**Meet the editor**

Dr. Peng Xi obtained his PhD in optical engineering from Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. He then worked as a postdoctoral Research Associate in Hong Kong University of Science and Technology (2003-2004), Purdue University (2005-2006), and Michigan State University (2006- 2007). From 2008 to 2009 he worked at Shanghai Jiao

Tong University as an Associate Professor. He is currently working at the Department of Biomedical Engineering, Peking University as an Associate Professor. He has been invited to give several keynote speeches and serve on the scientific committee board of Focus On Microscopy conference. His research interests include optical nanoscopy, multiphoton microscopy, as well as novel biomedical optical imaging techniques. Optical devices in co

Contents

**Preface IX** 

**Section 1 Advances in Theoretical Analysis 1** 

Chapter 1 **Zero Loss Condition Analysis on Optical** 

Mohammad Syuhaimi Ab-Rahman

Chapter 2 **Optical Resonators and Dynamic Maps 17** 

Chapter 3 **Electrodynamics of Evanescent Wave** 

**Section 2 Novel Structures in Optical Devices 53** 

Chapter 4 **Tunable and Memorable Optical Devices** 

Chapter 5 **Self-Organized Three-Dimensional Optical Circuits** 

**Prototypes, Fabrications and Devices 107** 

**Symmetrical Metal Cladding Waveguides 127** 

**Solar Cells, and Cancer Therapy 81** 

Feng Liu, Biqin Dong and Xiaohan Liu

Wei Li and Xunya Jiang

**Hybrid Structures 55**  Po-Chang Wu and Wei Lee

Tetsuzo Yoshimura

Chapter 7 **Optical Devices Based on** 

Lin Chen

Chapter 6 **Bio-Inspired Photonic Structures:** 

**Cross Add and Drop Multiplexer (OXADM)** 

**Operational Scheme in Point-to-Point Network 3** 

V. Aboites, Y. Barmenkov, A. Kir'yanov and M. Wilson

**with One-Dimensional Photonic-Crystal/Liquid-Crystal** 

**and Molecular Layer Deposition for Optical Interconnects,** 

**in Negative Refractive Index Superlens 37** 

### Contents

#### **Preface XI**


X Contents



### Preface

Optical devices in communication and computation have indeed a significant impact on our daily life and will continually be the leading revolutionizing technology in upcoming decades. This book presents a comprehensive account on recent advances in optical devices in communication and computing. The first section, advances in theoretical analysis, gives solid mathematical analysis on zero loss condition for optical communication, dynamic maps in laser resonator, as well as evanescent wave for superlens effect. In the following section a series of novel structures aiming at applications such as solar cells, inter-connections, waveguide, optical memory, nanoplasmonic filtering, etc. are presented. Not only that the novel structural materials are used in biomedical cancer therapy, but also the nature inspires the design of innovative optical structures. In the third section, functional optical materials, such as molecular level hybridization and fluidic optical lens are reported. This book may serve as an invaluable reference for researchers working in optical communications and photonics as well as for engineers who are conceiving new developments based on the advances in this field.

> **Peng Xi** Peking University, Beijing, China

**Section 1** 

**Advances in Theoretical Analysis** 

**Section 1** 

**Advances in Theoretical Analysis** 

**Chapter 1** 

© 2012 Ab-Rahman, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Zero Loss Condition Analysis on Optical** 

Mohammad Syuhaimi Ab-Rahman

http://dx.doi.org/10.5772/51006

**1. Introduction** 

Additional information is available at the end of the chapter

**Cross Add and Drop Multiplexer (OXADM)** 

**Operational Scheme in Point-to-Point Network** 

OXADMs are element which provide the capabilities of add and drop function and cross connecting traffic in the network, similar to OADM and OXC. OXADM consists of three main subsystem; a wavelength selective demultiplexer, a switching subsystem and a wavelength multiplexer. Each OXADM is expected to handle at least two distinct wavelength channels each with a coarse granularity of 2.5 Gbps of higher (signals with finer granularities are handled by logical switch node such as SDH/SONET digital cross connects or ATM switches). There are eight ports for add and drop functions, which are controlled by four lines of MEMs optical switch. The other four lines of MEMs switches are used to control the wavelength routing function between two different paths. The functions of OXADM include node termination, drop and add, routing, multiplexing and also providing mechanism of restoration for point-to-point, ring and mesh metropolitan and also customer access network in FTTH. The asymmetrical architecture of OXADM consists of 3 parts; selective port, add/drop operation, and path routing. Selective port permits only the interest wavelength pass through and acts as a filter. While add and drop function can be implemented in second part of OXADM architecture. The signals can then be re-routed to any port of output or/and perform an accumulation function which multiplex all signals onto one path and then exit to any interest output port. This will be done by the third part. OXADM can also perform 'U' turn to enable the line protection (Ring Protection) in the event of breakdown condition. This will be done by the first and third part. These two features have differed OXADM with the other existing device such as OADM and OXC. The purpose of this study was to obtain the maximum allowed loss for the device OXADM and input power required to maintain the satisfactory performance of the BER (BER <10-9) in the specific loss value. Ideal situation is a situation where all the devices that form the optical

## **Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network**

Mohammad Syuhaimi Ab-Rahman

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51006

#### **1. Introduction**

OXADMs are element which provide the capabilities of add and drop function and cross connecting traffic in the network, similar to OADM and OXC. OXADM consists of three main subsystem; a wavelength selective demultiplexer, a switching subsystem and a wavelength multiplexer. Each OXADM is expected to handle at least two distinct wavelength channels each with a coarse granularity of 2.5 Gbps of higher (signals with finer granularities are handled by logical switch node such as SDH/SONET digital cross connects or ATM switches). There are eight ports for add and drop functions, which are controlled by four lines of MEMs optical switch. The other four lines of MEMs switches are used to control the wavelength routing function between two different paths. The functions of OXADM include node termination, drop and add, routing, multiplexing and also providing mechanism of restoration for point-to-point, ring and mesh metropolitan and also customer access network in FTTH. The asymmetrical architecture of OXADM consists of 3 parts; selective port, add/drop operation, and path routing. Selective port permits only the interest wavelength pass through and acts as a filter. While add and drop function can be implemented in second part of OXADM architecture. The signals can then be re-routed to any port of output or/and perform an accumulation function which multiplex all signals onto one path and then exit to any interest output port. This will be done by the third part. OXADM can also perform 'U' turn to enable the line protection (Ring Protection) in the event of breakdown condition. This will be done by the first and third part. These two features have differed OXADM with the other existing device such as OADM and OXC. The purpose of this study was to obtain the maximum allowed loss for the device OXADM and input power required to maintain the satisfactory performance of the BER (BER <10-9) in the specific loss value. Ideal situation is a situation where all the devices that form the optical

© 2012 Ab-Rahman, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

device were considered to have zero loss. However, this loss is replaced in the BER measurement with the use of optical attenuator is set at 25 dB. The value of 25 dB will represent the total loss in the OXADM device. In zero loss condition, the only contributor to the system loss is the non-linear effect of power penalty. The decrement of data transmission rate with the increment of loss and maximum loss for each operation in the network OXADM point is also studied. The relationship between allowable power loss and the magnitude of input signal is shown in proposed equation. Optical fiber with nonlinear dispersion (attenuation constant, α = 0.25 dB/km) used for connecting two nodes OXADM at a distance of 60 km.

Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network 5

wavelength transfer between two different cores of fiber will increase the flexibility, survivability and also efficiency of the network structure. To make device operational more efficient by reducing the power penalty, zero leakage MEMs switches are used to control the mechanism of operation such as wavelength add/drop and wavelength routing operation. As a result, the switching performed within the optical layer will be able to achieve high speed restoration against failure/degradation of cables, fibers and optical amplifiers which had been proposed in [Rahman et al. 2006a][Rahman et al. 2006b]. We had proposed previously the migration of topology will be easier and reduce the restructuring process by eliminating the installation of new nodes because OXADMs are applicable for both types of topologies beside provide efficiency, reliability and survivability to the network [Rahman et

OXADMs are element which provide the capabilities of add and drop function and cross connecting traffic in the network, similar to OADM and OXC. OXADM consists of three main subsystem; a wavelength selective demultiplexer, a switching subsystem and a wavelength multiplexer. Each OXADM is expected to handle at least two distinct wavelength channels each with a coarse granularity of 2.5 Gbps of higher (signals with finer granularities are handled by logical switch node such as SDH/SONET digital cross connects or ATM switches. There are eight ports for add and drop functions, which are controlled by four lines of MEMs optical switch. The other four lines of MEMs switches are used to control the wavelength routing function between two different paths. The functions of OXADM include node termination, drop and add, routing, multiplexing and also providing mechanism of restoration for point-to-point, ring and mesh metropolitan and also customer access network in FTTH. With the setting of the MEMs optical switch configuration, the device can be programmed to function as another optical devices such as multiplexer, demultiplexer, coupler, wavelength converter (with fiber grating filter configuration), OADM, wavelength round about an etc for the single application. The designed 4-channel OXADM device is expected to have maximum operational loss of 0.06 dB for each channel when device components are in ideal/zero loss condition. The maximum insertion loss when considering the component loss at every channel is less than 6 dB [Rahman et al. 2006a]-

In this paper we analyze the performance of OXADM in zero loss condition to obtain the achievable loss of point-to-point network at a specific receiver sensitivity value. Finally to address the operational loss and can be called as power penalty to each function or

Table 1 shows the modulated launched power to characterize the insertion loss of OXADM operation. Since the launch of the four modulated wavelength operation is almost similar, therefore the process of leveling (equating the amplitude of) the wavelength is not necessary. Specification for the characterization of the insertion loss calculation is as

al. 2006c][Rahman & Shaari 2007].

[Rahman 2008].

follows:

operation performed by this device.

**2.1. Insertion loss calculation** 

This paper also measured the operational loss value for three main operation of OXADM such as pass through, dropping and adding signal. The relationship between minimum input power and attenuation given by the linear equation, y = x + 25 to intercept the y axis is 25 dB (maximum loss in the input power 0 dBm). Gradient, m = 1 shows no change at 1 dBm of input power will change the power loss of 1 dB. The restoration scheme offers by OXADM is also been investigated. We examine the relationship between the attenuation/loss at optical node on output power and the BER performance of the ring protection mechanism is activated. The simulation study also seeks to obtain the magnitude of the attenuation is allowed during the operation of this ring of protection (if attenuation increases due to inclusion of other optical devices and connectors). Rate of decreasing of output power due to attenuation increased will also be studied and based on the value of the internal amplifier gain can be determined relatively. Finally, the proposed value of the internal amplifier which is suitable for miniaturization compensate signal to a directional orientation to the West and East to have the same attenuation as a ring of protection is turned on.

#### **2. OXADM device**

Optical switch based devices is one of the most promising element that is used in optical communication network. Starting with Modulator at the receiver site, then moving to Optical Add and Drop Multiplexing (OADM) and Optical Cross Connect (OXC) at the distribution site and finally ending with Receiver (demodulator) at recovery site have shown the significant useful of the device. However, the rapid change and evolvement in optical network and service today has required the new type of optical switching device to be developed. Optical Cross Node, Tuneable Ring Node, Customer Access Protection Switch (CAPU), Arrayed Waveguide Grating Multiplexing are amongst the new generation of optical switch device [Mutafungwa 2000][ Eldada & Nunen 2000][Aziz et al. 2009]. In this paper we introducing of new architecture of switch device that is designed to overcome drawbacks that occur in wavelength management in expected. The device is called optical cross add and drop multiplexing (OXADM) which use combination concept of OXC and OADM. Its enable the operating wavelength on two different optical trunks to be switched to each other and implementing accumulating function simultaneously. Here, the operating wavelengths can be multiplexed together and exit to any interested output port. The wavelength transfer between two different cores of fiber will increase the flexibility, survivability and also efficiency of the network structure. To make device operational more efficient by reducing the power penalty, zero leakage MEMs switches are used to control the mechanism of operation such as wavelength add/drop and wavelength routing operation. As a result, the switching performed within the optical layer will be able to achieve high speed restoration against failure/degradation of cables, fibers and optical amplifiers which had been proposed in [Rahman et al. 2006a][Rahman et al. 2006b]. We had proposed previously the migration of topology will be easier and reduce the restructuring process by eliminating the installation of new nodes because OXADMs are applicable for both types of topologies beside provide efficiency, reliability and survivability to the network [Rahman et al. 2006c][Rahman & Shaari 2007].

OXADMs are element which provide the capabilities of add and drop function and cross connecting traffic in the network, similar to OADM and OXC. OXADM consists of three main subsystem; a wavelength selective demultiplexer, a switching subsystem and a wavelength multiplexer. Each OXADM is expected to handle at least two distinct wavelength channels each with a coarse granularity of 2.5 Gbps of higher (signals with finer granularities are handled by logical switch node such as SDH/SONET digital cross connects or ATM switches. There are eight ports for add and drop functions, which are controlled by four lines of MEMs optical switch. The other four lines of MEMs switches are used to control the wavelength routing function between two different paths. The functions of OXADM include node termination, drop and add, routing, multiplexing and also providing mechanism of restoration for point-to-point, ring and mesh metropolitan and also customer access network in FTTH. With the setting of the MEMs optical switch configuration, the device can be programmed to function as another optical devices such as multiplexer, demultiplexer, coupler, wavelength converter (with fiber grating filter configuration), OADM, wavelength round about an etc for the single application. The designed 4-channel OXADM device is expected to have maximum operational loss of 0.06 dB for each channel when device components are in ideal/zero loss condition. The maximum insertion loss when considering the component loss at every channel is less than 6 dB [Rahman et al. 2006a]- [Rahman 2008].

In this paper we analyze the performance of OXADM in zero loss condition to obtain the achievable loss of point-to-point network at a specific receiver sensitivity value. Finally to address the operational loss and can be called as power penalty to each function or operation performed by this device.

#### **2.1. Insertion loss calculation**

4 Optical Devices in Communication and Computation

a distance of 60 km.

turned on.

**2. OXADM device** 

device were considered to have zero loss. However, this loss is replaced in the BER measurement with the use of optical attenuator is set at 25 dB. The value of 25 dB will represent the total loss in the OXADM device. In zero loss condition, the only contributor to the system loss is the non-linear effect of power penalty. The decrement of data transmission rate with the increment of loss and maximum loss for each operation in the network OXADM point is also studied. The relationship between allowable power loss and the magnitude of input signal is shown in proposed equation. Optical fiber with nonlinear dispersion (attenuation constant, α = 0.25 dB/km) used for connecting two nodes OXADM at

This paper also measured the operational loss value for three main operation of OXADM such as pass through, dropping and adding signal. The relationship between minimum input power and attenuation given by the linear equation, y = x + 25 to intercept the y axis is 25 dB (maximum loss in the input power 0 dBm). Gradient, m = 1 shows no change at 1 dBm of input power will change the power loss of 1 dB. The restoration scheme offers by OXADM is also been investigated. We examine the relationship between the attenuation/loss at optical node on output power and the BER performance of the ring protection mechanism is activated. The simulation study also seeks to obtain the magnitude of the attenuation is allowed during the operation of this ring of protection (if attenuation increases due to inclusion of other optical devices and connectors). Rate of decreasing of output power due to attenuation increased will also be studied and based on the value of the internal amplifier gain can be determined relatively. Finally, the proposed value of the internal amplifier which is suitable for miniaturization compensate signal to a directional orientation to the West and East to have the same attenuation as a ring of protection is

Optical switch based devices is one of the most promising element that is used in optical communication network. Starting with Modulator at the receiver site, then moving to Optical Add and Drop Multiplexing (OADM) and Optical Cross Connect (OXC) at the distribution site and finally ending with Receiver (demodulator) at recovery site have shown the significant useful of the device. However, the rapid change and evolvement in optical network and service today has required the new type of optical switching device to be developed. Optical Cross Node, Tuneable Ring Node, Customer Access Protection Switch (CAPU), Arrayed Waveguide Grating Multiplexing are amongst the new generation of optical switch device [Mutafungwa 2000][ Eldada & Nunen 2000][Aziz et al. 2009]. In this paper we introducing of new architecture of switch device that is designed to overcome drawbacks that occur in wavelength management in expected. The device is called optical cross add and drop multiplexing (OXADM) which use combination concept of OXC and OADM. Its enable the operating wavelength on two different optical trunks to be switched to each other and implementing accumulating function simultaneously. Here, the operating wavelengths can be multiplexed together and exit to any interested output port. The

Table 1 shows the modulated launched power to characterize the insertion loss of OXADM operation. Since the launch of the four modulated wavelength operation is almost similar, therefore the process of leveling (equating the amplitude of) the wavelength is not necessary. Specification for the characterization of the insertion loss calculation is as follows:

Attenuation = 25 dB (representing insertion loss) Photodetector sensitivity = -28.4 dBm at1550 nm Data transmission rate = 2.5 Gps (OC-48) WDM analyzer resolution bandwidth = 0.1 nm Photodetector thermal noise = 1x10-23 W/Hz Launched power (before modulation) = 0 dBm

The word 'sensitivity' is used in this paper are based on the simulation using optisystem tool. 'Sensitivity' is actually referring to the power allocation or budget power in actual application. The actual sensitivity in photodetector is defined as

$$\text{Photodectector Sensitivity} \left( \text{dBm} \right) \ = - \left( \text{Power Boundget} + \text{Safety Margin} \right) \tag{1}$$

Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network 7

Figure 2 shows the effects of attenuation on the BER for the operation of additional signals into the device OXADM. Attenuation value is set starting at 20 dB to 29 dB. The purpose of this characterization was to obtain the actual value of the total insertion loss is acceptable to

**Figure 2.** Effect of attenuation to BER performance for four different wavelengths for new additional

From the graph, the value of the attenuation that gave readings equivalent to the BER is 1x10-9 at 25 dB. This means that the maximum acceptable amount of insertion loss in the OXADM device is 25 dB. However, this value can be increased by increasing the sensitivity

Figure 3 shows the effect of attenuation on the BER measurements for the operation of pass through to the signal. At 25 dB attenuation values give the same BER measurement readings 1x10-9. This value is equal to the value obtained for the operation of adding a new signal of OXADM. This shows OXADM single unit provides good performance in the value of the

Conclusions from the studies on this part of the overall estimated value of OXADM device is 25 dB. Studies in the next section (the theory of product) will have an estimated value of

**2.3. The effect of attenuation to the BER** 

**a) Addition Signal to the Output Signal**

maintain the BER measurement of 1x10-9.

of the system depends on the receiver system used.

maximum insertion loss of 25 dB to the sensitivity of -28.4 dBm.

**b) Launched Signal to Output Signal** 

signal.


**Table 1.** Modulated launched power which injected to OXADM device.

#### **2.2. Attenuation representing network total loss**

The purpose of this simulation study was to determine allowable loss of OXADM to maintain the network performance in point to point network and be tested under ideal condition. The decrement of data transmission rate with the increment of loss and maximum loss for each operation in the network OXADM point is also studied. The relationship between allowable power loss and the magnitude of input signal is shown in equation (1). Optical fiber with nonlinear dispersion (attenuation constant, α = 0.25 dB/km) used for connecting two nodes OXADM at a distance of 60 km (Figure 1).

**Figure 1.** Experimental set up of point-to-point network which uses OXADM as an optical node. The value of OXADM insertion loss is determined by adjusting the attenuator.

#### **2.3. The effect of attenuation to the BER**

#### **a) Addition Signal to the Output Signal**

6 Optical Devices in Communication and Computation

Attenuation = 25 dB (representing insertion loss) Photodetector sensitivity = -28.4 dBm at1550 nm

application. The actual sensitivity in photodetector is defined as

**Table 1.** Modulated launched power which injected to OXADM device.

used for connecting two nodes OXADM at a distance of 60 km (Figure 1).

60 km

60 km

value of OXADM insertion loss is determined by adjusting the attenuator.

**2.2. Attenuation representing network total loss** 

Tx

1510 nm, 1530

1550 nm, 1570

Source 1

Tx

Source 1

The word 'sensitivity' is used in this paper are based on the simulation using optisystem tool. 'Sensitivity' is actually referring to the power allocation or budget power in actual

Photodetector Sensitivity dBm Power Budget Safety Margin (1)

**Wavelength Launched Power (Watt) Launched Power (dBm)** 

1510 nm 4.680 x 10-4 -3.297 1530 nm 4.808 x 10-4 -3.180 1550 nm 4.872 x 10-4 -3.123 1570 nm 4.808 x 10-4 -3.180

The purpose of this simulation study was to determine allowable loss of OXADM to maintain the network performance in point to point network and be tested under ideal condition. The decrement of data transmission rate with the increment of loss and maximum loss for each operation in the network OXADM point is also studied. The relationship between allowable power loss and the magnitude of input signal is shown in equation (1). Optical fiber with nonlinear dispersion (attenuation constant, α = 0.25 dB/km)

RX

Variable Attenuator 1

> Variable Attenuator 2

Receiver 1

RX

Receiver 2

**Figure 1.** Experimental set up of point-to-point network which uses OXADM as an optical node. The

OXADM 1 OXADM 2

Data transmission rate = 2.5 Gps (OC-48) WDM analyzer resolution bandwidth = 0.1 nm Photodetector thermal noise = 1x10-23 W/Hz Launched power (before modulation) = 0 dBm

Figure 2 shows the effects of attenuation on the BER for the operation of additional signals into the device OXADM. Attenuation value is set starting at 20 dB to 29 dB. The purpose of this characterization was to obtain the actual value of the total insertion loss is acceptable to maintain the BER measurement of 1x10-9.

**Figure 2.** Effect of attenuation to BER performance for four different wavelengths for new additional signal.

From the graph, the value of the attenuation that gave readings equivalent to the BER is 1x10-9 at 25 dB. This means that the maximum acceptable amount of insertion loss in the OXADM device is 25 dB. However, this value can be increased by increasing the sensitivity of the system depends on the receiver system used.

#### **b) Launched Signal to Output Signal**

Figure 3 shows the effect of attenuation on the BER measurements for the operation of pass through to the signal. At 25 dB attenuation values give the same BER measurement readings 1x10-9. This value is equal to the value obtained for the operation of adding a new signal of OXADM. This shows OXADM single unit provides good performance in the value of the maximum insertion loss of 25 dB to the sensitivity of -28.4 dBm.

Conclusions from the studies on this part of the overall estimated value of OXADM device is 25 dB. Studies in the next section (the theory of product) will have an estimated value of

real power for the provision of optical networks based on different values OXADM 25 dB with the insertion loss of OXADM which measured in the product theory.

Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network 9

The loss under zero loss condition is also measured for each operation of OXADM. Table 2 listing the operational loss or power penalty for three OXADM operations; pass through, dropping, adding signal. The values is range from 0.05 to 0.18 depend to the number of

**Figure 4.** Effect of Input Power to the BER performance at different attenuation values (1530 nm)

**Figure 5.** The required input power by OXADM to maintain the performance at different attenuation

**Input Power(dBm)**


y = x + 25

20

21

22

23

24

25

26

27

switch device involve of each operation.

(λ=1530 nm, BER=3.98x10-9).

**Attenuation (dB)**

**Figure 3.** Effect of attenuation to BER performance for four different wavelengths for pass through operation.

#### **2.4. Input signal to BER performance**

Figure 4 shows the effect of input power diode laser (before the signal is modulated with data) on BER performance in a variety of attenuation. Attenuation value is set between 20 dB to 26 dB. The purpose of this characterization is to obtain the minimum power required by the device OXADM to operate in a satisfactory condition. The relationship between minimum input power and attenuation given by the linear equation, y = x + 25 to intercept the y axis is 25 dB (maximum loss in the input power 0 dBm). Gradient, m = 1 shows no change at 1 dBm of input power will change the power loss of 1 dB. The changes are shown in Figure 5.

The insertion loss under ideal condition is called as operational loss. The magnitude is rely on the operation functioned by OXADM. This term can also be used as power penalty. Power penalty is the other loss need to be compensated instead of insertion loss. Power penalty is the loss due to the non-linear effect such as SRS, FWM and others.

The loss under zero loss condition is also measured for each operation of OXADM. Table 2 listing the operational loss or power penalty for three OXADM operations; pass through, dropping, adding signal. The values is range from 0.05 to 0.18 depend to the number of switch device involve of each operation.

8 Optical Devices in Communication and Computation

operation.

1.0E-74 1.0E-69 1.0E-64 1.0E-59 1.0E-54 1.0E-49 1.0E-44 1.0E-39 1.0E-34 1.0E-29 1.0E-24 1.0E-19 1.0E-14 1.0E-09 1.0E-04

**BER**

in Figure 5.

**2.4. Input signal to BER performance** 

real power for the provision of optical networks based on different values OXADM 25 dB

**Figure 3.** Effect of attenuation to BER performance for four different wavelengths for pass through

20 21 22 23 24 25 26 27 28 29 30

1510 nm 1530 nm 1550 nm 1570 nm

**Attenuation (dB)**

Figure 4 shows the effect of input power diode laser (before the signal is modulated with data) on BER performance in a variety of attenuation. Attenuation value is set between 20 dB to 26 dB. The purpose of this characterization is to obtain the minimum power required by the device OXADM to operate in a satisfactory condition. The relationship between minimum input power and attenuation given by the linear equation, y = x + 25 to intercept the y axis is 25 dB (maximum loss in the input power 0 dBm). Gradient, m = 1 shows no change at 1 dBm of input power will change the power loss of 1 dB. The changes are shown

The insertion loss under ideal condition is called as operational loss. The magnitude is rely on the operation functioned by OXADM. This term can also be used as power penalty. Power penalty is the other loss need to be compensated instead of insertion loss. Power

penalty is the loss due to the non-linear effect such as SRS, FWM and others.

with the insertion loss of OXADM which measured in the product theory.

**Figure 4.** Effect of Input Power to the BER performance at different attenuation values (1530 nm)

**Figure 5.** The required input power by OXADM to maintain the performance at different attenuation (λ=1530 nm, BER=3.98x10-9).

#### **2.5. Attenuation over distance**

The purpose of this simulation study is to determine the performance of the OXADM in point to point network under the certain loss value. The decrement of achievable distance due to the increment of loss value is also studied. As a result, the relationship between the achievable distances for point to point network to the OXADM insertion loss has been defined in equation (2). Optical fiber with nonlinear dispersion (attenuation constant, α = 0.25 dB / km) is used for connecting two nodes OXADM at a distance of 60 km (Figure 1). Five value if insertion loss (which has a value nearly equal to the loss of each operation OXADM) were selected to estimate the BER performance in this network.

Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network 11

**Figure 6.** Effect of distance to the BER performance in npoint-to-point network at zero attenuation.

**Figure 7.** Effect of distance to the BER performance in point-to-point network at attenuation of 10 dB.


**Table 2.** Power Penalty for several OXADM operations under ideal condition.

Figure 6 until Figure 10 shows the effect of distance of data transmission to the BER performance of the point to point networks at different attenuation value. The attenuation is set at 0 dB to 20 dB. Observed in these graphs, the boundary lines for the BER = 10-9 shifted to the left with the increment of value of attenuation. This shows the increment of device loss, distance of data transmission is also decreased. At zero power loss the boundary lines on the BER is at 95 km but when the loss at 20 dB, BER = 10-9 boundary is located at 14 km. This shows the distance is inversely proportional to the devices insertion loss (Saleh & Teich 1991). The decrement rate of distance is 3.92 km/dB, as shown in Figure 11 and equations (2).

$$\mathbf{y} = -3.9151\mathbf{x} + 94.434\tag{2}$$

The purpose of this simulation study is to determine the performance of the OXADM in point to point network under the certain loss value. The decrement of achievable distance due to the increment of loss value is also studied. As a result, the relationship between the achievable distances for point to point network to the OXADM insertion loss has been defined in equation (2). Optical fiber with nonlinear dispersion (attenuation constant, α = 0.25 dB / km) is used for connecting two nodes OXADM at a distance of 60 km (Figure 1). Five value if insertion loss (which has a value nearly equal to the loss of each operation

**Wavelength (nm) Insertion Loss (dB)** 

1510 0.1185 1530 0.1171 1550 0.1128 1570 0.1144

1510 0.0938 1530 0.0931 1550 0.0891 1570 0.0903

1510 0.0600 1530 0.0584 1550 0.0599 1570 0.0572

Figure 6 until Figure 10 shows the effect of distance of data transmission to the BER performance of the point to point networks at different attenuation value. The attenuation is set at 0 dB to 20 dB. Observed in these graphs, the boundary lines for the BER = 10-9 shifted to the left with the increment of value of attenuation. This shows the increment of device loss, distance of data transmission is also decreased. At zero power loss the boundary lines on the BER is at 95 km but when the loss at 20 dB, BER = 10-9 boundary is located at 14 km. This shows the distance is inversely proportional to the devices insertion loss (Saleh & Teich 1991). The decrement rate of distance is 3.92 km/dB, as shown in

y 3.9151x 94.434 (2)

OXADM) were selected to estimate the BER performance in this network.

i. Launched Power (dBm)-Output Power (dBm)

ii. Launched Power (dBm)-Drop Power (dBm)

iii. Add Power (dBm)-Output Power (dBm)

Figure 11 and equations (2).

**Table 2.** Power Penalty for several OXADM operations under ideal condition.

**2.5. Attenuation over distance** 

**Figure 6.** Effect of distance to the BER performance in npoint-to-point network at zero attenuation.

**Figure 7.** Effect of distance to the BER performance in point-to-point network at attenuation of 10 dB.

Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network 13

**Figure 10.** Effect of distance to the BER performance in npoint-to-point network at attenuation of 20 dB.

**Figure 11.** Achievable distance at specific attenuation values in point-to-point network at sensitivity -

28.4 dBm (1550 nm at OC-48).

**Figure 8.** Effect of distance to the BER performance in npoint-to-point network at attenuation of 15 dB.

**Figure 9.** Effect of distance to the BER performance in npoint-to-point network at attenuation of 17dB.

**Figure 8.** Effect of distance to the BER performance in npoint-to-point network at attenuation of 15 dB.

**Figure 9.** Effect of distance to the BER performance in npoint-to-point network at attenuation of 17dB.

**Figure 10.** Effect of distance to the BER performance in npoint-to-point network at attenuation of 20 dB.

**Figure 11.** Achievable distance at specific attenuation values in point-to-point network at sensitivity - 28.4 dBm (1550 nm at OC-48).

Wavelength of operation of the network is point to point can be divided into two groups: the group A (wavelength 1550 nm and 1570 nm) and group B (wavelength 1510 nm and 1530 nm). Observed in Figure 6, curve B group is under the curve A. But in Figure 7 until Figure 10, the movement to the right occurs at the curvature of the group B that eventually bend the curve B is above the group A. This shows the effect of attenuation to the BER performance is different at different wavelengths. The reduction in the distance occurs suddenly at a wavelength of Group B with the increasing of attenuation compared with the wavelength A.

Achievable distance (maximum span) in point-to-point network is define bu equation (3)

$$L = \frac{P - l\_{OXADM}}{\alpha} \tag{3}$$

Zero Loss Condition Analysis on Optical Cross Add and Drop Multiplexer (OXADM) Operational Scheme in Point-to-Point Network 15

This project is supported by Ministry of Science, Technology and Innovation (MOSTI), Government of Malaysia, through the National Top-Down Project fund and National Science Fund (NSF). The authors would like to thank the Photonic Technology Laboratory in Institute of Micro Engineering and Nanoelectronics (IMEN), Universiti Kebangsaan Malaysia (UKM), Malaysia, for providing the facilities to conduct the experiments. The OXADM had firstly been exhibited in 19th International Invention, Innovation and Technology Exhibition (ITEX 2008), Malaysia, and was awarded with Bronze medal in

Mutafungwa, E. An improved wavelength-selective all fiber cross-connect node, *IEEE* 

Eldada, L. & Nunen, J.v. Architecture and performance requirements of optical metro ring nodes in implementing optical add/drop and protection functions, *Telephotonics Review*.

Rahman, M.S.A.; Husin, H.; Ehsan A.A., & Shaari, S. Analytical modeling of optical cross add and drop multiplexing switch", *Proceeding 2006 IEEE International Conference on Semiconductor* Electronics, pub. IEEE Malaysia Section. pp 290-293.

Rahman, M.S.A.; Shaari, S. OXADM restoration scheme: Approach to optical ring network

Rahman, M.S.A.; Ehsan, A.A. & Shaari, S. Mesh upgraded ring in metropolitan network using OXADM, *Proceeding of the 5th International Conference on Optical Communications and Networks & the 2nd International Symposium on Advances and* 

Rahman, M.S.A. & Shaari, S. 2007. *Survivable Mesh Upgraded Ring in Metropolitan Network*,

Rahman, M.S.A. 2008. *First Experimental on OXADM restoration scheme Using Point-to-Point Configuration*. Journal of Optical Communication, JOC (German). 29(2008)3. Pp. 174-

Aziz, S.A.C.; Ab-Rahman, M.S. & Jumari,K., 2009 Customer access protection unit for survivable FTTH network. Proceedings of International Conference on Space Science

protection, *IEEE International Conference on Networks*. pp 371-376. 2006b.

Journal of Optical Communication, JOC (German). 28(2007)3, pp. 206-211

**Author details** 

**Acknowledgement** 

telecommunication category.

*Journal of Applied Optics. pp 63-69. 2000.*

**4. References** 

2000

2006a.

177.

*Trends in Fiber. 2006c.*

*Malaysia* 

Mohammad Syuhaimi Ab-Rahman *Universiti Kebangsaan Malaysia (UKM),* 

L = Achievable distance, km

P = Power Budget, dB (ideal condition or zero loss)

*l*OXADM = Insertion loss of OXADM, dB (product theory condition)

α = fiber constant, dB/km

#### **3. Conclusion**

We have introduced a new switching device which utilizes the combined concepts of optical add and drop multiplexing and optical cross connect operation through the development of an optical cross add and drop multiplexer (OXADM). Ideal situation is a situation where all the devices that form the optical device were considered to have zero loss. However, this loss is replaced in the BER measurement with the use of optical attenuator is set at 25 dB. The value of 25 dB will represent the total loss in the OXADM device. The purpose of this study was to obtain the maximum allowed loss for the device OXADM and input power required to maintain the satisfactory performance of the BER (BER <10-9) in the specific loss value. In zero loss condition, the only contributor to the loss is the non-linear effect of power penalty.

The experimental results show the value of crosstalk and return loss is bigger than 60 dB and 40 dB respectively.We have obtained the achievable distance associated with insertion loss for the OXADM device at specific fiber used. The result will be the mathematical equation that describe about these parameter relationship as mentioned in equation (3). As a result, analysis using the value of insertion loss was less than 0.06 dB under ideal condition, the maximum length that can be achieved is 94 km. While when considering the loss, with the transmitter power of 0 dBm and sensitivity –22.8 dBm at a point-to-point configuration with safety margin, the required transmission is 71 km with OXADM.

#### **Author details**

14 Optical Devices in Communication and Computation

wavelength A.

L = Achievable distance, km

α = fiber constant, dB/km

**3. Conclusion** 

penalty.

OXADM.

P = Power Budget, dB (ideal condition or zero loss)

*l*OXADM = Insertion loss of OXADM, dB (product theory condition)

(3)

Wavelength of operation of the network is point to point can be divided into two groups: the group A (wavelength 1550 nm and 1570 nm) and group B (wavelength 1510 nm and 1530 nm). Observed in Figure 6, curve B group is under the curve A. But in Figure 7 until Figure 10, the movement to the right occurs at the curvature of the group B that eventually bend the curve B is above the group A. This shows the effect of attenuation to the BER performance is different at different wavelengths. The reduction in the distance occurs suddenly at a wavelength of Group B with the increasing of attenuation compared with the

Achievable distance (maximum span) in point-to-point network is define bu equation

*P lOXADM <sup>L</sup>* 

We have introduced a new switching device which utilizes the combined concepts of optical add and drop multiplexing and optical cross connect operation through the development of an optical cross add and drop multiplexer (OXADM). Ideal situation is a situation where all the devices that form the optical device were considered to have zero loss. However, this loss is replaced in the BER measurement with the use of optical attenuator is set at 25 dB. The value of 25 dB will represent the total loss in the OXADM device. The purpose of this study was to obtain the maximum allowed loss for the device OXADM and input power required to maintain the satisfactory performance of the BER (BER <10-9) in the specific loss value. In zero loss condition, the only contributor to the loss is the non-linear effect of power

The experimental results show the value of crosstalk and return loss is bigger than 60 dB and 40 dB respectively.We have obtained the achievable distance associated with insertion loss for the OXADM device at specific fiber used. The result will be the mathematical equation that describe about these parameter relationship as mentioned in equation (3). As a result, analysis using the value of insertion loss was less than 0.06 dB under ideal condition, the maximum length that can be achieved is 94 km. While when considering the loss, with the transmitter power of 0 dBm and sensitivity –22.8 dBm at a point-to-point configuration with safety margin, the required transmission is 71 km with

(3)

Mohammad Syuhaimi Ab-Rahman *Universiti Kebangsaan Malaysia (UKM), Malaysia* 

#### **Acknowledgement**

This project is supported by Ministry of Science, Technology and Innovation (MOSTI), Government of Malaysia, through the National Top-Down Project fund and National Science Fund (NSF). The authors would like to thank the Photonic Technology Laboratory in Institute of Micro Engineering and Nanoelectronics (IMEN), Universiti Kebangsaan Malaysia (UKM), Malaysia, for providing the facilities to conduct the experiments. The OXADM had firstly been exhibited in 19th International Invention, Innovation and Technology Exhibition (ITEX 2008), Malaysia, and was awarded with Bronze medal in telecommunication category.

#### **4. References**


and Communication, 2009. 26-27 Oct, pp: 71 – 73, Negeri Sembilan, 10.1109/ICONSPACE.2009.5352668

**Chapter 2** 

© 2012 Aboites et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

The power performance of a phase conjugated laser oscillator can be significantly improved introducing intracavity nonlinear elements, e.g. Eichler et al. [2] and O'Connor et al. [3] showed that a stimulated-Brillouin-scattering (SBS) phase conjugating cell placed inside the resonator of a solid-state laser reduces its optical coherence length, because each axial mode

and reproduction in any medium, provided the original work is properly cited.

**Optical Resonators and Dynamic Maps** 

In recent years, optical phase conjugation (OPC) has been an important research subject in the field of lasers and nonlinear optics. OPC defines a link between two coherent optical beams propagating in opposite directions with reversed wave front and identical transverse amplitude distributions. The distinctive characteristic of a pair of phase-conjugate beams is that the aberration influence imposed on the forward beam passed through an inhomogeneous or disturbing medium can be automatically removed for the backward beam passed through the same disturbing medium. There are three main approaches that are efficiently able to produce the backward phase-conjugate beam. The first one is based on the degenerate (or partially degenerate) four-wave mixing processes (FWM), the second is based on a variety of backward simulated (e.g. Brillouin, Raman or Kerr) scattering processes, and the third is based on one-photon or multi-photon pumped backward stimulated emission (lasing) processes. Among these different approaches, there is a common physical mechanism in generating a backward phase-conjugate beam, which is the formation of the induced holographic grating and the subsequent wave-front restoration via a backward reading beam. In most experimental studies, certain types of resonance enhancements of induced refractive-index changes are desirable for obtaining higher grating-refraction efficiency. OPC-associated techniques can be effectively utilized in many different application areas: such as high-brightness laser oscillator/amplifier systems, cavityless lasing devices, laser target-aiming systems, aberration correction for coherent-light transmission and reflection through disturbing media, long distance optical fiber communications with ultra-high bit-rate, optical phase locking and coupling systems, and novel optical data storage and processing systems (see Ref. [1] and references therein).

V. Aboites, Y. Barmenkov, A. Kir'yanov and M. Wilson

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51854

**1. Introduction** 

Saleh, B. E.A.& Teich, M.C. Fundamentals of photonics. Wiley (New York). 1991

#### **Chapter 2**

### **Optical Resonators and Dynamic Maps**

V. Aboites, Y. Barmenkov, A. Kir'yanov and M. Wilson

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51854

#### **1. Introduction**

16 Optical Devices in Communication and Computation

10.1109/ICONSPACE.2009.5352668

and Communication, 2009. 26-27 Oct, pp: 71 – 73, Negeri Sembilan,

Saleh, B. E.A.& Teich, M.C. Fundamentals of photonics. Wiley (New York). 1991

In recent years, optical phase conjugation (OPC) has been an important research subject in the field of lasers and nonlinear optics. OPC defines a link between two coherent optical beams propagating in opposite directions with reversed wave front and identical transverse amplitude distributions. The distinctive characteristic of a pair of phase-conjugate beams is that the aberration influence imposed on the forward beam passed through an inhomogeneous or disturbing medium can be automatically removed for the backward beam passed through the same disturbing medium. There are three main approaches that are efficiently able to produce the backward phase-conjugate beam. The first one is based on the degenerate (or partially degenerate) four-wave mixing processes (FWM), the second is based on a variety of backward simulated (e.g. Brillouin, Raman or Kerr) scattering processes, and the third is based on one-photon or multi-photon pumped backward stimulated emission (lasing) processes. Among these different approaches, there is a common physical mechanism in generating a backward phase-conjugate beam, which is the formation of the induced holographic grating and the subsequent wave-front restoration via a backward reading beam. In most experimental studies, certain types of resonance enhancements of induced refractive-index changes are desirable for obtaining higher grating-refraction efficiency. OPC-associated techniques can be effectively utilized in many different application areas: such as high-brightness laser oscillator/amplifier systems, cavityless lasing devices, laser target-aiming systems, aberration correction for coherent-light transmission and reflection through disturbing media, long distance optical fiber communications with ultra-high bit-rate, optical phase locking and coupling systems, and novel optical data storage and processing systems (see Ref. [1] and references therein).

The power performance of a phase conjugated laser oscillator can be significantly improved introducing intracavity nonlinear elements, e.g. Eichler et al. [2] and O'Connor et al. [3] showed that a stimulated-Brillouin-scattering (SBS) phase conjugating cell placed inside the resonator of a solid-state laser reduces its optical coherence length, because each axial mode

© 2012 Aboites et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of the phase conjugated oscillator experiences a frequency shift at every reflection by the SBS cell resulting in a multi-frequency lasing spectrum, that makes the laser insensitive to changing operating conditions such as pulse repetition frequency, pump energy, etc. This ability is very important for many laser applications including ranging and remote sensing. The intracavity cell is also able to compensate optical aberrations from the resonator and from thermal effects in the active medium, resulting in near diffraction limited output [4], and eliminate the need for a conventional Q-switch as well, because its intensity-dependent reflectivity acts as a passive Q-switch, typically producing a train of nanosecond pulses of diffraction limited beam quality. One more significant use of OPC is a so-called short hologram, which does not exhibit in-depth diffraction deformation of the fine speckle pattern of the recording fields [5]. A thermal hologram in the output mirror was recorded by two speckle waves produced as a result of this recording a ring Nd:YAG laser [6]. Phase conjugation by SBS represents a fundamentally promising approach for achieving power scaling of solid-state lasers [7, 8] and optical fibers [9].

Optical Resonators and Dynamic Maps 19

well as the general case for each beams in a ring phase conjugated resonator. Finally Section

Any optical element may be described by a 2×2 matrix in paraxial optics. Assuming cylindrical symmetry around the optical axis, and defining at a given position *z* both the perpendicular distance of any ray to the optical axis and its angle with the same axis as *y*(z) and *θ*(z), when the ray undergoes a transformation as it travels through an optical system represented by the matrix [*A,B,C,D*], the resultant values of *y* and *θ* are given by

For any optical system, one may obtain the total [*A,B,C,D*] matrix, by carrying out the matrix

For passive optical elements such as lenses, interfaces between two media, reflections, propagation, and many others, the elements *A, B, C, D* are constants and the determinant Det[*A,B,C,D*] = *nn*/*nn*+1, where *nn* and *nn*+1 are the refraction index before and after the optical element described by the matrix. Since typically *nn* and *nn*+1 are the same, it holds that

However, for active or non-linear optical elements the *A, B, C, D* matrix elements are not constant but may be functions of various parameters. The following three examples are

Due to the electro-optic Kerr effect the refraction index of an optical media *n* is a function of the electric field strength *E* [18]. The change of the refraction index is given by Δ*n* = *λKE*2, where *λ* is the wavelength and *K* is the Kerr constant of the media. For example, the [*A,B,C,D*] matrix of a curved surface of radius of curvature *r* separating two regions of refractive index *n*1 and *n*2 (taking the center of the radius of curvature positive to the right in

> 2 1

*n n r*

1 0

. 1

(2)

. *n n n n y A B y*

 

*C D* (1)

 

1 1

product of the matrices describing each one of the optical elements in the system.

6 presents the conclusions.

**2. ABCD matrix optics** 

**2.1. Constant ABCD elements** 

**2.2. Non constant ABCD elements** 

the zone of refractive index *n*2) is given as:

*2.2.1. Curved interface with a Kerr electro-optic material* 

Det[*A,B,C,D*] = 1.

worth mentioning.

[17]:

There are several theoretical models to describe OPC in resonators and lasers. One of them is to use the SBS reflection as one of the cavity mirrors of a laser resonator to form a socalled linear phase conjugate resonator [10], however ring-phase conjugate resonators are also possible [11]. The theoretical model of an OPC laser in transient operation [12] considers the temporal and spatial dynamic of the input field the Stokes field and the acoustic-wave amplitude in the SBS cell. On the other hand the spatial mode analysis of a laser may be carried out using transfer matrices, also know as ABCD matrices, which are a useful mathematical tool when studying the propagation of light rays through complex optical systems. They provide a simple way to obtain the final key characteristics (position and angle) of the ray. As an important example we could mention that transfer matrices have been used to study self-adaptive laser resonators where the laser oscillator is made out of a plane output coupler and an infinite nonlinear FWM medium in a self-intersecting loop geometry [13].

In this chapter we put forward an approach where the intracavity element is presented in the context of an iterative map (e.g. Tinkerbell, Duffing and Hénon) whose state is determined by its previous state. It is shown that the behavior of a beam within a ring optical resonator may be well described by a particular iterative map and the necessary conditions for its occurrence are discussed. In particular, it is shown that the introduction of a specific element within a ring phase-conjugated resonator may produce beams described by a Duffing, Tinkerbell or Hénon map, which we call "Tinkerbell, Duffing or Hénon beams". The idea of introducing map generating elements in optical resonators from a mathematical viewpoint was originally explored in [14-16] and this chapter is mainly based on those results.

This chapter is organized as follows: Section 2 discusses the matrix optics elements on which this work is based. Section 3 presents as an illustration some basic features of Tinkerbell, Duffing and Hénon maps, Sections 4,5 and 6 show, each one of them, the main characteristics of the map generation matrix and Tinkerbell, Duffing and Hénon Beams, as well as the general case for each beams in a ring phase conjugated resonator. Finally Section 6 presents the conclusions.

#### **2. ABCD matrix optics**

18 Optical Devices in Communication and Computation

scaling of solid-state lasers [7, 8] and optical fibers [9].

geometry [13].

on those results.

of the phase conjugated oscillator experiences a frequency shift at every reflection by the SBS cell resulting in a multi-frequency lasing spectrum, that makes the laser insensitive to changing operating conditions such as pulse repetition frequency, pump energy, etc. This ability is very important for many laser applications including ranging and remote sensing. The intracavity cell is also able to compensate optical aberrations from the resonator and from thermal effects in the active medium, resulting in near diffraction limited output [4], and eliminate the need for a conventional Q-switch as well, because its intensity-dependent reflectivity acts as a passive Q-switch, typically producing a train of nanosecond pulses of diffraction limited beam quality. One more significant use of OPC is a so-called short hologram, which does not exhibit in-depth diffraction deformation of the fine speckle pattern of the recording fields [5]. A thermal hologram in the output mirror was recorded by two speckle waves produced as a result of this recording a ring Nd:YAG laser [6]. Phase conjugation by SBS represents a fundamentally promising approach for achieving power

There are several theoretical models to describe OPC in resonators and lasers. One of them is to use the SBS reflection as one of the cavity mirrors of a laser resonator to form a socalled linear phase conjugate resonator [10], however ring-phase conjugate resonators are also possible [11]. The theoretical model of an OPC laser in transient operation [12] considers the temporal and spatial dynamic of the input field the Stokes field and the acoustic-wave amplitude in the SBS cell. On the other hand the spatial mode analysis of a laser may be carried out using transfer matrices, also know as ABCD matrices, which are a useful mathematical tool when studying the propagation of light rays through complex optical systems. They provide a simple way to obtain the final key characteristics (position and angle) of the ray. As an important example we could mention that transfer matrices have been used to study self-adaptive laser resonators where the laser oscillator is made out of a plane output coupler and an infinite nonlinear FWM medium in a self-intersecting loop

In this chapter we put forward an approach where the intracavity element is presented in the context of an iterative map (e.g. Tinkerbell, Duffing and Hénon) whose state is determined by its previous state. It is shown that the behavior of a beam within a ring optical resonator may be well described by a particular iterative map and the necessary conditions for its occurrence are discussed. In particular, it is shown that the introduction of a specific element within a ring phase-conjugated resonator may produce beams described by a Duffing, Tinkerbell or Hénon map, which we call "Tinkerbell, Duffing or Hénon beams". The idea of introducing map generating elements in optical resonators from a mathematical viewpoint was originally explored in [14-16] and this chapter is mainly based

This chapter is organized as follows: Section 2 discusses the matrix optics elements on which this work is based. Section 3 presents as an illustration some basic features of Tinkerbell, Duffing and Hénon maps, Sections 4,5 and 6 show, each one of them, the main characteristics of the map generation matrix and Tinkerbell, Duffing and Hénon Beams, as Any optical element may be described by a 2×2 matrix in paraxial optics. Assuming cylindrical symmetry around the optical axis, and defining at a given position *z* both the perpendicular distance of any ray to the optical axis and its angle with the same axis as *y*(z) and *θ*(z), when the ray undergoes a transformation as it travels through an optical system represented by the matrix [*A,B,C,D*], the resultant values of *y* and *θ* are given by [17]:

$$
\begin{pmatrix} y\_{n+1} \\ \theta\_{n+1} \end{pmatrix} = \begin{pmatrix} A & B \\ C & D \end{pmatrix} \begin{pmatrix} y\_n \\ \theta\_n \end{pmatrix}. \tag{1}
$$

For any optical system, one may obtain the total [*A,B,C,D*] matrix, by carrying out the matrix product of the matrices describing each one of the optical elements in the system.

#### **2.1. Constant ABCD elements**

For passive optical elements such as lenses, interfaces between two media, reflections, propagation, and many others, the elements *A, B, C, D* are constants and the determinant Det[*A,B,C,D*] = *nn*/*nn*+1, where *nn* and *nn*+1 are the refraction index before and after the optical element described by the matrix. Since typically *nn* and *nn*+1 are the same, it holds that Det[*A,B,C,D*] = 1.

#### **2.2. Non constant ABCD elements**

However, for active or non-linear optical elements the *A, B, C, D* matrix elements are not constant but may be functions of various parameters. The following three examples are worth mentioning.

#### *2.2.1. Curved interface with a Kerr electro-optic material*

Due to the electro-optic Kerr effect the refraction index of an optical media *n* is a function of the electric field strength *E* [18]. The change of the refraction index is given by Δ*n* = *λKE*2, where *λ* is the wavelength and *K* is the Kerr constant of the media. For example, the [*A,B,C,D*] matrix of a curved surface of radius of curvature *r* separating two regions of refractive index *n*1 and *n*2 (taking the center of the radius of curvature positive to the right in the zone of refractive index *n*2) is given as:

$$
\begin{pmatrix} 1 & 0 \\ -\frac{\left(n\_2 - n\_1\right)}{r} & 1 \end{pmatrix} \tag{2}
$$

Having vacuum (*n*1 = 1) on the left of the interface and a Kerr electro-optic material on the right, the above [*ABCD*] matrix becomes

$$
\begin{pmatrix}
1 & 0 \\ 
\end{pmatrix}.
\tag{3}
$$

Optical Resonators and Dynamic Maps 21

*<sup>g</sup> <sup>l</sup>* (7)

(8)

 

> 

 , <sup>30</sup> . *L th B*

The modeling of a real stimulated Brillouin scattering phase conjugate mirror usually takes into account a Gaussian aperture of radius *a* at intensity 1/*e*2 placed before an ideal phase conjugator. In this way the reflected beam is Gaussian and only the parts of the Gaussian incident beam with intensity above threshold are phase conjugate reflected. The matrix of

 <sup>2</sup> 1 0 , <sup>1</sup> *<sup>i</sup> a*

where the aperture *a* is a function of the incident light intensity *a*(*IL*) (*IL* must reach threshold to initiate the scattering process). As we can see, depending on the model, the *ABCD* matrix elements of a phase conjugated mirror may depend on several parameters such as the Brillouin downshifting frequency, the Gaussian aperture radius and the incident

At last, as third example we may consider a system with hysteresis. It is well known that such systems exhibit memory. There are many examples of materials with electric, magnetic and elastic hysteresis, as well as systems in neuroscience, biology, electronics, energy and even economics which show hysteresis. As it is known in a system with no hysteresis, it is possible to predict the system's output at an instant in time given only its input at that instant in time. However in a system with hysteresis, this is not possible; there is no way to predict the output without knowing the system's previous state and there is no way to know the system's state without looking at the history of the input. This means that it is necessary to know the path that the input followed before it reached its current value. For an optical element with hysteresis the *ABCD* matrix elements are function of the *yn*, *yn*-1, …*yn*-i and *θn*, *θn*-1, …, *θn*-i and its knowledge is necessary in order to find the state *yn*+1, *θn*+1. In general, taking into account hysteresis, the [*A,B,C,D*] matrix of

 

 

 

An extensive list of two-dimensional maps may be found in Ref. [20]. A few examples are Tinkerbell, Duffing and Hénon maps. As will be shown next they may be written as a matrix

*A B Ay y y By y y*

dynamical system such as the one described by Eq. (1) or equivalently as

*C D Cy y y Dy y y* (9)

11 11 11 11 , ,... , , ,... , ,... , , ,... . , ,... , , ,... , ,... , , ,... *n n ni n n ni n n ni n n ni n n ni n n ni n n ni n n ni*

 

*I*

this aperture is given by:

light intensity [19].

**2.3. Systems with hysteresis** 

Eq. (1) may be written as:

**3. Dynamic maps** 

Clearly the elements *A, B, D* are constants but element *C* is a function of the electric field *E*.

#### *2.2.2. Phase conjugate mirror*

A second example is a phase conjugate mirror. The process of phase conjugation has the property of retracing an incoming ray along the same incident path [7]. The ideal ABCD phase conjugate matrix is

$$
\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}. \tag{4}
$$

One may notice that the determinant of this particular matrix is not 1 but -1. The ABCD matrix of a real phase conjugated mirror must take into account the specific process to produce the phase conjugation. As already mentioned, typically phase conjugation is achieved in two ways; Four Wave Mixing or using a stimulated scattering process such as Brillouin, i.e. SBS. However upon reflection on a stimulated SBS phase conjugated mirror, the reflected wave has its frequency *ω* downshifted to *ω – δ* = *ω*(1 – *δ*/*ω*) where *δ* is the characteristic Brillouin downshift frequency of the mirror material (typically *δ*/*ω* « 1). In a non-ideal (i.e. real) case one must take the downshifting frequency into account and the ABCD matrix reads

$$
\begin{pmatrix}
1 - \frac{\delta}{\delta \nu} & 0 \\
0 & -1
\end{pmatrix}.
\tag{5}
$$

Furthermore, since in phase conjugation by SBS a light intensity threshold must be reached in order to have an exponential amplification of the scattered light, the above ideal matrix (4) must be modified. The scattered light intensity at position *z* in the medium is given as

$$I\_S\left(z\right) = I\_S\left(0\right) \exp\left(\mathcal{g}\_B I\_L l\right)\_\prime \tag{6}$$

where *IS*(0) is the initial level of scattering, *gB* denotes the characteristic exponential gain coefficient of the scattering process, *IL* is the intensity of the incident light beam, and *l* is the interaction length over which amplification takes place. Given the amplification *G* = exp(*gB*(ν)*ILl*) the threshold gain factor is commonly taken as *G* ~ exp(30) ≈ 1013 which corresponds to a threshold intensity

Optical Resonators and Dynamic Maps 21

$$I\_{L,th} = \frac{30}{\mathcal{g}\_B l}.\tag{7}$$

The modeling of a real stimulated Brillouin scattering phase conjugate mirror usually takes into account a Gaussian aperture of radius *a* at intensity 1/*e*2 placed before an ideal phase conjugator. In this way the reflected beam is Gaussian and only the parts of the Gaussian incident beam with intensity above threshold are phase conjugate reflected. The matrix of this aperture is given by:

$$
\begin{pmatrix} 1 & 0 \\ -\frac{i\lambda}{\pi a^2} & 1 \end{pmatrix}'\tag{8}
$$

where the aperture *a* is a function of the incident light intensity *a*(*IL*) (*IL* must reach threshold to initiate the scattering process). As we can see, depending on the model, the *ABCD* matrix elements of a phase conjugated mirror may depend on several parameters such as the Brillouin downshifting frequency, the Gaussian aperture radius and the incident light intensity [19].

#### **2.3. Systems with hysteresis**

20 Optical Devices in Communication and Computation

right, the above [*ABCD*] matrix becomes

*2.2.2. Phase conjugate mirror* 

phase conjugate matrix is

ABCD matrix reads

corresponds to a threshold intensity

*E*.

Having vacuum (*n*1 = 1) on the left of the interface and a Kerr electro-optic material on the

1 0

1 . 1

(3)

1 0 . 0 1 (4)

(5)

0 exp , *S S B L I z I gIl* (6)

 2

Clearly the elements *A, B, D* are constants but element *C* is a function of the electric field

A second example is a phase conjugate mirror. The process of phase conjugation has the property of retracing an incoming ray along the same incident path [7]. The ideal ABCD

> 

One may notice that the determinant of this particular matrix is not 1 but -1. The ABCD matrix of a real phase conjugated mirror must take into account the specific process to produce the phase conjugation. As already mentioned, typically phase conjugation is achieved in two ways; Four Wave Mixing or using a stimulated scattering process such as Brillouin, i.e. SBS. However upon reflection on a stimulated SBS phase conjugated mirror, the reflected wave has its frequency *ω* downshifted to *ω – δ* = *ω*(1 – *δ*/*ω*) where *δ* is the characteristic Brillouin downshift frequency of the mirror material (typically *δ*/*ω* « 1). In a non-ideal (i.e. real) case one must take the downshifting frequency into account and the

 1 0 . 0 1

Furthermore, since in phase conjugation by SBS a light intensity threshold must be reached in order to have an exponential amplification of the scattered light, the above ideal matrix (4) must be modified. The scattered light intensity at position *z* in the medium is given as

where *IS*(0) is the initial level of scattering, *gB* denotes the characteristic exponential gain coefficient of the scattering process, *IL* is the intensity of the incident light beam, and *l* is the interaction length over which amplification takes place. Given the amplification *G* = exp(*gB*(ν)*ILl*) the threshold gain factor is commonly taken as *G* ~ exp(30) ≈ 1013 which

*n E r*

> At last, as third example we may consider a system with hysteresis. It is well known that such systems exhibit memory. There are many examples of materials with electric, magnetic and elastic hysteresis, as well as systems in neuroscience, biology, electronics, energy and even economics which show hysteresis. As it is known in a system with no hysteresis, it is possible to predict the system's output at an instant in time given only its input at that instant in time. However in a system with hysteresis, this is not possible; there is no way to predict the output without knowing the system's previous state and there is no way to know the system's state without looking at the history of the input. This means that it is necessary to know the path that the input followed before it reached its current value. For an optical element with hysteresis the *ABCD* matrix elements are function of the *yn*, *yn*-1, …*yn*-i and *θn*, *θn*-1, …, *θn*-i and its knowledge is necessary in order to find the state *yn*+1, *θn*+1. In general, taking into account hysteresis, the [*A,B,C,D*] matrix of Eq. (1) may be written as:

$$
\begin{pmatrix} A & B \\ C & D \end{pmatrix} = \begin{pmatrix} A \begin{pmatrix} y\_{n'} y\_{n-1} \dots y\_{n-i}, \theta\_n, \theta\_{n-1} \dots \theta\_{n-i} \end{pmatrix} & \mathcal{B} \begin{pmatrix} y\_{n'} y\_{n-1} \dots y\_{n-i}, \theta\_n, \theta\_{n-1} \dots \theta\_{n-i} \end{pmatrix} \\ \mathcal{C} \begin{pmatrix} y\_{n'} y\_{n-1} \dots y\_{n-i}, \theta\_n, \theta\_{n-1} \dots \theta\_{n-i} \end{pmatrix} & \mathcal{D} \begin{pmatrix} y\_{n'} y\_{n-1} \dots y\_{n-i}, \theta\_n, \theta\_{n-1} \dots \theta\_{n-i} \end{pmatrix} \end{pmatrix} . \tag{9}
$$

#### **3. Dynamic maps**

An extensive list of two-dimensional maps may be found in Ref. [20]. A few examples are Tinkerbell, Duffing and Hénon maps. As will be shown next they may be written as a matrix dynamical system such as the one described by Eq. (1) or equivalently as

$$\begin{aligned} \mathbf{y}\_{n+1} &= A\mathbf{y}\_n + B\boldsymbol{\theta}\_{n'} & \text{ (a)}\\ \boldsymbol{\theta}\_{n+1} &= \mathbf{C}\mathbf{y}\_n + D\boldsymbol{\theta}\_n. & \text{ (b)} \end{aligned} \tag{10}$$

Optical Resonators and Dynamic Maps 23

(18)

(19)

1 1

 

instance, Ref. [25]) and its fixed points are given by:

And the corresponding eigenvalues are

**3.3. Duffing map** 

<sup>1</sup> <sup>1</sup>

*n n n n n n <sup>y</sup> <sup>y</sup> <sup>y</sup> <sup>y</sup>* 

where *yn* and *θn* are the scalar state variables which can be measured as time series and α and *β* the map parameters. In many control systems α is a control parameter. The Jacobian *β* (0 ≤ *β* ≤ 1) is related to dissipation. The dynamics of the Hénon map is well studied (see, for

> 1 1 1 1 ( 1) 4 (,) , <sup>2</sup> *<sup>y</sup> <sup>y</sup>*

1,2 

1

 

*y*

*n n*

 

constants but depend on *θn* and the Duffing map parameters are as follows:

1

2 2 2

 

The study of the stability and chaos of the Duffing map has been the topic of many articles

[26-27]. The Duffing map is a dynamical system which may be written as follows:

*n n nn*

 

where *yn* and *θn* are the scalar state variables and α and *β* the map parameters. In order to write the Duffing map equations as a matrix system Eq. (1) the following values for the coefficients *A, B, C* and *D* must hold. It should be noted that these coefficients are not

> *C*() ,

<sup>2</sup> ( ,) . *<sup>D</sup> n n*

 

Therefore as an ABCD matrix system the Duffing map may be written as:

*y*

 

 

0

2

2

2

3

, (b)

(22)

*A* 0, (23)

*B* 1, (24)

(26)

(25)

, (a)

 

   

 

*y y* () . (21)

1 ( 1) 4 (,) , . <sup>2</sup> *y y* (20)

#### **3.1. Tinkerbell map**

The Tinkerbell map [21, 22] is a discrete-time dynamical system given by the equations:

$$\begin{aligned} y\_{n+1} &= y\_n^2 - \theta\_n^2 + \alpha \ y\_n + \beta \ \theta\_n \text{ (a)}\\ \theta\_{n+1} &= 2y\_n \theta\_n + \gamma \ y\_n + \delta \ \theta\_n. \end{aligned} \tag{11}$$

where *yn* and *θn* are the scalar state variables and *α*, *β*, *γ*, and *δ* the map parameters. In order to write the Tinkerbell map as a matrix system such as Eq. (1) the following values for the coefficients *A, B, C* and *D* must hold:

$$A\left(y\_{n'}\alpha\right) = y\_n + \alpha\_{n'} \tag{12}$$

$$B\left(\theta\_{n'}\beta\right) = -\theta\_n + \beta\_{n'} \tag{13}$$

$$\mathbb{C}(\theta\_{n'}\gamma) = \mathbb{Z}\theta\_n + \gamma. \tag{14}$$

$$D(\mathcal{S}) = \mathcal{S}.\tag{15}$$

It should be noted that these coefficients are not constants but depend on the state variables *yn* and *θn* and the Tinkerbell map parameters *α*, *β*, *γ*, and *δ*. Therefore as an *ABCD* matrix system the Tinkerbell map may be written as:

$$
\begin{pmatrix} y\_{n+1} \\ \theta\_{n+1} \end{pmatrix} = \begin{pmatrix} y\_n + \alpha & -\; \theta\_n + \beta \\ 2\theta\_n + \gamma & \delta \end{pmatrix} \begin{pmatrix} y\_n \\ \theta\_n \end{pmatrix}. \tag{16}
$$

#### **3.2. Hénon map**

The Hénon map has been widely studied due to its nonlinear chaotic dynamics. Hénon map is a popular example of a two-dimensional quadratic mapping which produces a discretetime system with chaotic behavior. The Hénon map is described by the following two difference equations [23, 24]:

$$\begin{aligned} y\_{n+1} &= 1 - \alpha y\_n^2 + \theta\_{n'} \\ \theta\_{n+1} &= \beta y\_n. \end{aligned} \qquad \text{(a)} \tag{17}$$

Following similar steps as those of the Tinkerbell map, this map may be written as a dynamic matrix system:

#### Optical Resonators and Dynamic Maps 23

$$
\begin{pmatrix} y\_{n+1} \\ \theta\_{n+1} \end{pmatrix} = \begin{pmatrix} 1 \\ y\_n \\ \beta \end{pmatrix} \begin{pmatrix} y\_n \\ \theta\_n \end{pmatrix} \tag{18}
$$

where *yn* and *θn* are the scalar state variables which can be measured as time series and α and *β* the map parameters. In many control systems α is a control parameter. The Jacobian *β* (0 ≤ *β* ≤ 1) is related to dissipation. The dynamics of the Hénon map is well studied (see, for instance, Ref. [25]) and its fixed points are given by:

$$\delta(y\_1, \theta\_1) = \left(\frac{-\beta - 1 - \sqrt{\left(\beta + 1\right)^2 + 4\alpha}}{2\alpha}, -\beta y\_1\right) \tag{19}$$

$$\Psi(y\_2, \theta\_2) = \left(\frac{-\beta - 1 + \sqrt{\left(\beta + 1\right)^2 + 4a}}{2a}, -\beta y\_2\right). \tag{20}$$

And the corresponding eigenvalues are

$$
\mathcal{A}\_{1,2} = -\alpha y \pm \sqrt{(\alpha y)^2 - \beta}. \tag{21}
$$

#### **3.3. Duffing map**

22 Optical Devices in Communication and Computation

coefficients *A, B, C* and *D* must hold:

system the Tinkerbell map may be written as:

**3.2. Hénon map** 

difference equations [23, 24]:

dynamic matrix system:

1 1

> 1 1

 

*n n y y y* 

 

 

 

**3.1. Tinkerbell map** 

1 1

 

1 1

 

*n nn n nn y Ay B Cy D*

The Tinkerbell map [21, 22] is a discrete-time dynamical system given by the equations:

*n nn n n n nn n n*

where *yn* and *θn* are the scalar state variables and *α*, *β*, *γ*, and *δ* the map parameters. In order to write the Tinkerbell map as a matrix system such as Eq. (1) the following values for the

2 2

*yy y y y* 

 

 ,

 ,

> 

, (a) . (b)

, (a)

(10)

(11)

, *Ay y n n* (12)

, *n n B* (13)

(14)

(15)

 

2 . (b)

 

 

( ,) 2 , *C n n*

*D*() . 

It should be noted that these coefficients are not constants but depend on the state variables *yn* and *θn* and the Tinkerbell map parameters *α*, *β*, *γ*, and *δ*. Therefore as an *ABCD* matrix

> *nn n n n n n y y y*

The Hénon map has been widely studied due to its nonlinear chaotic dynamics. Hénon map is a popular example of a two-dimensional quadratic mapping which produces a discretetime system with chaotic behavior. The Hénon map is described by the following two

2

 

Following similar steps as those of the Tinkerbell map, this map may be written as a

*n nn*

1 , (a) . (b)

. <sup>2</sup>

   

(17)

(16)

 

 

 

The study of the stability and chaos of the Duffing map has been the topic of many articles [26-27]. The Duffing map is a dynamical system which may be written as follows:

$$\begin{aligned} y\_{n+1} &= \theta\_{n'} \\ \theta\_{n+1} &= -\beta y\_n + \alpha \theta\_n - \theta\_{n'}^3 \end{aligned} \qquad \text{(a)}$$

$$\begin{aligned} \theta\_{n+1} &= -\beta y\_n + \alpha \theta\_n - \theta\_{n'}^3 \end{aligned} \qquad \text{(b)} \tag{22}$$

where *yn* and *θn* are the scalar state variables and α and *β* the map parameters. In order to write the Duffing map equations as a matrix system Eq. (1) the following values for the coefficients *A, B, C* and *D* must hold. It should be noted that these coefficients are not constants but depend on *θn* and the Duffing map parameters are as follows:

$$A = 0,\tag{23}$$

$$B = \mathbf{1}\_{\prime} \tag{24}$$

$$C(\beta) = -\beta,\tag{25}$$

$$D(\theta\_n, \alpha) = \alpha - \theta\_n^2. \tag{26}$$

Therefore as an ABCD matrix system the Duffing map may be written as:

$$
\begin{pmatrix} y\_{n+1} \\ \theta\_{n+1} \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ -\beta & \alpha - \theta\_n^2 \end{pmatrix} \begin{pmatrix} y\_n \\ \theta\_n \end{pmatrix} \tag{27}
$$

Optical Resonators and Dynamic Maps 25

(29)

(30)

(31)

For this system, the total transformation matrix [*A,B,C,D*] for a complete round trip is:

The above one round trip total transformation matrix is

map dynamics for (*yn*,*θn*).

**5. Tinkerbell beams** 

to (15) must be equated to Eq. (29), that is:

*cd d a b a cd e*

*c e*

As can be seen, the elements of this matrix depend on the elements of the map generating matrix device [*a,b,c,e*]. If one does want a specific map to be reproduced by a ray in the ring optical resonator, then each round trip a ray described by (*yn*,*θn*) has to be considered as an iteration of the desired map. Then, the *ABCD* matrix of the map system (16), (18), (27) must be equated to the total *ABCD* matrix of the resonator (29), this in order to generate a specific

It should be noticed that the results given by equations (28) and (29) are only valid for *b* small (*b* ≈ 0). This is due to the fact that before and after the matrix element [*a,b,c,e*] we have

> 1 0 1 10 1 1 10 1 2 2 0 10101 <sup>0101</sup> 01 01

*<sup>c</sup> a b d b c b a cd e d a cd e*

 

Matrix (29) describes a simplified ideal case whereas matrix (31) describes a general more complex and realistic case. These results will be widely used in the next three sections.

This section presents an optical resonator that produces beams following the Tinkerbell map dynamics; these beams will be called "Tinkerbell beams". Equation (29) is the one round trip total transformation matrix of the resonator. If one does want a particular map to be reproduced by a ray in the optical resonator, each round trip described by (*yn*, *θn*), has to be considered as an iteration of the selected map. In order to obtain Tinkerbell beams, Eqs. (12)

*c bc cd e*

<sup>1</sup> <sup>2</sup> 3 2 2 3 32 3 2 2 4 . <sup>1</sup> 3 2 2

*db db <sup>A</sup> Bd a b d*

a propagation of *d*/2. For a general case, expression (29) has to be substituted by:

*C D c e*

Therefore the round trip total transformation matrix is:

3 3 (2 3 2 ) 2 4 . <sup>3</sup>

2

*cd*

*A B d da bd d*

1 0 1 10 1 2 1 2 10 1 . 0 101010 1 0 1 0101

*C D c e* (28)

#### **4. Maps in a ring phase-conjugated resonator**

In this section an optical resonator with a specific map behavior for the variables *y* and *θ* is presented. Figure 1 shows a ring phase-conjugated resonator consisting of two ideal mirrors, an ideal phase conjugate mirror and a yet unknown optical element described by a matrix [*a,b,c,e*]. The two perfect plain mirrors [M] and the ideal phase conjugated mirror [PM] are separated by a distance *d*. The matrices involved in this resonator are: the identity matrix: 1 0 0 1 for the plane mirrors [M], 1 0 0 1 for the ideal phase conjugated mirror [PM], 1 0 1 *<sup>d</sup>* for a distance *<sup>d</sup>* translation and, in addition, the unknown map generating device matrix represented by *a b c e* , is located between the plain mirrors [M] at distance *d*/2 from each one.

**Figure 1.** Ring phase conjugated laser resonator with chaos generating element.

For this system, the total transformation matrix [*A,B,C,D*] for a complete round trip is:

$$
\begin{pmatrix} A & B \\ C & D \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} 1 & d \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & d/2 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} a & b \\ c & e \end{pmatrix} \begin{pmatrix} 1 & d/2 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & d \\ 0 & 1 \end{pmatrix}.\tag{28}
$$

The above one round trip total transformation matrix is

24 Optical Devices in Communication and Computation

plane mirrors [M],

 *a b*

 1 0

**4. Maps in a ring phase-conjugated resonator** 

  1

1

In this section an optical resonator with a specific map behavior for the variables *y* and *θ* is presented. Figure 1 shows a ring phase-conjugated resonator consisting of two ideal mirrors, an ideal phase conjugate mirror and a yet unknown optical element described by a matrix [*a,b,c,e*]. The two perfect plain mirrors [M] and the ideal phase conjugated mirror [PM] are separated by

0 1 for the ideal phase conjugated mirror [PM],

translation and, in addition, the unknown map generating device matrix represented by

a b c e

M M d/2 d/2

PM

**Figure 1.** Ring phase conjugated laser resonator with chaos generating element.

d d

a distance *d*. The matrices involved in this resonator are: the identity matrix:

*c e* , is located between the plain mirrors [M] at distance *d*/2 from each one.

0 1 *n n n n n*

*<sup>y</sup> <sup>y</sup>* (27)

 1 0 0 1

*<sup>d</sup>* for a distance *<sup>d</sup>*

 1 0 1

for the

2

$$
\begin{pmatrix} a + \frac{3cd}{2} & b + \frac{3d}{4}(2a + 3cd + 2e) \\\\ -c & -\frac{3cd}{2} - e \end{pmatrix} . \tag{29}
$$

As can be seen, the elements of this matrix depend on the elements of the map generating matrix device [*a,b,c,e*]. If one does want a specific map to be reproduced by a ray in the ring optical resonator, then each round trip a ray described by (*yn*,*θn*) has to be considered as an iteration of the desired map. Then, the *ABCD* matrix of the map system (16), (18), (27) must be equated to the total *ABCD* matrix of the resonator (29), this in order to generate a specific map dynamics for (*yn*,*θn*).

It should be noticed that the results given by equations (28) and (29) are only valid for *b* small (*b* ≈ 0). This is due to the fact that before and after the matrix element [*a,b,c,e*] we have a propagation of *d*/2. For a general case, expression (29) has to be substituted by:

$$
\begin{pmatrix} A & B \\ C & D \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} 1 & d \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & \frac{d-b}{2} \\ 0 & 1 \end{pmatrix} \begin{pmatrix} a & b \\ c & e \end{pmatrix}
\begin{pmatrix} 1 & \frac{d-b}{2} \\ 0 & 1 \end{pmatrix} \begin{pmatrix} 1 & d \\ 0 & 1 \end{pmatrix} \tag{30}
$$

Therefore the round trip total transformation matrix is:

$$\begin{bmatrix} a - \frac{c}{2}(b - 3d) & \frac{1}{4} \Big[ b^2c - 2b(-2 + a + 3cd + e) + 3d(2a + 3cd + 2e) \Big] \\\\ -c & \frac{1}{2}(bc - 3cd - 2e) \end{bmatrix} . \tag{31}$$

Matrix (29) describes a simplified ideal case whereas matrix (31) describes a general more complex and realistic case. These results will be widely used in the next three sections.

#### **5. Tinkerbell beams**

This section presents an optical resonator that produces beams following the Tinkerbell map dynamics; these beams will be called "Tinkerbell beams". Equation (29) is the one round trip total transformation matrix of the resonator. If one does want a particular map to be reproduced by a ray in the optical resonator, each round trip described by (*yn*, *θn*), has to be considered as an iteration of the selected map. In order to obtain Tinkerbell beams, Eqs. (12) to (15) must be equated to Eq. (29), that is:

$$a + \frac{\Im cd}{2} = a + y\_{n'} \tag{32}$$

Optical Resonators and Dynamic Maps 27

(40)

**Figure 2.** Computer calculation of the magnitude of matrix element *b* of the Tinkerbell map generating device for a resonator with *d* = 1 and Tinkerbell parameters *α* = 0, *β* = -0.6, *γ* = 0 and *δ* = -1 for the first 100

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>100</sup> <sup>0</sup>

n

Matrix-element b

To obtain the Eqs. (36-39) *b*, the thickness of the Tinkerbell generating device, has to be very small (close to zero), so the translations before and after the device can be over the same distance *d*/2. In the previous numeric simulation *b* takes values up to 0.2, so the general case where the map generating element *b* does not have to be small must be studied. As

From Eqs. (16) and (31) we obtain the following system of equations for the matrix elements

( 3) , 2 *<sup>n</sup> <sup>c</sup> a bd y*

<sup>1</sup> <sup>2</sup> ( 2 ( 2 3 ) 3 (2 3 2 )) ,

<sup>4</sup> *<sup>n</sup> b c b a cd e d a cd e* (41)

 

round trips.

0.05

0.1

0.15

size(m)

0.2

0.25

*a*, *b*, *c* and *e*:

**5.1. Tinkerbell beams: General case** 

previously explained Eq. (28) must be substituted by Eq. (30).

$$a \, b + \frac{3d}{4} (2a + 3cd + 2e) = \beta - \theta\_{n'} \tag{33}$$

$$\mathfrak{c} = -\gamma - \mathfrak{D}\theta\_{n'} \tag{34}$$

$$e + \frac{3cd}{2} = -\delta.\tag{35}$$

Equations (32-35) define a system for the matrix elements *a, b, c, e*, that guarantees a Tinkerbell map behaviour for a given ray (*yn*, *θn*). These elements can be written in terms of the map parameters (*α*, *β*, *γ* and *δ*), the resonator's main parameter *d* and the ray state variables *yn* and *θn* as:

$$a = \alpha + \frac{\mathfrak{Z}}{2}\gamma d + \mathfrak{Z}d\theta\_n + y\_{n'} \tag{36}$$

$$a \, b = \frac{1}{4} \left( 4\beta - 6ad + 6\delta d - 9\gamma d^2 - 4\theta\_n - 18d^2 \theta\_n - 6dy\_n \right) \,\tag{37}$$

$$
\mathcal{L} = -\mathcal{D}\theta\_n - \mathcal{Y}\_n \tag{38}
$$

$$e = -\mathcal{S} + \frac{3}{2}d\left(\mathcal{Y} + 2\theta\_n\right). \tag{39}$$

The introduction of the above values for the *a b c e* matrix in Eq. (28) enables us to obtain

Eq. (16). For any transfer matrix elements *A* and *D* describe the lateral magnification while *C* describe the focal length, whereas the device's optical thickness is given by *B* = *L*/*n*, where *L* is its length and *n* its refractive index. From Eqs. (36-39) it must be noted that the upper elements (*a* and *b*) of the device matrix depend on both state variables (*yn* and *θn*) while the lower elements (*c* and *e*) only on the state variable *θn*. The study of the stability and chaos of the Tinkerbell map in terms of its parameters is a well-known topic [21,22]. The behaviour of element *b* is quite interesting; figure 2 shows a computer calculation for the first 100 round trips of matrix element *b* of the Tinkerbell map generating device for a resonator of unitary length (*d* = 1) and map parameters *α* = 0, *β* = -0.6, γ = 0 and *δ* = -1, these parameters were found using brute force calculations and they were selected due to the matrix-element *b* behaviour (i.e. we were looking for behaviour able to be achievable in experiments). As can be seen, the optical length of the map generating device varies on each round trip in a periodic form, this would require that the physical length of the device, its refractive index or a combination of both- change in time. The actual design of a physical Tinkerbell map generating device for a unitary ring resonator must satisfy Eqs. (36-39), to do so its elements (*a*, *b*, *c* and *e*) must vary accordingly.

**Figure 2.** Computer calculation of the magnitude of matrix element *b* of the Tinkerbell map generating device for a resonator with *d* = 1 and Tinkerbell parameters *α* = 0, *β* = -0.6, *γ* = 0 and *δ* = -1 for the first 100 round trips.

#### **5.1. Tinkerbell beams: General case**

26 Optical Devices in Communication and Computation

variables *yn* and *θn* as:

 

 2 , 

<sup>3</sup> , <sup>2</sup> *<sup>n</sup> cd*

<sup>3</sup> 23 2 , <sup>4</sup> *<sup>n</sup>*

<sup>3</sup> . <sup>2</sup> *cd e*

Equations (32-35) define a system for the matrix elements *a, b, c, e*, that guarantees a Tinkerbell map behaviour for a given ray (*yn*, *θn*). These elements can be written in terms of the map parameters (*α*, *β*, *γ* and *δ*), the resonator's main parameter *d* and the ray state

> 

 

 

 2 , 

 <sup>3</sup> 2 .

> *a b*

Eq. (16). For any transfer matrix elements *A* and *D* describe the lateral magnification while *C* describe the focal length, whereas the device's optical thickness is given by *B* = *L*/*n*, where *L* is its length and *n* its refractive index. From Eqs. (36-39) it must be noted that the upper elements (*a* and *b*) of the device matrix depend on both state variables (*yn* and *θn*) while the lower elements (*c* and *e*) only on the state variable *θn*. The study of the stability and chaos of the Tinkerbell map in terms of its parameters is a well-known topic [21,22]. The behaviour of element *b* is quite interesting; figure 2 shows a computer calculation for the first 100 round trips of matrix element *b* of the Tinkerbell map generating device for a resonator of unitary length (*d* = 1) and map parameters *α* = 0, *β* = -0.6, γ = 0 and *δ* = -1, these parameters were found using brute force calculations and they were selected due to the matrix-element *b* behaviour (i.e. we were looking for behaviour able to be achievable in experiments). As can be seen, the optical length of the map generating device varies on each round trip in a periodic form, this would require that the physical length of the device, its refractive index or a combination of both- change in time. The actual design of a physical Tinkerbell map generating device for a unitary ring resonator must satisfy Eqs. (36-39), to do so its elements

 

The introduction of the above values for the

(*a*, *b*, *c* and *e*) must vary accordingly.

 

> 

 

*a y* (32)

*<sup>n</sup> c* (34)

<sup>3</sup> 3 , <sup>2</sup> *n n a dd y* (36)

*<sup>n</sup> <sup>c</sup>* (38)

*c e* matrix in Eq. (28) enables us to obtain

<sup>2</sup> *<sup>n</sup> e d* (39)

 <sup>1</sup> 2 2 4 6 6 9 4 18 6 , <sup>4</sup> *n nn b ddd d dy* (37)

(35)

*<sup>d</sup> b a cd e* (33)

To obtain the Eqs. (36-39) *b*, the thickness of the Tinkerbell generating device, has to be very small (close to zero), so the translations before and after the device can be over the same distance *d*/2. In the previous numeric simulation *b* takes values up to 0.2, so the general case where the map generating element *b* does not have to be small must be studied. As previously explained Eq. (28) must be substituted by Eq. (30).

From Eqs. (16) and (31) we obtain the following system of equations for the matrix elements *a*, *b*, *c* and *e*:

$$a - \frac{c}{2}(b - 3d) = a + y\_{n'} \tag{40}$$

$$\frac{1}{4}(b^2c - 2b(-2 + a + 3cd + e) + 3d(2a + 3cd + 2e)) = \beta - \theta\_{n'} \tag{41}$$

$$-\mathcal{c} = \mathcal{y} + \mathcal{D}\theta\_{n'} \tag{42}$$

Optical Resonators and Dynamic Maps 29

**Figure 3.** Computer calculation of the magnitude of matrix element *b* of the Tinkerbell map generating device for a resonator with *d* = 1 and Tinkerbell parameters *α* = 0.4, *β* = -0.4, *γ* = -0.3 and *δ* = 0.225 for the

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>70</sup> <sup>80</sup> <sup>90</sup> <sup>100</sup> <sup>0</sup>

Matrix-element b

n

This section presents an optical resonator that produces beams following the Duffing map dynamics; these beams will be called "Duffing beams". Equation (29) is the one round trip total transformation matrix of the resonator. If one does want a particular map to be reproduced by a ray in the optical resonator, each round trip described by (*yn*, *θn*), has to be considered as an iteration of the selected map. In order to obtain Duffing beams, Eqs. (23) to

*cd*

 <sup>3</sup> 2 3 2 1, <sup>4</sup>

> *c*

 

*cd*

of a Duffing map for the *y*n and *θ*n state variables. Its solution is:

 <sup>3</sup> <sup>2</sup> . <sup>2</sup> *<sup>n</sup>*

Equations (48-51) define a system for the matrix elements of *a, b, c, e,* enabling the generation

 <sup>3</sup> , <sup>2</sup> *d*

*a* (48)

, (50)

*e* (51)

*a* (52)

*<sup>d</sup> b a cd e* (49)

first 100 round trips.

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

size(m)

**6. Duffing beams** 

(26) must be equated to Eq. (29), that is:

<sup>3</sup> 0, <sup>2</sup>

$$\frac{bc - \Im cd - \Im e}{2} = \delta. \tag{43}$$

The solution to this new system is written as:

$$a = \alpha + \frac{3}{2}\gamma d + 3d\theta\_n + y\_n + \frac{1}{2\gamma + 4\theta\_n} \begin{pmatrix} \gamma \left( 2 - \alpha + \delta - 3\gamma d - 12d\theta\_n - y\_n \right) \\ + \theta\_n \left( 4 - 2\alpha + 2\delta - 12d\theta\_n - 2y\_n \right) \\ - \left( -\frac{\gamma}{2} - \theta\_n \right) \sqrt{\mathbf{P}^2 - \mathbf{Q}} \end{pmatrix},\tag{44}$$

$$b = \frac{1}{\chi + 2\theta\_n} \left( -2 + \alpha - \delta + 3\gamma d + 6d\theta\_n + y\_n + \frac{\sqrt{P^2 - Q}}{2} \right) \tag{45}$$

$$
\mathbf{c} = -\boldsymbol{\gamma} - \boldsymbol{\mathcal{D}} \boldsymbol{\theta}\_{n'} \tag{46}
$$

$$c = \delta + \frac{3}{2}\gamma d + 3d\theta\_n + \frac{1}{2\gamma + 4\theta\_n} \begin{pmatrix} \gamma \left( 2 - \alpha + \delta - 3\gamma d - 12d\theta\_n - y\_n \right) \\ + \theta\_n \left( 4 - 2\alpha + 2\delta - 12d\theta\_n - 2y\_n \right) \\ - \left( -\frac{\gamma}{2} - \theta\_n \right) \sqrt{P^2 - Q} \end{pmatrix},\tag{47}$$

where:

$$P = 4 - 2\alpha + 2\delta - 6\gamma d - 12d\theta\_n - 2y\_n$$

and

$$Q = \left(4\gamma + 8\theta\_n\right)\left(-4\beta + 6\gamma d - 6\delta d + 9\gamma d^2 + 4\theta\_n + 18d^2\theta\_n + 6dy\_n\right).$$

It should be noted that if one takes into account the thickness of the map generating element, the equations complexity is substantially increased. Now only *c* has a simple relation with *θn* and *γ*, on the other hand *a, b* and *e* are dependent on both state variables, on all Tinkerbell parameters, as well as on the resonator length. When the calculation is performed for this new matrix with the following map parameters: *α* = 0.4, *β* = -0.4, *γ* = -0.3 and *δ* = 0.225, figure 3 is obtained. The behaviour observed in figure 3 for the matrix-element *b* can be obtained for several different parameters' combinations, as well as other dynamical regimes with a lack of relevance to our work. One can note that after a few iterations the device's optical thickness is small and constant, this should make easier a physical implementation of this device.

**Figure 3.** Computer calculation of the magnitude of matrix element *b* of the Tinkerbell map generating device for a resonator with *d* = 1 and Tinkerbell parameters *α* = 0.4, *β* = -0.4, *γ* = -0.3 and *δ* = 0.225 for the first 100 round trips.

#### **6. Duffing beams**

28 Optical Devices in Communication and Computation

The solution to this new system is written as:

where:

and

 

*n*

 

> 

 

implementation of this device.

 

   2 , 

3 2 . <sup>2</sup>

 

*a dd y d y*

*n*

 

 2 , 

*e dd d y*

*n*

 

 4 2 2 6 12 2 

 

2 2 4 8 4 6 6 9 4 18 6 . *Q d n n <sup>n</sup> <sup>n</sup> <sup>d</sup> d d dy*

It should be noted that if one takes into account the thickness of the map generating element, the equations complexity is substantially increased. Now only *c* has a simple relation with *θn* and *γ*, on the other hand *a, b* and *e* are dependent on both state variables, on all Tinkerbell parameters, as well as on the resonator length. When the calculation is performed for this new matrix with the following map parameters: *α* = 0.4, *β* = -0.4, *γ* = -0.3 and *δ* = 0.225, figure 3 is obtained. The behaviour observed in figure 3 for the matrix-element *b* can be obtained for several different parameters' combinations, as well as other dynamical regimes with a lack of relevance to our work. One can note that after a few iterations the device's optical thickness is small and constant, this should make easier a physical

*n n P d d y*

 

 

2

 

3 1 <sup>3</sup> 4 2 2 12 2 , 2 24

 

*n*

 

> 

*n n n n*

 <sup>2</sup> <sup>1</sup> 2 36 , 2 2 *n n*

3 1 3 4 <sup>2</sup> <sup>2</sup> <sup>12</sup> <sup>2</sup> , 2 2 <sup>4</sup>

 

*n n n n n*

 

2

   

*n*

*P Q <sup>b</sup> dd y* (45)

 

 

 

2 3 12

 2

*P Q*

*<sup>n</sup> c* (42)

*bc cd e* (43)

 

 2

*P Q*

 

 

*ddy*

*n n*

(44)

(47)

 

*<sup>n</sup> c* (46)

 

*ddy*

*n n*

 

 

 

2 3 12

This section presents an optical resonator that produces beams following the Duffing map dynamics; these beams will be called "Duffing beams". Equation (29) is the one round trip total transformation matrix of the resonator. If one does want a particular map to be reproduced by a ray in the optical resonator, each round trip described by (*yn*, *θn*), has to be considered as an iteration of the selected map. In order to obtain Duffing beams, Eqs. (23) to (26) must be equated to Eq. (29), that is:

$$a + \frac{3cd}{2} = 0,\tag{48}$$

$$b + \frac{3d}{4}(2a + 3cd + 2e) = 1,\tag{49}$$

$$-c = -\mathcal{B}\_1 \tag{50}$$

$$-\frac{\Im cd}{2} - e = \alpha - \theta\_n^2. \tag{51}$$

Equations (48-51) define a system for the matrix elements of *a, b, c, e,* enabling the generation of a Duffing map for the *y*n and *θ*n state variables. Its solution is:

$$a = -\frac{3\beta d}{2},$$
 
$$\text{(52)}$$

$$b = \frac{1}{4} \Big( 4 + 6ad + 9\,\theta d^2 - 6d\theta\_n^2 \Big) \tag{53}$$

$$
\sigma = \beta\_\prime \tag{54}
$$

Optical Resonators and Dynamic Maps 31

parameters *α* = 1.04 and *β* = -1 for the first 100 round trips. As it is well known, depending on the *α* and *β* map parameters different dynamic states may be obtained including chaos. As can be seen the optical length of the map generating device given by the *B* matrix element varies on each round trip. This requires that either the physical length of the device or its refractive index, or a combination of both, changes as shown in Figure 4. The design of a physical Duffing map generating device for this resonator must satisfy Eqs. (52-55). A physical implementation of this device is possible as long as its *ABCD* elements vary

The results given by Eqs. (52-55) are valid only when the *b* element of the [*a,b,c,e*] matrix is small. As can be seen from Eq. (28), the thickness of the Duffing map generating element (described by matrix [*a,b,c,e*]) must be close to zero. This because in Eq. (28) the matrix before and after the [*a,b,c,e*] is a matrix for a *d*/2 translation which is possible only if *b* = 0 or very small. The previous numeric simulation shows that the *b* element takes the values of up to 0.3. Therefore one must consider a general case where the map generating element *b* has not the limitation of being asked to be small. For a general case, Eq. (28) must be substituted by Eq. (30) and (31). From expressions (27) and (31) we obtain the following system of

( 3 ) 0,

3 2 <sup>2</sup> . <sup>2</sup> *<sup>n</sup>*

2 2 <sup>2</sup> 2 2 <sup>2</sup> 4 (1 3) 2 (2 ) (2 ) , <sup>2</sup> *n n <sup>n</sup> d*

2 2 <sup>2</sup> 2 2 2 3 4 (1 3) 2 (2 ) (2 ) , *n n <sup>n</sup> d d*

2 2 <sup>2</sup> 2 2 <sup>2</sup> 4 (1 3) 2 (2 ) (2 ) . <sup>2</sup> *n n <sup>n</sup> d*

 

 

> 

<sup>1</sup> <sup>2</sup> ( 2 ( 2 3 ) 3 (2 3 2 )) 1,

*c* 

*<sup>c</sup> a bd* (56)

(59)

, (58)

 

> 

, (62)

 

*b c b a cd e d a cd e* (57)

 

 

(63)

 

(60)

 

(61)

2

*bc cd e*

 

   

according to these equations.

**6.1. Duffing beams: General case** 

equations for the matrix elements *a, b, c, e*:

4

 

   

The solution to this system is given by:

*a*

*e*

 

*c*

*b*

$$e = -\alpha - \frac{\Im d\beta}{2} + \theta\_n^2. \tag{55}$$

**Figure 4.** Computer calculation of the magnitude of matrix element *b* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = -1 for the first 100 round trips.

As can be seen these matrix elements depend on the Duffing parameters *α* and *β* as well as on the resonator main parameter *d* and on the state variable *θ*n. These are the values which must be substituted for the [*a,b,c,e*] matrix in equation (28) for the round trip matrix. As expected, the introduction of the above [*a,b,c,e*] matrix elements in Eq. (29) produces the *ABCD* matrix of the Duffing Map, Eq. (27). For a general *ABCD* transfer matrix, elements *A* and *D* are related to the lateral magnification and element *C* to the focal length, whereas element *B* gives the optical length of the device. The optical thickness of the *ABCD* is; *B* = *L*/*n*, where *L* is the physical length of the device and *n* its refractive index. From Eqs. (52-55) we may see that the *A* and *C* elements of the matrix [*a,b,c,e*] are constants depending only on the resonator parameter *d* and the Duffing parameters *α* and *β*. However matrix elements *B* and *D* are dynamic ones and depend on the state variable *θ*n. Of special interest is element *B* of the map generating matrix [*a,b,c,e*]. Figure 4 shows a computer calculation of matrix element *B* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = -1 for the first 100 round trips. As it is well known, depending on the *α* and *β* map parameters different dynamic states may be obtained including chaos. As can be seen the optical length of the map generating device given by the *B* matrix element varies on each round trip. This requires that either the physical length of the device or its refractive index, or a combination of both, changes as shown in Figure 4. The design of a physical Duffing map generating device for this resonator must satisfy Eqs. (52-55). A physical implementation of this device is possible as long as its *ABCD* elements vary according to these equations.

#### **6.1. Duffing beams: General case**

30 Optical Devices in Communication and Computation

 

> 

 <sup>3</sup> <sup>2</sup> . <sup>2</sup> *<sup>n</sup> d*

*c* 

**Figure 4.** Computer calculation of the magnitude of matrix element *b* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = -1 for the first 100 round trips.

As can be seen these matrix elements depend on the Duffing parameters *α* and *β* as well as on the resonator main parameter *d* and on the state variable *θ*n. These are the values which must be substituted for the [*a,b,c,e*] matrix in equation (28) for the round trip matrix. As expected, the introduction of the above [*a,b,c,e*] matrix elements in Eq. (29) produces the *ABCD* matrix of the Duffing Map, Eq. (27). For a general *ABCD* transfer matrix, elements *A* and *D* are related to the lateral magnification and element *C* to the focal length, whereas element *B* gives the optical length of the device. The optical thickness of the *ABCD* is; *B* = *L*/*n*, where *L* is the physical length of the device and *n* its refractive index. From Eqs. (52-55) we may see that the *A* and *C* elements of the matrix [*a,b,c,e*] are constants depending only on the resonator parameter *d* and the Duffing parameters *α* and *β*. However matrix elements *B* and *D* are dynamic ones and depend on the state variable *θ*n. Of special interest is element *B* of the map generating matrix [*a,b,c,e*]. Figure 4 shows a computer calculation of matrix element *B* of the Duffing map generating device for a resonator with *d* = 1 and Duffing

 

<sup>1</sup> 2 2 46 9 6 , <sup>4</sup> *<sup>n</sup> b d dd* (53)

*e* (55)

, (54)

The results given by Eqs. (52-55) are valid only when the *b* element of the [*a,b,c,e*] matrix is small. As can be seen from Eq. (28), the thickness of the Duffing map generating element (described by matrix [*a,b,c,e*]) must be close to zero. This because in Eq. (28) the matrix before and after the [*a,b,c,e*] is a matrix for a *d*/2 translation which is possible only if *b* = 0 or very small. The previous numeric simulation shows that the *b* element takes the values of up to 0.3. Therefore one must consider a general case where the map generating element *b* has not the limitation of being asked to be small. For a general case, Eq. (28) must be substituted by Eq. (30) and (31). From expressions (27) and (31) we obtain the following system of equations for the matrix elements *a, b, c, e*:

$$a - \frac{c}{2}(b - \Im d) = 0,\tag{56}$$

$$\frac{1}{4}(b^2c - 2b(-2 + a + 3cd + e) + 3d(2a + 3cd + 2e)) = 1,\tag{57}$$

$$-\mathcal{c} = -\mathcal{B} \, , \tag{58}$$

$$\frac{bc - 3cd - 2e}{2} = a - \theta\_n^2. \tag{59}$$

The solution to this system is given by:

$$a = \frac{2 + a - \theta\_n^2 + \sqrt{a^2 + 4\beta(-1 + 3d) - 2a(-2 + \theta\_n^2) + (-2 + \theta\_n^2)^2}}{2},\tag{60}$$

$$b = \frac{2 + \alpha + 3\beta d - \theta\_n^2 + \sqrt{\alpha^2 + 4\beta(-1 + 3d) - 2\alpha(-2 + \theta\_n^2) + (-2 + \theta\_n^2)^2}}{\beta},\tag{61}$$

$$
\mathfrak{c} = \beta,\tag{62}
$$

$$e = \frac{2 - \alpha + \theta\_n^2 + \sqrt{\alpha^2 + 4\beta(-1 + 3d) - 2\alpha(-2 + \theta\_n^2) + (-2 + \theta\_n^2)^2}}{2}.\tag{63}$$

As we may see, taking into account the thickness of the map generating element device described by matrix [*a,b,c,e*] greatly increases its complexity. Now only the *C* matrix element is constant, being elements *A, B* and *D* dependent on the state variable *θ*n and on the Duffing parameters *α* and *β* as well as on the resonator main parameter *d.* Figure 5 shows a computer calculation of the matrix element *B* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = - 0.6 for the first 100 round trips. As can be seen, the optical thickness variation of the map generating device now is rather small, which means that the length and/or refractive index variation of the map generating element is also small and favors a physical realization of this device.

Optical Resonators and Dynamic Maps 33

(64)

(68)

, (70)

(71)

(69)

, (66)

*cd e* (67)

*<sup>d</sup> b a cd e* (65)

3 1 , <sup>2</sup> *<sup>n</sup> n*

<sup>3</sup> 2 3 2 1, <sup>4</sup>

<sup>3</sup> 0. 2

The solution for the Hénon chaos matrix elements [*a,b,c,e*], able to produce Hénon beams in

*d a y <sup>y</sup>* 

3 1 , <sup>2</sup> *<sup>n</sup> n*

31 3 1 ( ), 2 2 *<sup>n</sup> n <sup>d</sup> bd y <sup>y</sup>*

> 3 . 2 *d*

As can be seen the matrix elements depend on the Hénon parameters α and *β* as well as on the resonator main parameter *d* and on the state variable *y*n. However when analyzing the behavior of element "*b*" (Eq. (69)) we may see that there is a problem caused by the term 1/*y*n. While for the case of Tinkerbell and Duffing beams we were able to look at the behavior of the obtained "*b*" element for small values of *y*n, as it is shown in figures (2-5), this is not possible for the Henon case because small values of *y*n will produce very large values for "*b*", therefore making very difficult to obtain solutions with practical value.

In an analogous way to the two previous cases, using expression (18) and (31) we obtain for

 2 2 <sup>3</sup> <sup>2</sup> <sup>4</sup> 12 14 2 2 2 6 4 , <sup>2</sup> *nn n n nn n*

 

*y*

2 2 <sup>3</sup> <sup>2</sup> <sup>4</sup> 1 23 14 2 2 2 6 4 , <sup>2</sup>

*n*

*dy y y dy y y <sup>b</sup> y* 

*y y y dy y y*

*nn n nnn*

(73)

(72)

 
> 

 

 

> *c*

*e*

terms of the Hénon Map are the following:

**7.1. Hénon beams: General case** 

*a*

the general Hénon chaos matrix elements [*a,b,c,e*]:

  *c*  *cd a y <sup>y</sup>* 

**Figure 5.** Computer calculation of the magnitude of matrix element *b* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = -0.6 for the first 100 round trips.

#### **7. Hénon beams**

This section presents an optical resonator that produces beams following the Hénon map dynamics; these beams will be called "Hénon beams". Equation (29) is the one round trip total transformation matrix of the resonator. If one does want a particular map to be reproduced by a ray in the optical resonator, each round trip described by (*yn*, *θn*), has to be considered as an iteration of the selected map. In order to obtain Hénon beams, the [*A, B, C, D*] elements of Eq. (18) must be equated to Eq. (29), that is:

Optical Resonators and Dynamic Maps 33

$$a + \frac{\Im cd}{2} = \frac{1}{y\_n} - \alpha y\_{n'} \tag{64}$$

$$a + \frac{3d}{4}(2a + 3cd + 2e) = 1,\tag{65}$$

$$-c = \beta\_\prime \tag{66}$$

$$-\frac{3cd}{2} - e = 0.\tag{67}$$

The solution for the Hénon chaos matrix elements [*a,b,c,e*], able to produce Hénon beams in terms of the Hénon Map are the following:

$$a = \frac{3\beta d}{2} + \frac{1}{y\_n} - \alpha y\_{n'} \tag{68}$$

$$b = 1 + \frac{3}{2}d(-\frac{1}{y\_n} + \alpha y\_n - \frac{3d\beta}{2}),\tag{69}$$

$$
\mathcal{L} = -\mathcal{B}\_{\prime} \tag{70}
$$

$$e = \frac{\Im d\beta}{2}.\tag{71}$$

As can be seen the matrix elements depend on the Hénon parameters α and *β* as well as on the resonator main parameter *d* and on the state variable *y*n. However when analyzing the behavior of element "*b*" (Eq. (69)) we may see that there is a problem caused by the term 1/*y*n. While for the case of Tinkerbell and Duffing beams we were able to look at the behavior of the obtained "*b*" element for small values of *y*n, as it is shown in figures (2-5), this is not possible for the Henon case because small values of *y*n will produce very large values for "*b*", therefore making very difficult to obtain solutions with practical value.

#### **7.1. Hénon beams: General case**

32 Optical Devices in Communication and Computation

device.

trips.

**7. Hénon beams** 

As we may see, taking into account the thickness of the map generating element device described by matrix [*a,b,c,e*] greatly increases its complexity. Now only the *C* matrix element is constant, being elements *A, B* and *D* dependent on the state variable *θ*n and on the Duffing parameters *α* and *β* as well as on the resonator main parameter *d.* Figure 5 shows a computer calculation of the matrix element *B* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = - 0.6 for the first 100 round trips. As can be seen, the optical thickness variation of the map generating device now is rather small, which means that the length and/or refractive index variation of the map generating element is also small and favors a physical realization of this

**Figure 5.** Computer calculation of the magnitude of matrix element *b* of the Duffing map generating device for a resonator with *d* = 1 and Duffing parameters *α* = 1.04 and *β* = -0.6 for the first 100 round

This section presents an optical resonator that produces beams following the Hénon map dynamics; these beams will be called "Hénon beams". Equation (29) is the one round trip total transformation matrix of the resonator. If one does want a particular map to be reproduced by a ray in the optical resonator, each round trip described by (*yn*, *θn*), has to be considered as an iteration of the selected map. In order to obtain Hénon beams, the [*A, B, C,* 

*D*] elements of Eq. (18) must be equated to Eq. (29), that is:

In an analogous way to the two previous cases, using expression (18) and (31) we obtain for the general Hénon chaos matrix elements [*a,b,c,e*]:

$$a = \frac{-1 - 2y\_n + \alpha y\_n^2 + \sqrt{1 - 4y\_n - 2\left(-2 + \alpha - 2\beta + 6\beta d\right)y\_n^2 + 4\alpha y\_n^3 + \alpha^2 y\_n^4}}{2y\_n},\tag{72}$$

$$b = \frac{1 + \left(-2 + 3\beta d\right)y\_n - \alpha y\_n^2 + \sqrt{1 - 4y\_n - 2\left(-2 + \alpha - 2\beta + 6\beta d\right)y\_n^2 + 4\alpha y\_n^3 + \alpha^2 y\_n^4}}{2y\_n},\tag{73}$$

$$
\mathcal{L} = -\mathcal{B}\_{\prime} \tag{74}
$$

**9. References** 

504

1996), p. 259

697-702 (2002)

3309

374

435.

3333

96-97

Optical Resonators and Dynamic Maps 35

[1] G.S. He, Optical Phase Conjugation: Principles, Techniques and Applications, Progress

[4] M. Ostermeyer, A. Heuer, V. Watermann, and R. Menzel in Int. Quantum Electronics Conf., 1996 OSA Technical Digest Series (Optical Society of America, Washington, DC,

[5] Bel'dyugin I.M., Galushkin M.G., and Zemskov E.M. Kvantovaya Elektron., 11, 887 (1984) [Sov. J. Quantum Electron., 14, 602 (1984); Bespalov V.I. and Betin A.A. Izv.

[6] V.V. Yarovoi, A.V. Kirsanov, Phase conjugation of speckle-inhomogeneous radiation in a holographic Nd:YAG laser with a short thermal hologram, Quantum Electronics 32(8)

[7] M.J. Damzen, V.I. Vlad, V. Babin, and A. Mocofanescu, Stimulated Brillouin Scattering:

[8] D. A. Rockwell, A review of phase-conjugate solid-state lasers, IEEE Journal of

[9] Dämmig, M., Zinner, G., Mitschke, F., Welling, H. Stimulated Brillouin scattering in fibers with and without external feedback (1993) Physical Review A, 48 (4), pp. 3301-

[12] B. Barrientos, V. Aboites, and M. Damzen, Temporal dynamics of a ring dye laser with a stimulated Brillouin scattering mirror, Applied Optics, 35 (27) 5386-5391 (1996) [13] E. Rosas, V. Aboites, M.J. Damzen, FWM interaction transfer matrix for self-adaptive

[15] V. Aboites and M. Wilson, Int. J. of Pure and Applied Mathematics, 54 No. 3 (2009) 429-

[16] V. Aboites, A.N. Pisarchik, A. Kiryanov, X. Gomez-Mont, Opt. Comm., 283, (2010) 3328-

[17] A. Gerrard and J.M. Burch, Introduction to Matrix Methods in Optics, Dover

[18] Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, Advanced Materials, 17 No.1 (2005)

[21] R.L. Davidchack, Y.C. Lai, A.Klebanoff, E.M. Bollt, Physics Letters A, 287 (2001) 99-104

[10] P.J. Soan, M.J. Damzen, V. Aboites and M.H.R. Hutchinson, Opt. Lett. 19 (1994), 783 [11] A.D. Case, P.J. Soan, M.J. Damzen and M.H.R. Hutchinson, J. Opt. Soc. Am. B 9 (1992)

Fundamentals and Applications, Institute of Physics, Bristol (2003)

laser oscillators, Optics Communications 174 243-247 (2000)

[19] A.V. Kir'yanov, V. Aboites and N.N. Il'ichev, JOSA B, 17 (2000) 11-17

[22] P.E. McSharry, P.R.C. Ruffino, Dynamical Systems, 18, No. 3 (2003) 191-200

Publications Inc., New York (1994).

[20] http://en.wikipedia.org/wiki/List\_of\_chaotic\_maps

[14] V. Aboites, Int. J. of Pure and Applied Mathematics, 36, No. 4 (2007) 345-352.

[2] H.-J. Eichler, R. Menzel, and D. Schumann, Appl. Opt., 31 No. 24 (1992) 5038-5043 [3] M. O'Connor, V. Devrelis, and J. Munch, in Proc. Int. Conf. on Lasers'95 (1995) pp. 500-

in Quantum Electronics 26, No, 3, (2002), 61p.

Akad. Nauk SSSR., Ser. Fiz., 53 1496 (1989)

Quantum Electronics 24, No. 6, (1988) 1124-1140

$$e = \frac{-1 + 2y\_n + \alpha y\_n^2 - \sqrt{1 - 4y\_n - 2(-2 + \alpha - 2\beta + 6\beta d)y\_n^2 + 4\alpha y\_n^3 + \alpha^2 + y\_n^4}}{2y\_n}.\tag{75}$$

#### **8. Conclusions**

This chapter presents a description of the application of non-constant ABCD matrix in the description of ring optical phase conjugated resonators. It is shown how the introduction of a particular map generating device in a ring optical phase-conjugated resonator can generate beams with the behavior of a specific two dimensional map. In this way beams that behave according to the Tinkerbell, Duffing or Henon Maps which we call "Tinkerbell, Duffing or Henon Beams", are obtained.

In particular, this chapter shows how Tinkerbell beams can be produced if a particular device is introduced in a ring optical phase-conjugated resonator. The difference equations of the Tinkerbell map are explicitly introduced in an *ABCD* transfer matrix to control the beams behaviour. The matrix elements *a*, *b*, *c* and *e* of a map generating device are found in terms of the map parameters (*α*, *β*, *γ* and *δ*), the state variables (*yn* and *θn*) and the resonator length. The mathematical characteristics of an optical device inside an optical resonator capable to produce Tinkerbell beams are found. In the general case a device with fixed size was obtained, opening the possibility of a continuance of this work; that is the actual building of an optical device with these *a*, *b*, *c* and *d* matrix elements according to the description given and the experimental observation of Tinkerbell beams.

Also, it is explicitly shown how the difference equations of the Duffing map can be used to describe the dynamic behavior of what we call Duffing beams i.e. beams that behave according to the Duffing map. The matrix elements *a, b, c, e* of a map generating device are found in terms of α and β, the Duffing parameters, the state variable *θ*n and the resonator parameter *d*.

Finally it is shown that the difference equations of the Hénon map can be used to describe the dynamical behavior of Hénon beams. The matrix elements *a, b, c, e* of a chaos generating device are found in terms of α and β the Hénon parameters, and *d* the resonator parameter.

#### **Author details**

V. Aboites\* , Y. Barmenkov and A. Kir'yanov *Centro de Investigaciones en Óptica, México* 

M. Wilson *Université des Sciences et Technologies de Lille, France* 

<sup>\*</sup> Corresponding Author

#### **9. References**

34 Optical Devices in Communication and Computation

Duffing or Henon Beams", are obtained.

*e*

**8. Conclusions** 

parameter *d*.

resonator parameter.

**Author details** 

Corresponding Author

V. Aboites\*

M. Wilson

 \*

*c* 

2 2 <sup>3</sup> <sup>2</sup> <sup>4</sup> 1 2 1 4 2( 2 2 6 ) 4 . <sup>2</sup> *nn n nn n n y y y dy y y*

(75)

*y* 

This chapter presents a description of the application of non-constant ABCD matrix in the description of ring optical phase conjugated resonators. It is shown how the introduction of a particular map generating device in a ring optical phase-conjugated resonator can generate beams with the behavior of a specific two dimensional map. In this way beams that behave according to the Tinkerbell, Duffing or Henon Maps which we call "Tinkerbell,

In particular, this chapter shows how Tinkerbell beams can be produced if a particular device is introduced in a ring optical phase-conjugated resonator. The difference equations of the Tinkerbell map are explicitly introduced in an *ABCD* transfer matrix to control the beams behaviour. The matrix elements *a*, *b*, *c* and *e* of a map generating device are found in terms of the map parameters (*α*, *β*, *γ* and *δ*), the state variables (*yn* and *θn*) and the resonator length. The mathematical characteristics of an optical device inside an optical resonator capable to produce Tinkerbell beams are found. In the general case a device with fixed size was obtained, opening the possibility of a continuance of this work; that is the actual building of an optical device with these *a*, *b*, *c* and *d* matrix elements according to the

Also, it is explicitly shown how the difference equations of the Duffing map can be used to describe the dynamic behavior of what we call Duffing beams i.e. beams that behave according to the Duffing map. The matrix elements *a, b, c, e* of a map generating device are found in terms of α and β, the Duffing parameters, the state variable *θ*n and the resonator

Finally it is shown that the difference equations of the Hénon map can be used to describe the dynamical behavior of Hénon beams. The matrix elements *a, b, c, e* of a chaos generating device are found in terms of α and β the Hénon parameters, and *d* the

description given and the experimental observation of Tinkerbell beams.

, Y. Barmenkov and A. Kir'yanov

*Université des Sciences et Technologies de Lille, France* 

*Centro de Investigaciones en Óptica, México* 

 

, (74)

	- [23] E. Eschenazi, H.G. Solari, and R. Gilmore, Phys. Rev. A 39 (1989) 2609.
	- [24] M. Hénon, Commun. Math. Phys. 50 (1976) 69.
	- [25] R.L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, Redwood City (1989).
	- [26] L.M. Saha and R. Tehri, Int. J. of Appl. Math and Mech., 6 (1) (2010) 86-93
	- [27] C. Murakami, W. Murakami, K. Hirose and W.H. Ichikawa, Chaos, Solitons & Fractals, 16 (2) (2003) 233-244

**1. Introduction**

Wei Li and Xunya Jiang

http://dx.doi.org/10.5772/50025

cannot be rigorous.

cited.

Early in 1968, Veselago[1] predicted that a new type of artificial metamaterial, which possesses simultaneously negative permittivity and permeability, could function as a lens to focus electromagnetic waves. These research direction was promoted by Pendry's work[2, 3] and other latter works [4–26]. They show that with such a metamaterial lens, not only the radiative waves but also the evanescent waves, can be collected at its image, so the lens could be a superlens which can break through or overcome the diffraction limit of the conventional imaging system. This beyond-limit property gives us a new window to design devices.

**Electrodynamics of Evanescent Wave in** 

**Chapter 3**

**Negative Refractive Index Superlens** 

Additional information is available at the end of the chapter

It is well-known that evanescent wave plays an important role in the beyond-limit property of the metamaterial superlens. Furthermore, evanescent waves become more and more important when the metamaterial devices enter sub-wavelength scales[27, 28]. Therefore, the quantitatively study of *pure* evanescent waves in the metamaterial superlens is very significant. However, the quantitatively effects of *pure* evanescent wave in the metamaterial superlens have not been intensively studied, since so far almost all studies were only interested in the image properties with global field[8, 9], which is the summation of radiative wave and evanescent wave. On the other hand, many theoretical works were performed to study the metamaterial superlens, employing either finite-difference-time domain (FDTD) simulations[16] or some approximate approaches[29, 30]. However, one cannot obtain the rigorous *pure* evanescent wave by these numerical methods, since the image field of the metamaterial superlens obtained by FDTD is global field, and other approximate approaches

In reviewing these existing efforts, we feel desirable to develop a rigorous method that can be used to study quantitatively the transient phenomena of the evanescent wave in the image of the metamaterial superlens. In this paper, we will present a new method based on the Green's function[7, 8] to serve this purpose. Our method can be successfully used to calculate the evanescent wave, as well as the radiative wave and the global field. The main idea of our method can be briefly illustrated as follows. Since the metamaterial superlens is a linear

and reproduction in any medium, provided the original work is properly cited.

©2012 Li and Jiang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Chapter 3**

## **Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens**

Wei Li and Xunya Jiang

36 Optical Devices in Communication and Computation

Redwood City (1989).

16 (2) (2003) 233-244

[24] M. Hénon, Commun. Math. Phys. 50 (1976) 69.

[23] E. Eschenazi, H.G. Solari, and R. Gilmore, Phys. Rev. A 39 (1989) 2609.

[26] L.M. Saha and R. Tehri, Int. J. of Appl. Math and Mech., 6 (1) (2010) 86-93

[25] R.L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley,

[27] C. Murakami, W. Murakami, K. Hirose and W.H. Ichikawa, Chaos, Solitons & Fractals,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50025

#### **1. Introduction**

Early in 1968, Veselago[1] predicted that a new type of artificial metamaterial, which possesses simultaneously negative permittivity and permeability, could function as a lens to focus electromagnetic waves. These research direction was promoted by Pendry's work[2, 3] and other latter works [4–26]. They show that with such a metamaterial lens, not only the radiative waves but also the evanescent waves, can be collected at its image, so the lens could be a superlens which can break through or overcome the diffraction limit of the conventional imaging system. This beyond-limit property gives us a new window to design devices.

It is well-known that evanescent wave plays an important role in the beyond-limit property of the metamaterial superlens. Furthermore, evanescent waves become more and more important when the metamaterial devices enter sub-wavelength scales[27, 28]. Therefore, the quantitatively study of *pure* evanescent waves in the metamaterial superlens is very significant. However, the quantitatively effects of *pure* evanescent wave in the metamaterial superlens have not been intensively studied, since so far almost all studies were only interested in the image properties with global field[8, 9], which is the summation of radiative wave and evanescent wave. On the other hand, many theoretical works were performed to study the metamaterial superlens, employing either finite-difference-time domain (FDTD) simulations[16] or some approximate approaches[29, 30]. However, one cannot obtain the rigorous *pure* evanescent wave by these numerical methods, since the image field of the metamaterial superlens obtained by FDTD is global field, and other approximate approaches cannot be rigorous.

In reviewing these existing efforts, we feel desirable to develop a rigorous method that can be used to study quantitatively the transient phenomena of the evanescent wave in the image of the metamaterial superlens. In this paper, we will present a new method based on the Green's function[7, 8] to serve this purpose. Our method can be successfully used to calculate the evanescent wave, as well as the radiative wave and the global field. The main idea of our method can be briefly illustrated as follows. Since the metamaterial superlens is a linear

©2012 Li and Jiang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 2 Will-be-set-by-IN-TECH 38 Optical Devices in Communication and Computation Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens <sup>3</sup>

system, so all dynamical processes can be solved by sum of multi-frequency components. And each frequency component can be solved by sum of multi-wavevector components. So we can use Green's function of multi-frequency components to obtain the strict numerical results. Therefore, our method based on the Green's function is strict, and it is quite a universe method in any linear system, for example, it can be used to study the two dimensional (2D) and three dimensional (3D) metamaterial superlens.

Therefore, Eq.(3) becomes:

; *t* − *t* �

the frequency domain, which satisfies

→→ *G* (*r*,*r*�

By Fourier transforming the electric field

*E*(*r*, *ω*), satisfying

Considering the general properties:

and →→

Eq.(12) exhibits the role of →→

region for simplicity. If

, *ω*) =

i.e., *Es*(*r*�

where

*Es*(*r*�

frequency domain between *r* and *r*�

*E*(*r*�

∇×∇× +*�*(*r*)*μ*(*r*)*�*0*μ*<sup>0</sup>

) is known, then the

*E*(*r*, *t*) = −*μ*<sup>0</sup>

∇×∇×−*μ*(*r*, *<sup>ω</sup>*)*�*(*r*, *<sup>ω</sup>*)*�*0*μ*0*ω*<sup>2</sup>

; *t* − *t* � ) = <sup>1</sup> 2*π dω* →→ *G* (*r*,*r*�

*<sup>E</sup>*(*r*, *<sup>t</sup>*) = <sup>1</sup>

*G* (*r*,*r*�

Substituting Eq.(8), Eq.(9), Eq(10) and Eq.(11) into Eq.(6), we can obtain

*<sup>E</sup>*(*r*, *<sup>ω</sup>*) = →→

, *ω*), then Eq.(12) can be rewritten as:

*<sup>E</sup>*(*r*, *<sup>ω</sup>*) = →→

*E*(*r*�

*G* (*r*,*r*�

, *ω*) is the spectrum of the exciting source.

2*π dωe* −*iωt*

*�*(*r*, −*ω*) = *�*(*r*, *ω*)∗,

*μ*(*r*, −*ω*) = *μ*(*r*, *ω*)∗,

; <sup>−</sup>*ω*) = →→

*G* (*r*,*r*�

*G* (*r*,*r*�

; *<sup>ω</sup>*) that →→

*G* (*r*,*r*�

; *<sup>ω</sup>*) · *E*(*r*�

. Here we have supposed that *σ*(*r*�

; *<sup>ω</sup>*) · *Es*(*r*�

, *ω*) is the exciting source's electric field in the frequency domain,

*G* (*r*,*r*�

dispersive material at a frequency *<sup>ω</sup>*, respectively, and →→

*∂*2 *∂t*<sup>2</sup>

> →→ *G* (*r*,*r*�

By Fourier transforming Eq.(5) from time domain to frequency domain, we obtain

 →→ *G* (*r*,*r*�

; *t* − *t* �

*E* field can be found as

; *t* − *t* � ) ·*<sup>J</sup>*(*r*� , *t* � )*dr*�

 →→ *G* (*r*,*r*�

where *�*(*r*, *ω*) and *μ*(*r*, *ω*) are the relative permittivity and the relative permeability of the

) = *δ*(*r* − *r*�

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 39

; *ω*) = *δ*(*r* − *r*�

−*iω*(*t*−*t* �

*E*(*r*, *t*) in time domain to the frequency domain, we

*G* (*r*,*r*�

; *ω*)*e*

)*δ*(*t* − *t* � ) →→

> ) →→

*E*(*r*, *ω*) (9)

; *ω*)∗. (11)

, *ω*). (12)

, *ω*) (13)

, *t*) = 1 in the source

; *ω*) is a propagator for the field in the

*I* (5)

*dt*� (6)

; *ω*) is the Green's Function in

) (8)

(10)

*I* (7)

If →→ *G* (*r*,*r*�

obtain

The content of the chapter is organized as follows. We mainly focus on the details of our theory and method in Section 2. After that, in Section 3, we will calculate the field of the image of a NIR superlens by using our method, including radiative waves, evanescent waves, SEWs, and global field. The method will be confirmed by using FDTD simulations. In Section 4, we will present our study on the group delay of evanescent wave in the superlens by using our method. Finally, conclusions are presented in Section 5.

#### **2. Theoretical method**

In this section, we will focus on the theoretical details of our method. First, a time-dependent Green's function will be introduced. Then, based on the Green's function, the method to obtain evanescent waves as well as radiative waves will be presented.

#### **2.1. A time-dependent Green's function**

First, we would like to introduce a very useful time-dependent Green's function for the solution of inhomogeneous media. The time-dependent Green's function can be applied to study the dynamical scattering processes[7, 22]. In the inhomogeneous media, the problem we study can be solved by Maxwell equations:

$$\begin{aligned} \nabla \times \vec{E}(r, t) &= -\mu(r)\mu\_0 \frac{\partial}{\partial t} \vec{H}(r, t), \\\\ \nabla \times \vec{H}(r, t) &= \epsilon(r)\epsilon\_0 \frac{\partial}{\partial t} \vec{E}(r, t) + \vec{J}(r, t), \end{aligned} \tag{1}$$

where *J*(*r*, *t*) = *σ*(*r*, *t*) *E*(*r*, *t*) is the current density and *σ*(*r*, *t*) is the conductivity. We rewrite Eq.(1) as:

$$\nabla \times \nabla \times \vec{E}(r,t) + \epsilon(r)\mu(r)\epsilon\_0\mu\_0 \frac{\partial^2}{\partial t^2} \vec{E}(r,t) = -\mu(r)\mu\_0 \frac{\partial}{\partial t} [\sigma(r,t)\vec{E}(r,t)] \tag{2}$$

To solve Eq.(2), we introduce a dynamic Green's function →→ *G* (*r*,*r*� ; *t*, *t* � ), which satisfies:

$$\left(\nabla \times \nabla \times + \epsilon(r)\mu(r)\epsilon\_0\mu\_0 \frac{\partial^2}{\partial t^2}\right) \stackrel{\rightarrow}{G} (r, r'; t, t') = \delta(r - r')\delta(t - t') \stackrel{\rightarrow}{I} \tag{3}$$

where →→ *<sup>I</sup>* is a unit dyad. In this system, when *<sup>r</sup>* and *<sup>r</sup>*� is given, →→ *G* (*r*,*r*� ; *t*, *t* � ) is just a function of (*t* − *t* � ) in time domain, so it yields

$$\stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; t, t') = \stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; t - t'). \tag{4}$$

Therefore, Eq.(3) becomes:

2 Will-be-set-by-IN-TECH

system, so all dynamical processes can be solved by sum of multi-frequency components. And each frequency component can be solved by sum of multi-wavevector components. So we can use Green's function of multi-frequency components to obtain the strict numerical results. Therefore, our method based on the Green's function is strict, and it is quite a universe method in any linear system, for example, it can be used to study the two dimensional (2D) and three

The content of the chapter is organized as follows. We mainly focus on the details of our theory and method in Section 2. After that, in Section 3, we will calculate the field of the image of a NIR superlens by using our method, including radiative waves, evanescent waves, SEWs, and global field. The method will be confirmed by using FDTD simulations. In Section 4, we will present our study on the group delay of evanescent wave in the superlens by using

In this section, we will focus on the theoretical details of our method. First, a time-dependent Green's function will be introduced. Then, based on the Green's function, the method to

First, we would like to introduce a very useful time-dependent Green's function for the solution of inhomogeneous media. The time-dependent Green's function can be applied to study the dynamical scattering processes[7, 22]. In the inhomogeneous media, the problem

> *∂ ∂t*

*∂ ∂t* 

*∂*2 *∂t*<sup>2</sup> 

 →→ *G* (*r*,*r*� *H* (*r*, *t*),

*E*(*r*, *t*) +*J*(*r*, *t*),

*E*(*r*, *t*) is the current density and *σ*(*r*, *t*) is the conductivity. We rewrite

*∂ ∂t*

> ; *t*, *t* �

*G* (*r*,*r*�

*G* (*r*,*r*�

) = *δ*(*r* − *r*�

[*σ*(*r*, *t*)

)*δ*(*t* − *t* � ) →→

> ; *t*, *t* �

). (4)

*E*(*r*, *t*) = −*μ*(*r*)*μ*<sup>0</sup>

; *t*, *t* �

*G* (*r*,*r*�

; *t* − *t* �

*E*(*r*, *t*) = −*μ*(*r*)*μ*<sup>0</sup>

∇ × *<sup>H</sup>* (*r*, *<sup>t</sup>*) = *�*(*r*)*�*<sup>0</sup>

*∂*2 *∂t*<sup>2</sup>

*<sup>I</sup>* is a unit dyad. In this system, when *<sup>r</sup>* and *<sup>r</sup>*� is given, →→

; *t*, *t* � ) = →→

dimensional (3D) metamaterial superlens.

**2.1. A time-dependent Green's function**

we study can be solved by Maxwell equations:

∇ ×

*E*(*r*, *t*) + *�*(*r*)*μ*(*r*)*�*0*μ*<sup>0</sup>

To solve Eq.(2), we introduce a dynamic Green's function →→

→→ *G* (*r*,*r*�

∇×∇× +*�*(*r*)*μ*(*r*)*�*0*μ*<sup>0</sup>

) in time domain, so it yields

**2. Theoretical method**

where *J*(*r*, *t*) = *σ*(*r*, *t*)

∇×∇×

Eq.(1) as:

where →→

of (*t* − *t* �

our method. Finally, conclusions are presented in Section 5.

obtain evanescent waves as well as radiative waves will be presented.

$$\left(\nabla \times \nabla \times + \epsilon(r)\mu(r)\epsilon\_0\mu\_0 \frac{\partial^2}{\partial t^2}\right) \stackrel{\rightarrow}{G} (r, r'; t - t') = \delta(r - r')\delta(t - t') \stackrel{\rightarrow}{I} \tag{5}$$

If →→ *G* (*r*,*r*� ; *t* − *t* � ) is known, then the *E* field can be found as

$$\vec{E}(r,t) = -\mu\_0 \int \stackrel{\rightarrow}{G}(r,r';t-t') \cdot \vec{f}(r',t') dr' dt' \tag{6}$$

By Fourier transforming Eq.(5) from time domain to frequency domain, we obtain

$$\left(\nabla \times \nabla \times -\mu(r,\omega)\epsilon(r,\omega)\epsilon\_0\mu\_0\omega^2\right)^{\xrightarrow{\longrightarrow}}\stackrel{\longrightarrow}{G}\left(r,r';\omega\right) = \delta(r-r')\stackrel{\longrightarrow}{I} \tag{7}$$

where *�*(*r*, *ω*) and *μ*(*r*, *ω*) are the relative permittivity and the relative permeability of the dispersive material at a frequency *<sup>ω</sup>*, respectively, and →→ *G* (*r*,*r*� ; *ω*) is the Green's Function in the frequency domain, which satisfies

$$\stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; t - t') = \frac{1}{2\pi} \int d\omega \stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega) e^{-i\omega(t - t')}\tag{8}$$

By Fourier transforming the electric field *E*(*r*, *t*) in time domain to the frequency domain, we obtain *E*(*r*, *ω*), satisfying

$$\vec{E}(r,t) = \frac{1}{2\pi} \int d\omega e^{-i\omega t} \vec{E}(r,\omega) \tag{9}$$

Considering the general properties:

$$\begin{aligned} \varepsilon(r, -\omega) &= \varepsilon(r, \omega)^\*, \\ \mu(r, -\omega) &= \mu(r, \omega)^\*, \end{aligned} \tag{10}$$

and →→

(1)

*E*(*r*, *t*)] (2)

*I* (3)

) is just a function

), which satisfies:

$$\stackrel{\rightarrow}{G}(r, r'; -\omega) = \stackrel{\rightarrow}{G}(r, r'; \omega)^\*.\tag{11}$$

Substituting Eq.(8), Eq.(9), Eq(10) and Eq.(11) into Eq.(6), we can obtain

$$
\vec{E}(r,\omega) = \stackrel{\rightarrow}{G}(r,r';\omega) \cdot \vec{E}(r',\omega). \tag{12}
$$

Eq.(12) exhibits the role of →→ *G* (*r*,*r*� ; *<sup>ω</sup>*) that →→ *G* (*r*,*r*� ; *ω*) is a propagator for the field in the frequency domain between *r* and *r*� . Here we have supposed that *σ*(*r*� , *t*) = 1 in the source region for simplicity. If *E*(*r*� , *ω*) is the exciting source's electric field in the frequency domain, i.e., *Es*(*r*� , *ω*) = *E*(*r*� , *ω*), then Eq.(12) can be rewritten as:

$$
\vec{E}(r,\omega) = \stackrel{\rightarrow}{G}(r,r';\omega) \cdot \vec{E}\_{\sf s}(r',\omega) \tag{13}
$$

where *Es*(*r*� , *ω*) is the spectrum of the exciting source.

#### 4 Will-be-set-by-IN-TECH 40 Optical Devices in Communication and Computation Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens <sup>5</sup>

So the field � *E*(*r*, *t*) can be obtained by the inverse Fourier transformation:

$$\vec{E}(r,t) = \frac{1}{2\pi} \int d\omega e^{-i\omega t} \vec{E}(r,\omega),\tag{14}$$

where *J*0(*z*) and *J*2(*z*) are the usual zeroth-order Bessel function and second-order Bessel

*<sup>l</sup>*(*ω*/*c*)2, *<sup>k</sup>*<sup>2</sup>

in the region (0 < *z* < *d*) and the region (*z* < 0, *z* > *d*) respectively. Here, *TTE* and *TTM* are the

� <sup>+</sup> *<sup>k</sup>*<sup>2</sup>

*e*−*ikzd*

*<sup>k</sup>*<sup>2</sup> *<sup>T</sup>TM*(*k*�)(*J*0(*k*�*x*) + *<sup>J</sup>*2(*k*�*x*))*k*�*dk*�],

, *ω*) = *σ*(*r*�

*TTE*(*kx*)*e*

*TTE*(0)*e*

; *ω*) is obtained, we can obtain the field in the frequency domain in the region



<sup>−</sup>*ikz <sup>z</sup>*[*TTE*(*k*�)(*J*0(*k*�*x*) <sup>−</sup> *<sup>J</sup>*2(*k*�*x*))

*<sup>z</sup>* = (*ω*/*c*)<sup>2</sup> are the dispersion relation

, *ω*). *σ*(*r*�

*ikz zdkx*. (20)

<sup>−</sup>*ikz*. (21)

, *ω*) has been

(19)

(� <sup>+</sup> <sup>1</sup>)2*e*−*iklzd* <sup>−</sup> (� − <sup>1</sup>)2*eiklzd* , (17)

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 41

(�� <sup>+</sup> <sup>1</sup>)2*e*−*iklzd* <sup>−</sup> (�� <sup>−</sup> <sup>1</sup>)2*eiklzd* , (18)

, *ω*)� *Es*(*r*�

*<sup>z</sup>* = *ω*2/*c*2, where *c* is the light velocity in the vacuum. In

*E* polarized), respectively,

function, respectively, and *k*<sup>2</sup>

which are respectively given by

*kzμ<sup>r</sup> l*

And for the 3D case, we have

dispersion relation as follows: *k*<sup>2</sup>

After →→

*G* (*r*,*r*�

can be obtained.

the case of *k*<sup>2</sup>

While if *k*<sup>2</sup>

→→ *G* (*r*,*r*�

and �� <sup>=</sup> *klz*

For the 2D case, the wave vector *<sup>k</sup>*� <sup>=</sup> *kx*, we have

→→ *G* (*r*,*r*�

*kz�<sup>r</sup> l* .

; *<sup>ω</sup>*) = <sup>−</sup> *<sup>i</sup>*

, *ω*) = 1. So Eq(16) becomes:

+ *k*2 *z*

→→ *G* (*r*,*r*�

8*π*

 1 *kz e*

; *<sup>ω</sup>*) = <sup>−</sup> *<sup>i</sup>*

**2.2. The Green's function for radiative waves and evanescent waves**


4*π*

; *<sup>ω</sup>*) = <sup>−</sup> *<sup>i</sup>*

 *eikx <sup>x</sup> kz*

2*k*

*z* > *d* by Eq.(12). And then by the inverse Fourier transformation, the field in time domain

Now, we will apply a time-dependent Green's function for a radiative wave and an evanescent wave. This Green's function can be directly developed from the Green's function introduced in the Sec.2.1. The schematic model is shown in Fig.1. As we know, the plane solution wave for the electric field in vacuum is of the form *Ez*(*r*||, *<sup>z</sup>*, *<sup>t</sup>*) = *Ez*0exp(*i*(*k*||*r*|| <sup>+</sup> *kzz* <sup>−</sup> *<sup>ω</sup>t*)), where *<sup>k</sup>*|| and *kz* are wave numbers along the *xy* plane and *z* directions respectively, and they satisfy the

, *ω*) is the conductivity in source region, i.e., �*J*(*r*�

and

*σ*(*r*�

where � <sup>=</sup> *klz*

assumed to be *σ*(*r*�

� <sup>+</sup> *<sup>k</sup>*<sup>2</sup>

*lz* <sup>=</sup> *�<sup>r</sup> l μr*

*<sup>T</sup>TE*(*k*�) = <sup>4</sup>�*e*−*ikzd*

*<sup>T</sup>TM*(*k*�) = <sup>4</sup>��

transmission coefficients for TE wave (*H*� polarized) and TM wave (�

where *ω*<sup>0</sup> is the working frequency of the exciting source.

**Figure 1.** The shematic of the three-layer inhomogeneous medium.

Now the remaining problem is to solve Eq(7) to get →→ *G* (*r*,*r*� ; *ω*). With the exciting source *Es*(*r*� , *t*) (whose spectrum is *Es*(*r*� , *<sup>ω</sup>*)), after obtain →→ *G* (*r*,*r*� ; *ω*), then we can calculate � *E*(*r*, *ω*) directly by Eq.(12).

As a typical example, the time-dependent Green's function for the three-layer inhomogeneous media is presented, which is shown in Fig.1. The inhomogeneous media of the system can be described by:

$$
\varepsilon(r)\varepsilon\_{0\prime}\mu(r)\mu\_0 = \begin{cases}
\varepsilon\_{0\prime}\mu\_0 & z > d \\
\varepsilon\_I^r \varepsilon\_{0\prime} \mu\_I^r \mu\_0 & 0 < z < d \\
\varepsilon\_{0\prime}\mu\_0 & z < 0
\end{cases} \tag{15}
$$

→→ *G* (*r*,*r*� ; *ω*) is related to the transmission coefficient and/or reflection coefficient which are dependent on the boundary conditions of each layer. Here, we only consider the Green's function in the region that *<sup>z</sup>* <sup>&</sup>gt; *<sup>d</sup>*. Under these conditions, →→ *G* (*r*,*r*� ; *ω*) has been obtained in Ref.[7]. →→ *G* (*r*,*r*� ; *ω*) is different in different spatial dimensions. For three-dimension, we can rewrite →→ *G* (*r*,*r*� ; *ω*) as follows:

$$\begin{split} \stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega) &= -\frac{i\sigma(r', \omega)}{8\pi} \int \frac{1}{k\_z} e^{-ik\_z z} [T^{TE}(k\_{\parallel})(f\_0(k\_{\parallel} \mathbf{x}) - f\_2(k\_{\parallel} \mathbf{x})) \\ &+ \frac{k\_z^2}{k^2} T^{TM}(k\_{\parallel})(f\_0(k\_{\parallel} \mathbf{x}) + f\_2(k\_{\parallel} \mathbf{x})) k\_{\parallel} dk\_{\parallel} ], \end{split} \tag{16}$$

where *J*0(*z*) and *J*2(*z*) are the usual zeroth-order Bessel function and second-order Bessel function, respectively, and *k*<sup>2</sup> � <sup>+</sup> *<sup>k</sup>*<sup>2</sup> *lz* <sup>=</sup> *�<sup>r</sup> l μr <sup>l</sup>*(*ω*/*c*)2, *<sup>k</sup>*<sup>2</sup> � <sup>+</sup> *<sup>k</sup>*<sup>2</sup> *<sup>z</sup>* = (*ω*/*c*)<sup>2</sup> are the dispersion relation in the region (0 < *z* < *d*) and the region (*z* < 0, *z* > *d*) respectively. Here, *TTE* and *TTM* are the transmission coefficients for TE wave (*H*� polarized) and TM wave (� *E* polarized), respectively, which are respectively given by

$$T^{TE}(k\_{\parallel}) = \frac{4\triangle e^{-ik\_{\perp}d}}{ (\triangle + 1)^2 e^{-ik\_{\parallel}d} - (\triangle - 1)^2 e^{ik\_{\parallel}d}} \,\tag{17}$$

and

4 Will-be-set-by-IN-TECH

*G* (*r*,*r*�

*<sup>l</sup> μ*<sup>0</sup> 0 < *z* < *d*

*G* (*r*,*r*�

<sup>−</sup>*ikz <sup>z</sup>*[*TTE*(*k*�)(*J*0(*k*�*x*) <sup>−</sup> *<sup>J</sup>*2(*k*�*x*))

*G* (*r*,*r*�

*�*0, *μ*<sup>0</sup> *z* > *d*

*�*0, *μ*<sup>0</sup> *z* < 0

; *ω*) is different in different spatial dimensions. For three-dimension, we can

; *ω*) is related to the transmission coefficient and/or reflection coefficient which are

*<sup>k</sup>*<sup>2</sup> *<sup>T</sup>TM*(*k*�)(*J*0(*k*�*x*) + *<sup>J</sup>*2(*k*�*x*))*k*�*dk*�],

*E*(*r*, *ω*), (14)

; *ω*). With the exciting source

; *ω*) has been obtained in

*E*(*r*, *ω*)

(15)

(16)

; *ω*), then we can calculate �

*E*(*r*, *t*) can be obtained by the inverse Fourier transformation:

2*π* � *dωe* −*iωt*�

, *<sup>ω</sup>*)), after obtain →→

As a typical example, the time-dependent Green's function for the three-layer inhomogeneous media is presented, which is shown in Fig.1. The inhomogeneous media of the system can be

> *�r <sup>l</sup> �*0, *<sup>μ</sup><sup>r</sup>*

dependent on the boundary conditions of each layer. Here, we only consider the Green's

⎧ ⎨ ⎩

�

where *ω*<sup>0</sup> is the working frequency of the exciting source.

**Figure 1.** The shematic of the three-layer inhomogeneous medium.

Now the remaining problem is to solve Eq(7) to get →→

*�*(*r*)*�*0, *μ*(*r*)*μ*<sup>0</sup> =

, *ω*) 8*π*

� 1 *kz e*

function in the region that *<sup>z</sup>* <sup>&</sup>gt; *<sup>d</sup>*. Under these conditions, →→

; *<sup>ω</sup>*) = <sup>−</sup> *<sup>i</sup>σ*(*r*�

+ *k*2 *z*

; *ω*) as follows:

, *t*) (whose spectrum is *Es*(*r*�

*<sup>E</sup>*(*r*, *<sup>t</sup>*) = <sup>1</sup>

So the field �

*Es*(*r*�

→→ *G* (*r*,*r*�

directly by Eq.(12).

described by:

Ref.[7]. →→

rewrite →→

*G* (*r*,*r*�

*G* (*r*,*r*�

→→ *G* (*r*,*r*�

$$T^{TM}(k\_{\parallel}) = \frac{4\triangle' e^{-ik\_{z}d}}{ (\triangle' + 1)^{2} e^{-ik\_{\parallel z}d} - (\triangle' - 1)^{2} e^{ik\_{\parallel z}d} } \tag{18}$$

where � <sup>=</sup> *klz kzμ<sup>r</sup> l* and �� <sup>=</sup> *klz kz�<sup>r</sup> l* .

*σ*(*r*� , *ω*) is the conductivity in source region, i.e., �*J*(*r*� , *ω*) = *σ*(*r*� , *ω*)� *Es*(*r*� , *ω*). *σ*(*r*� , *ω*) has been assumed to be *σ*(*r*� , *ω*) = 1. So Eq(16) becomes:

$$\begin{split} \stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega) &= -\frac{i}{8\pi} \int \frac{1}{k\_z} e^{-i k\_\parallel z} [T^{\text{TE}}(k\_{\parallel})(f\_0(k\_{\parallel} \mathbf{x}) - f\_2(k\_{\parallel} \mathbf{x})) \\ &+ \frac{k\_z^2}{k^2} T^{TM}(k\_{\parallel})(f\_0(k\_{\parallel} \mathbf{x}) + f\_2(k\_{\parallel} \mathbf{x})) k\_{\parallel} dk\_{\parallel} ], \end{split} \tag{19}$$

For the 2D case, the wave vector *<sup>k</sup>*� <sup>=</sup> *kx*, we have

$$\stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega) = -\frac{i}{4\pi} \int \frac{e^{ik\_x x}}{k\_z} T^{TE}(k\_x) e^{ik\_z z} dk\_x. \tag{20}$$

And for the 3D case, we have

$$\stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega) = -\frac{i}{2k} T^{TE}(0) e^{-ikz}.\tag{21}$$

After →→ *G* (*r*,*r*� ; *ω*) is obtained, we can obtain the field in the frequency domain in the region *z* > *d* by Eq.(12). And then by the inverse Fourier transformation, the field in time domain can be obtained.

#### **2.2. The Green's function for radiative waves and evanescent waves**

Now, we will apply a time-dependent Green's function for a radiative wave and an evanescent wave. This Green's function can be directly developed from the Green's function introduced in the Sec.2.1. The schematic model is shown in Fig.1. As we know, the plane solution wave for the electric field in vacuum is of the form *Ez*(*r*||, *<sup>z</sup>*, *<sup>t</sup>*) = *Ez*0exp(*i*(*k*||*r*|| <sup>+</sup> *kzz* <sup>−</sup> *<sup>ω</sup>t*)), where *<sup>k</sup>*|| and *kz* are wave numbers along the *xy* plane and *z* directions respectively, and they satisfy the dispersion relation as follows: *k*<sup>2</sup> || <sup>+</sup> *<sup>k</sup>*<sup>2</sup> *<sup>z</sup>* = *ω*2/*c*2, where *c* is the light velocity in the vacuum. In the case of *k*<sup>2</sup> || <sup>&</sup>lt; *<sup>ω</sup>*2/*c*2, *kz* is real, corresponding to the radiative waves along the *<sup>z</sup>* direction. While if *k*<sup>2</sup> || <sup>&</sup>gt; *<sup>ω</sup>*2/*c*2, *kz* is imaginary, corresponding to the evanescent waves along the *<sup>z</sup>*

#### 6 Will-be-set-by-IN-TECH 42 Optical Devices in Communication and Computation Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens <sup>7</sup>

direction. Similarly, in the slab region, the real or imaginary *klz* corresponds to the radiative wave or the evanescent wave along *z* direction, respectively.

For simplicity, we first consider the 2D system, in which *<sup>k</sup>*|| <sup>=</sup> *kx*. The global field of image region is the superposition of radiative waves and evanescent waves. We can rewrite Eq.(20),Eq.(13) and Eq(14) as follows:

$$\stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega; k\_{\rm min}, k\_{\rm max}) = -\frac{i}{4\pi} \int\_{k\_{\rm min}}^{k\_{\rm max}} \frac{e^{ik\_{\rm x}}}{k\_{z}} T^{\rm TE}(k\_{\rm x}) e^{ik\_{z}z} \, dk\_{\rm x} \tag{22}$$

also be obtained from Eq.(22) to Eq.(24) such that

*G SEW*(*r*,*r*�

Green's function can be obtained easily from Eq.(28) as:

; *ω*)|

→→ *G eva*(*r*,*r*�

*G rad*(*r*,*r*�

discussion, i.e., just replace *kx* by *<sup>k</sup>*|| and let *<sup>k</sup>*<sup>2</sup>

; *ω*)|

*kmax*=*k<sup>b</sup> x kmin*=*ka x* = →→ *G* (*r*,*r*�

*kmax*=1.2*ω*/*c kmin*=1.1*ω*/*<sup>c</sup>* <sup>=</sup> <sup>−</sup> *<sup>i</sup>*

; *<sup>ω</sup>*), the evanescent wave Green's function →→

**3. Electromagnetic waves in the image of the superlens**

<sup>=</sup> <sup>−</sup> *<sup>i</sup>* 4*π*

As an typical example, a SEW with an integral range [*kmin* = 1.1*ω*/*c*, *kmax* = 1.2*ω*/*c*], whose

4*π*

In this way, we can obtain the Green's function for the SEW with any integral range. Obviously, evanescent wave could be regarded as the superposition of SEWs. Therefore, we

From Eq.(28), Eq.(26), Eq.(25), and Eq.(27), one can obtain the SEW Green's function

respectively. Substituting them to Eq.(23) and Eq.(24) respectively, we can obtain the field of the SEW, the evanescent wave, the radiative wave, and the global field, respectively.

For the 3D system, obviously, the methods to get Green's function for the SEW, the evanescent wave, the radiative wave, and the global field are respectively very similar with the above

In this section, we will discuss the image's field of a 2D metamaterial superlens, which is shown in Fig.2. The thickness of the metamaterial slab is *d*, which is placed at the *xy*-*plane* between *z* = *d*/2 and *z* = 3*d*/2. The source is set in the object plane at (*z* = 0). Obviously, the image will be formed in the image plane at *z* = 2*d*. The source is the quasi-monochromatic random source with the field expressed as *Es*(*r*, *t*)=*Us*(*r*, *t*)*exp*(−*iω*0*t*), where *Us*(*r*, *t*) is a slow-varying random function, *<sup>ω</sup>*<sup>0</sup> <sup>=</sup> 1.33 <sup>×</sup> 1015/*<sup>s</sup>* is the central frequency of our random source (the details of the random source can be seen in Ref.[29]). The exciting source *Es*(*r*, *t*)

the TM modes are investigated (the TM modes have the electric field perpendicular to the

is a quasi-monochromatic field with the central frequency *ω*0, whose electric field

The inhomogeneous media of the metamaterial superlens system are described by:


; *ω*) = ∑ *SEWs* ; *k<sup>a</sup> <sup>x</sup>*, *<sup>k</sup><sup>b</sup> x*)

 *<sup>k</sup><sup>b</sup> x ka x*

 1.2*ω*/*c* 1.1*ω*/*c*

→→

*G SEW*(*r*,*r*�

; *<sup>ω</sup>*), and the global field Green's function →→

*<sup>x</sup>* + *k*<sup>2</sup>

*Es*(*ω*) are shown in Fig.3(a) and Fig.3(b), respectively. In this paper, only

*eikx <sup>x</sup> kz*

*TTE*(*kx*)*e*

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 43

*TTE*(*kx*)*e*

*eikx <sup>x</sup> kz*

*G eva*(*r*,*r*�

*ikz zdkx*.

*ikz zdkx*.

; *ω*). (29)

*<sup>y</sup>* in Eq.(28), Eq.(26), Eq.(25), and

; *ω*), the radiative wave

*G glob*(*r*,*r*�

; *ω*),

*Es*(*t*) and

(28)

→→

→→

have

→→

*G SEW*(*r*,*r*�

Green's function →→

Eq.(27), respectively.

frequency spectrum

two-dimensional plane of our model).

*G SEW*(*r*,*r*�

$$
\vec{E}(r; \omega; k\_{\rm min}, k\_{\rm max}) = \stackrel{\rightarrow}{G}(r, r'; \omega; k\_{\rm min}, k\_{\rm max}) \cdot \vec{E}\_{\rm s}(r', \omega), \tag{23}
$$

and

$$\vec{E}(r;t;k\_{\rm min},k\_{\rm max}) = \frac{1}{2\pi} \int d\omega e^{-i\omega t} \vec{E}(r;\omega;k\_{\rm min},k\_{\rm max}),\tag{24}$$

where *kmin* < *kx* < *kmax* is the integral range. The integral range is of great significance, since different integral range corresponds to different wave. For example, the integral range [*kmin* → −∞, *kmax* → ∞] is for global field, and the range [*kmin* = −*ω*/*c*, *kmax* = *ω*/*c*] is for radiative wave. Obviously, for linear system, the integral range can be chosen arbitrarily.

From Eq.(22) to Eq.(24), we can directly calculate the radiative wave and evanescent wave. In the case of radiative wave (*k*<sup>2</sup> *<sup>x</sup>* <sup>&</sup>lt; *<sup>ω</sup>*2/*c*2), the integral range is [*kmin* <sup>=</sup> <sup>−</sup>*ω*/*c*, *kmax* <sup>=</sup> *<sup>ω</sup>*/*c*], so the radiative wave Green's function →→ *G rad*(*r*,*r*� ; *ω*) satisfies

$$\begin{aligned} \stackrel{\rightarrow}{G}\_{rad}(r, r'; \omega) &= \stackrel{\rightarrow}{G}^{\rightarrow}(r, r'; \omega; k\_{\rm min} = -\omega/c, k\_{\rm max} = \omega/c) \\ &= -\frac{\stackrel{\rightarrow}{\mathbf{1}}}{4\pi} \int\_{-\omega/c}^{\omega/c} \frac{e^{ik\_{\rm x}\mathbf{x}}}{k\_{\rm z}} T^{TE}(k\_{\rm x}) e^{ik\_{\rm z}\mathbf{z}} dk\_{\rm x} \end{aligned} \tag{25}$$

for radiative waves.

In the case of evanescent wave (*k*<sup>2</sup> *<sup>x</sup>* <sup>&</sup>gt; *<sup>ω</sup>*2/*c*2), the integral range is *kx*>|*ω*/*c*|, so the evanescent wave Green's function →→ *G eva*(*r*,*r*� ; *ω*) satisfies:

$$\begin{aligned} \stackrel{\rightarrow}{G}\_{\text{eva}}(r, r'; \omega) &= 2 \lim\_{k\_{\text{max}} \to \infty} \stackrel{\rightarrow}{G}(r, r'; \omega; k\_{\text{min}} = \omega/c, k\_{\text{max}}) \\ &= -\frac{i}{2\pi} \lim\_{k\_{\text{max}} \to \infty} \int\_{\omega/c}^{k\_{\text{max}}} \frac{e^{ik\_{\text{x}}}}{k\_{z}} T^{TE}(k\_{\text{x}}) e^{ik\_{\text{z}} z} dk\_{\text{x}} \end{aligned} \tag{26}$$

for evanescent waves.

And for the global field, the global field Green's function →→ *G glob*(*r*,*r*� ; *ω*) satisfies:

$$\stackrel{\rightarrow}{G}\_{glob}^{\rightarrow}(r, r'; \omega) = \stackrel{\rightarrow}{G}\_{rad}^{\rightarrow}(r, r'; \omega) + \stackrel{\rightarrow}{G}\_{eva}^{\rightarrow}(r, r'; \omega) \tag{27}$$

Additionally, we can also focus our observation on the *subdivided evanescent wave* (SEW), with a certain integral range [*kmin* = *k<sup>a</sup> <sup>x</sup>*, *kmax* = *k<sup>b</sup> <sup>x</sup>*]. The SEW, with a certain integral range, can also be obtained from Eq.(22) to Eq.(24) such that

6 Will-be-set-by-IN-TECH

direction. Similarly, in the slab region, the real or imaginary *klz* corresponds to the radiative

For simplicity, we first consider the 2D system, in which *<sup>k</sup>*|| <sup>=</sup> *kx*. The global field of image region is the superposition of radiative waves and evanescent waves. We can rewrite

4*π*

where *kmin* < *kx* < *kmax* is the integral range. The integral range is of great significance, since different integral range corresponds to different wave. For example, the integral range [*kmin* → −∞, *kmax* → ∞] is for global field, and the range [*kmin* = −*ω*/*c*, *kmax* = *ω*/*c*] is for radiative wave. Obviously, for linear system, the integral range can be chosen arbitrarily.

From Eq.(22) to Eq.(24), we can directly calculate the radiative wave and evanescent wave. In

; *ω*) satisfies

*eikx <sup>x</sup> kz*

*G* (*r*,*r*�

2*π dωe* −*iωt*�

*G rad*(*r*,*r*�

 *ω*/*c* −*ω*/*c*

*G* (*r*,*r*�

; *ω*) satisfies:

*kmax*→∞

→→ *G* (*r*,*r*�

*lim kmax*→∞

*G rad*(*r*,*r*�

Additionally, we can also focus our observation on the *subdivided evanescent wave* (SEW), with

 *kmax ω*/*c*

*eikx <sup>x</sup> kz*

; *<sup>ω</sup>*) + →→

; *<sup>ω</sup>*) = →→

*G eva*(*r*,*r*�

And for the global field, the global field Green's function →→

<sup>=</sup> <sup>−</sup> *<sup>i</sup>* 4*π*

; *ω*) = 2 lim

<sup>=</sup> <sup>−</sup> *<sup>i</sup>* 2*π*

; *<sup>ω</sup>*) = →→

*<sup>x</sup>*, *kmax* = *k<sup>b</sup>*

 *kmax kmin*

*eikx <sup>x</sup> kz*

; *<sup>ω</sup>*; *kmin*, *kmax*) · �

*<sup>x</sup>* <sup>&</sup>lt; *<sup>ω</sup>*2/*c*2), the integral range is [*kmin* <sup>=</sup> <sup>−</sup>*ω*/*c*, *kmax* <sup>=</sup> *<sup>ω</sup>*/*c*], so

; *ω*; *kmin* = −*ω*/*c*, *kmax* = *ω*/*c*)

*ikz zdkx*

*<sup>x</sup>* <sup>&</sup>gt; *<sup>ω</sup>*2/*c*2), the integral range is *kx*>|*ω*/*c*|, so the evanescent

; *ω*; *kmin* = *ω*/*c*, *kmax*)

*TTE*(*kx*)*e*

*G glob*(*r*,*r*�

*G eva*(*r*,*r*�

*ikz zdkx*

*<sup>x</sup>*]. The SEW, with a certain integral range, can

; *ω*) satisfies:

; *ω*) (27)

*TTE*(*kx*)*e*

*TTE*(*kx*)*e*

*Es*(*r*�

*E*(*r*; *ω*; *kmin*, *kmax*), (24)

*ikz zdkx*, (22)

, *ω*), (23)

(25)

(26)

wave or the evanescent wave along *z* direction, respectively.

; *<sup>ω</sup>*; *kmin*, *kmax*) = <sup>−</sup> *<sup>i</sup>*

*<sup>E</sup>*(*r*; *<sup>ω</sup>*; *kmin*, *kmax*) = →→

*<sup>E</sup>*(*r*; *<sup>t</sup>*; *kmin*, *kmax*) = <sup>1</sup>

Eq.(20),Eq.(13) and Eq(14) as follows:

→→ *G* (*r*,*r*�

�

�

the radiative wave Green's function →→

→→ *G rad*(*r*,*r*�

In the case of evanescent wave (*k*<sup>2</sup>

→→ *G eva*(*r*,*r*�

> →→ *G glob*(*r*,*r*�

a certain integral range [*kmin* = *k<sup>a</sup>*

wave Green's function →→

for evanescent waves.

the case of radiative wave (*k*<sup>2</sup>

for radiative waves.

and

$$\begin{split} \stackrel{\rightarrow}{\mathbf{G}}^{\rightarrow} \stackrel{\rightarrow}{\mathbf{G}}^{\rightarrow} (r, r'; \omega) \vert\_{k\_{\text{min}} = \mathbf{k}\_{\text{x}}^{b}}^{k\_{\text{max}} = \mathbf{k}\_{\text{x}}^{b}} &= \stackrel{\rightarrow}{\mathbf{G}}^{\rightarrow} (r, r'; \mathbf{k}\_{\text{x}}^{a}, \mathbf{k}\_{\text{x}}^{b}) \\ &= -\frac{\mathrm{i}}{4\pi} \int\_{\mathbf{k}\_{\text{x}}^{a}}^{\mathbf{k}\_{\text{x}}^{b}} \frac{e^{i\mathbf{k}\_{\text{x}} \cdot \mathbf{r}}}{k\_{\text{z}}} T^{TE}(k\_{\text{x}}) e^{i\mathbf{k}\_{\text{z}} \cdot \mathbf{z}} d\mathbf{k}\_{\text{x}}. \end{split} \tag{28}$$

As an typical example, a SEW with an integral range [*kmin* = 1.1*ω*/*c*, *kmax* = 1.2*ω*/*c*], whose Green's function can be obtained easily from Eq.(28) as:

$$\stackrel{\rightarrow}{G}^{\rightarrow}\_{SEW}(r,r';\omega)|\_{k\_{\text{min}}=1.1\omega/c}^{k\_{\text{max}}=1.2\omega/c} = -\frac{i}{4\pi} \int\_{1.1\omega/c}^{1.2\omega/c} \frac{e^{ik\_{\text{x}}\mathbf{x}}}{k\_{\text{z}}} T^{\text{TE}}(k\_{\text{x}}) e^{ik\_{\text{z}}z} dk\_{\text{x}}.$$

In this way, we can obtain the Green's function for the SEW with any integral range. Obviously, evanescent wave could be regarded as the superposition of SEWs. Therefore, we have

$$\stackrel{\rightarrow}{G}\_{\text{eva}}^{\rightarrow}(r, r'; \omega) = \sum\_{SEWs} \stackrel{\rightarrow}{G}\_{SEW}^{\rightarrow}(r, r'; \omega). \tag{29}$$

From Eq.(28), Eq.(26), Eq.(25), and Eq.(27), one can obtain the SEW Green's function →→ *G SEW*(*r*,*r*� ; *<sup>ω</sup>*), the evanescent wave Green's function →→ *G eva*(*r*,*r*� ; *ω*), the radiative wave Green's function →→ *G rad*(*r*,*r*� ; *<sup>ω</sup>*), and the global field Green's function →→ *G glob*(*r*,*r*� ; *ω*), respectively. Substituting them to Eq.(23) and Eq.(24) respectively, we can obtain the field of the SEW, the evanescent wave, the radiative wave, and the global field, respectively.

For the 3D system, obviously, the methods to get Green's function for the SEW, the evanescent wave, the radiative wave, and the global field are respectively very similar with the above discussion, i.e., just replace *kx* by *<sup>k</sup>*|| and let *<sup>k</sup>*<sup>2</sup> || <sup>=</sup> *<sup>k</sup>*<sup>2</sup> *<sup>x</sup>* + *k*<sup>2</sup> *<sup>y</sup>* in Eq.(28), Eq.(26), Eq.(25), and Eq.(27), respectively.

#### **3. Electromagnetic waves in the image of the superlens**

In this section, we will discuss the image's field of a 2D metamaterial superlens, which is shown in Fig.2. The thickness of the metamaterial slab is *d*, which is placed at the *xy*-*plane* between *z* = *d*/2 and *z* = 3*d*/2. The source is set in the object plane at (*z* = 0). Obviously, the image will be formed in the image plane at *z* = 2*d*. The source is the quasi-monochromatic random source with the field expressed as *Es*(*r*, *t*)=*Us*(*r*, *t*)*exp*(−*iω*0*t*), where *Us*(*r*, *t*) is a slow-varying random function, *<sup>ω</sup>*<sup>0</sup> <sup>=</sup> 1.33 <sup>×</sup> 1015/*<sup>s</sup>* is the central frequency of our random source (the details of the random source can be seen in Ref.[29]). The exciting source *Es*(*r*, *t*) is a quasi-monochromatic field with the central frequency *ω*0, whose electric field *Es*(*t*) and frequency spectrum *Es*(*ω*) are shown in Fig.3(a) and Fig.3(b), respectively. In this paper, only the TM modes are investigated (the TM modes have the electric field perpendicular to the two-dimensional plane of our model).

The inhomogeneous media of the metamaterial superlens system are described by:

**Figure 2.** The schematic diagram of our model.

$$\varepsilon(r), \mu(r) = \begin{cases} \varepsilon\_{0\prime}\mu\_0 & z > 3/2d \\ \varepsilon\_0 \varepsilon\_{1\prime}^r \mu\_0 \mu\_1^r & 1/2d < z < 3/2d \\ \varepsilon\_{0\prime}\mu\_0 & z < 1/2d \end{cases} \tag{30}$$

The negative relative permittivity *�<sup>r</sup> <sup>l</sup>* and the negative relative permeability *<sup>μ</sup><sup>r</sup> <sup>l</sup>* of metamaterial are phenomenologically introduced by the Lorenz model. The negative relative permittivity *�r <sup>l</sup>* and the negative relative permeability *<sup>μ</sup><sup>r</sup> <sup>l</sup>* are satisfied as follows:

$$\epsilon\_l^r(\omega) = \mu\_l^r(\omega) = 1 + \omega\_p^2 / (\omega\_a^2 - \omega^2 - i\Delta\omega \cdot \omega) \tag{31}$$

**Figure 3.** (a) Electric field of the source. (b) Spectrum of the source (top) and the image obtained by using our method (bottom) in units of *ω*0. (c) Electric field of the image vs time. The global field calculated by using our method (top) and by using FDTD (bottom). (d) The evanescent wave of the

*<sup>G</sup> glob*(2*d*, 0; *<sup>ω</sup>*) ·

*<sup>G</sup> eva*(2*d*, 0; *<sup>ω</sup>*) ·

The numerical results calculated by our method are shown in Fig.3. Fig.3(c)(up, the blue one), (d) and (e) show the global field, the evanescent wave, and two typical SEWs respectively. The integral *kx* range of the two SEWs are [*kmin* = 1.1*ω*/*c*, *kmax* = 1.2*ω*/*c*] (shown in Fig.3(e)(up, the black one)), and [*kmin* = 1.3*ω*/*c*, *kmax* = 1.4*ω*/*c*] (shown in Fig.3(e)(down, the blue one)),

*<sup>G</sup> SEW*(2*d*, 0; *<sup>ω</sup>*) ·

*Es*(*ω*)

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 45

*Es*(*ω*).

(33)

*Es*(*ω*)

image calculated by using our method. (e) Two typical SEWs of the image.

*Eglob*(2*d*, *<sup>ω</sup>*) = →→

*Eeva*(2*d*, *<sup>ω</sup>*) = →→

*ESEW*(2*d*, *<sup>ω</sup>*) = →→

respectively, where

respectively.

where *<sup>ω</sup><sup>a</sup>* <sup>=</sup> 1.884 <sup>×</sup> <sup>10</sup>15/*<sup>s</sup>* and <sup>Δ</sup>*<sup>ω</sup>* <sup>=</sup> 1.88 <sup>×</sup> 1014/*<sup>s</sup>* are the resonant frequency and the resonant line-width of the "resonators" in the metamaterial respectively, and *ω<sup>p</sup>* = 10 × *ω<sup>a</sup>* is the plasma frequency. At *ω* = *ω*0, we have *�<sup>r</sup> <sup>l</sup>* <sup>=</sup> *<sup>μ</sup><sup>r</sup> <sup>l</sup>* = −1.0 + *i*0.0029.

In order to excite the evanescent wave strong enough in the image of the metamaterial superlens, the distance *d*/2 between the source and the superlens should be small enough. Here we choose *d* = *λ*0/2, where *λ*<sup>0</sup> = 1.42*μm* is the wavelength corresponding to the central frequency *ω*0.

For this metamaterial superlens system, it is very easy to obtain →→ *G glob*(*r*,*r*� ; *ω*), →→ *G eva*(*r*,*r*� ; *<sup>ω</sup>*), and →→ *G SEW*(*r*,*r*� ; *ω*) from Eq.(26) to Eq.(28), respectively. Let *r* = 2*d* and *r*� = 0, and thus the Green's functions for the image will be obtained. After that, we can obtain the global field, the evanescent wave and the SEW of the image via:

$$
\vec{E}\_{glob}(2d,t) = \frac{1}{2\pi} \int d\omega e^{-i\omega t} \vec{E}\_{glob}(2d,\omega)
$$

$$
\vec{E}\_{eva}(2d,t) = \frac{1}{2\pi} \int d\omega e^{-i\omega t} \vec{E}\_{eva}(2d,\omega) \tag{32}
$$

$$
\vec{E}\_{SEW}(2d,t) = \frac{1}{2\pi} \int d\omega e^{-i\omega t} \vec{E}\_{SEW}(2d,\omega)
$$

**Figure 3.** (a) Electric field of the source. (b) Spectrum of the source (top) and the image obtained by using our method (bottom) in units of *ω*0. (c) Electric field of the image vs time. The global field calculated by using our method (top) and by using FDTD (bottom). (d) The evanescent wave of the image calculated by using our method. (e) Two typical SEWs of the image.

respectively, where

8 Will-be-set-by-IN-TECH

**Figure 2.** The schematic diagram of our model.

The negative relative permittivity *�<sup>r</sup>*

; *<sup>ω</sup>*), and →→

*<sup>l</sup>* and the negative relative permeability *<sup>μ</sup><sup>r</sup>*

the plasma frequency. At *ω* = *ω*0, we have *�<sup>r</sup>*

*�r*

*<sup>l</sup>*(*ω*) = *<sup>μ</sup><sup>r</sup>*

*G SEW*(*r*,*r*�

�

�

�

*�r*

frequency *ω*0.

→→ *G eva*(*r*,*r*� *�*(*r*), *μ*(*r*) =

⎧ ⎪⎪⎨

*�*0, *μ*<sup>0</sup> *z* > 3/2*d*

*�*0, *μ*<sup>0</sup> *z* < 1/2*d*

*p*/(*ω*<sup>2</sup>

are phenomenologically introduced by the Lorenz model. The negative relative permittivity

where *<sup>ω</sup><sup>a</sup>* <sup>=</sup> 1.884 <sup>×</sup> <sup>10</sup>15/*<sup>s</sup>* and <sup>Δ</sup>*<sup>ω</sup>* <sup>=</sup> 1.88 <sup>×</sup> 1014/*<sup>s</sup>* are the resonant frequency and the resonant line-width of the "resonators" in the metamaterial respectively, and *ω<sup>p</sup>* = 10 × *ω<sup>a</sup>* is

*<sup>l</sup>* <sup>=</sup> *<sup>μ</sup><sup>r</sup>*

In order to excite the evanescent wave strong enough in the image of the metamaterial superlens, the distance *d*/2 between the source and the superlens should be small enough. Here we choose *d* = *λ*0/2, where *λ*<sup>0</sup> = 1.42*μm* is the wavelength corresponding to the central

*r*� = 0, and thus the Green's functions for the image will be obtained. After that, we can

*<sup>l</sup>* 1/2*d* < *z* < 3/2*d*

*<sup>l</sup>* = −1.0 + *i*0.0029.

; *ω*) from Eq.(26) to Eq.(28), respectively. Let *r* = 2*d* and

*Eglob*(2*d*, *ω*)

*Eeva*(2*d*, *ω*)

*ESEW*(2*d*, *ω*)

*<sup>l</sup>* and the negative relative permeability *<sup>μ</sup><sup>r</sup>*

*<sup>l</sup>* are satisfied as follows:

(30)

*<sup>l</sup>* of metamaterial

*G glob*(*r*,*r*�

; *ω*),

(32)

*<sup>a</sup>* <sup>−</sup> *<sup>ω</sup>*<sup>2</sup> <sup>−</sup> *<sup>i</sup>*Δ*<sup>ω</sup>* · *<sup>ω</sup>*) (31)

⎪⎪⎩

*�*0*�<sup>r</sup> <sup>l</sup>* , *<sup>μ</sup>*0*μ<sup>r</sup>*

*<sup>l</sup>*(*ω*) = <sup>1</sup> <sup>+</sup> *<sup>ω</sup>*<sup>2</sup>

For this metamaterial superlens system, it is very easy to obtain →→

2*π* � *dωe* −*iωt*�

2*π* � *dωe* −*iωt*�

2*π* � *dωe* −*iωt*�

obtain the global field, the evanescent wave and the SEW of the image via:

*Eglob*(2*d*, *<sup>t</sup>*) = <sup>1</sup>

*Eeva*(2*d*, *<sup>t</sup>*) = <sup>1</sup>

*ESEW*(2*d*, *<sup>t</sup>*) = <sup>1</sup>

$$
\vec{E}\_{glob}(2d,\omega) = \stackrel{\rightarrow}{G}\_{glob}(2d,0;\omega) \cdot \vec{E}\_s(\omega)
$$

$$
\vec{E}\_{\text{eva}}(2d,\omega) = \stackrel{\rightarrow}{G}\_{\text{eva}}(2d,0;\omega) \cdot \vec{E}\_s(\omega)\tag{33}
$$

$$
\vec{E}\_{SEW}(2d,\omega) = \stackrel{\rightarrow}{G}\_{SEW}(2d,0;\omega) \cdot \vec{E}\_s(\omega).
$$

The numerical results calculated by our method are shown in Fig.3. Fig.3(c)(up, the blue one), (d) and (e) show the global field, the evanescent wave, and two typical SEWs respectively. The integral *kx* range of the two SEWs are [*kmin* = 1.1*ω*/*c*, *kmax* = 1.2*ω*/*c*] (shown in Fig.3(e)(up, the black one)), and [*kmin* = 1.3*ω*/*c*, *kmax* = 1.4*ω*/*c*] (shown in Fig.3(e)(down, the blue one)), respectively.

In order to convince our method, FDTD simulation is also applied to calculate the field of the image, which is shown in Fig.3(c) (down, the green one). Comparison with the results calculated by our method and FDTD shown in Fig.3(c), we can see they coincide with each other very well. In addition, we also calculate the frequency sepctrum of the image by our method, as shown in Fig.3(b) (down, the red one). Comparing the spectra of source and image, we can find they are very close to each other. This result also agrees with the Ref.[29]. Therefore, our method is convincible, which can be used to obtain the pure evanescent waves, the SEWs, and the global field effectively.

#### **4. Group delay time of SEWs and its impacts on the temporal coherence**

#### **4.1. Group delay time of SEWs**

From Figs.3(c)-(e), we can find that the profile of evanescent wave and that of SEWs look like that of radiative wave with a group delay time *τr*. So the field evanescent wave *Eeva*(*t*), as well as that of SEWs *ESEW*(*t*), can be written as an expression such as *Eeva*(*SEW*)(*t*)= *fa*(*t*) *Erad*(*t* − *τr*), where *fa*(*τr*) is parameter function of *τr*. In order to quantitatively study the delay time *τr*, we introduce a function *y*(*τi*) which satisfies:

$$y(\pi\_i) = \int\_{\mathbf{t}} dt \, |\vec{E}\_{rad}(t)| \cdot |\vec{E}\_{\text{extra}}(t - \pi\_i)| \,\tag{34}$$

<sup>1</sup> 1.1 1.2 1.3 1.4 1.5 1.6 1.7 <sup>0</sup>

/c)

*ESEW*(*t*) = *A*(*τr*(*kx*))

*ESEW*(*t*)*dkx*

*A*(*τr*(*kx*))

**4.2. Impacts of the group delay of SEWs on temporal coherence gain in the image**

One of the most interesting impacts of the group delay of SEWs is related to the first-order temporal coherence gain (CG). Here, we would like to discuss the CG caused by the SEWs in the image of the superlens. In our previous work [29, 30], we have investigated a prominent CG of the image by the radiative waves even when the frequency-filtering effects are very weak. Then, a natural question is what about the role of the evanescent waves play in the CG of a superlens? In this section, we will show that not only the radiative waves but also the evanescent waves, and the SEWs that can be responsible for the CG. Furthermore, we will show that the total CG in the image of a superlens is the weighted

The physical meaning of *A*(*τr*) and its impacts will be discussed in the following.

Since the field profile of SEWs looks like that of a radiative wave, so we can write the field of

where *A*(*τr*(*kx*)) = *B*(*τr*(*kx*))*exp*(−2|*kz*(*kx*)|*d*), *B*(*τr*) is a slowly-verifying function of *τr*, and *exp*(−2|*kz*|*d*) is an exponentially-decreasing function of *kz* and a general-function of *τr*. Obviously, when *τr*(or *kx*) becomes larger, *A*(*τr*) will trends to become smaller. Then the field

<sup>1</sup> 1.1 1.2 1.3 1.4 1.5 1.6 1.7 <sup>5</sup>

/(ω<sup>0</sup> /c)

*Erad*(*t* − *τr*(*kx*)), (37)

(38)

SEWs kx

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 47

(a) (b)

*Erad*(*t* − *τr*(*kx*))*dkx*.

10

15

20

25

ρcoh(a.u.)

30

35

40

SEWs kmx/(<sup>ω</sup><sup>0</sup>

the SEW with the integral range [*kx* − *δkx*, *kx* + *δkx*] as follows:

*Eeva*(*t*) can be obtained by:

= 

*Eeva*(*t*) =

**Figure 4.** (a) The group delay time *τ<sup>r</sup>* of SEWs. (b) *ρcoh* of SEWs.

original data polynomial fitting curve

200

400

600

800

τ

of evanescent wave

**of the superlens**

/δ

r

t

1000

1200

1400

1600

1800

where *Erad*(*t*) and *Eeva*(*t*) are the field of radiative wave and the evanescent wave respectively, *τ<sup>i</sup>* is an independent variable with the time dimension. Since the profile of the radiative wave and the evanescent wave are very similar, obviously, the function *y*(*τi*) will get the maximal value when *τ<sup>i</sup>* = *τr*. Therefore, the delay time can be defined quantitatively as follows:

$$\pi\_r = [\operatorname{Max}(y(\pi\_i))]^{-1}.\tag{35}$$

Here [··· ] <sup>−</sup><sup>1</sup> means the inverse function.

Similarly, we can also study the group delay time of the SEWs. We rewrite Eq.(34) as follows:

$$y(\pi\_i) = \int\_t dt \left| \vec{E}\_{rad}(t) \right| \cdot \left| \vec{E}\_{SEW}(t - \pi\_i) \right| \,, \tag{36}$$

where *ESEW*(*t*) is the field of the SEW with a certain integral *kx* range. So we can calculate the delay time of the SEWs from Eq.(36) and Eq.(35).

In our numerical experiment, in order to calculate the group delay time of the SEWs, we choose 70 SEWs with integral *kx* range as [*kmx* − 0.01*ω*0/*c*, *kmx* + 0.01*ω*0/*c*], where *kmx*=1.01*ω*0/*c*, 1.02*ω*0/*c*, ···, 1.69*ω*0/*c*, 1.7*ω*0/*c* , respectively. The delay time of the 70 SEWs is shown in Fig.4(a). In this figure, we can see that the SEW with larger integral variable *kx* will have a larger delay time. Obviously, the function *τ<sup>r</sup>* = *τr*(*kx*) is a continuous-monotone increasing function, when the integral range [*kx* − *dkx*, *kx* + *dkx*] is infinitesimal (*dkx*→0). The result can be obtained by using a polynomial fitting, as shown in Fig.4(a). Therefore, from Fig.4(a), we can find that the SEWs with larger integral variable *kx* corresponds to a larger delay time, which means the group velocity of SEWs with larger integral variable is smaller in the superlens system.

**Figure 4.** (a) The group delay time *τ<sup>r</sup>* of SEWs. (b) *ρcoh* of SEWs.

10 Will-be-set-by-IN-TECH

In order to convince our method, FDTD simulation is also applied to calculate the field of the image, which is shown in Fig.3(c) (down, the green one). Comparison with the results calculated by our method and FDTD shown in Fig.3(c), we can see they coincide with each other very well. In addition, we also calculate the frequency sepctrum of the image by our method, as shown in Fig.3(b) (down, the red one). Comparing the spectra of source and image, we can find they are very close to each other. This result also agrees with the Ref.[29]. Therefore, our method is convincible, which can be used to obtain the pure evanescent waves,

**4. Group delay time of SEWs and its impacts on the temporal coherence**

From Figs.3(c)-(e), we can find that the profile of evanescent wave and that of SEWs look like

*τr*), where *fa*(*τr*) is parameter function of *τr*. In order to quantitatively study the delay time

*Erad*(*t*)|·|

*τ<sup>i</sup>* is an independent variable with the time dimension. Since the profile of the radiative wave and the evanescent wave are very similar, obviously, the function *y*(*τi*) will get the maximal value when *τ<sup>i</sup>* = *τr*. Therefore, the delay time can be defined quantitatively as follows:

Similarly, we can also study the group delay time of the SEWs. We rewrite Eq.(34) as follows:

*Erad*(*t*)|·|

where *ESEW*(*t*) is the field of the SEW with a certain integral *kx* range. So we can calculate the

In our numerical experiment, in order to calculate the group delay time of the SEWs, we choose 70 SEWs with integral *kx* range as [*kmx* − 0.01*ω*0/*c*, *kmx* + 0.01*ω*0/*c*], where *kmx*=1.01*ω*0/*c*, 1.02*ω*0/*c*, ···, 1.69*ω*0/*c*, 1.7*ω*0/*c* , respectively. The delay time of the 70 SEWs is shown in Fig.4(a). In this figure, we can see that the SEW with larger integral variable *kx* will have a larger delay time. Obviously, the function *τ<sup>r</sup>* = *τr*(*kx*) is a continuous-monotone increasing function, when the integral range [*kx* − *dkx*, *kx* + *dkx*] is infinitesimal (*dkx*→0). The result can be obtained by using a polynomial fitting, as shown in Fig.4(a). Therefore, from Fig.4(a), we can find that the SEWs with larger integral variable *kx* corresponds to a larger delay time, which means the group velocity of SEWs with larger integral variable is smaller

*Eeva*(*t*) are the field of radiative wave and the evanescent wave respectively,

*τ<sup>r</sup>* = [*Max*(*y*(*τi*))]<sup>−</sup>1. (35)

*Eeva*(*t*), as well

*Erad*(*t* −

*Eeva*(*SEW*)(*t*)= *fa*(*t*)

*Eeva*(*t* − *τi*)|, (34)

*ESEW*(*t* − *τi*)|, (36)

that of radiative wave with a group delay time *τr*. So the field evanescent wave

 *t dt*<sup>|</sup>

*ESEW*(*t*), can be written as an expression such as

the SEWs, and the global field effectively.

*τr*, we introduce a function *y*(*τi*) which satisfies:

<sup>−</sup><sup>1</sup> means the inverse function.

delay time of the SEWs from Eq.(36) and Eq.(35).

*y*(*τi*) =

*y*(*τi*) =

 *t dt*<sup>|</sup>

**4.1. Group delay time of SEWs**

as that of SEWs

*Erad*(*t*) and

in the superlens system.

where

Here [··· ]

Since the field profile of SEWs looks like that of a radiative wave, so we can write the field of the SEW with the integral range [*kx* − *δkx*, *kx* + *δkx*] as follows:

$$
\vec{E}\_{\rm SEW}(t) = A(\tau\_r(k\_\chi))\vec{E}\_{rad}(t - \tau\_r(k\_\chi)),
\tag{37}
$$

where *A*(*τr*(*kx*)) = *B*(*τr*(*kx*))*exp*(−2|*kz*(*kx*)|*d*), *B*(*τr*) is a slowly-verifying function of *τr*, and *exp*(−2|*kz*|*d*) is an exponentially-decreasing function of *kz* and a general-function of *τr*. Obviously, when *τr*(or *kx*) becomes larger, *A*(*τr*) will trends to become smaller. Then the field of evanescent wave *Eeva*(*t*) can be obtained by:

$$\begin{split} \vec{E}\_{\text{eva}}(t) &= \int \vec{E}\_{\text{SEW}}(t) dk\_{\text{x}} \\ &= \int A(\tau\_{\text{r}}(k\_{\text{x}})) \vec{E}\_{\text{rad}}(t - \tau\_{\text{r}}(k\_{\text{x}})) dk\_{\text{x}}. \end{split} \tag{38}$$

The physical meaning of *A*(*τr*) and its impacts will be discussed in the following.

#### **4.2. Impacts of the group delay of SEWs on temporal coherence gain in the image of the superlens**

One of the most interesting impacts of the group delay of SEWs is related to the first-order temporal coherence gain (CG). Here, we would like to discuss the CG caused by the SEWs in the image of the superlens. In our previous work [29, 30], we have investigated a prominent CG of the image by the radiative waves even when the frequency-filtering effects are very weak. Then, a natural question is what about the role of the evanescent waves play in the CG of a superlens? In this section, we will show that not only the radiative waves but also the evanescent waves, and the SEWs that can be responsible for the CG. Furthermore, we will show that the total CG in the image of a superlens is the weighted averaged of evanescent-wave coherence gain (ECG), radiative-wave coherence gain (RCG), radiative-wave and evanescent-wave coherence gain (RECG).

First of all, let's consider the contributions of the evanescent waves on the CG. For this, we calculate the normalized first-order temporal coherence *g*(1)(*r*, *τ*) of the superlens with the random source *Es*(*t*) exciting, which are shown in Fig.5. Here, the normalized first-order temporal coherence function *g*(1)(*r*, *τ*) is defined by

$$g^{(1)}(r,\tau) = \frac{G^{(1)}(r,\tau)}{G^{(1)}(r,0)} = \frac{<\vec{E}^\*(r,t)\vec{E}(r,t+\tau\_r)>}{<\vec{E}^\*(r,t)\vec{E}(r,t)>}\tag{39}$$

where *G*(1)(*r*, *τ*) is a coherence function, which is defined by

$$G^{(1)}(r,\tau) = <\vec{E}^\*(r,t)\vec{E}(r,t+\tau\_r) > \tag{40}$$

To show how the ECG is produced from the interference of the SEWs with different group

*mx*)) and both of them are close to a certain constant *A*.

*Eα*

*<sup>r</sup>* , respectively. The two SEWs can be expressed by Eq.(37). We assume

*<sup>r</sup>* ) + *A*(*τr*(*k*

*E*∗

*rad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*<sup>r</sup>* + *<sup>τ</sup>*) + �

*E*∗

*β mx*))�

*<sup>r</sup>* )),

*rad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*<sup>r</sup>* )�

*<sup>r</sup>* )�

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>α</sup>*

*<sup>r</sup>* |. This condition can always be satisfied between SEWs

*<sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*<sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*mx* are far from each other, so the value of <sup>|</sup>*A*(*τ<sup>α</sup>*

*SEW*(*t*) and �

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 49

*Eβ*

*mx* � *k β*

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*<sup>r</sup>* |. Unfortunately, the two conditions could

Δ*τr*(*kx*) (44)

*<sup>r</sup>* + *τ*) >,

*r* )

*<sup>r</sup>* + *τ*)+

*<sup>r</sup>* | of SEWs are responsible

*<sup>r</sup>* | is large, which also means

*<sup>r</sup>* ) <sup>−</sup> *<sup>A</sup>*(*τ<sup>β</sup>*

*r* )|

*mx*] respectively, which correspond to the

*SEW*(*t*) with the range

*mx*, and so we have

(42)

(43)

delay time, we assume there are only two SEWs, such as �

*β mx* − *δk β mx*, *k β mx* + *δk β*

the two SEWs have an integral range very close to each other, i.e., *k<sup>α</sup>*

*SEW*(*t*) + �

*mx*))�

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>α</sup>*

*Eeva*(*t* + *τ*) >

*<sup>r</sup>* )�

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

*<sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

since *<sup>τ</sup><sup>r</sup>* is a continuous variable. So the relative delay time <sup>|</sup>*τ<sup>α</sup>*

*mx*)); and (2) *<sup>τ</sup>* � |*τ<sup>α</sup>*

*β*

not always be satisfied at the same time. When *<sup>τ</sup>* � |*τ<sup>α</sup>*

*mx* and *k*

then the temporal coherence of the evanescent wave in the image is given by

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>α</sup>*

*Eβ SEW*(*t*)

*Erad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>α</sup>*

*<sup>r</sup>* ) + �

*<sup>r</sup>* + *τ*) + �

The first two terms are the same as the coherence function of the radiative wave, so they do not contribute to ECG. The last two terms are from the interference between SEWs, they can be

Therefore, ECG can always exist in the superlens when two conditions are satisfied: (1)

*<sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup>*

will be very large, and thus the former condition could not be satisfied. The condition that *A*(*τr*(*kx*)) � *A*(*τr*(*kmx*)) is the direct reflection that *only the interference of those SEWs with*

Here the integral variable "*kx close* to *kmx*" means when *kmx* is given, for any *kx* satisfying |*kx* − *kmx*| → *δkmx*, the condition *A*(*τr*(*kx*)) � *A*(*τr*(*kmx*)) is always satisfied, where *δkmx* is a threshold value with small positive value near zero(for example *δkmx*=0.01). For two SEWs with the integral range [*kmx* − *δkmx*, *kmx* + *δkmx*] and [*kx* − *δkx*, *kx* + *δkx*] respectively, we can obtain the relative delay time Δ*τr*(*kx*) = |*τr*(*kx*) − *τr*(*kmx*)|. As the discussion above, the relative delay time Δ*τ<sup>r</sup>* is responsible to the ECG. When *kx* is *close* to *kmx*, Δ*τr*(*kx*) is a monotonic increasing function of *kx* in the range [*kmx*, *kmx* + *δkmx*], which gives a threshold

*kx*→*kmx*+*δ*.*kmx*

*τd*(*kx*) = *lim*

*mx*] and [*k*

[*kα mx* <sup>−</sup> *<sup>δ</sup>k<sup>α</sup>*

*mx*, *k<sup>α</sup>*

*mx*)) � *A*(*τr*(*k*

delay time *τ<sup>α</sup>*

*A*(*τr*(*k<sup>α</sup>*

for ECG .

*A*(*τr*(*k<sup>α</sup>*

value *τ<sup>d</sup>* as:

*mx* + *δk<sup>α</sup>*

*β*

*Eeva*(*t*) = �

*E*∗ *eva*(*t*)�

*rad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>α</sup>*

*β*

*close integral variable kx can produce the ECG.*

=< � *E*∗

From Eq.(38), we have the evanescent wave field:

*Eα*

= *A*(*τr*(*k<sup>α</sup>*

� *<sup>A</sup>* · (�

*rad*(*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup><sup>α</sup>*

*<sup>r</sup>* )�

*<sup>r</sup>* and *<sup>τ</sup><sup>β</sup>*

�

*Geva*(*τ*) =< �

� *E*∗

very large at the condition *<sup>τ</sup>* � |*τ<sup>α</sup>*

*mx*)) � *A*(*τr*(*k*

the integral variable *k<sup>α</sup>*

or

$$G^{(1)}(r,\tau) = \lim\_{T \to \infty} \frac{1}{2T} \int\_{-T}^{T} \vec{E}^\*(r,t)\vec{E}(r,t+\tau)dt,\tag{41}$$

here < ··· > means the statistic average (ensemble average) and *τ* is time delay. From Fig.5, we can see that the temporal coherence of image of evanescent wave, radiative wave and global field, are all obviously better than that of source. Comparing with the temporal coherence of source and image, there are three kinds of coherence gain as follows. The first one is the radiative-wave coherence gain (RCG, this mechanism has been discussed in our previous work[29, 30]), which is determined by the radiative waves. The second one is the evanescent-wave coherence gain (ECG), which is determined by the evanescent waves. The last one is the global field coherence gain (GCG), which is from the global field with the co-effect of RCG and ECG.

**Figure 5.** The first temporal coherence of image and source. The dashed-dotted one is the *g*(1)(*r*, *τ*) of the source. Others are for the image, i.e., the red one, the black one (and also the green one), and the blue one are the *g*(1)(*r*, *τ*) of the evanescent waves, the global field, and the radiative waves, respectively.

To show how the ECG is produced from the interference of the SEWs with different group delay time, we assume there are only two SEWs, such as � *Eα SEW*(*t*) and � *Eβ SEW*(*t*) with the range [*kα mx* <sup>−</sup> *<sup>δ</sup>k<sup>α</sup> mx*, *k<sup>α</sup> mx* + *δk<sup>α</sup> mx*] and [*k β mx* − *δk β mx*, *k β mx* + *δk β mx*] respectively, which correspond to the delay time *τ<sup>α</sup> <sup>r</sup>* and *<sup>τ</sup><sup>β</sup> <sup>r</sup>* , respectively. The two SEWs can be expressed by Eq.(37). We assume the two SEWs have an integral range very close to each other, i.e., *k<sup>α</sup> mx* � *k β mx*, and so we have *A*(*τr*(*k<sup>α</sup> mx*)) � *A*(*τr*(*k β mx*)) and both of them are close to a certain constant *A*.

From Eq.(38), we have the evanescent wave field:

12 Will-be-set-by-IN-TECH

averaged of evanescent-wave coherence gain (ECG), radiative-wave coherence gain (RCG),

First of all, let's consider the contributions of the evanescent waves on the CG. For this, we calculate the normalized first-order temporal coherence *g*(1)(*r*, *τ*) of the superlens with the random source *Es*(*t*) exciting, which are shown in Fig.5. Here, the normalized first-order

*E*∗(*r*, *t*)�

*E*∗(*r*, *t*)�

source radiative wave evanescent wave global field (Green's function) global field(approximate GFCG)

< �

*E*∗(*r*, *t*)�

 *T* −*T* � *E*∗(*r*, *t*)�

here < ··· > means the statistic average (ensemble average) and *τ* is time delay. From Fig.5, we can see that the temporal coherence of image of evanescent wave, radiative wave and global field, are all obviously better than that of source. Comparing with the temporal coherence of source and image, there are three kinds of coherence gain as follows. The first one is the radiative-wave coherence gain (RCG, this mechanism has been discussed in our previous work[29, 30]), which is determined by the radiative waves. The second one is the evanescent-wave coherence gain (ECG), which is determined by the evanescent waves. The last one is the global field coherence gain (GCG), which is from the global field with the

<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>2000</sup> <sup>2500</sup> <sup>3000</sup> <sup>3500</sup> <sup>4000</sup> <sup>0</sup>

δ t

**Figure 5.** The first temporal coherence of image and source. The dashed-dotted one is the *g*(1)(*r*, *τ*) of the source. Others are for the image, i.e., the red one, the black one (and also the green one), and the blue one are the *g*(1)(*r*, *τ*) of the evanescent waves, the global field, and the radiative waves, respectively.

*E*(*r*, *t* + *τr*) >

(39)

*E*(*r*, *t*) >

*E*(*r*, *t* + *τr*) > (40)

*E*(*r*, *t* + *τ*)*dt*, (41)

*<sup>G</sup>*(1)(*r*, 0) <sup>=</sup> <sup>&</sup>lt; �

1 2*T*

(*r*, *τ*) =< �

*T*→∞

radiative-wave and evanescent-wave coherence gain (RECG).

where *G*(1)(*r*, *τ*) is a coherence function, which is defined by

*G*(1)

(*r*, *τ*) = *lim*

(*r*, *<sup>τ</sup>*) = *<sup>G</sup>*(1)(*r*, *<sup>τ</sup>*)

temporal coherence function *g*(1)(*r*, *τ*) is defined by

*G*(1)

co-effect of RCG and ECG.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


(τ)|

*g*(1)

or

$$\begin{split} \vec{E}\_{\text{eva}}(t) &= \vec{E}\_{SEW}^{a}(t) + \vec{E}\_{SEW}^{\mathcal{B}}(t) \\ &= A(\tau\_{r}(k\_{\text{mx}}^{a})) \vec{E}\_{\text{rad}}(t - \tau\_{r}^{a}) + A(\tau\_{r}(k\_{\text{mx}}^{\mathcal{B}})) \vec{E}\_{\text{rad}}(t - \tau\_{r}^{\mathcal{B}}) \\ &\simeq A \cdot (\vec{E}\_{\text{rad}}(t - \tau\_{r}^{a}) + \vec{E}\_{\text{rad}}(t - \tau\_{r}^{\mathcal{B}})) ,\end{split} \tag{42}$$

then the temporal coherence of the evanescent wave in the image is given by

$$\begin{split} \mathbf{G}\_{\rm rad}(\tau) &= < \vec{E}\_{\rm rad}^{\*}(t) \vec{E}\_{\rm rad}(t + \tau) \\ &= < \vec{E}\_{\rm rad}^{\*}(t - \tau\_{r}^{a}) \vec{E}\_{\rm rad}(t - \tau\_{r}^{a} + \tau) + \vec{E}\_{\rm rad}^{\*}(t - \tau\_{r}^{\mathcal{B}}) \vec{E}\_{\rm rad}(t - \tau\_{r}^{\mathcal{B}} + \tau) + \\ &\vec{E}\_{\rm rad}^{\*}(t - \tau\_{r}^{a}) \vec{E}\_{\rm rad}(t - \tau\_{r}^{\mathcal{B}} + \tau) + \vec{E}\_{\rm rad}^{\*}(t - \tau\_{r}^{\mathcal{B}}) \vec{E}\_{\rm rad}(t - \tau\_{r}^{a} + \tau) >, \end{split} \tag{43}$$

The first two terms are the same as the coherence function of the radiative wave, so they do not contribute to ECG. The last two terms are from the interference between SEWs, they can be very large at the condition *<sup>τ</sup>* � |*τ<sup>α</sup> <sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup> <sup>r</sup>* |. This condition can always be satisfied between SEWs since *<sup>τ</sup><sup>r</sup>* is a continuous variable. So the relative delay time <sup>|</sup>*τ<sup>α</sup> <sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup> <sup>r</sup>* | of SEWs are responsible for ECG .

Therefore, ECG can always exist in the superlens when two conditions are satisfied: (1) *A*(*τr*(*k<sup>α</sup> mx*)) � *A*(*τr*(*k β mx*)); and (2) *<sup>τ</sup>* � |*τ<sup>α</sup> <sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup> <sup>r</sup>* |. Unfortunately, the two conditions could not always be satisfied at the same time. When *<sup>τ</sup>* � |*τ<sup>α</sup> <sup>r</sup>* <sup>−</sup> *<sup>τ</sup><sup>β</sup> <sup>r</sup>* | is large, which also means the integral variable *k<sup>α</sup> mx* and *k β mx* are far from each other, so the value of <sup>|</sup>*A*(*τ<sup>α</sup> <sup>r</sup>* ) <sup>−</sup> *<sup>A</sup>*(*τ<sup>β</sup> r* )| will be very large, and thus the former condition could not be satisfied. The condition that *A*(*τr*(*kx*)) � *A*(*τr*(*kmx*)) is the direct reflection that *only the interference of those SEWs with close integral variable kx can produce the ECG.*

Here the integral variable "*kx close* to *kmx*" means when *kmx* is given, for any *kx* satisfying |*kx* − *kmx*| → *δkmx*, the condition *A*(*τr*(*kx*)) � *A*(*τr*(*kmx*)) is always satisfied, where *δkmx* is a threshold value with small positive value near zero(for example *δkmx*=0.01). For two SEWs with the integral range [*kmx* − *δkmx*, *kmx* + *δkmx*] and [*kx* − *δkx*, *kx* + *δkx*] respectively, we can obtain the relative delay time Δ*τr*(*kx*) = |*τr*(*kx*) − *τr*(*kmx*)|. As the discussion above, the relative delay time Δ*τ<sup>r</sup>* is responsible to the ECG. When *kx* is *close* to *kmx*, Δ*τr*(*kx*) is a monotonic increasing function of *kx* in the range [*kmx*, *kmx* + *δkmx*], which gives a threshold value *τ<sup>d</sup>* as:

$$\pi\_d(k\_\mathcal{x}) = \lim\_{k\_\mathcal{x} \to k\_{\max} + \delta, k\_{\max}} \Delta \pi\_\mathcal{r}(k\_\mathcal{x}) \tag{44}$$

#### 14 Will-be-set-by-IN-TECH 50 Optical Devices in Communication and Computation Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens <sup>15</sup>

*τ<sup>d</sup>* shows the upper-limit of the effective coherent relative delay time that only the Δ*τ<sup>r</sup>* ≤ *τ<sup>d</sup>* is the effective responsible to ECG. As Δ*τ<sup>r</sup>* increasing, when Δ*τ<sup>r</sup>* > *τd*, which means |*kx* − *kmx*| > *δkmx* (i.e. *kx* and *kmx* is not close to each other), the difference between *A*(*τr*(*kx*)) and *A*(*τr*(*kmx*)) becomes greater, and so their interference becomes weaker and their contribution to the coherence gain will decrease rapidly. While when Δ*τ<sup>r</sup>* � *τd*, which means the integral variable *kx* and *kmx* are very far from each other, then the SEW with the much larger integral variable one is too weak to have any effective interference, so their contribution to the coherence gain trends to be zero.

Therefore, the coherence gain from the interference of SEWs is limited by *τd*. The SEW with larger *τ<sup>d</sup>* corresponds larger coherence gain. In order to study the temperas coherence gain of SEWs, we introduce a parameter function as: *<sup>ρ</sup>coh*(*kx*) = *<sup>d</sup>τr*(*kx*) *dkx* , which is shown in Fig.4(b). The physical meaning of *ρcoh*(*kx*) is very clear, which gives a relation

$$
\pi\_d(k\_x) \simeq \rho\_{coh}(k\_x) \cdot \delta k\_x \tag{45}
$$

**5. Conclusion**

**Author details**

**6. References**

(2003).

(2003)

Wei Li and Xunya Jiang

and give us a new way to design new devices.

[1] V. C. Veselago, Sov. Phys. Usp. 10, 509 (1968). [2] J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000). [3] J. B. Pendry, Phys. Rev. Lett. 91, 099701 (2003).

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[12] A.C.Peacock and N.G.R.Broderick,11,2502 (2003).

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[16] X. S. Rao and C. K. Ong, Phys. Rev. E 68, 067601 (2003). [17] S. A. Cummer, Appl. Phys. Lett. 82, 1503 (2003).

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[24] R. Merlin, Appl. Phys. Lett. 84, 1290 (2004).

In conclusion, based on the Green's function, we have numerically and theoretically obtained the evanescent wave, as well as the SEWs, separating from the global field. This study could help us to investigate the effect of an evanescent wave on a metamaterial superlens directly

Electrodynamics of Evanescent Wave in Negative Refractive Index Superlens 51

*State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and*

[7] Y. Zhang, T. M. Grzegorczyk, and J. A. Kong, Prog. Electromagn. Res. 35, 271 (2002).

[9] Lei Zhou, Xueqin Huang and C.T. Chan, Photonics and Nanostructures 3, 100 (2005).

[11] Ilya V.Shadrivov, Andrey A.sukhorukov and Yuri S.Kivshar, Phys.Rev.E 67,057602

[14] E.Cubukcu,K.Aydin,E.Ozbay,S.Foteinopoulou,and C.M.Soukoulis,Nature 423,604

[15] D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A.Ramakrishna, and J.B. Pendry,

[18] P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, Phys. Rev. E

[19] S.Foteinopoulou, E.N.Economou, and C.M.Soukoulis, Phys,Rev.Lett.90,107402 (2003).

[26] R.Ruppin, Phys.Lett.A 277,61(2000); R.Ruppin, J.Phys.:Condens.Matter 13,1811 (2001). [27] W. Li, J. Chen, G. Nouet, L. Chen, and X. Jiang, Appl. Phys. Lett. 99, 051112 (2011).

[25] B.I.Wu, T.M.Grzegorczyk, Y.Zhang and J.A.Kong, J.Appl.Phys 93,9386 (2003).

*Information Technology, Chinese Academy of Sicences, Shanghai 200050, China*

[4] N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).

[10] Nader Engheta, IEEE Antennas and Wireless Propagation Lett. 1,10 (2002).

when *δkx* → 0, we can get *τ<sup>d</sup>* = *ρcohδkx*. Thus, *τ<sup>d</sup>* is proportional to *ρcoh*. From Fig.4(b) we can see that *ρcoh* is an increasing function of *kx*, so the SEWs with larger integral variable *kx* correspond larger *τ<sup>d</sup>* and stronger ECG, and so the field of the SEWs with larger integral various *kx* will have better temporal-coherence *g*(1)(*τ*).

**Figure 6.** *g*(1)(*τ*) of SEW1, SEW2, and SEW3, comparing with *g*(1)(*τ*) of evanescent wave.

To convince it, three SEWs (SWE1,SWE2,SWE3)with the different integral *kx* range [*kmin* = 1.0*ω*/*c*, *kmax* = 1.15*ω*/*c*], [*kmin* = 1.15*ω*/*c*, *kmax* = 1.3*ω*/*c*] and [*kmin* = 1.3*ω*/*c*, *kmax* = 1.45*ω*/*c*] respectively are chosen to calculate the normalized first-order temporal-coherence function *g*(1)(*τ*), which are shown in Fig.6. In this figure, we can see the temporal-coherence of SWE3 with the largest integral variable is the best (black), the temporal coherence of SWE2 with the second largest integral variable(red) is the second best, and the temporal coherence of SWE1 with the smallest integral variable is the worst, which is expected.

#### **5. Conclusion**

14 Will-be-set-by-IN-TECH

*τ<sup>d</sup>* shows the upper-limit of the effective coherent relative delay time that only the Δ*τ<sup>r</sup>* ≤ *τ<sup>d</sup>* is the effective responsible to ECG. As Δ*τ<sup>r</sup>* increasing, when Δ*τ<sup>r</sup>* > *τd*, which means |*kx* − *kmx*| > *δkmx* (i.e. *kx* and *kmx* is not close to each other), the difference between *A*(*τr*(*kx*)) and *A*(*τr*(*kmx*)) becomes greater, and so their interference becomes weaker and their contribution to the coherence gain will decrease rapidly. While when Δ*τ<sup>r</sup>* � *τd*, which means the integral variable *kx* and *kmx* are very far from each other, then the SEW with the much larger integral variable one is too weak to have any effective interference, so their

Therefore, the coherence gain from the interference of SEWs is limited by *τd*. The SEW with larger *τ<sup>d</sup>* corresponds larger coherence gain. In order to study the temperas coherence gain of

when *δkx* → 0, we can get *τ<sup>d</sup>* = *ρcohδkx*. Thus, *τ<sup>d</sup>* is proportional to *ρcoh*. From Fig.4(b) we can see that *ρcoh* is an increasing function of *kx*, so the SEWs with larger integral variable *kx* correspond larger *τ<sup>d</sup>* and stronger ECG, and so the field of the SEWs with larger integral

<sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>2000</sup> <sup>2500</sup> <sup>3000</sup> <sup>3500</sup> <sup>4000</sup> <sup>4500</sup> 0.1

δ t

To convince it, three SEWs (SWE1,SWE2,SWE3)with the different integral *kx* range [*kmin* = 1.0*ω*/*c*, *kmax* = 1.15*ω*/*c*], [*kmin* = 1.15*ω*/*c*, *kmax* = 1.3*ω*/*c*] and [*kmin* = 1.3*ω*/*c*, *kmax* = 1.45*ω*/*c*] respectively are chosen to calculate the normalized first-order temporal-coherence function *g*(1)(*τ*), which are shown in Fig.6. In this figure, we can see the temporal-coherence of SWE3 with the largest integral variable is the best (black), the temporal coherence of SWE2 with the second largest integral variable(red) is the second best, and the temporal coherence

**Figure 6.** *g*(1)(*τ*) of SEW1, SEW2, and SEW3, comparing with *g*(1)(*τ*) of evanescent wave.

of SWE1 with the smallest integral variable is the worst, which is expected.

*dkx*

*τd*(*kx*) � *ρcoh*(*kx*) · *δkx* (45)

, which is shown in Fig.4(b).

contribution to the coherence gain trends to be zero.

various *kx* will have better temporal-coherence *g*(1)(*τ*).

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SEW1 SEW2 SEW3 evanescent wave


(τ)|

SEWs, we introduce a parameter function as: *<sup>ρ</sup>coh*(*kx*) = *<sup>d</sup>τr*(*kx*)

The physical meaning of *ρcoh*(*kx*) is very clear, which gives a relation

In conclusion, based on the Green's function, we have numerically and theoretically obtained the evanescent wave, as well as the SEWs, separating from the global field. This study could help us to investigate the effect of an evanescent wave on a metamaterial superlens directly and give us a new way to design new devices.

#### **Author details**

Wei Li and Xunya Jiang

*State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sicences, Shanghai 200050, China*

#### **6. References**

	- [28] R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, New York, 1985).

**Novel Structures in Optical Devices** 


**Novel Structures in Optical Devices** 

16 Will-be-set-by-IN-TECH

[28] R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, New York,

[29] Peijun Yao, Wei Li, Songlin Feng and Xunya Jiang, Opt. Express 14, 12295 (2005). [30] Xunya Jiang, Wenda Han, Peijun Yao and Wei Li, Appl. Phys. Lett. 89, 221102 (2006).

1985).

**Chapter 4** 

© 2012 Wu and Lee, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Tunable and Memorable** 

Additional information is available at the end of the chapter

Po-Chang Wu and Wei Lee

http://dx.doi.org/10.5772/48127

**crystal/liquid-crystal hybrid cell** 

**1. Introduction** 

tunable defect layer.

**Optical Devices with One-Dimensional** 

**1.1. Concept of defect-mode tunability in a one-dimensional photonic-**

Photonic crystals (PCs) are a special class of artificial structures with spatially periodic dielectric permittivity and their investigations stem from 1987 when both Yablonovitch and John independently demonstrated their own findings (Yablonovitch, 1987; John, 1987). The most attractive feature of PCs is the existence of photonic bandgap (PBG), characterized by the spatial distribution of refractive index or dielectric constant. The PBG of PCs is analogous to the electronic bandgap of semiconductors, meaning that certain photons will be localized and forbidden in propagation through PCs. According to this characteristic, PCs can be of wide use; thus, various types of PCs have successively been proposed and devised for photonic applications. (Fleming & Lin, 1999; Imada et al., 1999; Knight, 2003; Krauss et al., 2000; Nelson et al., 2000; Park, 1999). If a defect layer is infiltrated in a PC to disrupt its periodicity, partial defect modes that allow the transmission of photons at specific wavelengths will be generated within the PBG. Based on this design of PCs with defect layers, several photonic devices made of two- or three-dimensional PCs have been suggested for lasers (Painter et al., 1999), optical fibers (Knight et al., 1998), and some other applications (Blanco et al., 2000; Chow et al., 2000). Notably, the spectral profile of a PC can be more flexible when the PBG is intrinsically tunable or when the PC is composed of a

Liquid crystals (LCs) are anisotropic materials whose physical properties such as electrical and optical anisotropy can be tuned by the electric field, magnetic field, temperature, and the like in that the LC molecules are susceptible to external stimuli. Depending on the

and reproduction in any medium, provided the original work is properly cited.

**Photonic-Crystal/Liquid-Crystal Hybrid Structures** 

## **Tunable and Memorable Optical Devices with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures**

Po-Chang Wu and Wei Lee

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48127

### **1. Introduction**

### **1.1. Concept of defect-mode tunability in a one-dimensional photoniccrystal/liquid-crystal hybrid cell**

Photonic crystals (PCs) are a special class of artificial structures with spatially periodic dielectric permittivity and their investigations stem from 1987 when both Yablonovitch and John independently demonstrated their own findings (Yablonovitch, 1987; John, 1987). The most attractive feature of PCs is the existence of photonic bandgap (PBG), characterized by the spatial distribution of refractive index or dielectric constant. The PBG of PCs is analogous to the electronic bandgap of semiconductors, meaning that certain photons will be localized and forbidden in propagation through PCs. According to this characteristic, PCs can be of wide use; thus, various types of PCs have successively been proposed and devised for photonic applications. (Fleming & Lin, 1999; Imada et al., 1999; Knight, 2003; Krauss et al., 2000; Nelson et al., 2000; Park, 1999). If a defect layer is infiltrated in a PC to disrupt its periodicity, partial defect modes that allow the transmission of photons at specific wavelengths will be generated within the PBG. Based on this design of PCs with defect layers, several photonic devices made of two- or three-dimensional PCs have been suggested for lasers (Painter et al., 1999), optical fibers (Knight et al., 1998), and some other applications (Blanco et al., 2000; Chow et al., 2000). Notably, the spectral profile of a PC can be more flexible when the PBG is intrinsically tunable or when the PC is composed of a tunable defect layer.

Liquid crystals (LCs) are anisotropic materials whose physical properties such as electrical and optical anisotropy can be tuned by the electric field, magnetic field, temperature, and the like in that the LC molecules are susceptible to external stimuli. Depending on the

© 2012 Wu and Lee, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

molecular orientation, LCs can serve as a phase retardation medium and an optical polarization rotator to manipulate the incoming light via the electrically controlled birefringence and polarization rotation, respectively. As a result, LCs are widely applied to various types of currently used electro-optical devices, especially the information display. As a matter of fact, certain LCs such as the cholesteric LC (CLC), blue phase LC (BP LC) and ferroelectric LC (FLC) can be regarded as PCs due to their periodical orientation of molecular helix. Among them, the PBG of CLCs depends on the LC and chiral parameters. The tunable CLC PCs can thus be realized by adjusting the external factors such as temperature (Morris et al., 2005; Hung et al., 2000), light irradiation (Bobrovsky et al., 2003; Lin et al., 2005), or electric field (Choi et al., 2009; Lin et al., 2005; Yu et al., 2005). Some other tunable PCs based on FLC (Kasano et al., 2003) or BP LC (Yokoyama et al., 2006) have also been demonstrated.

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 57

al., 2010). Their results conclude some attractive features for the tunable mechanism of defect modes within the PBG. First, the shift of defect-mode wavelengths depends on the change in effective refractive index (*n*eff) (Zyryanov et al., 2008, 2010). The decrease in *n*eff gives rise to the blueshift of defect-mode wavelengths whereas redshift occurs as *n*eff increases. In addition, a larger number of defect modes can be obtained by using LC with high refractive index or by increasing the thickness of the defect layer, enabling the 1D PC/LC structure to be applicable for the use of a narrow band filter. Moreover, they experimentally and theoretically demonstrated that the transmission tunability of defect modes can be achieved by placing the cell between crossed polarizers to allow "interference" between two orthogonal polarization components through vector sum in the projection direction along the transmission axis of the analyzer. As a result, the transmittance is increased when the defect-mode wavelength of an extraordinary

component overlaps that of an ordinary one (Zyryanov et al., 2008).

**Figure 1.** Schematic of a 1D PC/LC hybrid structure in a typical experimental setup.

**dynamic-mode liquid crystal** 

**1.2. Overview of the development of one-dimensional photonic crystals with a** 

Current available LC devices can be classified into two categories, dynamic-mode (DM) and memory-mode (MM)LCs, according to their operation as a function of applied electric field. The LC molecules in the DMLC have only one stable state, determined by the condition of the alignment film, and they are continuously reoriented with applied voltage. On the contrary, there are two or multistable states in the MMLC and the stable states can be switched from one to another by the applied voltage. In the DMLC, it can serve as a phase retarder or optical rotator and the light passing them is modified by electrically controlled birefringence (ECB) and polarization rotation effect, respectively. For the 1D PC/LC cells mentioned in Section 1.1, the LC defect layers used are DMLCs acting as phase retarders. The mechanism of the tunable defect modes in these cells can thus be explained in terms of the ordinary and extraordinary refractive indices (Ozaki et al., 2002, 2004b; Zyryanov et al., 2008). On the other hand, the twisted-nematic (TN) LC, in which the molecular orientation

By inserting a LC as defect layer in the PC, tunabilities in the profiles of defect modes are expected. The first tunable PC/LC hybrid structure was developed by Ozaki et al. when they used a planar aligned nematic LC as a defect layer sandwiched between two onedimensional (1D) periodical multilayers (i.e., dielectric mirrors) and successfully demonstrated the electrically tunable wavelength of defect modes (Ozaki et al., 2002). Their concept of tunability in the 1D PC/LC cell can briefly be described as follows: Figure 1 illustrates the setup for investigation of the transmission spectra of the PC/LC cell. Note that the configuration includes a single linear polarizer in front of the PC/LC cell. The LC with positive dielectric anisotropy is aligned homogeneously along the *x*-axis whereas the incoming light propagates in the *z*-axis. The multilayer consists of two dielectric materials, with high- and low-refractive-index layers stacked alternatively. When the incoming light is normally incident to the PC/LC cell with its polarization direction parallel to the LC molecular axis, the optical path length (OPL) is contributed by the sole extraordinary refractive index (*n*e). The appearance of peaks in the PBG of the transmission spectrum thus represents extraordinary defect modes. Once an electric field is applied across the cell to align the molecule along the *z*-axis, the contribution of the ordinary refractive index (*n*o) to the OPL leads to the shift of defect modes to the shorter wavelength in the spectrum. On the contrary, the wavelength positions of all defect modes remain unchanged under the field-on and field-off conditions when the polarization direction of the impinging light becomes parallel to the *y*-axis due to the equal contribution of the OPL. It is concluded that the tunability of defect modes is attributed to the change in refractive index as well as the OPL manipulated by the electric field. After the publication of the milestone paper by Ozaki et al. (Ozaki et al., 2002), the idea has been extended to the 1D PC/CLC color-tunable lasing (Matsuhisa et al., 2006, 2007; Ozaki et al., 2003a, 2005; Park et al., 2009) and fast-response PC/LC structure (Ozaki et al., 2003b). Furthermore, based on this mechanism, several approaches, such as varying the incident angle of light (Arkhipkin et al., 2007) and temperature (Arkhipkin et al., 2008) or using magnetic field (Zyryanov et al., 2008) to adjust the optical anisotropy of LCs, have successively been proposed for realization of tunable 1D PC/LC cells. Particularly, Zyryanov and colleagues further took the investigation of a 1D PC/LC cell to a new stage by setting the hybrid cell between crossed polarizers (Zyryanov et al., 2010). Their results conclude some attractive features for the tunable mechanism of defect modes within the PBG. First, the shift of defect-mode wavelengths depends on the change in effective refractive index (*n*eff) (Zyryanov et al., 2008, 2010). The decrease in *n*eff gives rise to the blueshift of defect-mode wavelengths whereas redshift occurs as *n*eff increases. In addition, a larger number of defect modes can be obtained by using LC with high refractive index or by increasing the thickness of the defect layer, enabling the 1D PC/LC structure to be applicable for the use of a narrow band filter. Moreover, they experimentally and theoretically demonstrated that the transmission tunability of defect modes can be achieved by placing the cell between crossed polarizers to allow "interference" between two orthogonal polarization components through vector sum in the projection direction along the transmission axis of the analyzer. As a result, the transmittance is increased when the defect-mode wavelength of an extraordinary component overlaps that of an ordinary one (Zyryanov et al., 2008).

56 Optical Devices in Communication and Computation

been demonstrated.

molecular orientation, LCs can serve as a phase retardation medium and an optical polarization rotator to manipulate the incoming light via the electrically controlled birefringence and polarization rotation, respectively. As a result, LCs are widely applied to various types of currently used electro-optical devices, especially the information display. As a matter of fact, certain LCs such as the cholesteric LC (CLC), blue phase LC (BP LC) and ferroelectric LC (FLC) can be regarded as PCs due to their periodical orientation of molecular helix. Among them, the PBG of CLCs depends on the LC and chiral parameters. The tunable CLC PCs can thus be realized by adjusting the external factors such as temperature (Morris et al., 2005; Hung et al., 2000), light irradiation (Bobrovsky et al., 2003; Lin et al., 2005), or electric field (Choi et al., 2009; Lin et al., 2005; Yu et al., 2005). Some other tunable PCs based on FLC (Kasano et al., 2003) or BP LC (Yokoyama et al., 2006) have also

By inserting a LC as defect layer in the PC, tunabilities in the profiles of defect modes are expected. The first tunable PC/LC hybrid structure was developed by Ozaki et al. when they used a planar aligned nematic LC as a defect layer sandwiched between two onedimensional (1D) periodical multilayers (i.e., dielectric mirrors) and successfully demonstrated the electrically tunable wavelength of defect modes (Ozaki et al., 2002). Their concept of tunability in the 1D PC/LC cell can briefly be described as follows: Figure 1 illustrates the setup for investigation of the transmission spectra of the PC/LC cell. Note that the configuration includes a single linear polarizer in front of the PC/LC cell. The LC with positive dielectric anisotropy is aligned homogeneously along the *x*-axis whereas the incoming light propagates in the *z*-axis. The multilayer consists of two dielectric materials, with high- and low-refractive-index layers stacked alternatively. When the incoming light is normally incident to the PC/LC cell with its polarization direction parallel to the LC molecular axis, the optical path length (OPL) is contributed by the sole extraordinary refractive index (*n*e). The appearance of peaks in the PBG of the transmission spectrum thus represents extraordinary defect modes. Once an electric field is applied across the cell to align the molecule along the *z*-axis, the contribution of the ordinary refractive index (*n*o) to the OPL leads to the shift of defect modes to the shorter wavelength in the spectrum. On the contrary, the wavelength positions of all defect modes remain unchanged under the field-on and field-off conditions when the polarization direction of the impinging light becomes parallel to the *y*-axis due to the equal contribution of the OPL. It is concluded that the tunability of defect modes is attributed to the change in refractive index as well as the OPL manipulated by the electric field. After the publication of the milestone paper by Ozaki et al. (Ozaki et al., 2002), the idea has been extended to the 1D PC/CLC color-tunable lasing (Matsuhisa et al., 2006, 2007; Ozaki et al., 2003a, 2005; Park et al., 2009) and fast-response PC/LC structure (Ozaki et al., 2003b). Furthermore, based on this mechanism, several approaches, such as varying the incident angle of light (Arkhipkin et al., 2007) and temperature (Arkhipkin et al., 2008) or using magnetic field (Zyryanov et al., 2008) to adjust the optical anisotropy of LCs, have successively been proposed for realization of tunable 1D PC/LC cells. Particularly, Zyryanov and colleagues further took the investigation of a 1D PC/LC cell to a new stage by setting the hybrid cell between crossed polarizers (Zyryanov et

**Figure 1.** Schematic of a 1D PC/LC hybrid structure in a typical experimental setup.

#### **1.2. Overview of the development of one-dimensional photonic crystals with a dynamic-mode liquid crystal**

Current available LC devices can be classified into two categories, dynamic-mode (DM) and memory-mode (MM)LCs, according to their operation as a function of applied electric field. The LC molecules in the DMLC have only one stable state, determined by the condition of the alignment film, and they are continuously reoriented with applied voltage. On the contrary, there are two or multistable states in the MMLC and the stable states can be switched from one to another by the applied voltage. In the DMLC, it can serve as a phase retarder or optical rotator and the light passing them is modified by electrically controlled birefringence (ECB) and polarization rotation effect, respectively. For the 1D PC/LC cells mentioned in Section 1.1, the LC defect layers used are DMLCs acting as phase retarders. The mechanism of the tunable defect modes in these cells can thus be explained in terms of the ordinary and extraordinary refractive indices (Ozaki et al., 2002, 2004b; Zyryanov et al., 2008). On the other hand, the twisted-nematic (TN) LC, in which the molecular orientation exhibits 90° twist, acts as an optical polarization rotator so that the light passing through the TN LC is characterized by the rotation of polarization. The hybrid structure configured by a 1D PC and a TN LC was demonstrated in 2010 (Lin et al., 2010). Several phenomena attributable to the adiabatic following are quite different from the tunability mechanism mentioned in the preceding section. To realize how the adiabatic following enables optical tunability, described here are the spectral characteristics of an electrically controlled 1D PC/TN cell acquired in both the single-polarizer (SP) and crossed-polarizer (CP) schemes.

In the study reported by Lin and coworkers (Lin et al., 2010), the 90° TN LC modes are divided into three groups, depending on the polarization angle *β* between the transmission axis of the first polarizer (i.e., input polarization) and the director axis (i.e., averaged molecular axis) lying in the front substrate. They are the ordinary-mode (O-mode), extraordinary-mode (E-mode), and mixed-mode (M-mode) TN satisfying the conditions of *β* = 90°, 0°, and 45°, respectively. It is worth mentioning that the M-mode TN considered by Lin et al. is only a specific one. Generally, the M-mode TN, abbreviated as MTN, combines the polarization-rotation effect as well as birefringence effect. A traditional TN is primarily characterized by its polarization-rotation effect, which is manifested when the multiplication of the mesogenic bulk thickness and the optical birefringence (i.e., optical anisotropy), *dn*, is larger than the Gooch–Tarry first minimum condition, namely, (√3/2) 0.866, where is the wavelength (Gooch & Tarry, 1975). If *dn* is smaller than that condition, then the polarization-rotation effect is incomplete. Another condition of MTN is that 0° *β* 90° without the requirement of the twisted angle to be 90°. Under such a circumstance, birefringence effect will also take place. The triumph of MTN is its wide use in reflective LC displays, including pico projectors (Wu & Wu, 1996). Figure 2 shows the phenomenon of the wavelength shift of defect modes in two PC/TN cells impregnated with two different nematic LC materials. Note that the birefringence of the LC material E7 is higher than that of CYLC43. Unlike the ECB-based tunable defect modes in some specific PC/LC cells, in which the defect modes for the ordinary-ray are independent of the applied voltage, the defectmode wavelengths in both the E-mode and O-mode PC/TN cell show blueshift when the applied voltage increases. Compared with the O-mode configuration, the E-mode has a more perceptible shift in wavelength (blueshift) due to significant change (decrease) in effective refractive index, dedicated by the unwinding process of the molecular helix. It is also clear from Fig. 2 that the extent of buleshift for E7 is greater than that for CYLC43. This result can be explained by their Mauguin parameters (Gooch & Tarry, 1975)

$$\mathbf{u} = \frac{\mathbf{2d} \mathbf{A} \mathbf{n}}{\mathbf{y}},\tag{1}$$

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 59

**Figure 2.** Voltage-induced blueshift of defect modes for two comparative 1D PC/LC cells with distinct

Figure 3 demonstrates an integrated effect on the transmission of defect modes in the Mmode PC/TN cell. One can obviously identify that the peaks of the M-mode spectrum are located at the exactly same positions of the E-mode and O-mode peaks in wavelength. This result indicates that each defect mode in the M-mode PC/TN is contributed by both the adiabatic following and birefringence effects. Moreover, the intensity of the transmitted light in either E- or O-mode spreads to the other, making the integrated intensity of the peaks in the M-mode almost the same as that in either E- or M-mode. This implies that the M-mode spectrum is a superposition of those of both E-mode and O-mode. Interestingly, while looking carefully into the spectra of E- and O-mode, small satellite peaks accompanying the defect modes are observed, presumably due to the unavoidable elliptic polarization of light in a conventional TN cell. This phenomenon has left untouched in other types of 1D PC/LC cells. Recently, it has been explained by the Mauguin condition violation and the coupling between the slow semi-longitudinal mode (i.e., twisted extraordinary mode) and fast semi-transverse mode (i.e., twisted ordinary mode) PC/TN cell (Timofeev et

In regard to a typical 90° TN cell, the linearly polarized light rotated approximately by 90° by the cell can almost "completely" pass the rear polarizer; i.e., the analyzer. There is no doubt that the spectra of the E-mode as well as the O-mode in the CP scheme (configured by two linear polarizers whose transmission axes are orthogonal to each other) are nearly identical to their corresponding ones under the SP scheme. Figure 4 reveals a distinctive profile in the spectrum for the M-mode because the light passing through the cell becomes non-linearly polarized light. Particularly, an outstanding peak, whose intensity is the strongest among the vast of peaks within the PBG, is located near 700 nm as shown in Fig. 4. This unique feature enables to extend the use of the PC/TN cell in the application of a

defect materials (adapted from Lin et al., 2010).

al., 2012).

giving superior adiabatic following capability of E7 (Lin et al., 2010). A perfect adiabatic following in the TN LC cell would enable the linearly polarized light to traverse the LC layer with the rotation of the molecular twist, which makes *n*eff for the incident beam nearly equal to *n*e in E-mode and *n*o in O-mode. In fact, the elliptic polarization can hardly be avoided in the TN LC (Yeh & Gu, 1999a); thus, *n*eff is no longer a constant in the O-mode TN LC but becomes a weak function of applied voltage. As a result, small shifts for the defect modes are observed in the O-mode PC/TN cells.

exhibits 90° twist, acts as an optical polarization rotator so that the light passing through the TN LC is characterized by the rotation of polarization. The hybrid structure configured by a 1D PC and a TN LC was demonstrated in 2010 (Lin et al., 2010). Several phenomena attributable to the adiabatic following are quite different from the tunability mechanism mentioned in the preceding section. To realize how the adiabatic following enables optical tunability, described here are the spectral characteristics of an electrically controlled 1D PC/TN cell acquired in both the single-polarizer (SP) and crossed-polarizer (CP) schemes.

In the study reported by Lin and coworkers (Lin et al., 2010), the 90° TN LC modes are divided into three groups, depending on the polarization angle *β* between the transmission axis of the first polarizer (i.e., input polarization) and the director axis (i.e., averaged molecular axis) lying in the front substrate. They are the ordinary-mode (O-mode), extraordinary-mode (E-mode), and mixed-mode (M-mode) TN satisfying the conditions of *β* = 90°, 0°, and 45°, respectively. It is worth mentioning that the M-mode TN considered by Lin et al. is only a specific one. Generally, the M-mode TN, abbreviated as MTN, combines the polarization-rotation effect as well as birefringence effect. A traditional TN is primarily characterized by its polarization-rotation effect, which is manifested when the multiplication of the mesogenic bulk thickness and the optical birefringence (i.e., optical anisotropy), *dn*,

is the wavelength (Gooch & Tarry, 1975). If *dn* is smaller than that condition, then the polarization-rotation effect is incomplete. Another condition of MTN is that 0° *β* 90° without the requirement of the twisted angle to be 90°. Under such a circumstance, birefringence effect will also take place. The triumph of MTN is its wide use in reflective LC displays, including pico projectors (Wu & Wu, 1996). Figure 2 shows the phenomenon of the wavelength shift of defect modes in two PC/TN cells impregnated with two different nematic LC materials. Note that the birefringence of the LC material E7 is higher than that of CYLC43. Unlike the ECB-based tunable defect modes in some specific PC/LC cells, in which the defect modes for the ordinary-ray are independent of the applied voltage, the defectmode wavelengths in both the E-mode and O-mode PC/TN cell show blueshift when the applied voltage increases. Compared with the O-mode configuration, the E-mode has a more perceptible shift in wavelength (blueshift) due to significant change (decrease) in effective refractive index, dedicated by the unwinding process of the molecular helix. It is also clear from Fig. 2 that the extent of buleshift for E7 is greater than that for CYLC43. This

0.866

, where

(1)

is larger than the Gooch–Tarry first minimum condition, namely, (√3/2)

result can be explained by their Mauguin parameters (Gooch & Tarry, 1975)

modes are observed in the O-mode PC/TN cells.

2d n u , 

giving superior adiabatic following capability of E7 (Lin et al., 2010). A perfect adiabatic following in the TN LC cell would enable the linearly polarized light to traverse the LC layer with the rotation of the molecular twist, which makes *n*eff for the incident beam nearly equal to *n*e in E-mode and *n*o in O-mode. In fact, the elliptic polarization can hardly be avoided in the TN LC (Yeh & Gu, 1999a); thus, *n*eff is no longer a constant in the O-mode TN LC but becomes a weak function of applied voltage. As a result, small shifts for the defect

**Figure 2.** Voltage-induced blueshift of defect modes for two comparative 1D PC/LC cells with distinct defect materials (adapted from Lin et al., 2010).

Figure 3 demonstrates an integrated effect on the transmission of defect modes in the Mmode PC/TN cell. One can obviously identify that the peaks of the M-mode spectrum are located at the exactly same positions of the E-mode and O-mode peaks in wavelength. This result indicates that each defect mode in the M-mode PC/TN is contributed by both the adiabatic following and birefringence effects. Moreover, the intensity of the transmitted light in either E- or O-mode spreads to the other, making the integrated intensity of the peaks in the M-mode almost the same as that in either E- or M-mode. This implies that the M-mode spectrum is a superposition of those of both E-mode and O-mode. Interestingly, while looking carefully into the spectra of E- and O-mode, small satellite peaks accompanying the defect modes are observed, presumably due to the unavoidable elliptic polarization of light in a conventional TN cell. This phenomenon has left untouched in other types of 1D PC/LC cells. Recently, it has been explained by the Mauguin condition violation and the coupling between the slow semi-longitudinal mode (i.e., twisted extraordinary mode) and fast semi-transverse mode (i.e., twisted ordinary mode) PC/TN cell (Timofeev et al., 2012).

In regard to a typical 90° TN cell, the linearly polarized light rotated approximately by 90° by the cell can almost "completely" pass the rear polarizer; i.e., the analyzer. There is no doubt that the spectra of the E-mode as well as the O-mode in the CP scheme (configured by two linear polarizers whose transmission axes are orthogonal to each other) are nearly identical to their corresponding ones under the SP scheme. Figure 4 reveals a distinctive profile in the spectrum for the M-mode because the light passing through the cell becomes non-linearly polarized light. Particularly, an outstanding peak, whose intensity is the strongest among the vast of peaks within the PBG, is located near 700 nm as shown in Fig. 4. This unique feature enables to extend the use of the PC/TN cell in the application of a monochromatic selector. In accordance with the simulation results published in the literature, this remarkable defect-mode peak is attributable to the intrinsic transmission characteristic of a MTN cell (Lin et al., 2010).

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 61

**Figure 4.** Transmission spectra of a 1D PC/TN cell at null voltage under crossed polarizers (adapted

Among the recent development of MMLCs, the bistable or multistable cells using dualfrequency LCs (DFLCs) enable the switching between optically stable states by applying frequency-modulated voltage pulses. The DFLC is a kind of LC material whose sign of dielectric anisotropy (*∆ε*) can be varied by the frequency of an externally applied electric field (Xianyu et al., 2009). The DFLC has a certain crossover frequency (*f*c) to discriminate the behavior of ∆*ε*. While the frequency is lower than *f*c, the ∆*ε* value is positive. Or it becomes negative if the frequency is higher than *f*c. Based on this mechanism, various types of MMLC cells composed of DFLC are demonstrated in the literature (Hsiao et al., 2011b; Hsu et al., 2004; Jhun et al., 2006; Yao et al., 2009). Among them, the bistable chiralhomeotropic nematic (BHN) LC and dual-frequency cholesteric LC (DFCLC) have been used as defect layer in the 1D PC/MMLC cell (Hsiao et al., 2011a, 2011c; Wu et al., 2011). As such, Section 2 details the cell configuration and operation principles of these two MMLC modes so that one can grasp the switching mechanisms in the description in the next two sections. The configuration of a 1D PC/MMLC cell, including the design of multilayers is schematically depicted in Session 3. In addition, the optical properties and the tunability in the defect modes of the cell switching among the stable and voltage-sustained states are reported in Session 3 as well. To realize a low-power-consumption optical device, in Session 4, the characteristics of defect modes in various memory states of both PC/BHN and PC/DFCLC cells are further discussed. The features of defect-mode switching between two stable states are confirmed. Particularly, a new scheme of a tristable PC device based on DFCLC is demonstrated using a polymer-stabilized cholesteric texture (PSCT) as a defect layer (Hsiao et al., 2011). Finally, the key findings of the properties of the 1D PC/MMLC cells discussed in the preceding sections are summarized. In accordance with the concluding remarks, suitable device applications of the tunable 1D PC/MMLC hybrid structures are

from Lin et al., 2010).

#### **1.3. Aim of this chapter**

Recently, electro-optical devices in line with the idea of energy saving and/or low power consumption become a popular research topic in that the green concept is globally promoted due to the great concern for energy shortage nowadays. The most representative one for alternative energy is the solar cell which has the ability to transfer natural energy from the sun to electric power. In view of the recent development in 1D PC/LC cells, the demonstrated features such as wavelength tunability and transmission tunablity enable their use for the application in various electro-optical devices, as described in Section 1.2. However, aforementioned features in 1D PC/LC cells are realized by the continuous-varying of electric field due to the use of DMLCs as the defect layer so that applications in green products are very limited. Lately, a new design of 1D PC with MMLC as a defect layer that brings the notion of multistability in defect modes has been demonstrated (Hsiao et al., 2011a, 2011c; Wu et al., 2011). In the 1D PC/MMLC cell, the spectral properties of defect modes in a memory state persist without applied voltage; such a cell supports a pathway for designing photonic devices with green concept. To interpret how the 1D PC/MMLC operates, this chapter reviews some previous works primarily done by this group and builds up the following three sections in the main body of this article to explicitly clarify the characteristics of such 1D PC/MMLC cells.

**Figure 3.** Transmission spectra of a PC/TN cell in the photonic bandgap in three different modes. The M-mode, E-mode and O-mode are represented by the thick solid line, thin solid line and dashed line, respectively (adapted from Lin et al., 2010).

characteristic of a MTN cell (Lin et al., 2010).

characteristics of such 1D PC/MMLC cells.

respectively (adapted from Lin et al., 2010).

**1.3. Aim of this chapter** 

monochromatic selector. In accordance with the simulation results published in the literature, this remarkable defect-mode peak is attributable to the intrinsic transmission

Recently, electro-optical devices in line with the idea of energy saving and/or low power consumption become a popular research topic in that the green concept is globally promoted due to the great concern for energy shortage nowadays. The most representative one for alternative energy is the solar cell which has the ability to transfer natural energy from the sun to electric power. In view of the recent development in 1D PC/LC cells, the demonstrated features such as wavelength tunability and transmission tunablity enable their use for the application in various electro-optical devices, as described in Section 1.2. However, aforementioned features in 1D PC/LC cells are realized by the continuous-varying of electric field due to the use of DMLCs as the defect layer so that applications in green products are very limited. Lately, a new design of 1D PC with MMLC as a defect layer that brings the notion of multistability in defect modes has been demonstrated (Hsiao et al., 2011a, 2011c; Wu et al., 2011). In the 1D PC/MMLC cell, the spectral properties of defect modes in a memory state persist without applied voltage; such a cell supports a pathway for designing photonic devices with green concept. To interpret how the 1D PC/MMLC operates, this chapter reviews some previous works primarily done by this group and builds up the following three sections in the main body of this article to explicitly clarify the

**Figure 3.** Transmission spectra of a PC/TN cell in the photonic bandgap in three different modes. The M-mode, E-mode and O-mode are represented by the thick solid line, thin solid line and dashed line,

**Figure 4.** Transmission spectra of a 1D PC/TN cell at null voltage under crossed polarizers (adapted from Lin et al., 2010).

Among the recent development of MMLCs, the bistable or multistable cells using dualfrequency LCs (DFLCs) enable the switching between optically stable states by applying frequency-modulated voltage pulses. The DFLC is a kind of LC material whose sign of dielectric anisotropy (*∆ε*) can be varied by the frequency of an externally applied electric field (Xianyu et al., 2009). The DFLC has a certain crossover frequency (*f*c) to discriminate the behavior of ∆*ε*. While the frequency is lower than *f*c, the ∆*ε* value is positive. Or it becomes negative if the frequency is higher than *f*c. Based on this mechanism, various types of MMLC cells composed of DFLC are demonstrated in the literature (Hsiao et al., 2011b; Hsu et al., 2004; Jhun et al., 2006; Yao et al., 2009). Among them, the bistable chiralhomeotropic nematic (BHN) LC and dual-frequency cholesteric LC (DFCLC) have been used as defect layer in the 1D PC/MMLC cell (Hsiao et al., 2011a, 2011c; Wu et al., 2011). As such, Section 2 details the cell configuration and operation principles of these two MMLC modes so that one can grasp the switching mechanisms in the description in the next two sections. The configuration of a 1D PC/MMLC cell, including the design of multilayers is schematically depicted in Session 3. In addition, the optical properties and the tunability in the defect modes of the cell switching among the stable and voltage-sustained states are reported in Session 3 as well. To realize a low-power-consumption optical device, in Session 4, the characteristics of defect modes in various memory states of both PC/BHN and PC/DFCLC cells are further discussed. The features of defect-mode switching between two stable states are confirmed. Particularly, a new scheme of a tristable PC device based on DFCLC is demonstrated using a polymer-stabilized cholesteric texture (PSCT) as a defect layer (Hsiao et al., 2011). Finally, the key findings of the properties of the 1D PC/MMLC cells discussed in the preceding sections are summarized. In accordance with the concluding remarks, suitable device applications of the tunable 1D PC/MMLC hybrid structures are

suggested in the last section of the chapter. A brief note will also be included on future perspectives of the development of 1D PC/MMLC cells.

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 63

frequency *f2* instantly follows the first one with frequency *f*1. Once the connecting pulse is applied to the cell, the cell first induces the pulse with frequency *f*<sup>1</sup> which results in the switching of cell from tH to bH state. As the frequency of the connecting pulse changes from *f*<sup>1</sup> and *f*2, where the dielectric anisotropy of the LC becomes negative (*∆ε* < 0), the dielectric coupling between the electric field and LC leads the molecules to align parallel to the substrate and induces flow effect. The cell is thus switched from bH state to another voltage-sustained state, called biased twisted (bT) state due to the backflow effect and applied electric field. The molecular in the bT state rotates about 2*π* in the azimuthal angle. The bT state subsequently relax to the stable tT state as the driving pulse ends. Both bT and tT state have 2*π*-twist molecular orientation but the tilted angle in bT state is higher than that in the tT state. As a result, a transition process of tH−bH−bT−tT is required within the switching from tH to tT

state. It is worth reminding that the tH and tT states are of optical stability.

**Figure 5.** Schematic illustration of the configuration of a BHN LC cell. R, the rubbing direction.

**Figure 6.** Bistable switching for a BHN LC cell upon the application of a frequency-modulated voltage

pulse (adapted from Hsu et al., 2007).

#### **2. Operation principles of memory-mode liquid crystals**

#### **2.1. Bistable chiral-tilted homeotropic nematic liquid crystals**

The BHN LC possesses two optically stable states—tilted-homeotropic (tH) and tilted-twist (tT) states, either of which remains optically stable without the need of continuous application of a voltage (Hsu et al., 2004). By means of a DFLC, switching between these two states is accomplished by the flow effect of LC molecules and frequency-revertible dielectric anisotropy of the DFLC. To fabricate a BHN LC cell, the thickness-to-pitch ratio *d*/*p* and the pretilt angle *θ* of LC molecules, measured from the substrate plane, play crucial roles in the stability of the tH and tT states. Typically, the BHN LC cell is made in the high-pretilt-angle regime with *d*/*p* around unity. To understand the optimized condition of *d*/*p* and *θ*, Liang and Lin determined the *d*/*p* ranges of the BHN LC cells with various pretilt angles based on their experimental and simulation results (Liang & Lin, 2007). They found that the *d*/*p* range for obtaining stable tH and tT state in the BHN LC cell is 0.6–1.14, 0.68–1.21, and 0.82–1.24 when the pretilt angle is equal to 62°, 72°, and 80°, respectively. In additional to the conventional (0, 2*π*) BHN LC, the two stable states can also be found in the (*π*/2, 3*π*/2) BHN LC under the condition of *θ* = 74° (Hsu, 2007).

According to the above-mentioned results, Fig. 5 illustrates the cell configuration of the BHN LC. The BHN cell is composed of a DFLC doped with a suitable concentration of a chiral agent sandwiched between two indium–tin-oxide (ITO)-coated glass substrates covered with alignment films. To achieve necessary tilted-homeotropic molecular orientation with a proper pretilt angle, one can simply coat a homeotropic polyimide or a mixed solution of homeotropic- and planar-alignment polyimide on the substrates as the aligning layers with the treatment of mechanical rubbing on the top and bottom substrates in anti-parallel direction. While the adaptable range of the pretilt angle is very limited in a BHN LC cell with homeotropic alignment, cells with mixed alignment enable the tunable pretilt angle in a wider range by adjusting its composition (Yeung et al., 2006).

On the basis of the switching mechanism of the BHN LC (Hsu et al., 2007; Liang et al., 2008), a brief illustration, shown in Fig. 6, is provided to summarize the operation between the two stable states in a BHN LC cell. Here, *f*<sup>1</sup> and *f*<sup>2</sup> are the frequencies satisfying the conditions of *f*<sup>1</sup> < *f*c and *f*2 > *f*c, and hence correspond to the positive and negative dielectric anisotropy (*∆ε*) of the DFLC, respectively. The solid and dash lines represent the texture transitions from tT to tH and tH to tT, respectively. Consider a tT state stabilized in the cell. The LC molecules will response to align perpendicular to the substrate when an electric field with frequency *f*1 is applied vertically to the cell because the LC exhibits positive dielectric anisotropy (*∆ε* > 0). The molecules are then oriented homeotropically (i.e., vertically) in the cell at high voltage. This voltage-sustained state is called biased homeotropic (bH) state. As the electric field is switched off, the molecules relax to the tH state with very high pretilt angle. Accordingly, the switching from tT to tH state follows a transition process of tT−bH−tH. To switch the cell from tH to tT state, a connecting pulse with frequencies *f*<sup>1</sup> and *f*<sup>2</sup> is used. Note that the second pulse with frequency *f2* instantly follows the first one with frequency *f*1. Once the connecting pulse is applied to the cell, the cell first induces the pulse with frequency *f*<sup>1</sup> which results in the switching of cell from tH to bH state. As the frequency of the connecting pulse changes from *f*<sup>1</sup> and *f*2, where the dielectric anisotropy of the LC becomes negative (*∆ε* < 0), the dielectric coupling between the electric field and LC leads the molecules to align parallel to the substrate and induces flow effect. The cell is thus switched from bH state to another voltage-sustained state, called biased twisted (bT) state due to the backflow effect and applied electric field. The molecular in the bT state rotates about 2*π* in the azimuthal angle. The bT state subsequently relax to the stable tT state as the driving pulse ends. Both bT and tT state have 2*π*-twist molecular orientation but the tilted angle in bT state is higher than that in the tT state. As a result, a transition process of tH−bH−bT−tT is required within the switching from tH to tT state. It is worth reminding that the tH and tT states are of optical stability.

62 Optical Devices in Communication and Computation

perspectives of the development of 1D PC/MMLC cells.

BHN LC under the condition of *θ* = 74° (Hsu, 2007).

**2. Operation principles of memory-mode liquid crystals** 

**2.1. Bistable chiral-tilted homeotropic nematic liquid crystals** 

suggested in the last section of the chapter. A brief note will also be included on future

The BHN LC possesses two optically stable states—tilted-homeotropic (tH) and tilted-twist (tT) states, either of which remains optically stable without the need of continuous application of a voltage (Hsu et al., 2004). By means of a DFLC, switching between these two states is accomplished by the flow effect of LC molecules and frequency-revertible dielectric anisotropy of the DFLC. To fabricate a BHN LC cell, the thickness-to-pitch ratio *d*/*p* and the pretilt angle *θ* of LC molecules, measured from the substrate plane, play crucial roles in the stability of the tH and tT states. Typically, the BHN LC cell is made in the high-pretilt-angle regime with *d*/*p* around unity. To understand the optimized condition of *d*/*p* and *θ*, Liang and Lin determined the *d*/*p* ranges of the BHN LC cells with various pretilt angles based on their experimental and simulation results (Liang & Lin, 2007). They found that the *d*/*p* range for obtaining stable tH and tT state in the BHN LC cell is 0.6–1.14, 0.68–1.21, and 0.82–1.24 when the pretilt angle is equal to 62°, 72°, and 80°, respectively. In additional to the conventional (0, 2*π*) BHN LC, the two stable states can also be found in the (*π*/2, 3*π*/2)

According to the above-mentioned results, Fig. 5 illustrates the cell configuration of the BHN LC. The BHN cell is composed of a DFLC doped with a suitable concentration of a chiral agent sandwiched between two indium–tin-oxide (ITO)-coated glass substrates covered with alignment films. To achieve necessary tilted-homeotropic molecular orientation with a proper pretilt angle, one can simply coat a homeotropic polyimide or a mixed solution of homeotropic- and planar-alignment polyimide on the substrates as the aligning layers with the treatment of mechanical rubbing on the top and bottom substrates in anti-parallel direction. While the adaptable range of the pretilt angle is very limited in a BHN LC cell with homeotropic alignment, cells with mixed alignment enable the tunable

On the basis of the switching mechanism of the BHN LC (Hsu et al., 2007; Liang et al., 2008), a brief illustration, shown in Fig. 6, is provided to summarize the operation between the two stable states in a BHN LC cell. Here, *f*<sup>1</sup> and *f*<sup>2</sup> are the frequencies satisfying the conditions of *f*<sup>1</sup> < *f*c and *f*2 > *f*c, and hence correspond to the positive and negative dielectric anisotropy (*∆ε*) of the DFLC, respectively. The solid and dash lines represent the texture transitions from tT to tH and tH to tT, respectively. Consider a tT state stabilized in the cell. The LC molecules will response to align perpendicular to the substrate when an electric field with frequency *f*1 is applied vertically to the cell because the LC exhibits positive dielectric anisotropy (*∆ε* > 0). The molecules are then oriented homeotropically (i.e., vertically) in the cell at high voltage. This voltage-sustained state is called biased homeotropic (bH) state. As the electric field is switched off, the molecules relax to the tH state with very high pretilt angle. Accordingly, the switching from tT to tH state follows a transition process of tT−bH−tH. To switch the cell from tH to tT state, a connecting pulse with frequencies *f*<sup>1</sup> and *f*<sup>2</sup> is used. Note that the second pulse with

pretilt angle in a wider range by adjusting its composition (Yeung et al., 2006).

**Figure 5.** Schematic illustration of the configuration of a BHN LC cell. R, the rubbing direction.

**Figure 6.** Bistable switching for a BHN LC cell upon the application of a frequency-modulated voltage pulse (adapted from Hsu et al., 2007).

#### **2.2. Dual-frequency cholesteric liquid crystals**

The optical bistability is one of the unique features in cholesteric LC (CLC) and its applications in electro-optical devices (Bao et al., 2009; Berreman & Heffner, 2006; Huang et al., 2003; Hsiao et al., 2011b; Xu & Yang, 1997). CLCs, also termed chiral nematic LCs because of their structural nature to be the chiral versions of the nematic molecules, have been widely investigated in the literature. In a typical bistable CLC cell, the two stable states are the transparent planar (P) state and light-scattering focal conic (FC) state. Switching between these two states can readily be achieved by adjusting the amplitude of applied electric field. For instance, when an electric field in square wave with a specific amplitude value is applied to the CLC cell, the texture will be changed from P to FC state. Further increasing the voltage over a critical value results in the transition of texture from FC to homeotropic (H) state. The texture in the H state can be switched back to the P state by turning off the field rapidly or to the lightscattering FC state by turning off the field slowly. As a result, the P-to-FC transition can be accomplished directly by the external applied field whereas the FC-to-P transition is indirect since an intermediate H state is required. In addition, it takes a few seconds to relax from H to P state, meaning that the response time for the FC-to-P transition is quite slow. This drawback limits the CLC device for practical applications. In contrast to the conventional CLCs, the DFCLC device empowers direct two-way switching between two cholesteric states due to its material property of the frequency-revertible dielectric anisotropy and thus yields a feature of fast response speed (Hsiao et al., 2011b; Ma et al., 2010).

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with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 65

**Figure 8.** Operation principle and texture transitions of a DFCLC cell under the application of various

To clarity how the cholesteric textures are switched by frequency-modulated voltage pulses, Fig. 8 illustrates operations among three cholesteric states (i.e., P, FC, and H) in a DFCLC cell (Hsiao et al., 2011a). It should be noted here again that, when a voltage pulse is applied to the DFCLC cell, the dielectric anisotropy is positive at low frequencies (*f*1) and negative at high frequencies (*f*2) beyond the temperature-dependent crossover frequency (*f*c). Once a voltage pulse with frequency *f*1 is applied vertically to the DFCLC cell, the dielectric coupling leads the molecules to reorientation in parallel to the field direction and the helix tends to be unwound. Consequently, direct P-to-FC and P-to-H switchings can be induced at voltages *V*1 and *V*2, respectively. The switching mechanism of the DFCLC cell in the increasing-voltage process is the same as that of a conventional CLC one. It is worth mentioning here that while applying a pulse with frequency *f*2, at which the molecules incline to align themselves homogeneously with respect to the substrate plane, the backward switching of the FC-to-P and H-to-P transitions can directly be accomplished at voltage *V*3 and *V*4, respectively. Noticeably, reversible direct-switching between FC and H state can also be achieved by individually applying a voltage pulse at voltage *V*<sup>2</sup> at *f*<sup>1</sup> and *f*2**.** Note that *V*<sup>2</sup> is higher than *V*1 (*V*<sup>2</sup> *> V*1) and *V*<sup>4</sup> is higher than *V3* (*V*4 *>V*3) because switching between P and H states requires more energy to make the molecules reach balance. In the bistable DFCLC device, the P and FC textures are essentially the stable states whereas the H texture is a voltage-sustained state. Upon incorporating a certain content of photo-curable monomer (or prepolymer) into DFCLC, another type of CLC device called polymerstabilized cholesteric texture (PSCT), can be created after adequate polymerization. In such a PSCT cell, the stabilization of polymer network throughout the bulk cell enables the possession of stable H state (Ma et al., 2010). Combining the switching mechanism of DFCLC with PSCT, a novel tristable PSCT in which the texture can permanently be stabilized optically in the P, FC, and H states, has been demonstrated very recently (Hsiao et al., 2011a). While thinking about the use of the DFCLC in practical applications there are some issues that should be taken into consideration. The common drawback of the DFCLC is its considerable sensitivity to temperature. Typically, high operation voltage results in

voltage pulses (adapted from Hsiao et al., 2011a).

Figure 7 depicts the cell configuration of a typical CLC or DFCLC cell prepared in homogeneous (i.e., planar) alignment. A (DF)LC host doped with a chiral agent in proper concentration is sandwiched between two conductive glass substrates coated with planar alignment films. The rubbing directions of the top and bottom substrates are set to be antiparallel. As a consequence, a planar texture is initially formed, exhibiting periodic helix structure with its optical axis perpendicular to the substrate plane. Such a molecular orientation in the CLC cell itself can be regarded as a photonic crystal structure with its bandgap located within a designated wavelength regime.

**Figure 7.** Schematic of the molecular configuration of a planar-alignment DFCLC cell. The helix axis is vertical in the initial state.

**2.2. Dual-frequency cholesteric liquid crystals** 

fast response speed (Hsiao et al., 2011b; Ma et al., 2010).

bandgap located within a designated wavelength regime.

vertical in the initial state.

The optical bistability is one of the unique features in cholesteric LC (CLC) and its applications in electro-optical devices (Bao et al., 2009; Berreman & Heffner, 2006; Huang et al., 2003; Hsiao et al., 2011b; Xu & Yang, 1997). CLCs, also termed chiral nematic LCs because of their structural nature to be the chiral versions of the nematic molecules, have been widely investigated in the literature. In a typical bistable CLC cell, the two stable states are the transparent planar (P) state and light-scattering focal conic (FC) state. Switching between these two states can readily be achieved by adjusting the amplitude of applied electric field. For instance, when an electric field in square wave with a specific amplitude value is applied to the CLC cell, the texture will be changed from P to FC state. Further increasing the voltage over a critical value results in the transition of texture from FC to homeotropic (H) state. The texture in the H state can be switched back to the P state by turning off the field rapidly or to the lightscattering FC state by turning off the field slowly. As a result, the P-to-FC transition can be accomplished directly by the external applied field whereas the FC-to-P transition is indirect since an intermediate H state is required. In addition, it takes a few seconds to relax from H to P state, meaning that the response time for the FC-to-P transition is quite slow. This drawback limits the CLC device for practical applications. In contrast to the conventional CLCs, the DFCLC device empowers direct two-way switching between two cholesteric states due to its material property of the frequency-revertible dielectric anisotropy and thus yields a feature of

Figure 7 depicts the cell configuration of a typical CLC or DFCLC cell prepared in homogeneous (i.e., planar) alignment. A (DF)LC host doped with a chiral agent in proper concentration is sandwiched between two conductive glass substrates coated with planar alignment films. The rubbing directions of the top and bottom substrates are set to be antiparallel. As a consequence, a planar texture is initially formed, exhibiting periodic helix structure with its optical axis perpendicular to the substrate plane. Such a molecular orientation in the CLC cell itself can be regarded as a photonic crystal structure with its

**Figure 7.** Schematic of the molecular configuration of a planar-alignment DFCLC cell. The helix axis is

**Figure 8.** Operation principle and texture transitions of a DFCLC cell under the application of various voltage pulses (adapted from Hsiao et al., 2011a).

To clarity how the cholesteric textures are switched by frequency-modulated voltage pulses, Fig. 8 illustrates operations among three cholesteric states (i.e., P, FC, and H) in a DFCLC cell (Hsiao et al., 2011a). It should be noted here again that, when a voltage pulse is applied to the DFCLC cell, the dielectric anisotropy is positive at low frequencies (*f*1) and negative at high frequencies (*f*2) beyond the temperature-dependent crossover frequency (*f*c). Once a voltage pulse with frequency *f*1 is applied vertically to the DFCLC cell, the dielectric coupling leads the molecules to reorientation in parallel to the field direction and the helix tends to be unwound. Consequently, direct P-to-FC and P-to-H switchings can be induced at voltages *V*1 and *V*2, respectively. The switching mechanism of the DFCLC cell in the increasing-voltage process is the same as that of a conventional CLC one. It is worth mentioning here that while applying a pulse with frequency *f*2, at which the molecules incline to align themselves homogeneously with respect to the substrate plane, the backward switching of the FC-to-P and H-to-P transitions can directly be accomplished at voltage *V*3 and *V*4, respectively. Noticeably, reversible direct-switching between FC and H state can also be achieved by individually applying a voltage pulse at voltage *V*<sup>2</sup> at *f*<sup>1</sup> and *f*2**.** Note that *V*<sup>2</sup> is higher than *V*1 (*V*<sup>2</sup> *> V*1) and *V*<sup>4</sup> is higher than *V3* (*V*4 *>V*3) because switching between P and H states requires more energy to make the molecules reach balance. In the bistable DFCLC device, the P and FC textures are essentially the stable states whereas the H texture is a voltage-sustained state. Upon incorporating a certain content of photo-curable monomer (or prepolymer) into DFCLC, another type of CLC device called polymerstabilized cholesteric texture (PSCT), can be created after adequate polymerization. In such a PSCT cell, the stabilization of polymer network throughout the bulk cell enables the possession of stable H state (Ma et al., 2010). Combining the switching mechanism of DFCLC with PSCT, a novel tristable PSCT in which the texture can permanently be stabilized optically in the P, FC, and H states, has been demonstrated very recently (Hsiao et al., 2011a). While thinking about the use of the DFCLC in practical applications there are some issues that should be taken into consideration. The common drawback of the DFCLC is its considerable sensitivity to temperature. Typically, high operation voltage results in dielectric heating, which shifts the crossover frequency to a higher value (Yin et al., 2006; Wen & Wu, 2005). On the other hand, a low-voltage pulse would be insufficient to induce the direct FC-to-P transition.

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 67

**Figure 10.** Transmittance of a dielectric mirror and an empty PC cell made of two identical dielectric

mission spectra of a multilayer film on a glass substrate and a combination of two multilayer-coated substrates with a central air gap (empty cell). In this example, the multilayer film has nine layers, including five high-index layers and four low-index layers. Obviously, the width of PBG is around 250 nm with the central wavelength near 620 nm in the single multilayer. While sandwiching a defect layer between two multilayers, a number of defect modes are generated within the PBG. Note that the insertion of the defect layer does not essentially affect the width of the PBG. The profile of defect modes is influenced by some parameters. Ozaki and associates report that increasing the layer number in the multilayer decreases the line width and transmittance of defect-mode peaks because the Bragg-reflected light, dictated by the multilayer, is limited to reach the defect layer (Ozaki et al., 2004a). On the other hand, it is concluded by Zyryanov and coauthors that the number of defect modes is increased with increasing thickness of the defect layer or using the

material with high refractive index as a defect layer (Zyryanov et al., 2008).

refractive index of an optically uniaxial material (Yeh & Gu, 1999b)

**3.2. One-dimensional photonic-crystal/bistable-chiral-tilted-homeotropic-**

According to the operation of a BHN LC discussed in Section 2.1, applying an external electric field to the PC/BHN hybrid cell enables the switching among four specific states; i.e., tH, bH, tT, and bT states. Due to different molecular orientation of LC as well as the contributions of effective refractive index (*n*eff), the transmission spectra of the 1D PC/BHN hybrid structure in four different states without employing any polarizer disclose dissimilar spectral profiles, as shown in Fig. 11. Recalling the mathematical expression of the effective

mirrors.

**nematic cells** 

### **3. Optical properties of one-dimensional photonic-crystal/memory-modeliquid-crystal cells**

#### **3.1. Definition of the cell configuration**

A 1D PC structure incorporated with LC as a defect layer is well known to have the ability on tuning the optical characteristics such as light intensities and wavelengths of the defect modes. While most of investigations of 1D PC/LC cells are demonstrated based on DMLCs, this section is dedicated to a new classification of 1D PC/LC cells formed by infiltrating with a MMLC as a defect layer. The configuration of a 1D PC/MMLC hybrid structure is schematically depicted in Fig. 9 (Hsiao et al., 2011c). Referring to the conventional 1D periodical structure, the 1D PC here is constructed with two identical dielectric mirrors having multilayer films deposited on the electrically conductive glass substrates. The MMLC, for example, the DFCLC whose electro-optical characteristic exhibits bistable or multistable switching, is infiltrated into the 1D PC as a defect layer with a thickness *d*. The dielectric multilayer consists of a number of high- and low-index materials stacked alternately.

To provide high reflectivity, the OPL of these two materials is theoretically set to be equal to one-quarter wavelength of the incident light, i.e., *n*H*d*H = *n*L*d*L = *λ*/4,where *n*H, *n*L, and *d*H, *d*<sup>L</sup> are the refractive indices and thicknesses of the high- and low-index materials in a multilayer, respectively, and *λ* is the center wavelength in the PBG. Note that the reflectivity of the cell can further be enhanced by additionally coating a high-index film on the top of the multilayer. In other words, the total number of layers is odd (Hecht, 2002). The width of the PBG can be enlarged by increasing the refractive-index difference (*n*<sup>H</sup> *n*L) and shifting the central wavelength to redder regime. Figure 10 compares the trans-

**Figure 9.** Cell configuration of a 1D PC/MMLC hybrid structure. The exemplary defect layer is a DFCLC (adapted from Hsiao et al., 2011c).

**3.1. Definition of the cell configuration** 

the direct FC-to-P transition.

**liquid-crystal cells** 

dielectric heating, which shifts the crossover frequency to a higher value (Yin et al., 2006; Wen & Wu, 2005). On the other hand, a low-voltage pulse would be insufficient to induce

**3. Optical properties of one-dimensional photonic-crystal/memory-mode-**

A 1D PC structure incorporated with LC as a defect layer is well known to have the ability on tuning the optical characteristics such as light intensities and wavelengths of the defect modes. While most of investigations of 1D PC/LC cells are demonstrated based on DMLCs, this section is dedicated to a new classification of 1D PC/LC cells formed by infiltrating with a MMLC as a defect layer. The configuration of a 1D PC/MMLC hybrid structure is schematically depicted in Fig. 9 (Hsiao et al., 2011c). Referring to the conventional 1D periodical structure, the 1D PC here is constructed with two identical dielectric mirrors having multilayer films deposited on the electrically conductive glass substrates. The MMLC, for example, the DFCLC whose electro-optical characteristic exhibits bistable or multistable switching, is infiltrated into the 1D PC as a defect layer with a thickness *d*. The dielectric

multilayer consists of a number of high- and low-index materials stacked alternately.

**Figure 9.** Cell configuration of a 1D PC/MMLC hybrid structure. The exemplary defect layer is a

DFCLC (adapted from Hsiao et al., 2011c).

the central wavelength to redder regime. Figure 10 compares the trans-

To provide high reflectivity, the OPL of these two materials is theoretically set to be equal to one-quarter wavelength of the incident light, i.e., *n*H*d*H = *n*L*d*L = *λ*/4,where *n*H, *n*L, and *d*H, *d*<sup>L</sup> are the refractive indices and thicknesses of the high- and low-index materials in a multilayer, respectively, and *λ* is the center wavelength in the PBG. Note that the reflectivity of the cell can further be enhanced by additionally coating a high-index film on the top of the multilayer. In other words, the total number of layers is odd (Hecht, 2002). The width of the PBG can be enlarged by increasing the refractive-index difference (*n*<sup>H</sup> *n*L) and shifting

**Figure 10.** Transmittance of a dielectric mirror and an empty PC cell made of two identical dielectric mirrors.

mission spectra of a multilayer film on a glass substrate and a combination of two multilayer-coated substrates with a central air gap (empty cell). In this example, the multilayer film has nine layers, including five high-index layers and four low-index layers. Obviously, the width of PBG is around 250 nm with the central wavelength near 620 nm in the single multilayer. While sandwiching a defect layer between two multilayers, a number of defect modes are generated within the PBG. Note that the insertion of the defect layer does not essentially affect the width of the PBG. The profile of defect modes is influenced by some parameters. Ozaki and associates report that increasing the layer number in the multilayer decreases the line width and transmittance of defect-mode peaks because the Bragg-reflected light, dictated by the multilayer, is limited to reach the defect layer (Ozaki et al., 2004a). On the other hand, it is concluded by Zyryanov and coauthors that the number of defect modes is increased with increasing thickness of the defect layer or using the material with high refractive index as a defect layer (Zyryanov et al., 2008).

#### **3.2. One-dimensional photonic-crystal/bistable-chiral-tilted-homeotropicnematic cells**

According to the operation of a BHN LC discussed in Section 2.1, applying an external electric field to the PC/BHN hybrid cell enables the switching among four specific states; i.e., tH, bH, tT, and bT states. Due to different molecular orientation of LC as well as the contributions of effective refractive index (*n*eff), the transmission spectra of the 1D PC/BHN hybrid structure in four different states without employing any polarizer disclose dissimilar spectral profiles, as shown in Fig. 11. Recalling the mathematical expression of the effective refractive index of an optically uniaxial material (Yeh & Gu, 1999b)

$$\mathbf{n}\_{\text{off}} = \frac{\mathbf{n}\_{\text{o}}\mathbf{n}\_{\text{o}}}{\left(\mathbf{n}\_{\text{o}}\cos^{2}\theta + \mathbf{n}\_{\text{o}}\sin^{2}\theta\right)^{1/2}},\tag{2}$$

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 69

low frequency *f*1 (see Section 2.1). Considering a forward switching from tH to bH state, the intensity of peaks in the extraordinary defect modes is reduced with increasing voltage due to the decrease in the effective refractive index. The intensity then reaches minima as the tH state transfers completely to the bH state. Similarly, backward switching from bH to tH state

Furthermore, Fig. 13 reveals the wavelength tunability of the defect modes in the bT state of the PC/BHN cell. Switching to the bT state is accomplished from bH state by adjusting the frequency from low frequency *f1* to high frequency *f2* (see Section 2.1). In the bT state, the tilted angle of molecular director is higher than that in the stable tT state, as illustrated in Fig. 6. Thus, while increasing the high-frequency voltage, the tilted angle is reduced and increases the contribution of *n*e component to the overall effective refractive index. As a result, redshift (Miroshnichenko et al., 2008a, 2008b; Zyryanov et al., 2008a) of the defect modes as a function

of increasing voltage is observed, demonstrating the ability of defect mode tunability.

**Figure 12.** Comparison of defect modes in the transmission spectra for the PC/BHN LC cell in tH and

**3.3. One-dimensional photonic-crystal/dual-frequency-cholesteric-liquid-crystal** 

The texture PC/DFCLC cell can be switched to three states, according to its operation mechanism illustrated in Fig. 7. These textures are P, FC, and H state. While the P and FC can be the stable states H state is the voltage-sustained state. Figure 14 shows the transmission spectra of the PC/DFCLC cell in two stable states. The cell in the transparent P state reveals a number of defect modes with transmission intensity around 25 to 60% in the

reproduces the original intensity of peaks.

bH state.

**cells** 

where *n*o and *n*e are the ordinary and extraordinary refractive indices of the LC, respectively and *θ* is the tilted angle of LC molecules measured from the substrate plane, one can comprehend that the defect modes in the bH state are attributed by sole *n*<sup>o</sup> because most of LC molecules in this state are aligned normal to the substrate (*θ* = 90°). In contrast, the molecules in the tH state are oriented at a high tilted angle with respect to the substrate plane whereas both the tT and bT state have a 2*π*-twist molecular orientation. Consequently, the defect modes have more peaks in all of the other three states due to the contribution of *n*<sup>e</sup> to the resulting *n*eff, which is larger than *n*o.

**Figure 11.** Transmission spectra of the four states of the PC/BHN LC cell within the photonic bandgap.

Similar to the tunable mechanism in the 1D PC/DMLC device, the tunability in defect modes of the PC/BHN cell can be realized by dynamic switching between two proper states. In the case of two homeotropic states, Fig. 12 shows defect modes of the tH and bH state in specific wavelength range without employing any polarizers. In the tH state, the peaks overlapped with those in the bH state characterizes the ordinary defect modes whereas other peaks are explained as the extraordinary defect modes. According to Eq. (2), the effective refractive index in the tH state is higher than that in the bH state, determined by their molecular orientation. In addition, it can also be conceived that operation between tH to bH state enables the control on the contribution of extraordinary index as well as the effective refractive index by the applied voltage. Accordingly, the transmission-intensity tunability in the extraordinary defect modes can be achieved by switching between these two states. For instance, the switching between tH and bH state is created by applying an electric field at low frequency *f*1 (see Section 2.1). Considering a forward switching from tH to bH state, the intensity of peaks in the extraordinary defect modes is reduced with increasing voltage due to the decrease in the effective refractive index. The intensity then reaches minima as the tH state transfers completely to the bH state. Similarly, backward switching from bH to tH state reproduces the original intensity of peaks.

68 Optical Devices in Communication and Computation

to the resulting *n*eff, which is larger than *n*o.

o e eff 2 2 1/2 o e n n <sup>n</sup> (n cos n sin )

where *n*o and *n*e are the ordinary and extraordinary refractive indices of the LC, respectively and *θ* is the tilted angle of LC molecules measured from the substrate plane, one can comprehend that the defect modes in the bH state are attributed by sole *n*<sup>o</sup> because most of LC molecules in this state are aligned normal to the substrate (*θ* = 90°). In contrast, the molecules in the tH state are oriented at a high tilted angle with respect to the substrate plane whereas both the tT and bT state have a 2*π*-twist molecular orientation. Consequently, the defect modes have more peaks in all of the other three states due to the contribution of *n*<sup>e</sup>

**Figure 11.** Transmission spectra of the four states of the PC/BHN LC cell within the photonic bandgap.

Similar to the tunable mechanism in the 1D PC/DMLC device, the tunability in defect modes of the PC/BHN cell can be realized by dynamic switching between two proper states. In the case of two homeotropic states, Fig. 12 shows defect modes of the tH and bH state in specific wavelength range without employing any polarizers. In the tH state, the peaks overlapped with those in the bH state characterizes the ordinary defect modes whereas other peaks are explained as the extraordinary defect modes. According to Eq. (2), the effective refractive index in the tH state is higher than that in the bH state, determined by their molecular orientation. In addition, it can also be conceived that operation between tH to bH state enables the control on the contribution of extraordinary index as well as the effective refractive index by the applied voltage. Accordingly, the transmission-intensity tunability in the extraordinary defect modes can be achieved by switching between these two states. For instance, the switching between tH and bH state is created by applying an electric field at

, (2)

Furthermore, Fig. 13 reveals the wavelength tunability of the defect modes in the bT state of the PC/BHN cell. Switching to the bT state is accomplished from bH state by adjusting the frequency from low frequency *f1* to high frequency *f2* (see Section 2.1). In the bT state, the tilted angle of molecular director is higher than that in the stable tT state, as illustrated in Fig. 6. Thus, while increasing the high-frequency voltage, the tilted angle is reduced and increases the contribution of *n*e component to the overall effective refractive index. As a result, redshift (Miroshnichenko et al., 2008a, 2008b; Zyryanov et al., 2008a) of the defect modes as a function of increasing voltage is observed, demonstrating the ability of defect mode tunability.

**Figure 12.** Comparison of defect modes in the transmission spectra for the PC/BHN LC cell in tH and bH state.

#### **3.3. One-dimensional photonic-crystal/dual-frequency-cholesteric-liquid-crystal cells**

The texture PC/DFCLC cell can be switched to three states, according to its operation mechanism illustrated in Fig. 7. These textures are P, FC, and H state. While the P and FC can be the stable states H state is the voltage-sustained state. Figure 14 shows the transmission spectra of the PC/DFCLC cell in two stable states. The cell in the transparent P state reveals a number of defect modes with transmission intensity around 25 to 60% in the PBG. When the texture is switched from P to FC state by a voltage pulse of *V*1 = 20 Vrms at *f*1 = 1 kHz, the intensity of defect modes drops dramatically to about 1% due to the formation of randomly oriented poly-domain in this state. Accordingly, the bistble switching between P and FC state results in the tunable defect modes between turning on and off state that enable the PC/DFCLC to serve as an electrically tunable light filter with features of fast switching speed and low power consumption. When the cell is switched between P and H state the tunability on the wavelength of the defect modes can be realized.

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 71

Figure 15 shows the transmission spectra of the PC/DFCLC cell in the P and H state. It can clearly be recognized that two separated sets of defect modes with comparable transmission strengths are obtained. In contrast to the defect modes in the P state, the defect modes in the H state shifts to the shorter wavelengths due to the decrease in the effective refractive index. Noticeably, the peaks of defect modes in one of the two states overlaps to the stop band in the other state indicating the complementary nature in wavelengths. Furthermore, Fig. 16 demonstrates a new approach for tuning the peak transmittance of the defect modes by varying the frequency of the applied voltage pulse. In this example, it is noted that the dielectric anisotropy of the DFLC is negative and it increases with increasing frequency in the frequency range from 20 to 100 kHz. Therefore, while a 20 kHz voltage pulse align the molecules in the FC state the cell subsequently transits to the planar state as the frequency increases due to the enhancement in the torque of dielectric coupling. As a result, the transmittance of peaks in the defect modes increases with increasing frequency due to the

**Figure 15.** Transmittance of the PC/DFCLC in the photonic bandgap with two different sets of defect

**4. Memorable multichannel devices based on one-dimensional photonic-**

**4.1. Bistable one-dimensional photonic-crystal/chiral-tilted-homeotropic-nematic** 

It is clarified from Section 3.2 that the electrically tunable defect modes in a 1D PC/BHN hybrid cell can be realized even for the light propagating through the cell without employing any polarizers. For instance, the transmittance tunabiltiy in the extraordinary

modes in the P and H states (adapted from Hsiao et al., 2011c).

**crystal/memory-mode-liquid-crystal cells** 

**cells under parallel polarizers** 

change of molecular orientation.

**Figure 13.** Redshift of the defect modes in the bT state with increasing voltage (adapted from Wu et al., 2011).

**Figure 14.** Transmission spectra of a PC/DFCLC in the photonic bandgap in two stable states (adapted from Hsiao et al., 2011c), demonstrating light-intensity tunability.

Figure 15 shows the transmission spectra of the PC/DFCLC cell in the P and H state. It can clearly be recognized that two separated sets of defect modes with comparable transmission strengths are obtained. In contrast to the defect modes in the P state, the defect modes in the H state shifts to the shorter wavelengths due to the decrease in the effective refractive index. Noticeably, the peaks of defect modes in one of the two states overlaps to the stop band in the other state indicating the complementary nature in wavelengths. Furthermore, Fig. 16 demonstrates a new approach for tuning the peak transmittance of the defect modes by varying the frequency of the applied voltage pulse. In this example, it is noted that the dielectric anisotropy of the DFLC is negative and it increases with increasing frequency in the frequency range from 20 to 100 kHz. Therefore, while a 20 kHz voltage pulse align the molecules in the FC state the cell subsequently transits to the planar state as the frequency increases due to the enhancement in the torque of dielectric coupling. As a result, the transmittance of peaks in the defect modes increases with increasing frequency due to the change of molecular orientation.

70 Optical Devices in Communication and Computation

2011).

tunability on the wavelength of the defect modes can be realized.

PBG. When the texture is switched from P to FC state by a voltage pulse of *V*1 = 20 Vrms at *f*1 = 1 kHz, the intensity of defect modes drops dramatically to about 1% due to the formation of randomly oriented poly-domain in this state. Accordingly, the bistble switching between P and FC state results in the tunable defect modes between turning on and off state that enable the PC/DFCLC to serve as an electrically tunable light filter with features of fast switching speed and low power consumption. When the cell is switched between P and H state the

**Figure 13.** Redshift of the defect modes in the bT state with increasing voltage (adapted from Wu et al.,

**Figure 14.** Transmission spectra of a PC/DFCLC in the photonic bandgap in two stable states (adapted

from Hsiao et al., 2011c), demonstrating light-intensity tunability.

**Figure 15.** Transmittance of the PC/DFCLC in the photonic bandgap with two different sets of defect modes in the P and H states (adapted from Hsiao et al., 2011c).

### **4. Memorable multichannel devices based on one-dimensional photoniccrystal/memory-mode-liquid-crystal cells**

#### **4.1. Bistable one-dimensional photonic-crystal/chiral-tilted-homeotropic-nematic cells under parallel polarizers**

It is clarified from Section 3.2 that the electrically tunable defect modes in a 1D PC/BHN hybrid cell can be realized even for the light propagating through the cell without employing any polarizers. For instance, the transmittance tunabiltiy in the extraordinary

defect modes is performed in the cell while switching between the tH and bH states, suggesting a potential application in light filter. Moreover, operation in bT state as a function of increasing voltage results in the tunable wavelength, shifting to the longer wavelengths, in the defect modes. Although above mentioned mechanisms enable the PC/BHN to extent its use in various optical devices without employing any polarizers, all of them are performed by the dynamic switching between one stable state and voltagesustained state. Here, a concept of wavelength-tunability in defect modes, characterized by the two stable states of the PC/BHN cell is proposed by setting the cell between two parallel polarizers (meaning linear polarizers with parallel transmission axes). Figure 17 depicts the transmission spectra of the PC/BHN cell in stable states with and without parallel polarizers. The angle between the rubbing direction of the cell and the transmission axis of either polarizer is denoted as *β*. While the incoming light passing through first polarizer at *β* = 0 represents as E-ray, it becomes O-ray at *β* = 90. It is known from Section 3.2 that the effective refractive index in the cell without any polarizers is contributed by both *n*o and *n*e; thus, forming minute defect modes in both the tH and tT states, as shown in Fig. 17(a). Along with pervious investigations of the spectral properties of 1D PC/LC cells with crossed polarizers (Lin et al., 2010; Zyryanov et al., 2010), except for the homeotropic state, the o-ray and e-ray propagating through the LC bulk senses *n*o and *n*e, respectively. Accordingly, when the cell is set between parallel polarizers with polarization angles of 90° and 0°, the defect modes associated with *n*o and *n*e are discriminative, respectively, as shown in Figs. 17(b) and (c). In addition, it is noticeable that two divided sets of defect modes corresponding to the two stable states are observed in the cell with parallel polarizers. This result implies a concept for multichannel applications, characterized by the optically bistable states.

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 73

**Figure 17.** Transmittance of a PC/BHN cell (a) without polarizers and with parallel polarizers at (b) *β* =

Based on the cell configuration of the DFCLC cell, a tristable PSCTs cell is created by incorporating photo-curable monomers into DFCLC with proper amounts due to the distribution of polymer networks throughout the cell. These three PSCTs are also referred to as the P, FC, and H states. According to the operation principle illustrated in Fig. 8, switching from one to another state in the PSCTs can be achieved by applying suitable frequency-modulated voltage pulses. In contrast to the electrical tunability mechanisms in the 1D PC/DFCLC cell, the 1D PC structure infiltrated with tristable PSCTs is expected to characterize the tunability on intensity and wavelength of defect modes by its tristable states. Figure 18 demonstrates the transmission spectra of the 1D PC/PSCTs cell in three stable states. Since the spectra profiles in these three states is revealed in Section 3.3, it can be understood from Fig. 18 that the mechanisms of tunable intensity and wavelength in the defect modes can also be performed in the PC/PSCT cell by operating between two stable states. In the case of intensity tunability, the FC state is certainly represented as the light off state because the transmission of defect modes in this state is the lowest. While switching

**4.2. Tristable one-dimensional photonic-crystal cell with polymer-stabilized** 

90° and (c) *β* = 0°.

**cholesteric textures** 

**Figure 16.** Transmittance of stable defect modes in the PBG induced by a 24.5-V voltage pulse at various frequencies.

defect modes is performed in the cell while switching between the tH and bH states, suggesting a potential application in light filter. Moreover, operation in bT state as a function of increasing voltage results in the tunable wavelength, shifting to the longer wavelengths, in the defect modes. Although above mentioned mechanisms enable the PC/BHN to extent its use in various optical devices without employing any polarizers, all of them are performed by the dynamic switching between one stable state and voltagesustained state. Here, a concept of wavelength-tunability in defect modes, characterized by the two stable states of the PC/BHN cell is proposed by setting the cell between two parallel polarizers (meaning linear polarizers with parallel transmission axes). Figure 17 depicts the transmission spectra of the PC/BHN cell in stable states with and without parallel polarizers. The angle between the rubbing direction of the cell and the transmission axis of either polarizer is denoted as *β*. While the incoming light passing through first polarizer at *β* = 0 represents as E-ray, it becomes O-ray at *β* = 90. It is known from Section 3.2 that the effective refractive index in the cell without any polarizers is contributed by both *n*o and *n*e; thus, forming minute defect modes in both the tH and tT states, as shown in Fig. 17(a). Along with pervious investigations of the spectral properties of 1D PC/LC cells with crossed polarizers (Lin et al., 2010; Zyryanov et al., 2010), except for the homeotropic state, the o-ray and e-ray propagating through the LC bulk senses *n*o and *n*e, respectively. Accordingly, when the cell is set between parallel polarizers with polarization angles of 90° and 0°, the defect modes associated with *n*o and *n*e are discriminative, respectively, as shown in Figs. 17(b) and (c). In addition, it is noticeable that two divided sets of defect modes corresponding to the two stable states are observed in the cell with parallel polarizers. This result implies a concept for

multichannel applications, characterized by the optically bistable states.

**Figure 16.** Transmittance of stable defect modes in the PBG induced by a 24.5-V voltage pulse at

various frequencies.

**Figure 17.** Transmittance of a PC/BHN cell (a) without polarizers and with parallel polarizers at (b) *β* = 90° and (c) *β* = 0°.

#### **4.2. Tristable one-dimensional photonic-crystal cell with polymer-stabilized cholesteric textures**

Based on the cell configuration of the DFCLC cell, a tristable PSCTs cell is created by incorporating photo-curable monomers into DFCLC with proper amounts due to the distribution of polymer networks throughout the cell. These three PSCTs are also referred to as the P, FC, and H states. According to the operation principle illustrated in Fig. 8, switching from one to another state in the PSCTs can be achieved by applying suitable frequency-modulated voltage pulses. In contrast to the electrical tunability mechanisms in the 1D PC/DFCLC cell, the 1D PC structure infiltrated with tristable PSCTs is expected to characterize the tunability on intensity and wavelength of defect modes by its tristable states. Figure 18 demonstrates the transmission spectra of the 1D PC/PSCTs cell in three stable states. Since the spectra profiles in these three states is revealed in Section 3.3, it can be understood from Fig. 18 that the mechanisms of tunable intensity and wavelength in the defect modes can also be performed in the PC/PSCT cell by operating between two stable states. In the case of intensity tunability, the FC state is certainly represented as the light off state because the transmission of defect modes in this state is the lowest. While switching

the cell from FC to either P or H state, the transmission of defect modes becomes intense, denoting the light on state. It is emphasized that all of the three states can be stabilized permanently after voltage pulse removal. On the other hand, the position of defect modes can be shifted by switching between the P and H states. The appearance of two individual sets of defect modes, characterized by the P and H states in the cell, is applicable for enhancing the performance of the multichannel device. While the transmission of the peaks in defect modes can be adjusted by frequency-modulated voltage pulses with fixed amplitude, Fig. 19 demonstrates that the transmittance-modulation in the defect modes is performed by modulating the amplitude of voltage pulse at fixed frequency. In this case, the initial state of the cell is H state and the frequency is *f*2 = 100 kHz, corresponding to the negative dielectric anisotropy of the DFLC. Accordingly, the PC/PSCTs cell is transferred from the initial P state to H-to-FC mixed state and FC state when the voltage increases from 0 to 40V. If the initial state is P state, it is comprehensible that the transmission tunability can be achieved by varying voltage at frequency *f*1. As a result, this powerful photonic device has potential to extend the application, permitting its use as an electrically controllable and optically tristable multichannel filter without requiring any polarizers.

Tunable and Memorable Optical Devices

with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 75

**Figure 19.** Transmittance of stable defect modes in the photonic bandgap induced by a voltage pulse at frequency *f*1 with various amplitudes, (adapted from Hsiao et al., 2011a). Note that the texture in the cell

In this chapter, two types of 1D PC/MMLC cells which exhibit both electrical tunability and optical bi- or tri-stability in the defect modes have been reviewed in accordance with our previously published papers. Several fascinating features have also been keynoted. In the case of the PC/BHN cell based on a chiral-agent-doped DFLC infiltrated as a defect layer, it can be switched in four different states by applying voltage pulses with designated waveforms. The dynamic switching in the voltage-sustained bT state results in the redshift of the defect modes with increasing voltage (at 100 kHz) due to the increase in the effective refractive index. Moreover, the tunable defect modes in the PC/BHN cell can be achieved by their two stable states (bH and bT) when the cell is set between parallel polarizers. Such bifunctional photonic devices pave a new pathway for the application in low-powerconsumption multichannel optical switches and integrated photonic devices. On the other hand, switching among the P, FC, and H states in a PC/DFCLC cell can be regulated rapidly, directly and reversibly by using frequency-modulated voltage pulses. The ability of wavelength tunability of defect modes in the PC/DFCLC cell is achieved by the texture transition from the stable P state to the voltage-sustained H state. Owing to the frequencydependent dielectric anisotropy of the DFLC, the transmittance of the defect modes can be tuned by both the voltage frequency and amplitude, providing a new way for intensity tunability through such a filter characterized by the defect modes. This device requires no polarizers and is of low power consumption. Noticeably, the voltage-sustained H state in the bistable DFCLC can further be a third optically stable state by incorporating an adequate amount of photo-curable monomer, oligomer, or prepolymer into the DFCLC material to

is transited from planar to focal conic state with increasing voltage.

**5. Conclusions** 

**Figure 18.** Transmission within the photonic bandgap of a PC/DFCLC cell in three stable states (adapted from Hsiao et al., 2011a).

**Figure 19.** Transmittance of stable defect modes in the photonic bandgap induced by a voltage pulse at frequency *f*1 with various amplitudes, (adapted from Hsiao et al., 2011a). Note that the texture in the cell is transited from planar to focal conic state with increasing voltage.

#### **5. Conclusions**

74 Optical Devices in Communication and Computation

the cell from FC to either P or H state, the transmission of defect modes becomes intense, denoting the light on state. It is emphasized that all of the three states can be stabilized permanently after voltage pulse removal. On the other hand, the position of defect modes can be shifted by switching between the P and H states. The appearance of two individual sets of defect modes, characterized by the P and H states in the cell, is applicable for enhancing the performance of the multichannel device. While the transmission of the peaks in defect modes can be adjusted by frequency-modulated voltage pulses with fixed amplitude, Fig. 19 demonstrates that the transmittance-modulation in the defect modes is performed by modulating the amplitude of voltage pulse at fixed frequency. In this case, the initial state of the cell is H state and the frequency is *f*2 = 100 kHz, corresponding to the negative dielectric anisotropy of the DFLC. Accordingly, the PC/PSCTs cell is transferred from the initial P state to H-to-FC mixed state and FC state when the voltage increases from 0 to 40V. If the initial state is P state, it is comprehensible that the transmission tunability can be achieved by varying voltage at frequency *f*1. As a result, this powerful photonic device has potential to extend the application, permitting its use as an electrically controllable and

optically tristable multichannel filter without requiring any polarizers.

**Figure 18.** Transmission within the photonic bandgap of a PC/DFCLC cell in three stable states

(adapted from Hsiao et al., 2011a).

In this chapter, two types of 1D PC/MMLC cells which exhibit both electrical tunability and optical bi- or tri-stability in the defect modes have been reviewed in accordance with our previously published papers. Several fascinating features have also been keynoted. In the case of the PC/BHN cell based on a chiral-agent-doped DFLC infiltrated as a defect layer, it can be switched in four different states by applying voltage pulses with designated waveforms. The dynamic switching in the voltage-sustained bT state results in the redshift of the defect modes with increasing voltage (at 100 kHz) due to the increase in the effective refractive index. Moreover, the tunable defect modes in the PC/BHN cell can be achieved by their two stable states (bH and bT) when the cell is set between parallel polarizers. Such bifunctional photonic devices pave a new pathway for the application in low-powerconsumption multichannel optical switches and integrated photonic devices. On the other hand, switching among the P, FC, and H states in a PC/DFCLC cell can be regulated rapidly, directly and reversibly by using frequency-modulated voltage pulses. The ability of wavelength tunability of defect modes in the PC/DFCLC cell is achieved by the texture transition from the stable P state to the voltage-sustained H state. Owing to the frequencydependent dielectric anisotropy of the DFLC, the transmittance of the defect modes can be tuned by both the voltage frequency and amplitude, providing a new way for intensity tunability through such a filter characterized by the defect modes. This device requires no polarizers and is of low power consumption. Noticeably, the voltage-sustained H state in the bistable DFCLC can further be a third optically stable state by incorporating an adequate amount of photo-curable monomer, oligomer, or prepolymer into the DFCLC material to

create polymer networks in the defect layer. Such a DFCLC cell exhibiting three stable states—P, FC, and H—is known as a tristable PSCT. Referring to the aforementioned tunability in the PC/DFCLC, the wavelength tunability and transmittance tunability of defect modes in the PC/PSCT cell can be achieved—the intensities of the defect modes can be regulated by the amplitude of voltage in the mixed states and the wavelengths be switched by the frequency in the H and P states. The cell can directly be switched from one to another stable state by employing a proper frequency- modulated voltage pulse on the cell.

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with One-Dimensional Photonic-Crystal/Liquid-Crystal Hybrid Structures 77

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1D PC/LC has received much attention in recent years due to its tunability in defect modes within the PBG. It has been established that this hybrid PC structure enables the control over the defect modes by electric field, magnetic field, and the like as a stimulus. The resulting features make it applicable for designing tunable photonic devices such as a multichannel filter, light shutter, and optical modulator. Specifically, incorporating MMLC as a defect layer in the 1D PC provides both the optically memorable and tunable defect modes characterized by the stable states, allowing the device to be of low power consumption. Such a 1D PC/MMLC device thus extends its use for green products.

### **Author details**

Po-Chang Wu

*Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan, Republic of China* 

Wei Lee

*Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan, Republic of China College of Photonics, National Chiao Tung University, Guiren Dist., Tainan, Taiwan, Republic of China* 

### **Acknowledgement**

The authors acknowledge the financial support from the National Science Council of the Republic of China (Taiwan) under grant Nos. NSC 98-2923-M-033-001-MY3 and NSC 98- 2112-M-009-023-MY3, and are grateful to Yu-Cheng Hsiao, Yu-Ting Lin, Ivan Timofeev, Chong-Yin Wu, Yi-Hong Zou, and Victor Ya. Zyryanov for their assistance with the preparation of this manuscript.

#### **6. References**

Arkhipkin, V. G.; Gunyakov, V. A.; Myslivets, S. A.; Gerasimov, V. P.; Zyryanov, V. Ya.; Vetrov, S. Ya. & Shabanov, V. F. (2008). One-Dimensional Photonic Crystals with a Planar Oriented Nematic Layer: Temperature and Angular Dependence of the Spectra of Defect Modes. *Journal of Experimental and Theoretical Physics,* Vol. 106, No. 2, pp. 388– 398

Arkhipkin, V. G.; Gunyakov, V. A.; Myslivets, S. A.; Zyryanov, V. Ya. & Shabanov, V. F. (2007). Angular Tuning of Defect Modes Spectrum in the One-Dimensional Photonic Crystal with Liquid-Crystal Layer. *European Physical Journal E,* Vol. 24, No. 3, pp. 297–302

76 Optical Devices in Communication and Computation

cell.

**Author details** 

Po-Chang Wu

*Republic of China* 

**6. References** 

398

**Acknowledgement** 

preparation of this manuscript.

Wei Lee

create polymer networks in the defect layer. Such a DFCLC cell exhibiting three stable states—P, FC, and H—is known as a tristable PSCT. Referring to the aforementioned tunability in the PC/DFCLC, the wavelength tunability and transmittance tunability of defect modes in the PC/PSCT cell can be achieved—the intensities of the defect modes can be regulated by the amplitude of voltage in the mixed states and the wavelengths be switched by the frequency in the H and P states. The cell can directly be switched from one to another stable state by employing a proper frequency- modulated voltage pulse on the

1D PC/LC has received much attention in recent years due to its tunability in defect modes within the PBG. It has been established that this hybrid PC structure enables the control over the defect modes by electric field, magnetic field, and the like as a stimulus. The resulting features make it applicable for designing tunable photonic devices such as a multichannel filter, light shutter, and optical modulator. Specifically, incorporating MMLC as a defect layer in the 1D PC provides both the optically memorable and tunable defect modes characterized by the stable states, allowing the device to be of low power

consumption. Such a 1D PC/MMLC device thus extends its use for green products.

*Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan, Republic of China* 

*Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan, Republic of China* 

The authors acknowledge the financial support from the National Science Council of the Republic of China (Taiwan) under grant Nos. NSC 98-2923-M-033-001-MY3 and NSC 98- 2112-M-009-023-MY3, and are grateful to Yu-Cheng Hsiao, Yu-Ting Lin, Ivan Timofeev, Chong-Yin Wu, Yi-Hong Zou, and Victor Ya. Zyryanov for their assistance with the

Arkhipkin, V. G.; Gunyakov, V. A.; Myslivets, S. A.; Gerasimov, V. P.; Zyryanov, V. Ya.; Vetrov, S. Ya. & Shabanov, V. F. (2008). One-Dimensional Photonic Crystals with a Planar Oriented Nematic Layer: Temperature and Angular Dependence of the Spectra of Defect Modes. *Journal of Experimental and Theoretical Physics,* Vol. 106, No. 2, pp. 388–

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**Chapter 5** 

© 2012 Yoshimura, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Self-Organized Three-Dimensional** 

**Solar Cells, and Cancer Therapy** 

Additional information is available at the end of the chapter

(FDTD) method and preliminary experiments.

**2. Core technologies** 

*2.1.1. Concept of SOLNET* 

**2.1. SOLNET** 

Tetsuzo Yoshimura

http://dx.doi.org/10.5772/48221

**1. Introduction** 

**Optical Circuits and Molecular Layer** 

**Deposition for Optical Interconnects,** 

Photonics is being coupled with the molecular nanotechnology to be a main technology in the information processing/communication, solar energy conversion, and bio/medical systems. We have developed two original core technologies for optical interconnects so far. One is Self-Organized Lightwave Network (SOLNET) [1-3] and the other is Molecular Layer Deposition (MLD) [4-6]. SOLNET is self-aligned optical waveguides formed in photoinduced refractive index increase (PRI) materials. MLD is a monomolecular-step growth process of tailored organic materials. Recently, we expanded our scope for the SOLNET/MLD applications toward the solar energy conversion and the bio/medical fields. In the present chapter, after SOLNET and MLD are reviewed, their applications to optical interconnects within computers [1,7-9], solar cells [4,10-12], and cancer therapy [4,10,13] are presented with some proof-of-concepts demonstrated by the finite difference time domain

The concept of SOLNET is shown in Figure 1 [1-3]. In one-beam-writing SOLNET, a write beam is introducqed into a PRI material from an optical device such as an optical waveguide, an optical fiber, a laser diode (LD), etc. In the PRI material, refractive index

and reproduction in any medium, provided the original work is properly cited.


Tetsuzo Yoshimura

80 Optical Devices in Communication and Computation

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Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48221

#### **1. Introduction**

Photonics is being coupled with the molecular nanotechnology to be a main technology in the information processing/communication, solar energy conversion, and bio/medical systems. We have developed two original core technologies for optical interconnects so far. One is Self-Organized Lightwave Network (SOLNET) [1-3] and the other is Molecular Layer Deposition (MLD) [4-6]. SOLNET is self-aligned optical waveguides formed in photoinduced refractive index increase (PRI) materials. MLD is a monomolecular-step growth process of tailored organic materials. Recently, we expanded our scope for the SOLNET/MLD applications toward the solar energy conversion and the bio/medical fields.

In the present chapter, after SOLNET and MLD are reviewed, their applications to optical interconnects within computers [1,7-9], solar cells [4,10-12], and cancer therapy [4,10,13] are presented with some proof-of-concepts demonstrated by the finite difference time domain (FDTD) method and preliminary experiments.

#### **2. Core technologies**

#### **2.1. SOLNET**

#### *2.1.1. Concept of SOLNET*

The concept of SOLNET is shown in Figure 1 [1-3]. In one-beam-writing SOLNET, a write beam is introducqed into a PRI material from an optical device such as an optical waveguide, an optical fiber, a laser diode (LD), etc. In the PRI material, refractive index

increases by write beam exposure. When the write beam propagates in the PRI material, the write beam propagation is affected by the refractive index distribution, which is generated by the write beam itself. Then, the write beam is concentrated along the propagation axis, inducing the self-focusing to construct an optical waveguide from the optical device. This is the SOLNET. SOLNET is also constructed by free-space light beams.

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 83

the "pulling water" effect. Finally, by the self-focusing, a self-aligned coupling waveguide is

Here, the wavelength filter can be replaced with a luminescent material. When a write beam from an optical waveguide is introduced onto the luminescent material through the PRI material, luminescence is generated from the material. The luminescence acts like the

In phosphor SOLNET (P-SOLNET), phosphor is doped in a part of an optical waveguide. By exposing the doped phosphor to an excitation light, a write beam generated from the phosphor propagates in the optical waveguide to be emitted into the PRI material. P-SOLNET is effective when write beams cannot be introduced from outside; for example, when SOLNET is formed in inner parts of three-dimensional (3-D) optoelectronic (OE)

The PRI materials are, for example, photopolymers, photo-definable materials, photorefractive crystals, etc. Figure 2 shows the mechanism of the refractive-index increase in a photopolymer. High-refractive-index monomers and low-refractive-index monomers are mixed. The high-refractive-index ones have higher photo-reactivity to write beams than the low-refractive-index ones. When the photopolymer is exposed to a write beam, highrefractive-index monomers are combined by photo-chemical reactions to produce new molecules. Then, high-refractive-index monomers diffuse into the exposed region from the surrounding area to compensate for the reduction of the high-refractive-index monomer concentration. Repeating this process increases the refractive index of the exposed region. The wavelength of the write beams typically ranges from ~350 to ~900 nm. The spectral

Some molecules are known to exhibit two-photon absorption [14]. As shown in Figure 3, in the four-level model, a photon with a wavelength of *λ*1 excites an electron from S0 state to S*<sup>n</sup>* state in a molecule. The excited electron in the S*n* state transfers to T0 state. Then, a photon with another wavelength of *λ*2 further excites the electron to T*n* state to induce chemical reactions. The chemical reactions occur only in places, where both *λ*1 photons and *λ*<sup>2</sup>

**Light Beam High-n Region Low-n Region**

formed between the optical waveguides.

response can be adjusted by sensitizers.

**Low-n Monomer**

**Figure 2.** Example of PRI materials

platforms.

**High-n Monomer**

reflected write beam to induce the "pulling water" effect.

*2.1.2. Photo-induced refractive index increase (PRI) materials* 

**Figure 1.** Concept of SOLNET

In multi-beam-writing SOLNET, a plurality of optical devices are put into a PRI material. Write beams are introduced into the PRI material from them. The write beams are attracted to each other and merge by the self-focusing to construct self-aligned coupling waveguides between the optical devices automatically. The coupling waveguides can be formed even when the optical devices are misaligned and have different core sizes.

In reflective SOLNET (R-SOLNET), some of the write beams in the multi-beam-writing SOLNET are replaced with reflected write beams from reflective elements on core edges of optical devices. In the example shown in Figure 1, a write beam from an optical waveguide and a reflected write beam from a wavelength filter on an edge of another optical waveguide overlap. In the overlap region, the refractive index of the PRI material increases, pulling the write beam to the wavelength filter location more and more. We call this effect the "pulling water" effect. Finally, by the self-focusing, a self-aligned coupling waveguide is formed between the optical waveguides.

Here, the wavelength filter can be replaced with a luminescent material. When a write beam from an optical waveguide is introduced onto the luminescent material through the PRI material, luminescence is generated from the material. The luminescence acts like the reflected write beam to induce the "pulling water" effect.

In phosphor SOLNET (P-SOLNET), phosphor is doped in a part of an optical waveguide. By exposing the doped phosphor to an excitation light, a write beam generated from the phosphor propagates in the optical waveguide to be emitted into the PRI material. P-SOLNET is effective when write beams cannot be introduced from outside; for example, when SOLNET is formed in inner parts of three-dimensional (3-D) optoelectronic (OE) platforms.

#### *2.1.2. Photo-induced refractive index increase (PRI) materials*

The PRI materials are, for example, photopolymers, photo-definable materials, photorefractive crystals, etc. Figure 2 shows the mechanism of the refractive-index increase in a photopolymer. High-refractive-index monomers and low-refractive-index monomers are mixed. The high-refractive-index ones have higher photo-reactivity to write beams than the low-refractive-index ones. When the photopolymer is exposed to a write beam, highrefractive-index monomers are combined by photo-chemical reactions to produce new molecules. Then, high-refractive-index monomers diffuse into the exposed region from the surrounding area to compensate for the reduction of the high-refractive-index monomer concentration. Repeating this process increases the refractive index of the exposed region. The wavelength of the write beams typically ranges from ~350 to ~900 nm. The spectral response can be adjusted by sensitizers.

**Figure 2.** Example of PRI materials

82 Optical Devices in Communication and Computation

**Optical Device, Free-Space Light Beam**

**Write Beam**

**Figure 1.** Concept of SOLNET

**Wavelength Filter or Luminescent Material**

*Reflective-SOLNET (R-SOLNET)*

increases by write beam exposure. When the write beam propagates in the PRI material, the write beam propagation is affected by the refractive index distribution, which is generated by the write beam itself. Then, the write beam is concentrated along the propagation axis, inducing the self-focusing to construct an optical waveguide from the optical device. This is

*One-Beam-Writing SOLNET*

**SOLNET**

*Multi-Beam-Writing SOLNET*

In multi-beam-writing SOLNET, a plurality of optical devices are put into a PRI material. Write beams are introduced into the PRI material from them. The write beams are attracted to each other and merge by the self-focusing to construct self-aligned coupling waveguides between the optical devices automatically. The coupling waveguides can be formed even

**Phosphor**

**Excitation Light**

*Phosphor SOLNET (P-SOLNET)*

In reflective SOLNET (R-SOLNET), some of the write beams in the multi-beam-writing SOLNET are replaced with reflected write beams from reflective elements on core edges of optical devices. In the example shown in Figure 1, a write beam from an optical waveguide and a reflected write beam from a wavelength filter on an edge of another optical waveguide overlap. In the overlap region, the refractive index of the PRI material increases, pulling the write beam to the wavelength filter location more and more. We call this effect

when the optical devices are misaligned and have different core sizes.

the SOLNET. SOLNET is also constructed by free-space light beams.

**Photo-Induced Refractive Index Increase (PRI) Material**

Some molecules are known to exhibit two-photon absorption [14]. As shown in Figure 3, in the four-level model, a photon with a wavelength of *λ*1 excites an electron from S0 state to S*<sup>n</sup>* state in a molecule. The excited electron in the S*n* state transfers to T0 state. Then, a photon with another wavelength of *λ*2 further excites the electron to T*n* state to induce chemical reactions. The chemical reactions occur only in places, where both *λ*1 photons and *λ*<sup>2</sup>

photons exist. By using the two-photon absorption in the multi-beam-writing SOLNET, smooth self-focusing is expected in the overlap regions. R-SOLNET might be formed by two-wavelength write beams using luminescent materials. Namely, R-SOLNET grows by a write beam of λ1 from an optical waveguide and luminescence of λ2 from the luminescent material.

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 85

**Figure 5.** Two-beam-writing SOLNET connecting two optical fibers in photopolymer

**Figure 6.** R-SOLNET formed between an optical fiber and a micromirror

MLD is a method to grow organic materials with designated molecular sequences as shown in Figure 7 [4-6]. The source molecules are designed so that the same molecules cannot be combined while different molecules can be combined by utilizing selective chemical reactions or the electrostatic force between them. Molecule A is provided onto a substrate surface to form a monomolecular layer of A. Once the surface is covered with A, the deposition of the molecules is automatically terminated by the self-limiting effect similarly to the atomic layer deposition (ALD) [16]. By switching source molecules sequentially as A,

MLD can grow organic tailored materials such as the molecular wire and the polymer multiple quantum dot (MQD), which means a polymer wire containing MQD. MLD can also grow ultra-thin/conformal organic layers on 3-D surfaces such as deep trenches, porous

Figure 9 shows an example of MLD using pyromellitic dianhydride (PMDA) and 4,4' diaminodiphenyl ether (DDE) [6]. Monomolecular-step growth to synthesize polyamic acid

B, C, D,…, materials with molecular sequences like A/B/C/D/… are obtained.

layers, particles etc. as schematically depicted in Figure 8.

**2.2. MLD** 

is observed.

**Figure 3.** Concept of R-SOLNET using two-wavelength write beams

#### *2.1.3. Experimental demonstrations of SOLNET*

Figure 4 shows SOLNET formed in a PRI sol-gel thin film with a 405-nm write beam at 200C. SOLNET grows toward the right-side edge. Figure 5 shows two-beam-writing SOLNET connecting two optical fibers with a core diameter of 9.5 μm in a photopolymer. For lateral misalignments of 1~9 μm, self-aligned coupling waveguides of SOLNET are constructed. For a lateral misalignment of 20 μm, optical waveguides grown from the two optical fibers do not merge, but, remain as separated two optical waveguides. This is due to insufficient overlap of the write beams.

Figure 6 shows experimental demonstration of R-SOLNET between a multi-mode optical fiber with a core diameter of 50 μm and an Al micromirror deposited on an edge of another optical fiber [15]. The optical fiber and the micromirror are placed with a gap of ~800 μm and a lateral misalignment of 60 μm in a photopolymer. When a write beam is introduced from the optical fiber into the photopolymer, R-SOLNET is formed, connecting the optical fiber to the misaligned micromirror. A probe beam of 650 nm in wavelength propagates in the S-shaped self-aligned waveguide of R-SOLNET.

**Figure 4.** SOLNET formed in PRI sol-gel thin film

**Figure 5.** Two-beam-writing SOLNET connecting two optical fibers in photopolymer

**Figure 6.** R-SOLNET formed between an optical fiber and a micromirror

#### **2.2. MLD**

84 Optical Devices in Communication and Computation

**Figure 3.** Concept of R-SOLNET using two-wavelength write beams

**T0**

**2**

**Tn**

**Chemical Reaction**

*2.1.3. Experimental demonstrations of SOLNET* 

*Two-Photon Absorption with Four Levels*

the S-shaped self-aligned waveguide of R-SOLNET.

**Figure 4.** SOLNET formed in PRI sol-gel thin film

insufficient overlap of the write beams.

material.

**S0**

**Sn**

**1**

photons exist. By using the two-photon absorption in the multi-beam-writing SOLNET, smooth self-focusing is expected in the overlap regions. R-SOLNET might be formed by two-wavelength write beams using luminescent materials. Namely, R-SOLNET grows by a write beam of λ1 from an optical waveguide and luminescence of λ2 from the luminescent

Figure 4 shows SOLNET formed in a PRI sol-gel thin film with a 405-nm write beam at 200C. SOLNET grows toward the right-side edge. Figure 5 shows two-beam-writing SOLNET connecting two optical fibers with a core diameter of 9.5 μm in a photopolymer. For lateral misalignments of 1~9 μm, self-aligned coupling waveguides of SOLNET are constructed. For a lateral misalignment of 20 μm, optical waveguides grown from the two optical fibers do not merge, but, remain as separated two optical waveguides. This is due to

**Luminescence <sup>2</sup>**

**1**

**Luminescent Material**

**1**

*R-SOLNET*

*Two-Beam-Writing SOLNET*

**2**

**PRI Material with Two-Photon Absorption**

**Optical Waveguide**

Figure 6 shows experimental demonstration of R-SOLNET between a multi-mode optical fiber with a core diameter of 50 μm and an Al micromirror deposited on an edge of another optical fiber [15]. The optical fiber and the micromirror are placed with a gap of ~800 μm and a lateral misalignment of 60 μm in a photopolymer. When a write beam is introduced from the optical fiber into the photopolymer, R-SOLNET is formed, connecting the optical fiber to the misaligned micromirror. A probe beam of 650 nm in wavelength propagates in MLD is a method to grow organic materials with designated molecular sequences as shown in Figure 7 [4-6]. The source molecules are designed so that the same molecules cannot be combined while different molecules can be combined by utilizing selective chemical reactions or the electrostatic force between them. Molecule A is provided onto a substrate surface to form a monomolecular layer of A. Once the surface is covered with A, the deposition of the molecules is automatically terminated by the self-limiting effect similarly to the atomic layer deposition (ALD) [16]. By switching source molecules sequentially as A, B, C, D,…, materials with molecular sequences like A/B/C/D/… are obtained.

MLD can grow organic tailored materials such as the molecular wire and the polymer multiple quantum dot (MQD), which means a polymer wire containing MQD. MLD can also grow ultra-thin/conformal organic layers on 3-D surfaces such as deep trenches, porous layers, particles etc. as schematically depicted in Figure 8.

Figure 9 shows an example of MLD using pyromellitic dianhydride (PMDA) and 4,4' diaminodiphenyl ether (DDE) [6]. Monomolecular-step growth to synthesize polyamic acid is observed.

*OE PCB*

**LSI LSI LSI**

*OE MCM*

waveguides of OE multi-chip module (MCM), OE printed circuit board (PCB) and OE

**LSI**

**Optical Waveguid**<sup>e</sup> *OE BP*

The 3-D stacked OE MCM shown in Figure 11 is the core unit for the integrated 3-D optical interconnects [1, 7-9]. OE films, in which thin-film flakes of light modulators and photodetectors (PDs) are embedded, are stacked together with films containing thinned LSIs. Optical signals generated in the light modulators driven by electrical signals from LSI outputs propagate to PDs, being converted into electrical signals for LSI inputs. In some cases, the optical signals are coupled to optical waveguides of the OE board by the back-side connection to be transmitted to other OE MCMs. The 3-D structure also provides the 3-D optical switching systems [1,17], where thin-film flakes of optical switches are embedded,

Since heat generation is a serious problem in the 3-D stacked OE MCM, light sources of cw or pulse trains are placed outside of the OE MCM. Implementation of the OE amplifier/driver-less substrate (OE-ADLES), where E-O and O-E conversions are respectively carried out by light modulators directly driven by LSI output signals and by PDs directly generating LSI input signals, is effective to realize "low power dissipation" and "high data rate" capability [1,7,8,18,19]. By implimenting light sources with a plurality of wavelengths and wavelength filters, wavelength division multiplexing (WDM)

The integrated 3-D optical interconnects are built from the scalable film optical link module (S-FOLM) shown in Figure 12 [1,7-9]. A set of OE films, in which thin-film device flakes are embedded, are prepared. The thin-film devices include optical waveguides, light modulators, optical switches, wavelength filters, vertical cavity surface emitting lasers (VCSELs), PDs, photovoltaic devices, interface ICs, LSIs, and so on. By combining the films in stacked configurations, various kinds of 3-D OE platforms are constructed. By stacking a VCSEL/PD-embedded film on an LSI, a smart pixel will be made. When a VCSEL/PDembedded optical waveguide film and an interface-IC-embedded film are stacked, an optical interconnect board will be made. If LSI-embedded films are added in the stack, 3-D stacked OE MCM will be made. Such scalability will contribute to system cost reductions.

backplane (BP) to reach inputs of LSIs.

**Figure 10.** Future image of high-performance computers

for the on-board reconfigurable network.

interconnects can be performed [1,2,7].

**Figure 8.** Deposition of ultra-thin/conformal layers on 3-D surfaces by MLD

**Figure 9.** Experimental demonstration of MLD.

#### **3. Applications to optical interconnects within computers**

#### **3.1. Integrated 3-D optical interconnects based on S-FOLM**

#### *3.1.1. Concept and advantages of S-FOLM*

A future image of high-performance computers is shown in Figure 10. Optical signals are generated at outputs of large-scale integrated circuits (LSIs) and transmitted through optical waveguides of OE multi-chip module (MCM), OE printed circuit board (PCB) and OE backplane (BP) to reach inputs of LSIs.

**Figure 10.** Future image of high-performance computers

86 Optical Devices in Communication and Computation

**Figure 8.** Deposition of ultra-thin/conformal layers on 3-D surfaces by MLD

**DDE**

*Ultra-Thin/Conformal Layers*

**Molecule A Molecule B Molecule C Molecule D**

**Repulsion Attraction**

**TS=80oC**

**PMDA DDE**

**Small Reactivity Large Reactivity**

**3. Applications to optical interconnects within computers** 

A future image of high-performance computers is shown in Figure 10. Optical signals are generated at outputs of large-scale integrated circuits (LSIs) and transmitted through optical

**0 120 240 360 480**

**Time (s)**

**3.1. Integrated 3-D optical interconnects based on S-FOLM** 

**Figure 9.** Experimental demonstration of MLD.

**PMDA**

**2**

**DDE**

**PMDA**

**1**

**Thickness Change (nm)**

**0**

*3.1.1. Concept and advantages of S-FOLM* 

**Figure 7.** Concept of MLD

The 3-D stacked OE MCM shown in Figure 11 is the core unit for the integrated 3-D optical interconnects [1, 7-9]. OE films, in which thin-film flakes of light modulators and photodetectors (PDs) are embedded, are stacked together with films containing thinned LSIs. Optical signals generated in the light modulators driven by electrical signals from LSI outputs propagate to PDs, being converted into electrical signals for LSI inputs. In some cases, the optical signals are coupled to optical waveguides of the OE board by the back-side connection to be transmitted to other OE MCMs. The 3-D structure also provides the 3-D optical switching systems [1,17], where thin-film flakes of optical switches are embedded, for the on-board reconfigurable network.

Since heat generation is a serious problem in the 3-D stacked OE MCM, light sources of cw or pulse trains are placed outside of the OE MCM. Implementation of the OE amplifier/driver-less substrate (OE-ADLES), where E-O and O-E conversions are respectively carried out by light modulators directly driven by LSI output signals and by PDs directly generating LSI input signals, is effective to realize "low power dissipation" and "high data rate" capability [1,7,8,18,19]. By implimenting light sources with a plurality of wavelengths and wavelength filters, wavelength division multiplexing (WDM) interconnects can be performed [1,2,7].

The integrated 3-D optical interconnects are built from the scalable film optical link module (S-FOLM) shown in Figure 12 [1,7-9]. A set of OE films, in which thin-film device flakes are embedded, are prepared. The thin-film devices include optical waveguides, light modulators, optical switches, wavelength filters, vertical cavity surface emitting lasers (VCSELs), PDs, photovoltaic devices, interface ICs, LSIs, and so on. By combining the films in stacked configurations, various kinds of 3-D OE platforms are constructed. By stacking a VCSEL/PD-embedded film on an LSI, a smart pixel will be made. When a VCSEL/PDembedded optical waveguide film and an interface-IC-embedded film are stacked, an optical interconnect board will be made. If LSI-embedded films are added in the stack, 3-D stacked OE MCM will be made. Such scalability will contribute to system cost reductions.

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 89

**SOLNET**

**Light Modulator**

**Photopolymer**

**R-SOLNET R-SOLNET**

*3.1.2. Self-organized 3-D integrated optical circuits with SOLNET* 

1. Enormous alignment efforts with micron or submicron accuracy

wiring in free spaces of SOLNET are respectively applicable for issue 1) and 2).

**Figure 13.** Concept of self-organized 3-D integrated optical circuits utilizing SOLNET

**Photopolymer**

even when a misalignment and a core size mismatching exist.

**PD/(VCSEL)**

the SOLNET to the target locations.

**Figure 14.** Optical solder of SOLNET

**R-SOLNET**

**Wavelength Filter or Luminescent Material**

Optical devices can be connected with self-aligned optical couplings by putting the optical solder of SOLNET betweent them. Figure 14 shows examples of the optical solder of R-SOLNET for couplings of devices that cannot emit write beams such as PDs, and light modulators. Wavelength filters or luminescent materials are placed on the devices to pull

Figure 15 shows an example of the free space optical wiring of R-SOLNET for optical Zconnections in 3-D optical circuits. A luminescent target is placed at a vertical mirror location of a waveguide film. By introducing a write beam from a waveguide in an OE board into a free space filled with a PRI material, the luminescent target generates luminescence to construct a self-aligned vertical waveguide of R-SOLNET between the waveguide film and the OE board

2. Vertical waveguide formation for the 3-D optical circuits

**Optical Device**

In future optical interconnects, a large number of optical couplings and optical Zconnections will be involved. In such cases, following two issues should be considered.

As a solution for them, the self-organized 3-D integrated optical circuit shown in Figure 13 is proposed [1,20]. After a precursor with optical devices distributed three-dimensionally is prepared, optical waveguides are formed between the devices in a self-aligned manner to construct 3-D optical circuits. This will be achieved by SOLNET. Optical solder and Optical

**Precursor Self-Organized 3-D Optical Circuit**

**Figure 11.** 3-D stacked OE MCM

**Figure 12.** Concept of S-FOLM

S-FOLM gives the following advantages over the conventional flip-chip-bonding-based packaging.


#### *3.1.2. Self-organized 3-D integrated optical circuits with SOLNET*

In future optical interconnects, a large number of optical couplings and optical Zconnections will be involved. In such cases, following two issues should be considered.


88 Optical Devices in Communication and Computation

**Waveguide Film PD Light Modulator Thinned LSI**

*Integrated 3-D Optical Interconnects*

*OE Films with Embedded Thin-Film Device Flakes*

**Light Modulator/Optical Switch/ Wavelength Filter/VCSEL/PD**

**Optical Switch Vertical Waveguide**

**Figure 11.** 3-D stacked OE MCM

**Light Source**

**OE Board**

 

**Figure 12.** Concept of S-FOLM

it is necessary.

selectively on substrates.


**Interface IC**

**Device-Embedded Optical Waveguide**

together into OE films by SORT [1,17].

improvement without knowledge of optics.

packaging.

S-FOLM gives the following advantages over the conventional flip-chip-bonding-based

**Optical Waveguide Smart Pixel**

*3-D Optical Switching Systems*

*3-D OE Platform*

**Optical Interconnect Board**

**3-D Stacked OE MCM**







photolithographic process like PL-Pack with SORT [1,17].

As a solution for them, the self-organized 3-D integrated optical circuit shown in Figure 13 is proposed [1,20]. After a precursor with optical devices distributed three-dimensionally is prepared, optical waveguides are formed between the devices in a self-aligned manner to construct 3-D optical circuits. This will be achieved by SOLNET. Optical solder and Optical wiring in free spaces of SOLNET are respectively applicable for issue 1) and 2).

**Figure 13.** Concept of self-organized 3-D integrated optical circuits utilizing SOLNET

Optical devices can be connected with self-aligned optical couplings by putting the optical solder of SOLNET betweent them. Figure 14 shows examples of the optical solder of R-SOLNET for couplings of devices that cannot emit write beams such as PDs, and light modulators. Wavelength filters or luminescent materials are placed on the devices to pull the SOLNET to the target locations.

Figure 15 shows an example of the free space optical wiring of R-SOLNET for optical Zconnections in 3-D optical circuits. A luminescent target is placed at a vertical mirror location of a waveguide film. By introducing a write beam from a waveguide in an OE board into a free space filled with a PRI material, the luminescent target generates luminescence to construct a self-aligned vertical waveguide of R-SOLNET between the waveguide film and the OE board even when a misalignment and a core size mismatching exist.

**Figure 14.** Optical solder of SOLNET

**Figure 17.** Simulation of optical Z-connections with vertical waveguides of R-SOLNET

arrangements, should be controlled by using MLD as shown in Figure 18.

of 430 pm/V [23], about 14 times that of LN.

molecular orbital calculations.

**3.2. Enhancement of pockels effect by controlling wavefunction shapes** 

In the integrated 3-D optical interconnects, high-speed/small-size optical modulators and optical switches are the key components, for which high-performance electro-optic (EO) materials are required. So far, EO materials such as LiNbO3 (LN) and quantum dots of III-V compound semiconductors [22] have been developed. As the next generation EO material, organic materials with π-conjugated systems attract interest because they have both "large optical nonlinearity" and "low dielectric constant" characteristics. For example, the styrylpyridinium cyanine dye (SPCD) thin film was found to exhibit a large EO coefficient *r*

Organic EO materials are classified into poled polymers, molecular crystals, and conjugated polymers. Among these, the polymer MQD with conjugated polymer backbones seems most promising because it enables a wavefunction control between the one dimensional and the zero-dimensional to enhance the EO effect. In order to apply the polymer MQD to EO waveguides, locations and orientations of the polymer wires, as well as molecular

In the below part of this subsection, the enhancement of the Pockels effect, which is an EO effect inducing refractive index changes proportional to applied electric fields, in the polymer MQD by controlling wavefunction shapes is theoretically predicted [4,24] using the

**Figure 15.** Self-organized vertical waveguides of R-SOLNET

#### *3.1.3. Simulation of self-organized vertical waveguides of R-SOLNET*

SOLNET simulator is based on the FDTD method as described in detail elsewhere [1,21]. Figure 16 shows an example of a simulation. A 650-nm write beam emitted from an input waveguide with core width of 500 nm is initially reflected upward with diffraction by a 45 wavelength filter. Then, the self-focusing gradually appears in the exposed part. Finally, the write beam is focused by SOLNET growth along the center axis of the write beam propagation.

Figure 17 shows a simulation of an optical Z-connection construction with a vertical waveguide of R-SOLNET [21]. A 2 μm-thick core with a total internal reflection (TIR) 45 mirror is on a 0.5 μm-thick under cladding layer to form an optical waveguide film. Two optical waveguide films are stacked with a gap filled with a PRI material. A wavelength filter is deposited at the TIR 45 mirror aperture in the upper optical waveguide film. Refractive index of the PRI material varies from 1.5 to 1.7 with write beam exposure. Wavelengths of write beams and probe beams are 650 nm and 850 nm, respectively. Polarization is *E*//*z*.

In Figure 17, negative and positive lateral misalignments respectively represent left-side and right-side dislocations of the upper optical waveguide film. In a lateral misalignment range from 0.12 to 0.75 μm, R-SOLNET is led to the wavelength filter location by the "pulling water" effect.

**Figure 16.** Simulation of the self-focusing of a write beam

90 Optical Devices in Communication and Computation

**PRI** 

**OE Board**

**Waveguide Film**

**Luminescent Target**

**Figure 15.** Self-organized vertical waveguides of R-SOLNET

**Material Write Beam**

**Figure 16.** Simulation of the self-focusing of a write beam

propagation.

Polarization is *E*//*z*.

water" effect.

*3.1.3. Simulation of self-organized vertical waveguides of R-SOLNET* 

**Luminescence**

SOLNET simulator is based on the FDTD method as described in detail elsewhere [1,21]. Figure 16 shows an example of a simulation. A 650-nm write beam emitted from an input waveguide with core width of 500 nm is initially reflected upward with diffraction by a 45 wavelength filter. Then, the self-focusing gradually appears in the exposed part. Finally, the write beam is focused by SOLNET growth along the center axis of the write beam

**R-SOLNET**

**"Pulling Water" Effect Self-Focusing** 

Figure 17 shows a simulation of an optical Z-connection construction with a vertical waveguide of R-SOLNET [21]. A 2 μm-thick core with a total internal reflection (TIR) 45 mirror is on a 0.5 μm-thick under cladding layer to form an optical waveguide film. Two optical waveguide films are stacked with a gap filled with a PRI material. A wavelength filter is deposited at the TIR 45 mirror aperture in the upper optical waveguide film. Refractive index of the PRI material varies from 1.5 to 1.7 with write beam exposure. Wavelengths of write beams and probe beams are 650 nm and 850 nm, respectively.

In Figure 17, negative and positive lateral misalignments respectively represent left-side and right-side dislocations of the upper optical waveguide film. In a lateral misalignment range from 0.12 to 0.75 μm, R-SOLNET is led to the wavelength filter location by the "pulling

**Figure 17.** Simulation of optical Z-connections with vertical waveguides of R-SOLNET

#### **3.2. Enhancement of pockels effect by controlling wavefunction shapes**

In the integrated 3-D optical interconnects, high-speed/small-size optical modulators and optical switches are the key components, for which high-performance electro-optic (EO) materials are required. So far, EO materials such as LiNbO3 (LN) and quantum dots of III-V compound semiconductors [22] have been developed. As the next generation EO material, organic materials with π-conjugated systems attract interest because they have both "large optical nonlinearity" and "low dielectric constant" characteristics. For example, the styrylpyridinium cyanine dye (SPCD) thin film was found to exhibit a large EO coefficient *r* of 430 pm/V [23], about 14 times that of LN.

Organic EO materials are classified into poled polymers, molecular crystals, and conjugated polymers. Among these, the polymer MQD with conjugated polymer backbones seems most promising because it enables a wavefunction control between the one dimensional and the zero-dimensional to enhance the EO effect. In order to apply the polymer MQD to EO waveguides, locations and orientations of the polymer wires, as well as molecular arrangements, should be controlled by using MLD as shown in Figure 18.

In the below part of this subsection, the enhancement of the Pockels effect, which is an EO effect inducing refractive index changes proportional to applied electric fields, in the polymer MQD by controlling wavefunction shapes is theoretically predicted [4,24] using the molecular orbital calculations.

> **0 10 20 30 40 Number of C Sites in a Polymer Wire**

**DA DAAD**

**DDAA**

**Detuning Energy : 0.2 eV**

substitution, and the numbers following them indicate the number of carbon sites *N*C, which corresponds to molecular lengths. The calculation, for which the details are described in articles published elsewhere [4,24], revealed that wavefunction separations increase in the

Figure 21(a) shows *r*, *r*gn, and *ρβ* of these model molecules. Here, *ρβ* is *β* per 1 nm in molecular lengths. *r* increases and *r*gn decreases in the order of DA34, DAAD34, and DDAA30, which makes *ρβ* of DAAD34 in between maximum. This parallels to the tendency of the qualitative guideline shown in Figure 19. It is found from Figure 21(b) that the molecular length affects *ρβ* and that adjusting the length improves the nonlinear optical effect. In DA and DAAD molecules, *ρβ* reaches the maximum values near *N*<sup>C</sup> = 20, corresponding to ~2 nm in molecular length. Assuming PDA wire density of 1.31014 1/cm2, the expected maximum EO coefficient of the DA and DAAD is about 3000 pm/V, which is 100 times larger than the EO coefficient *r*33 of LN. It is therefore concluded that a large EO effect will be obtained by controlling the wavefunction dimensionality and separation.

> **(10-30 esu/nm)**

**10**

**20**

**rgn, r (D)**

**0**

**1000**

**2000**

**3000 100 x r33 (LN)**

**0**

**Figure 21.** Hyperpolarizability of OE conjugated polymer wires (Simulation)

**DDAA30**

**DetuningEnergy : 0.2 eV**

**DAAD34**

**(a) (b)**

**r**

**rgn**

**0**

**DA34**

 **(10-30 esu/nm)**

**1000**

**2000**

order of DA34, DAAD34, and DDAA30.

**Figure 20.** Models of OE conjugated polymer wires

**Figure 18.** EO waveguides of the polymer MQD

Hyperpolarizability *β* is the measure of the second-order optical nonlinearity of molecules. The EO coefficient for the Pockels effect is proportional to *β*. In the two level model, 2 gn *r r* . Here, *r*gn and *r* are respectively the transition dipole moment and the dipole moment difference between the ground state and the excited state. Then, as schematically illustrated in Figure 19, the following guideline for EO coefficient enhancement is derived.


For three wavefunction shapes shown in Figure 19, from left to right, the wavefunction separation increases while the wavefunction overlap decreases, i.e., *r* increases and *r*gn decreases. Therefore, *β* is expected to have its maximum in a wavefunction shape of intermediate wavefunction separation with an appropriate conjugated system dimensionality existing somewhere between zero and one, i.e., between a quantum dot (QD) condition and a quantum wire condition.

**Figure 19.** Guidelines for EO coefficient enhancement

Such optimized wavefunction conditions can be obtained by adjusting the QD lengths and donor/acceptor substitution sites in the QDs using the push/pull effects of the donors/acceptors. Three types of models for conjugated polymer wires with polydiacetylene (PDA) backbones are considered as shown in Figure 20. –NH2 is the donor (D) and –NO2 the acceptor (A). DA, DAAD, and DDAA represent the types of donor/acceptor substitution, and the numbers following them indicate the number of carbon sites *N*C, which corresponds to molecular lengths. The calculation, for which the details are described in articles published elsewhere [4,24], revealed that wavefunction separations increase in the order of DA34, DAAD34, and DDAA30.

**Figure 20.** Models of OE conjugated polymer wires

92 Optical Devices in Communication and Computation

**Conjugated Polymer Wire Guided Light Beam**

**V**

**Figure 18.** EO waveguides of the polymer MQD

condition and a quantum wire condition.

**Figure 19.** Guidelines for EO coefficient enhancement

2 gn

increasing *r*gn.

increasing *r*.

2 *gn r*

**n g**

Hyperpolarizability *β* is the measure of the second-order optical nonlinearity of molecules. The EO coefficient for the Pockels effect is proportional to *β*. In the two level model,

**V**

 *r r* . Here, *r*gn and *r* are respectively the transition dipole moment and the dipole moment difference between the ground state and the excited state. Then, as schematically illustrated in Figure 19, the following guideline for EO coefficient enhancement is derived.



For three wavefunction shapes shown in Figure 19, from left to right, the wavefunction separation increases while the wavefunction overlap decreases, i.e., *r* increases and *r*gn decreases. Therefore, *β* is expected to have its maximum in a wavefunction shape of intermediate wavefunction separation with an appropriate conjugated system dimensionality existing somewhere between zero and one, i.e., between a quantum dot (QD)

Such optimized wavefunction conditions can be obtained by adjusting the QD lengths and donor/acceptor substitution sites in the QDs using the push/pull effects of the donors/acceptors. Three types of models for conjugated polymer wires with polydiacetylene (PDA) backbones are considered as shown in Figure 20. –NH2 is the donor (D) and –NO2 the acceptor (A). DA, DAAD, and DDAA represent the types of donor/acceptor

*r r gn* 2

*r*

Figure 21(a) shows *r*, *r*gn, and *ρβ* of these model molecules. Here, *ρβ* is *β* per 1 nm in molecular lengths. *r* increases and *r*gn decreases in the order of DA34, DAAD34, and DDAA30, which makes *ρβ* of DAAD34 in between maximum. This parallels to the tendency of the qualitative guideline shown in Figure 19. It is found from Figure 21(b) that the molecular length affects *ρβ* and that adjusting the length improves the nonlinear optical effect. In DA and DAAD molecules, *ρβ* reaches the maximum values near *N*<sup>C</sup> = 20, corresponding to ~2 nm in molecular length. Assuming PDA wire density of 1.31014 1/cm2, the expected maximum EO coefficient of the DA and DAAD is about 3000 pm/V, which is 100 times larger than the EO coefficient *r*33 of LN. It is therefore concluded that a large EO effect will be obtained by controlling the wavefunction dimensionality and separation.

**Figure 21.** Hyperpolarizability of OE conjugated polymer wires (Simulation)

The molecular orbital calculations revealed that energy gaps of DAAD molecules are smaller than those of PDA with no donor/acceptor substitution. Using the phenomena, it is possible to insert many DAAD molecules into a PDA backbone to construct a DAAD-type polymer MQD shown in Figure 22 [4].

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 95

**Light Absorption**

**V.B.**

**C.B.**

**(c) Polymer-MQD-Sensitized ZnO**

**Wavelength**

**ZnO Polymer MQD**

**V.B.**

**C.B.**

**Figure 24.** Schematic illustrations of energy levels and absorption spectra in Si, multi-dye-sensitized

**(b) Multi-Dye-Sensitized ZnO**

**Wavelength**

**ZnO Molecular Wire 1(p)**

**Light Absorption**

**V.B.**

**C.B.**

**2(n)**

**3(p)**

**4(n)**

**LUMO**

**HOMO**

In the multi-dye sensitization of ZnO, where molecular wires consisting of p-type and n-type dyes are grown on ZnO, the energy diagrams and absorption spectra are schematically drawn as Figure 24(b). The absorption wavelength region can be divided into narrow absorption bands of individual dyes, suppressing the energy loss arising from the excess photon energy. In the polymer-MQD sensitization, the similar effect is expected as drawn in Figure 24(c).

In Figure 25, the z-scheme-like sensitization is shown [4]. An electron excited by a photon with wavelength of λ1 in molecule 1 is injected into ZnO. An electron excited by a photon with λ2 in molecule 2 is transferred to HOMO of molecule 1. The hole left in molecule 2 is compensated by a redox system. This sensitization mechanism suppresses the energy loss arising from the excess photon energy, and at the same time, it increases the difference in energy between the Fermi level of ZnO and the standard electrode potential of the redox system to increase the generated voltage in the photo-voltaic device. The similar z-scheme-like sensitization might

arise from molecules with the four-level two-photon absorption characteristics [4].

**1**

**2**

**1**

**Molecular Wire**

**Redox System**

**2**

**ZnO**

**V.B.**

**C.B.**

**Electron**

ZnO, and polymer-MQD-sensitized ZnO

**(a) Si**

**Wavelength**

**C.B.**

**Heat**

**V.B.**

**Light Absorption**

**Figure 25.** Z-scheme-like sensitization

**Figure 22.** Polymer MQD containing DAAD18-type QDs

#### **4. Applications to solar cells**

#### **4.1. Sensitized solar cells**

#### *4.1.1. Concept of multi-dye sensitization and polymer-MQD sensitization*

Structures for the multi-dye sensitization and the polymer-MQD sensitization are shown in Figure 23 [4,10,11]. In the former [4,10], molecular wires consisting of dye molecules, and in the latter [4,11], polymer wires having MQDs with different dot lengths are grown on semiconductor surfaces by MLD.

In Si solar cells, as shown in Figure 24(a), since the band gap is narrow, excess energy of photons is considerably lost as heat. The similar energy loss occurs in the dye-sensitized solar cells using the black dye with wide absorption spectra.

**Figure 23.** Structures for the multi-dye sensitization and the polymer-MQD sensitization

**Figure 24.** Schematic illustrations of energy levels and absorption spectra in Si, multi-dye-sensitized ZnO, and polymer-MQD-sensitized ZnO

In the multi-dye sensitization of ZnO, where molecular wires consisting of p-type and n-type dyes are grown on ZnO, the energy diagrams and absorption spectra are schematically drawn as Figure 24(b). The absorption wavelength region can be divided into narrow absorption bands of individual dyes, suppressing the energy loss arising from the excess photon energy. In the polymer-MQD sensitization, the similar effect is expected as drawn in Figure 24(c).

In Figure 25, the z-scheme-like sensitization is shown [4]. An electron excited by a photon with wavelength of λ1 in molecule 1 is injected into ZnO. An electron excited by a photon with λ2 in molecule 2 is transferred to HOMO of molecule 1. The hole left in molecule 2 is compensated by a redox system. This sensitization mechanism suppresses the energy loss arising from the excess photon energy, and at the same time, it increases the difference in energy between the Fermi level of ZnO and the standard electrode potential of the redox system to increase the generated voltage in the photo-voltaic device. The similar z-scheme-like sensitization might arise from molecules with the four-level two-photon absorption characteristics [4].

**Figure 25.** Z-scheme-like sensitization

94 Optical Devices in Communication and Computation

polymer MQD shown in Figure 22 [4].

**Quantum Dot**

**C.B.**

**V.B.**

**Figure 22.** Polymer MQD containing DAAD18-type QDs

*4.1.1. Concept of multi-dye sensitization and polymer-MQD sensitization* 

**Figure 23.** Structures for the multi-dye sensitization and the polymer-MQD sensitization

**Polymer MQD Dye Molecule**

**Semiconductor**

solar cells using the black dye with wide absorption spectra.

**Molecular Wire**

Structures for the multi-dye sensitization and the polymer-MQD sensitization are shown in Figure 23 [4,10,11]. In the former [4,10], molecular wires consisting of dye molecules, and in the latter [4,11], polymer wires having MQDs with different dot lengths are grown on

In Si solar cells, as shown in Figure 24(a), since the band gap is narrow, excess energy of photons is considerably lost as heat. The similar energy loss occurs in the dye-sensitized

**Multi-Dye Sensitization Polymer-MQD Sensitization**

**Semiconductor**

**4. Applications to solar cells** 

**DAAD18**

semiconductor surfaces by MLD.

**4.1. Sensitized solar cells** 

The molecular orbital calculations revealed that energy gaps of DAAD molecules are smaller than those of PDA with no donor/acceptor substitution. Using the phenomena, it is possible to insert many DAAD molecules into a PDA backbone to construct a DAAD-type

#### *4.1.2. Experimental demonstration of multi-dye sensitization of ZnO*

As the first step toward the multi-dye sensitization, we grew a two-dye-molecule-stacked structure shown in Figure 26(a) by providing p-type dye molecules and n-type dye molecules successively on an n-type ZnO surface using the liquid-phase MLD (LP-MLD) [4,10].

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 97

As Figure 27(a) shows, absorption spectrum of CV is located in a longer wavelength region comparing with that of RB. Consequently, while the photocurrent is not observed at 633 nm in [ZnO/RB], the photocurrent spectrum extends to 633 nm in [ZnO/RB/CV], exhibiting the

**ZnO RB CV**

**Figure 27.** (a)Absorption spectra of RB and CV, and (b) photocurrent spectra of sensitized ZnO

**[ZnO/CV]**

ODH and TPA are alternately connected, resulting in very short QDs of ~0.8 nm long.

Figure 30 shows the absorption spectra of polymer MQDs. The absorption peak shifts to shorter wavelengths in the trend: OTPTPT, OTPT, and OT. This trend follows that of decreasing QD length, being attributed to the quantum confinement of π-electrons in the QDs. In 3QD, a broad absorption band extending from ~480 to ~300 nm appears. The

In Figure 28, polymer MQD structures of OTPTPT, OTPT, OT, and 3QD [4,11], which contains the OT, OTPT and OTPTPT structures in a wire, are shown, as well as a structure of poly-azomethine (poly-AM) quantum wire. These are formed by using terephthalaldehyde (TPA), *p*-phenylenediamine (PPDA) and oxalic dihydrazide (ODH) as source molecules with chemical reactions shown in Figure 29. In poly-AM, TPA and PPDA are alternately connected, so the wavefunction of π-electrons is delocalized across the polymer wire. For OTPTPT, molecules are connected in the sequence of -ODH-TPA-PPDA-TPA-PPDA-TPA-ODH---. The regions between ODHs are regarded as QDs of ~3 nm long. For OTPT, the molecular sequence of -ODH-TPA-PPDA-TPA-ODH--- yields QDs of ~2 nm long. For OT,

**400 500 600 700 Wavelength (nm)**

**[ZnO/RB] [ZnO/RB/CV]**

*4.1.3. Polymer Multiple Quantum Dots (MQDs)* 

**[ZnO]**

**(b) <sup>0</sup>**

**200**

**400**

**Photo**c**urrent (nA/mW)**

**600**

**(a) <sup>0</sup>**

**Absorption Coefficient** 

**(arb. units)**

**2**

**4**

spectral widennig arising from the superpositon of RB and CV.

**Applied Voltage: 8.5 V**

**Figure 26.** (a)Structure and (b) mechanism of two-dye sensitization

In the present experiments, we used rose bengal (RB) for the p-type dye and crystal violet (CV) for the n-type dye. Because the p-type dyes tend to accept electrons and the n-type dyes tend to donate electrons [25], the [n-type-Semiconductor/p-type-Dye/n-type-Dye] structure of [ZnO/RB/CV] can be formed by the electrostatic force. The surface potential was found to shift to negative side upon RB adsorption on [ZnO], and to shift to positive side upon CV adsorption on [ZnO/RB], indicating that the two-dye-molecule-stacked structure of [ZnO/RB/CV] was definitely constructed by LP-MLD.

Mechanism of the two-dye sensitization of ZnO is shown in Figure 26(b). The electrons excited in the p-type dye are injected into ZnO directly, and electrons excited in the n-type dye are injected into ZnO through the p-type dye [26]. Thus, by using the p/n-stacked structure, photocurrents arising from the p-type dye and the n-type dye are superposed to widen the spectra.

As Figure 27(a) shows, absorption spectrum of CV is located in a longer wavelength region comparing with that of RB. Consequently, while the photocurrent is not observed at 633 nm in [ZnO/RB], the photocurrent spectrum extends to 633 nm in [ZnO/RB/CV], exhibiting the spectral widennig arising from the superpositon of RB and CV.

**Figure 27.** (a)Absorption spectra of RB and CV, and (b) photocurrent spectra of sensitized ZnO

#### *4.1.3. Polymer Multiple Quantum Dots (MQDs)*

96 Optical Devices in Communication and Computation

[4,10].

**C.B.**

*4.1.2. Experimental demonstration of multi-dye sensitization of ZnO* 

**Figure 26.** (a)Structure and (b) mechanism of two-dye sensitization

**n-Type Dye Molecule**

**Electron**

**(a)**

**Photocurrent**

**p-Type Dye Molecule**

**E**

[ZnO/RB/CV] was definitely constructed by LP-MLD.

widen the spectra.

**ZnO (n-Type)**

**V.B.**

**++ <sup>+</sup>**

In the present experiments, we used rose bengal (RB) for the p-type dye and crystal violet (CV) for the n-type dye. Because the p-type dyes tend to accept electrons and the n-type dyes tend to donate electrons [25], the [n-type-Semiconductor/p-type-Dye/n-type-Dye] structure of [ZnO/RB/CV] can be formed by the electrostatic force. The surface potential was found to shift to negative side upon RB adsorption on [ZnO], and to shift to positive side upon CV adsorption on [ZnO/RB], indicating that the two-dye-molecule-stacked structure of

**(b)**

Mechanism of the two-dye sensitization of ZnO is shown in Figure 26(b). The electrons excited in the p-type dye are injected into ZnO directly, and electrons excited in the n-type dye are injected into ZnO through the p-type dye [26]. Thus, by using the p/n-stacked structure, photocurrents arising from the p-type dye and the n-type dye are superposed to

As the first step toward the multi-dye sensitization, we grew a two-dye-molecule-stacked structure shown in Figure 26(a) by providing p-type dye molecules and n-type dye molecules successively on an n-type ZnO surface using the liquid-phase MLD (LP-MLD)

> **n-Type Dye Molecule p-Type Dye Molecule n-Type ZnO Thin Film**

> > **p-Type Dye Molecule**

> > > **Wavelength**

**Widening Photocurrent Spectra**

**Two-Dye-**

**Structure**

**Molecule-Stacked**

**n-Type Dye Molecule**

> In Figure 28, polymer MQD structures of OTPTPT, OTPT, OT, and 3QD [4,11], which contains the OT, OTPT and OTPTPT structures in a wire, are shown, as well as a structure of poly-azomethine (poly-AM) quantum wire. These are formed by using terephthalaldehyde (TPA), *p*-phenylenediamine (PPDA) and oxalic dihydrazide (ODH) as source molecules with chemical reactions shown in Figure 29. In poly-AM, TPA and PPDA are alternately connected, so the wavefunction of π-electrons is delocalized across the polymer wire. For OTPTPT, molecules are connected in the sequence of -ODH-TPA-PPDA-TPA-PPDA-TPA-ODH---. The regions between ODHs are regarded as QDs of ~3 nm long. For OTPT, the molecular sequence of -ODH-TPA-PPDA-TPA-ODH--- yields QDs of ~2 nm long. For OT, ODH and TPA are alternately connected, resulting in very short QDs of ~0.8 nm long.

> Figure 30 shows the absorption spectra of polymer MQDs. The absorption peak shifts to shorter wavelengths in the trend: OTPTPT, OTPT, and OT. This trend follows that of decreasing QD length, being attributed to the quantum confinement of π-electrons in the QDs. In 3QD, a broad absorption band extending from ~480 to ~300 nm appears. The

measured spectrum is fairly coincident with the predicted spectrum that is the superposition of absorption bands of OT, OTPT and OTPTPT.

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 99

In the conventional dye-sensitized solar cells, in order to increase the number of adsorbed dye molecules on semiconductor surfaces, porous semiconductors are used. In this case, the crystallinity of the semiconductors is degraded and the porous structure narrows the

In the waveguide-type sensitized solar cell shown in Figure 31 [4,10], a thin-film semiconductor with a flat surface and high crystallinity is used. So, the internal resistivity decreases. However, if the "normally-incident light" configuration is used for light absorption, the light passes through only monomolecular layer of dye, resulting in very small light absorption. In the "guided light" configuration the light passes through a lot of dye molecules to enhance light absorption. Thus, high-performance sensitized solar cells are

We estimated the effect of the "guided light" configuration on the photocurrent enhancement using setups shown in Figure 32 [4,10]. Photocurrents were measured by a slit-type Al electrode. For the "normally-incident light" configuration, the light was introduced onto the ZnO surface from an optical fiber. For the "guided light" configuration, the light was introduced into the ZnO thin film from the edge. As shown in Figure 33, photocurrent enhancement by a factor of 5~15 is observed in the "guided light"

In the waveguide-type sensitized solar cells, the optical coupling to the thin-film semiconductor is a concern. SOLNET might be one of the solutions, enabling light beams to

**Electrolyte or** 

**Sensitizing Layer**

**Thin-Film Semiconductor**

**Molecular Wires with Dye Molecules**

**Polymer MQDs**

electron transporting channels, causing an increase in the internal resistivity.

**4.2. Waveguide-type sensitized solar cells** 

expected.

configuration.

be coupled efficiently into the film [4].

**Counter Electrode**

**Light**

**Figure 31.** Waveguide-type sensitized solar cell

**Electrode**

**Thin-Film Semiconductor**

**Figure 32.** Setups of photocurrent measurements

**Figure 28.** Quantum wire and polymer MQD structures

**Figure 29.** Source molecules and chemical reactions

**Figure 30.** Absorption spectra of polymer MQD structures

#### **4.2. Waveguide-type sensitized solar cells**

98 Optical Devices in Communication and Computation

superposition of absorption bands of OT, OTPT and OTPTPT.

**Figure 28.** Quantum wire and polymer MQD structures

**-- ODH – TPA–PPDA–TPA – ODH – TPA–PPDA–TPA – ODH --**

**N C N N**

**H C H N C H N**

**H**

**-- TPA–PPDA– TPA–PPDA– TPA–PPDA– TPA–PPDA– TPA –**

**N N N C**

**C N N H C O H C O N H**

**Quantum Dot**

**C H**

**N C**

**N C H**

**C C N N**

**C.B.**

**V.B.**

**C H**

**C H**

**O**

**TPA**

**TPA**

**1**

**Absorption Coefficient (arb. units)**

**0.5**

**0**

**H**

**C H**

**O**

**O**

**O**

**O O H N H N N C H C H N C H**

**N C H C H N C H**

**C.B. V.B.**

**Figure 29.** Source molecules and chemical reactions

**Measured Predicted OT/OTPT/OTPTPT**

**Figure 30.** Absorption spectra of polymer MQD structures

measured spectrum is fairly coincident with the predicted spectrum that is the

**H C O H C O N H**

**[OT] [OTPT] [OTPTPT]**

**N N C H C H**

**Poly-AM Quantum Wire OTPTPT**

**OTPT OT**

**-ODH-TPA-ODH-TPA-PPDA-TPA-ODH-TPA-PPDA-TPA-PPDA-TPA-ODH-**

**3QD**

**C + + N H2O**

**C H**

**O**

**H**

**Wavelength (nm)**

**300 400 500**

**OTPT**

**OTPTPT**

**OT**

**H2N N**

**O**

**-- ODH – TPA – ODH – TPA – ODH – TPA – ODH --**

**H**

**N C**

**N C H N**

**C C N N**

**-- ODH – TPA–PPDA–TPA–PPDA–TPA – ODH –**

**Quantum Dot**

**H C H**

**NH2**

**C O**

**H**

**NH2 + H2O**

**N N H C O C O N H C N**

**N N H C O C O N H C N**

**H C O**

**H**

**C O N H**

**H C H**

**C N N**

**N N H C O C O N H**

**C C N N**

**C H**

**C**

**H**

**N N H C O**

**Quantum Dot**

**O O H N H N N C H C H**

**O O H N H N N C H C H N C H**

**C N**

**N**

**H N NH2**

**+ C**

**ODH C C**

**H**

**H2N NH2 PPDA**

**O O**

**H C H**

In the conventional dye-sensitized solar cells, in order to increase the number of adsorbed dye molecules on semiconductor surfaces, porous semiconductors are used. In this case, the crystallinity of the semiconductors is degraded and the porous structure narrows the electron transporting channels, causing an increase in the internal resistivity.

In the waveguide-type sensitized solar cell shown in Figure 31 [4,10], a thin-film semiconductor with a flat surface and high crystallinity is used. So, the internal resistivity decreases. However, if the "normally-incident light" configuration is used for light absorption, the light passes through only monomolecular layer of dye, resulting in very small light absorption. In the "guided light" configuration the light passes through a lot of dye molecules to enhance light absorption. Thus, high-performance sensitized solar cells are expected.

We estimated the effect of the "guided light" configuration on the photocurrent enhancement using setups shown in Figure 32 [4,10]. Photocurrents were measured by a slit-type Al electrode. For the "normally-incident light" configuration, the light was introduced onto the ZnO surface from an optical fiber. For the "guided light" configuration, the light was introduced into the ZnO thin film from the edge. As shown in Figure 33, photocurrent enhancement by a factor of 5~15 is observed in the "guided light" configuration.

In the waveguide-type sensitized solar cells, the optical coupling to the thin-film semiconductor is a concern. SOLNET might be one of the solutions, enabling light beams to be coupled efficiently into the film [4].

**Figure 32.** Setups of photocurrent measurements

**Molecule B**

**Molecule D**

Figure 35 depicts how LP-MLD can be applied to cancer therapy [4,11,13]. In step 1, Molecule A is injected into a human body. Molecule A is adsorbed in cancer cells selectively, and extra Molecule A is excreted. In step 2, Molecule B is injected to be connected to Molecule A. Similarly, by injecting Molecule C and D successively, tailored materials having

**Step 2**

LP-MLD can be regarded as a kind of *in-situ* synthesis within human bodies. When a molecule of a drug is too large, as schematically illustrated in Figure 36(a), it might be difficult for the drug to reach deep inside the cancer through narrow channels. The deep drug delivery might become possible by building up the large drug from small component molecules at cancer sites *in situ* by LP-MLD as shown in Figure 36(b). For toxic drugs, they might be delivered without attacking normal cells by building them up from non-toxic

**Step 4**

Furthermore, using LP-MLD, multi-functional tailored structures are expected to grow

a structure of A/B/C/D can be constructed at the cancer sites.

**Cancer**

**Molecule A**

**Cancer**

**Molecule C**

**Figure 35.** Application of LP-MLD to cancer therapy

**5.1.** *In-situ* **selective drug synthesis** 

components *in situ* at cancer sites.

selectively at cancer sites as Figure 37 shows.

**5. Cancer therapy** 

**Step 1**

**Step 3**

**Figure 33.** Photocurrent enhancement induced by "guided light" configuration

#### **4.3. Film-based integrated solar cells**

Conventional solar cells are material-consuming since semiconductors are placed all over the modules. To reduce the semiconductor material consumption and to provide wide-angle light beam collecting capability to the systems, and at the same time, to make systems flexible and compact, we proposed the film-based integrated solar cell with optical waveguides [1,4]. Figure 34 shows the schematic illustration of the proposed solar cell, in which semiconductor flakes are placed partially in a light beam collecting film by the heterogeneous integration process such as PL-Pack with SORT [17]. Figure 34 also shows a photograph of an array of tapered vertical waveguides fabricated by the built-in mask method [20]. The light beam collecting efficiency in tapered vertical waveguides was estimated to be 1.5-4 times higher than that in straight vertical waveguides.

**Figure 34.** Film-based integrated solar cells utilizing optical waveguides

#### **5. Cancer therapy**

100 Optical Devices in Communication and Computation

**4.3. Film-based integrated solar cells** 

**Figure 33.** Photocurrent enhancement induced by "guided light" configuration

**[ZnO] 405 nm**

**0**

**5**

**Photocurrent Enhancement Ratio** 

**10**

estimated to be 1.5-4 times higher than that in straight vertical waveguides.

**Figure 34.** Film-based integrated solar cells utilizing optical waveguides

Conventional solar cells are material-consuming since semiconductors are placed all over the modules. To reduce the semiconductor material consumption and to provide wide-angle light beam collecting capability to the systems, and at the same time, to make systems flexible and compact, we proposed the film-based integrated solar cell with optical waveguides [1,4]. Figure 34 shows the schematic illustration of the proposed solar cell, in which semiconductor flakes are placed partially in a light beam collecting film by the heterogeneous integration process such as PL-Pack with SORT [17]. Figure 34 also shows a photograph of an array of tapered vertical waveguides fabricated by the built-in mask method [20]. The light beam collecting efficiency in tapered vertical waveguides was

**[ZnO/RB] 532 nm**

**Applied Voltage: 8.5 V**

**[ZnO/RB/CV] 633 nm**

Figure 35 depicts how LP-MLD can be applied to cancer therapy [4,11,13]. In step 1, Molecule A is injected into a human body. Molecule A is adsorbed in cancer cells selectively, and extra Molecule A is excreted. In step 2, Molecule B is injected to be connected to Molecule A. Similarly, by injecting Molecule C and D successively, tailored materials having a structure of A/B/C/D can be constructed at the cancer sites.

**Figure 35.** Application of LP-MLD to cancer therapy

#### **5.1.** *In-situ* **selective drug synthesis**

LP-MLD can be regarded as a kind of *in-situ* synthesis within human bodies. When a molecule of a drug is too large, as schematically illustrated in Figure 36(a), it might be difficult for the drug to reach deep inside the cancer through narrow channels. The deep drug delivery might become possible by building up the large drug from small component molecules at cancer sites *in situ* by LP-MLD as shown in Figure 36(b). For toxic drugs, they might be delivered without attacking normal cells by building them up from non-toxic components *in situ* at cancer sites.

Furthermore, using LP-MLD, multi-functional tailored structures are expected to grow selectively at cancer sites as Figure 37 shows.

**Luminescence**

**Beam**

**Write Beam**

**R-SOLNET Surgery**

**(4) R-SOLNET Formation (5) Inspection/Surgery**

**(1) LP-MLD (2) PRI Material Insertion (3) Write Beam Exposure**

**Figure 38.** Concept of SOLNET-assisted laser surgery

**Luminescent Molecules**

**Cancer**

**Organ**

In the model shown in Figure 39, a 600-nm wide luminescent target is placed in a PRI material with a lateral offset of 600 nm from the axis of the optical waveguide with core width of 1.2 μm. The wavelengths of the write beam, the luminescence, and the surgery beam are 650, 700, and 650 nm, respectively. Luminescence efficiency is 0.36. It is found that, with writing time, R-SOLNET is gradually constructed between the optical waveguide and

**Optical Fiber**

**PRI Material**

the target. As a result, the surgery beam is guided to the target site [1,13].

**Figure 39.** Simulation of R-SOLNET using a luminescent target

*5.2.2. Simulation by FDTD method* 

**Figure 36.** *In-situ* drug synthesis

**Figure 37.** Selective delivery of multi-functional materials to cancer cells by LP-MLD

#### **5.2. SOLNET-assisted laser surgery**

#### *5.2.1. Concept of SOLNET-assisted laser surgery*

Figure 38 shows the concept of the SOLNET-assisted laser surgery. Luminescent molecules are attached to cancer cells by LP-MLD. After inserting an optical fiber and a PRI material around the cancer sites, a write beam is introduced from the optical fiber to construct R-SOLNET between the optical fiber and the cancer sites. By introducing surgery beams into the R-SOLNET via the optical fiber, cancer cells are destroyed selectively. By detecting the luminescence emitted from the luminescent molecules, *in-situ* monitoring might be possible.

**Figure 38.** Concept of SOLNET-assisted laser surgery

#### *5.2.2. Simulation by FDTD method*

102 Optical Devices in Communication and Computation

**Cancer**

**Large Drug Toxic Drug**

**(a) Conventional Drug Delivery**

**Step 1 Step 2 Step 3 Step 4**

**Molecule A: Anchor for Growth Initiation** 

**Molecule B, C, D: Functional Molecules**

**-Sensitizer for Photodynamic Therapy (PDT) -Paramagnetic Agent for MRI Labeling and Magnetically-Actuated Systems -Agent for Radio-Enhancement**

**-Agent for Near Infrared Light Absorption**

**-Emissive Agent for Imaging**

**(b***) In-Situ* **Drug Synthesis**

**Figure 36.** *In-situ* drug synthesis

**5.2. SOLNET-assisted laser surgery** 

might be possible.

*5.2.1. Concept of SOLNET-assisted laser surgery* 

**Figure 37.** Selective delivery of multi-functional materials to cancer cells by LP-MLD

Figure 38 shows the concept of the SOLNET-assisted laser surgery. Luminescent molecules are attached to cancer cells by LP-MLD. After inserting an optical fiber and a PRI material around the cancer sites, a write beam is introduced from the optical fiber to construct R-SOLNET between the optical fiber and the cancer sites. By introducing surgery beams into the R-SOLNET via the optical fiber, cancer cells are destroyed selectively. By detecting the luminescence emitted from the luminescent molecules, *in-situ* monitoring In the model shown in Figure 39, a 600-nm wide luminescent target is placed in a PRI material with a lateral offset of 600 nm from the axis of the optical waveguide with core width of 1.2 μm. The wavelengths of the write beam, the luminescence, and the surgery beam are 650, 700, and 650 nm, respectively. Luminescence efficiency is 0.36. It is found that, with writing time, R-SOLNET is gradually constructed between the optical waveguide and the target. As a result, the surgery beam is guided to the target site [1,13].

**Figure 39.** Simulation of R-SOLNET using a luminescent target

#### *5.2.3. Experimental demonstration*

In order to demonstrate R-SOLNET with luminescent materials, a luminescent target of tris(8-hydroxyquinolinato)aluminum (Alq3) was put in a photopolymer. As Figure 40 shows, when a write beam of 405 nm in wavelength was introduced into the photopolymer from an optical fiber, blue-green luminescence was emitted from the Alq3 target. It is found that the blue write beam is pulled to the Alq3 target and a red probe beam of 650 nm is guided toward the target. These results indicate that R-SOLNET with luminescent materials was successfully formed by the write beam and the luminescence from the target [1,13,27].

Self-Organized Three-Dimensional Optical Circuits and Molecular Layer Deposition for Optical Interconnects, Solar Cells, and Cancer Therapy 105

**Author details** 

Tetsuzo Yoshimura

**7. References** 

Patent 6,081,632.

*Tokyo University of Technology, School of Computer Science, Hachioji, Tokyo, Japan* 

Pan Stanford Publishing Pte. Ltd., Singapore.

Components Technol. Conf. (ECTC): 962–969.

Proc. 3rd IEMT/IMC Symposium: 140–145.

Electrochem. Soc. 158: 51-55.

J. Vac. Sci. Technol. A. 29: 051510-1-6.

Renewable Sustainable Energy. 1: 033106 1-15.

Applications. CRC/Taylor & Francis, Boca Raton, Florida.

film, fabrication and use thereof. US Patent 5,444,811.

[1] Yoshimura T (2012) Optical Electronics: Self-Organized Integration and Applications.

[2] Yoshimura T, Sotoyama W, Motoyoshi K, Ishitsuka T, Tsukamoto K, Tatsuura S, Soda H, Yamamoto T (2000) Method of producing optical waveguide system, optical device and optical coupler employing the same, optical network and optical circuit board. U.S.

[3] Yoshimura T, Roman J, Takahashi Y, Wang W.V, Inao M, Ishitsuka T, Tsukamoto K, Motoyoshi K, Sotoyama W (2000) Self-Organizing Waveguide Coupling Method 'SOLNET' and Its Application to Film Optical Circuit Substrates. Proc. 50th Electron.

[4] Yoshimura T (2011) Thin-Film Organic Photonics: Molecular Layer Deposition and

[5] Yoshimura T, Yano E, Tatsuura S, Sotoyama W (1995) Organic functional optical thin

[6] Yoshimura T, Tatsuura S, Sotoyama W (1991) Polymer films formed with monolayer

[7] Yoshimura T, Takahashi Y, Inao M, Lee M, Chou W, Beilin S, Wang W.V, Roman J, Massingill T (2002) Systems Based on Opto-Electronic Substrates with Electrical and

[8] Yoshimura T, Roman J, Takahashi Y, Lee M, Chou B, Beilin S.I, Wang W.V, Inao M (1999) Proposal of Optoelectronic Substrate with Film/Z-Connection Based on OE-Film.

[9] Yoshimura T, Roman J, Takahashi Y, Lee M, Chou B, Beilin S.I, Wang W.V, Inao M (2000) Optoelectronic Scalable Substrates Based on Film/Z-connection and Its

[10] Yoshimura T, Watanabe H, Yoshino C (2011) Liquid-Phase Molecular Layer Deposition (LP-MLD): Potential Applications to Multi-Dye Sensitization and Cancer Therapy. J.

[11] Yoshimura T, Ebihara R, Oshima A (2011) Polymer Wires with Quantum Dots Grown by Molecular Layer Deposition of Three Source Molecules for Sensitized Photovoltaics.

[12] Shioya R, Yoshimura T (2009) Design of Solar Beam Collectors Consisting of Multi-Layer Optical Waveguide Films for Integrated Solar Energy Conversion Systems. J.

[13] Yoshimura T, Yoshino C, Sasaki K, Sato T, Seki M (2012) Cancer Therapy Utilizing Molecular Layer Deposition (MLD) and Self-Organized Lightwave Network (SOLNET)

growth steps by molecular layer deposition. Appl. Phys. Lett. 59: 482-484.

Optical Interconnections and Methods for Making. U.S. Patent 6,343,171 B1.

Application to Film Optical Link Module (FOLM). Proc. SPIE. 3952: 202–213.

**Figure 40.** R-SOLNET formed between an optical fiber and a luminescent target

#### **6. Summary**

Our core technologies, SOLNET and MLD, were reviewed, and their applications to optical interconnects within computers, solar cells, and cancer therapy were presented.

In the integrated optical interconnects within computers based on the self-organized 3-D optical circuits, SOLNET is used for vertical waveguides in optical Z-connections and the optical solder for self-aligned optical couplings. MLD is expected to contribute to improving the light modulator/optical switch performance. In the sensitized solar cells, MLD is used for growth of the multi-dye molecular wires and the polymer MQDs that are sensitizing layers on thin films of oxide semiconductors. SOLNET is expected to couple light beams efficiently into the thin films. In cancer therapy, MLD enables selective delivery of large/toxic drugs and multi-functional materials to cancer cells, as well as the SOLNETassisted laser surgery for the self-aligned laser beam guiding to cancer sites.

#### **Author details**

104 Optical Devices in Communication and Computation

In order to demonstrate R-SOLNET with luminescent materials, a luminescent target of tris(8-hydroxyquinolinato)aluminum (Alq3) was put in a photopolymer. As Figure 40 shows, when a write beam of 405 nm in wavelength was introduced into the photopolymer from an optical fiber, blue-green luminescence was emitted from the Alq3 target. It is found that the blue write beam is pulled to the Alq3 target and a red probe beam of 650 nm is guided toward the target. These results indicate that R-SOLNET with luminescent materials was successfully formed by the write beam and the luminescence from the target [1,13,27].

**Figure 40.** R-SOLNET formed between an optical fiber and a luminescent target

interconnects within computers, solar cells, and cancer therapy were presented.

assisted laser surgery for the self-aligned laser beam guiding to cancer sites.

Our core technologies, SOLNET and MLD, were reviewed, and their applications to optical

In the integrated optical interconnects within computers based on the self-organized 3-D optical circuits, SOLNET is used for vertical waveguides in optical Z-connections and the optical solder for self-aligned optical couplings. MLD is expected to contribute to improving the light modulator/optical switch performance. In the sensitized solar cells, MLD is used for growth of the multi-dye molecular wires and the polymer MQDs that are sensitizing layers on thin films of oxide semiconductors. SOLNET is expected to couple light beams efficiently into the thin films. In cancer therapy, MLD enables selective delivery of large/toxic drugs and multi-functional materials to cancer cells, as well as the SOLNET-

*5.2.3. Experimental demonstration* 

**6. Summary** 

Tetsuzo Yoshimura

*Tokyo University of Technology, School of Computer Science, Hachioji, Tokyo, Japan* 

#### **7. References**



**Chapter 0**

**Chapter 6**

**Bio-Inspired Photonic Structures:**

Feng Liu, Biqin Dong and Xiaohan Liu

way by nano-fabrication technologies today.

greater success than ever before.

cited.

http://dx.doi.org/10.5772/50199

**1. Introduction**

Additional information is available at the end of the chapter

**Prototypes, Fabrications and Devices**

Like the ability of electron regulation of electronic semiconductors, the photonic analogs usually considered as photonic structure materials are regarded as essential for light manipulation [1, 2]. With particular designs of photonic structures, they are expected to achieve different far-field and near-field optical features and thus lead to a perspective in all-optical circuit [3]. Though humankind has entered the nano-scale realm several decades ago, it is still a hard task for engineers to explore novel optical functional devices due to the limited experiences and originalities on artificial photonic structures design and the desired optical features. Additionally, it is also great challenges to fabricate photonic structures, owing to their sub-optical-wavelength to sub-micron featured sizes, especially in a high dimensional

By contrast, nature are found to develop photonic structures millions of years before our initial attempts. Diversified photonic structures, most of which are sophisticated and hierarchic, are revealed in beetles, butterflies, sea animals and even plants in recent surveys [4–10]. The exhibited optical features are regarded to have particular biological functions such as signal communications, conspecific recognition, and camouflage, which are optimized under selection pressure. Naturally, the occurring photonic structures provide us ideal 'blueprints' on design and stimulate similar optical functional devices. Various fabrication methods of bio-inspired photonic structures are explored [11–16]. By chemical methods (e.g. Sol-Gel, colloidal crystallization, chemical systhesis), nanoimprint lithography and nanocasting, physical layer deposition (PLD), atomic layer deposition (ALD), and etc., bio-inspired photonic structures, their reverse counterparts, and applications are achieving

This Chapter will review the typical bio-inspired photonic structures and focus on the biomimetic fabrications, the corresponding optical functions and the prototypes of optical devices. It is organized as follows: four subsections are introduced in Section 2, in which each describes one catagory of bio-inspired optical functional devices. In every subsection, the nature prototype is introduced first, then followed by biomimetic fabrication methods and

and reproduction in any medium, provided the original work is properly cited.

©2012 Liu et al. , licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,


**Chapter 0 Chapter 6**

## **Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices**

Feng Liu, Biqin Dong and Xiaohan Liu

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50199

#### **1. Introduction**

106 Optical Devices in Communication and Computation

Nonlinear Opt. 22: 453–456:.

Quantum Electron. 17: 566-570.

Patent 6,294,794B1.

B40: 6292–6298.

Nanotechnologies. Proc. SPIE. 6126: 612609-1-15.

Lett. 7: 177–179.

Biophotonics 1. May/June [to be published].


[14] Brauchle C, Wild U.P, Burland D.M, Bjorkund G.C, Alvares D.C (1982) Two-Photon Holographic Recording with Continuous-Wave Lasers in the 750–1100 nm Range. Opt.

[15] Yoshimura T, Kaburagi H (2008) Self-Organization of Optical Waveguides between Misaligned Devices Induced by Write-Beam Reflection. Appl. Phys. Express. 1: 06200. [16] Pessa M, Makela R, Suntola T (1981) Characterization of Surface Exchange Reactions

[17] Yoshimura T, Ojima M, Arai Y, Asama K (2003) Three-Dimensional Self-Organized Micro Optoelectronic Systems for Board-Level Reconfigurable Optical Interconnects — Performance Modeling and Simulation. IEEE J. Select. Top. Quantum Electron. 9: 492–511. [18] Yoshimura T, Roman J, Takahashi Y, Beilin S.I, Wang W.V, Inao M (1999) Optoelectronic Amplifier/Driver-Less Substrate <OE-ADLES> for Polymer-Waveguide-Based Board-Level Interconnection — Calculation of Delay and Power Dissipation.

[19] Yoshimura T, Suzuki Y, Shimoda N, Kofudo T, Okada K, Arai Y, Asama K (2006) Three-Dimensional Chip-Scale Optical Interconnects and Switches with Self-Organized Wiring Based on Device-Embedded Waveguide Films and Molecular

[20] Yoshimura T, Inoguchi T, Yamamoto T, Moriya S, Teramoto Y, Arai Y, Namiki T, Asama K (2004) Self-Organized Lightwave Network Based on Waveguide Films for Three-Dimensional Optical Wiring Within Boxes. J. Lightwave. Technol. 22:2091-2100. [21] Yoshimura T, Wakabayashi K, Ono S (2011) Analysis of Reflective Self-Organized Lightwave Network (R-SOLNET) for Z-Connections in Three-Dimensional Optical Circuits by the Finite Difference Time Domain Method. IEEE J. Select. Topics in

[22] Yoshimura T, Futatsugi T (2001) Non-linear optical device using quantum dots. U.S.

[23] Yoshimura T (1987) Characterization of the EO effect in styrylpyridinium cyanine dye

[24] Yoshimura T (1989) Enhancing Second-Order Nonlinear Optical Properties by Controlling the Wave Function in One-Dimensional Conjugated Molecules. Phys. Rev.

[25] Yoshimura T, Kiyota K, Ueda H, Tanaka M (1979) Contact Potential Difference of ZnO Layer Adsorbing p-Type Dye and n-Type Dye. Jpn. J. Appl. Phys. 18: 2315-2316. [26] Yoshimura T, Kiyota K, Ueda H, Tanaka M (1981) Mechanism of Spectral Sensitization of ZnO Coadsorbing p-Type and n-Type Dyes. Jpn. J. Appl. Phys. 20: 1671-1674. [27] Seki M, Yoshimura T (2012) Proposal and FDTD Simulation of Reflective Self-Organizing Lightwave Network (R-SOLNET) Using Phosphor. Proc. SPIE. 8267 82670V-1 - 9.

thin-film crystals by an ac modulation method. J. Appl. Phys. 62: 2028-2032.

Used to Grow Compound Films. Appl. Phys. Lett. 31: 131-133.

Like the ability of electron regulation of electronic semiconductors, the photonic analogs usually considered as photonic structure materials are regarded as essential for light manipulation [1, 2]. With particular designs of photonic structures, they are expected to achieve different far-field and near-field optical features and thus lead to a perspective in all-optical circuit [3]. Though humankind has entered the nano-scale realm several decades ago, it is still a hard task for engineers to explore novel optical functional devices due to the limited experiences and originalities on artificial photonic structures design and the desired optical features. Additionally, it is also great challenges to fabricate photonic structures, owing to their sub-optical-wavelength to sub-micron featured sizes, especially in a high dimensional way by nano-fabrication technologies today.

By contrast, nature are found to develop photonic structures millions of years before our initial attempts. Diversified photonic structures, most of which are sophisticated and hierarchic, are revealed in beetles, butterflies, sea animals and even plants in recent surveys [4–10]. The exhibited optical features are regarded to have particular biological functions such as signal communications, conspecific recognition, and camouflage, which are optimized under selection pressure. Naturally, the occurring photonic structures provide us ideal 'blueprints' on design and stimulate similar optical functional devices. Various fabrication methods of bio-inspired photonic structures are explored [11–16]. By chemical methods (e.g. Sol-Gel, colloidal crystallization, chemical systhesis), nanoimprint lithography and nanocasting, physical layer deposition (PLD), atomic layer deposition (ALD), and etc., bio-inspired photonic structures, their reverse counterparts, and applications are achieving greater success than ever before.

This Chapter will review the typical bio-inspired photonic structures and focus on the biomimetic fabrications, the corresponding optical functions and the prototypes of optical devices. It is organized as follows: four subsections are introduced in Section 2, in which each describes one catagory of bio-inspired optical functional devices. In every subsection, the nature prototype is introduced first, then followed by biomimetic fabrication methods and

©2012 Liu et al. , licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Figure 1.** Antireflection structures. (a) Hexagonal arranged tapered pillars root in the surface of cicada wings in top view (tilted view of the pillar array is showed in the inset) [19]; (b) The tapered pillars lead to gradual refraction index variation in view of effective theory and then minimize the reflection according to Fresnel relations.

optical features of artificial analogs, finally closed on the bio-inspired optical devices. A brief perspective is given in Section 3.

#### **2. Bio-inspired optical functional devices**

#### **2.1. Anti-reflection devices**

#### *2.1.1. Prototypes*

In arthropodal animals such as butterflies, nipple arrays with typical spacing of optical wavelength or subwavelength are commonly found on surfaces of their compound eyes, which are believed helpful to the light-harvest efficiency of the biological visual system [17]. With optical impedance matching to the ambience, the light transmission are enhanced. Another analogous examples are the transparent wings of some lepidoptera insects like hawkmoths [18] and cicada [19] (Fig.1 (a)). The tapered pillars lead to gradual changes of refraction index in view of effective medium theory (Fig.1 (b)) and therefore play a key role in minimizing the reflection over broadband and large viewangles. In order to physically explain the anti-reflection origin, the Fresnel equations are given as follows.

$$r\_s = |\frac{n\_1 \cos i\_1 - n\_2 \cos i\_2}{n\_1 \cos i\_1 + n\_2 \cos i\_2}|\,, \tag{1}$$

quasi omnidirectional anti-reflection.

respectively [22].

the substrate finally [24].

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 109

**Figure 2.** Improved antireflection of biomimetic nanotips by ECR plasma etching technique [25, 27]. (a) Schematic diagram for the silicon nanotip formation on silicon wafer; (b) and (c) show a tilted top view and a cross-sectional view of silicon nanotips, respectively; (d) Compared with polished silicon wafer (left), 6-inch silicon wafer coated with silicon nanotips (right) show greatly improved broadband and

evaporated-film-by-rotation (CEFR), colloidal lithography, self-masked dry etching,

Oblique angle deposition (OAD) is usually employed to fabricate anisotropic film which is originated from the oblique growth of contained nanorods with a tilted angle to the substrate surface normal. The so-called CEFR method, which rotates the substrates at a high speed under OAD, leads to the straight growth of a dense array columns to substrate surface rather than helical structures which are formed under low rotation rate. That is, CEFR method is suitable for conformal replication of the photonic structure with a curved surface even under thick film deposition. With compound eyes of the fruit fly as bio-templates, it is reported artificial replica is successfully fabricated and hence similar optical features are inherited,

Many lithography techniques are applied for fabricating antireflection structures, among which colloidal lithography is a much simpler approach [23]. With colloidal crystals as masks, the silicon substrate is etched by reaction ion etching (RIE). During the fabrication duration, the colloidal spheres are etched by RIE gradually firstly, leading to a reduced transverse cross section of the spheres and thus an increasing exposure of the substrate. Attributed to the features of RIE, the etching rates of the apex and the junction parts of the spheres are not uniform, resulting in the etching morphology modification from frustum to cone arrays on

Electron cyclotron resonance (ECR) plasma etching technique is employed by researchers to fabricate antireflection structures with much higher aspect ratio surfaces [25–27]. With the selected gas-mixture consisting of SiH4, CH4, Ar, and H2, one step and self-masked dry etching are realized for fabricating high density nanotip arrays on a 6-inch silicon wafer. The fabrication progress is illustrated in the schematic diagram of Fig. 2(a). In brief, SiC clusters, which size and density can be tuned via process temperature, gas pressure, and composition, are formed on surfaces of the silicon substrate due to the reaction of SiH4 and CH4 plasma.

nanoimprint lithography (NIL), ALD and other approaches, are realized [16].

$$r\_p = |\frac{n\_1 \cos i\_2 - n\_2 \cos i\_1}{(n\_1 \cos i\_2 + n\_2 \cos i\_1)}|\,,\tag{2}$$

where *rs* and *rp* refer to reflection coefficients of *s* polarised light (the electric field of the light perpendicular to the incident plane) and *p* polarised light (the electric field in the incident light plane), *n*<sup>1</sup> and *n*<sup>2</sup> are refraction indices of neighboring mediums, respectively. The relationship between incident angle *i*<sup>1</sup> and refraction angle *i*<sup>2</sup> is given by Snell's Law *n*1sin*i*1=*n*2sin*i*2. From the equations, e.g., for normal incidence, *rs* and *rp* are suppressed to near zero if *n*<sup>1</sup> and *n*<sup>2</sup> have very close values [20, 21].

#### *2.1.2. Bio-inspired fabrications*

Inspired by nature, many efforts are made in exploring techniques for fabricating the anti-reflection nanostructures and a variety of methods, e.g., conformal108 Optical Devices in Communication and Computation Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices <sup>3</sup> Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 109

2 Will-be-set-by-IN-TECH

**Figure 1.** Antireflection structures. (a) Hexagonal arranged tapered pillars root in the surface of cicada wings in top view (tilted view of the pillar array is showed in the inset) [19]; (b) The tapered pillars lead to gradual refraction index variation in view of effective theory and then minimize the reflection

optical features of artificial analogs, finally closed on the bio-inspired optical devices. A brief

In arthropodal animals such as butterflies, nipple arrays with typical spacing of optical wavelength or subwavelength are commonly found on surfaces of their compound eyes, which are believed helpful to the light-harvest efficiency of the biological visual system [17]. With optical impedance matching to the ambience, the light transmission are enhanced. Another analogous examples are the transparent wings of some lepidoptera insects like hawkmoths [18] and cicada [19] (Fig.1 (a)). The tapered pillars lead to gradual changes of refraction index in view of effective medium theory (Fig.1 (b)) and therefore play a key role in minimizing the reflection over broadband and large viewangles. In order to physically

> *n*1*cosi*<sup>1</sup> − *n*2*cosi*<sup>2</sup> *n*1*cosi*<sup>1</sup> + *n*2*cosi*<sup>2</sup>

*n*1*cosi*<sup>2</sup> − *n*2*cosi*1) (*n*1*cosi*<sup>2</sup> + *n*2*cosi*<sup>1</sup>

where *rs* and *rp* refer to reflection coefficients of *s* polarised light (the electric field of the light perpendicular to the incident plane) and *p* polarised light (the electric field in the incident light plane), *n*<sup>1</sup> and *n*<sup>2</sup> are refraction indices of neighboring mediums, respectively. The relationship between incident angle *i*<sup>1</sup> and refraction angle *i*<sup>2</sup> is given by Snell's Law *n*1sin*i*1=*n*2sin*i*2. From the equations, e.g., for normal incidence, *rs* and *rp* are suppressed to near zero if *n*<sup>1</sup> and *n*<sup>2</sup>

Inspired by nature, many efforts are made in exploring techniques for fabricating the anti-reflection nanostructures and a variety of methods, e.g., conformal-



explain the anti-reflection origin, the Fresnel equations are given as follows.

*rs* = |

*rp* = |

according to Fresnel relations.

perspective is given in Section 3.

**2.1. Anti-reflection devices**

have very close values [20, 21].

*2.1.2. Bio-inspired fabrications*

*2.1.1. Prototypes*

**2. Bio-inspired optical functional devices**

**Figure 2.** Improved antireflection of biomimetic nanotips by ECR plasma etching technique [25, 27]. (a) Schematic diagram for the silicon nanotip formation on silicon wafer; (b) and (c) show a tilted top view and a cross-sectional view of silicon nanotips, respectively; (d) Compared with polished silicon wafer (left), 6-inch silicon wafer coated with silicon nanotips (right) show greatly improved broadband and quasi omnidirectional anti-reflection.

evaporated-film-by-rotation (CEFR), colloidal lithography, self-masked dry etching, nanoimprint lithography (NIL), ALD and other approaches, are realized [16].

Oblique angle deposition (OAD) is usually employed to fabricate anisotropic film which is originated from the oblique growth of contained nanorods with a tilted angle to the substrate surface normal. The so-called CEFR method, which rotates the substrates at a high speed under OAD, leads to the straight growth of a dense array columns to substrate surface rather than helical structures which are formed under low rotation rate. That is, CEFR method is suitable for conformal replication of the photonic structure with a curved surface even under thick film deposition. With compound eyes of the fruit fly as bio-templates, it is reported artificial replica is successfully fabricated and hence similar optical features are inherited, respectively [22].

Many lithography techniques are applied for fabricating antireflection structures, among which colloidal lithography is a much simpler approach [23]. With colloidal crystals as masks, the silicon substrate is etched by reaction ion etching (RIE). During the fabrication duration, the colloidal spheres are etched by RIE gradually firstly, leading to a reduced transverse cross section of the spheres and thus an increasing exposure of the substrate. Attributed to the features of RIE, the etching rates of the apex and the junction parts of the spheres are not uniform, resulting in the etching morphology modification from frustum to cone arrays on the substrate finally [24].

Electron cyclotron resonance (ECR) plasma etching technique is employed by researchers to fabricate antireflection structures with much higher aspect ratio surfaces [25–27]. With the selected gas-mixture consisting of SiH4, CH4, Ar, and H2, one step and self-masked dry etching are realized for fabricating high density nanotip arrays on a 6-inch silicon wafer. The fabrication progress is illustrated in the schematic diagram of Fig. 2(a). In brief, SiC clusters, which size and density can be tuned via process temperature, gas pressure, and composition, are formed on surfaces of the silicon substrate due to the reaction of SiH4 and CH4 plasma.

4 Will-be-set-by-IN-TECH 110 Optical Devices in Communication and Computation Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices <sup>5</sup>

**(a) (b)**

**(d) nanodome solar cells thin film solar cells**

close to the Yablonovitch limit at an equivalent thickness of 2 *μ*m.

double-sided antireflection structure design (Fig. 4(e) and (f))[34].

larger enhancement for large viewing angles.

resulting in a more reliable three-axis attitude information.

**(e)**

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 111

TCO a-Si:H

Ag

**Figure 4.** (Color online) Solar cells coating antireflection structures [32, 34]. (a) Nanodome solar cells in top view. Scale bar 500 nm; (b) Schematic diagram of the cross-sectional structures of the solar cells; (c) The photographs of nanodome solar cells (left) and flat film solar cells (right); (d) Dark and light I-V curve corresponding to (c); (e) and (f) The optimized double-sided nanostructure yields a photocurrent

Due to the high reflectance of silicon solar cells (more than 30%) induced by the high index contrast of silicon and air according to the Fresnel equations, scientists are already aware of the vital roles of high-quality antireflection coatings at early ages of solar cell fabrications [30]. Inspired by antireflection structures found in moth eyes, nanodomes or similar architectures are reproduced on surfaces of solar cells, leading to a dramatic light absorption increase and therefore a superior efficiency improvements than that of quarter-wavelength antireflection coating [31–33], as shown in Fig. 4(a)-(d). The recent theoretical investigations even report a high light trapping close to the Yablonovitch limit in the silicon solar cell by optimizing a

The biomimetic antireflection structures can also play a key role in light extraction of light-emitting devices (LEDs) [35–37]. Because of the total internal reflection and the waveguiding modes in the glass substrate, only about 20% amount of the generated light can irradiate from the LEDs. By fabricating silica cone arrays on the surfaces of the ITO glass substrate to modulate the above two bottleneck factors, the light luminance efficiency of white LEDs is significantly improved by a factor of 1.4 in the normal direction and even

Another fascinating application of the inspired antireflection structures is the use in the micro Sun sensor for Mars rovers [38]. On the basis of the recorded image by an active pixel sensor, the location coordinates of the rover can be calculated. However, the ghost image originating from the multiple internal reflection of the optical system leads to severe limitation of the accuracy. By fabricating dense nanotip arrays on the surfaces of the sensor, the internal reflection is minimized to be nearly 3 orders of magnitude lower than that of no treatments,

**(f)**

**(c)**

*2.1.3. Potential applications*

**Figure 3.** Cicada wing structure fabrication by NIL [19]. (a) Schematic diagram of NIL using cicada wings as bio-templates; (b) The fabricated structures and (c) the natural photonic structures show similar morphology from the SEM images.

Ar and H2 are responsible for the dry etching process. The SiC clusters then act as nanomasks or nanocaps to protect the underlying substrate from etching, thus forming an aperiodic array of silicon nanotips with their lengths varying from ∼1000 nm to ∼ 16 *μ*m finally (Fig. 2(b) and (c)). Even superior to natural prototypes, the biomimetic antireflection structures exhibit striking omnidirectional low reflection shown in Fig. 2(d) over a broad range of wavelengths from ultraviolet to terahertz region, irrespective of polarization.

Avoiding time-consuming and complicated mask fabrication, scientists also attempt to directly use cicada wings or insect eyes as bio-templates [19, 28, 29]. For example, the nipple arrays on wing surfaces are stamped under certain pressure on glass-phase PMMA, which is at higher degree than its glass-transition temperature, supported by silicon wafer. A release process makes the polymer reverse nanostructures of the bio-templates. With the patterned PMMA as a mask or a mold, inverse or similar structures of the cicada wing are achieved by RIE or thermodeposition. A schematic diagram of the NIL, the fabricated structures, and the natural templates for comparison are illustrated in Fig. 3(a), Fig. 3(b), and Fig. 3(c), respectively. It is also worthy to note that an extra advantage of using bio-templates in NIL process is the notable low-surface-tension, which is vital for the release process, due to the wax layer commonly found on surfaces of plants and insects.

Taking advantages of accurate thickness control and three-dimensional (3D) fabrication of ALD, conformal replica is accomplished after ALD growth and sintering the hybrid structures with fly eyes as bio-templates, achieving similar anti-reflective features in the artificial analog finally [29].

**Figure 4.** (Color online) Solar cells coating antireflection structures [32, 34]. (a) Nanodome solar cells in top view. Scale bar 500 nm; (b) Schematic diagram of the cross-sectional structures of the solar cells; (c) The photographs of nanodome solar cells (left) and flat film solar cells (right); (d) Dark and light I-V curve corresponding to (c); (e) and (f) The optimized double-sided nanostructure yields a photocurrent close to the Yablonovitch limit at an equivalent thickness of 2 *μ*m.

#### *2.1.3. Potential applications*

4 Will-be-set-by-IN-TECH

**Figure 3.** Cicada wing structure fabrication by NIL [19]. (a) Schematic diagram of NIL using cicada wings as bio-templates; (b) The fabricated structures and (c) the natural photonic structures show similar

from ultraviolet to terahertz region, irrespective of polarization.

wax layer commonly found on surfaces of plants and insects.

Ar and H2 are responsible for the dry etching process. The SiC clusters then act as nanomasks or nanocaps to protect the underlying substrate from etching, thus forming an aperiodic array of silicon nanotips with their lengths varying from ∼1000 nm to ∼ 16 *μ*m finally (Fig. 2(b) and (c)). Even superior to natural prototypes, the biomimetic antireflection structures exhibit striking omnidirectional low reflection shown in Fig. 2(d) over a broad range of wavelengths

Avoiding time-consuming and complicated mask fabrication, scientists also attempt to directly use cicada wings or insect eyes as bio-templates [19, 28, 29]. For example, the nipple arrays on wing surfaces are stamped under certain pressure on glass-phase PMMA, which is at higher degree than its glass-transition temperature, supported by silicon wafer. A release process makes the polymer reverse nanostructures of the bio-templates. With the patterned PMMA as a mask or a mold, inverse or similar structures of the cicada wing are achieved by RIE or thermodeposition. A schematic diagram of the NIL, the fabricated structures, and the natural templates for comparison are illustrated in Fig. 3(a), Fig. 3(b), and Fig. 3(c), respectively. It is also worthy to note that an extra advantage of using bio-templates in NIL process is the notable low-surface-tension, which is vital for the release process, due to the

Taking advantages of accurate thickness control and three-dimensional (3D) fabrication of ALD, conformal replica is accomplished after ALD growth and sintering the hybrid structures with fly eyes as bio-templates, achieving similar anti-reflective features in the artificial analog

morphology from the SEM images.

finally [29].

Due to the high reflectance of silicon solar cells (more than 30%) induced by the high index contrast of silicon and air according to the Fresnel equations, scientists are already aware of the vital roles of high-quality antireflection coatings at early ages of solar cell fabrications [30]. Inspired by antireflection structures found in moth eyes, nanodomes or similar architectures are reproduced on surfaces of solar cells, leading to a dramatic light absorption increase and therefore a superior efficiency improvements than that of quarter-wavelength antireflection coating [31–33], as shown in Fig. 4(a)-(d). The recent theoretical investigations even report a high light trapping close to the Yablonovitch limit in the silicon solar cell by optimizing a double-sided antireflection structure design (Fig. 4(e) and (f))[34].

The biomimetic antireflection structures can also play a key role in light extraction of light-emitting devices (LEDs) [35–37]. Because of the total internal reflection and the waveguiding modes in the glass substrate, only about 20% amount of the generated light can irradiate from the LEDs. By fabricating silica cone arrays on the surfaces of the ITO glass substrate to modulate the above two bottleneck factors, the light luminance efficiency of white LEDs is significantly improved by a factor of 1.4 in the normal direction and even larger enhancement for large viewing angles.

Another fascinating application of the inspired antireflection structures is the use in the micro Sun sensor for Mars rovers [38]. On the basis of the recorded image by an active pixel sensor, the location coordinates of the rover can be calculated. However, the ghost image originating from the multiple internal reflection of the optical system leads to severe limitation of the accuracy. By fabricating dense nanotip arrays on the surfaces of the sensor, the internal reflection is minimized to be nearly 3 orders of magnitude lower than that of no treatments, resulting in a more reliable three-axis attitude information.

#### 6 Will-be-set-by-IN-TECH 112 Optical Devices in Communication and Computation Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices <sup>7</sup>

(a) (b)

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 113

(c) (d)

**Figure 6.** (Color online) Structural color printing using 'M-Ink' [57]. (a) Three-phase material system of 'M-Ink'; (b) 'M-Ink' particles align in a chain under external magnetic field, which acts as basic coloration units of color pattern after fixing by UV light; (c) Reflection images of multicolored structural colors (upper) and transmission photographs of the same sample (below) by gradually increasing magnetic fields; (d) High-resolution multiple structural color patterns. Scale bars: (b) 1*μ*m, (c) and (d) 100 *μ*m.

*Dynastes hercules* which can alter their appearance from khaki-green to black providing the ambience changes from dry to a high humidity level [54–56] (Fig. 5(g) and (h)). The 3D photonic crystal structures (nanoporous structures) are filled with water instead of air voids in dry status, rendering different refraction index contrast and thus the variation of Bragg scattering (Fig. 5(i), here only 2D cross section is illustrated). However, the underlying physics of coloration change induced by high-dimensional photonic structures is no other than that of

Due to the obvious appearance changes which are easy to be picked up with the naked eye, color-tunable devices are explored to identify the status changes by temperature, vapor, solvent, humidity in ambience, the applied mechanical force, electric field, magnetic field and etc. Besides the sensors, some novel writing system ('paper and ink') are developed. The key idea is to modify period (*d*), refraction index (*n*), viewangle (*θ*) or their combinations of

Because of relatively simple control by the environmental stimuli and large spectral variation which can be recognized by the naked eye, approaches on the modulation of photonic structure period are always of scientist interests in obtaining tunable color applications.

'M-Ink' is a mixture of colloidal nanocrystal clusters (CNCs), solvent and photocurable resin (Fig. 6(a)). With the superparamagnetic Fe3O4 nanocrystals encapsulated by silica shell, 'M-Ink' can response to external magnetic fields. The role of the resin is to provide repulsive force which balances the attractive force of the CNCs. Without external magnetic fields, CNCs are randomly dispersed (infinite period) in liquid resin. The exhibited coloration is consistent with the magnetite, to be brown. After applying magnetic fields, the CNCs are assembled to form chain-like structures along the magnetic field lines (Fig. 6(b)). The additional magnetic force, the intrinsic force among the CNCs, and the repulsive force by resin

their 1D counterparts.

2.2.2.1. *d* variation

*2.2.2. Bio-inspired fabrications and applications*

photonic structures, just like nature shows us.

**Figure 5.** (Color online) Color tuning mechanisms found in nature [50, 53, 56]. The coloration of (a) longhorn beetles, (d) iridophore of tropic fish neon tetra, and (g) hercules beetles can reversibly change their coloration to (b), (e), and (h), which are intrinsically induced by (c) period *d*, (f) tilting angle *θ*, (i) refraction index *n* variation, respectively. Scale bars: (a) and (b) 10 mm, (d) and (e) 20 *μ*m.

#### **2.2. Color-tunable devices**

#### *2.2.1. Prototypes*

Besides the well known coloration change strategy via migrations and volumes change of pigment granules such as chameleons, nature develops a second approach which is known as structural coloration change (SCC). By varying photonic structure characterizations, incident light angle, or the refraction index contrast of the color-produced optical system via the environmental stimuli, reversible coloration changes, which are basically passive, are revealed in fishes, beetles, and birds [39–46]. Most structural basis of SCC are attributed to the one-dimensional (1D) reflectors. For example, the damselfish *Chrysiptera cyanea* can change its color from blue to ultraviolet rapidly under stressful conditions, which is triggered by the simultaneous change in the spacing of adjoining reflecting plates made of guanine in the iridophore cell [47–49]. In insect world, the coloration change of longhorn beetles *Tmesisternus isabellae* from golden to red is revealed to originate from the swollen multilayer after water absorption [50] (Fig. 5(a), (b) and (c)). Another origin of structural coloration change is the tilted angle variability of the nanoplates with respect to incident light, which is found in tropic fish neon tetra *Paracheirodon innesi* [51–53] (Fig. 5(d), (e), and (f)). Physically, the underlying mechanism of the coloration change in the mentioned 1D biological photonic structures can be understood according to the given formula

$$
\lambda\_{\max} = \mathcal{D}(n\_1 d\_1 \cos \theta\_1 + n\_2 d\_2 \cos \theta\_2),
\tag{3}
$$

where *d* is the layer thickness, *n* is refraction index, and *θ* is angle of refraction. The subscripts represent the layer index. The angle of refraction at different layers *θ*<sup>1</sup> and *θ*<sup>2</sup> can be obtained from Snell's law *n*1*sinθ*1=*n*1*sinθ*1=*sinθ*0, where *θ*<sup>0</sup> is the incident angle from air. From the equation, it is easy to elucidate that either *n*, *d*, or *θ*<sup>0</sup> is related to the optical path in the multilayer and thus leads to shifting interference peaks at different wavelengths.

In biological system, high-dimensional photonic structures responsible for the coloration change are also discovered, though they are rare. An intriguing example is hercules beetles 112 Optical Devices in Communication and Computation Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices <sup>7</sup> Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 113

**Figure 6.** (Color online) Structural color printing using 'M-Ink' [57]. (a) Three-phase material system of 'M-Ink'; (b) 'M-Ink' particles align in a chain under external magnetic field, which acts as basic coloration units of color pattern after fixing by UV light; (c) Reflection images of multicolored structural colors (upper) and transmission photographs of the same sample (below) by gradually increasing magnetic fields; (d) High-resolution multiple structural color patterns. Scale bars: (b) 1*μ*m, (c) and (d) 100 *μ*m.

*Dynastes hercules* which can alter their appearance from khaki-green to black providing the ambience changes from dry to a high humidity level [54–56] (Fig. 5(g) and (h)). The 3D photonic crystal structures (nanoporous structures) are filled with water instead of air voids in dry status, rendering different refraction index contrast and thus the variation of Bragg scattering (Fig. 5(i), here only 2D cross section is illustrated). However, the underlying physics of coloration change induced by high-dimensional photonic structures is no other than that of their 1D counterparts.

#### *2.2.2. Bio-inspired fabrications and applications*

Due to the obvious appearance changes which are easy to be picked up with the naked eye, color-tunable devices are explored to identify the status changes by temperature, vapor, solvent, humidity in ambience, the applied mechanical force, electric field, magnetic field and etc. Besides the sensors, some novel writing system ('paper and ink') are developed. The key idea is to modify period (*d*), refraction index (*n*), viewangle (*θ*) or their combinations of photonic structures, just like nature shows us.

#### 2.2.2.1. *d* variation

6 Will-be-set-by-IN-TECH

**platelet (f)**

**Figure 5.** (Color online) Color tuning mechanisms found in nature [50, 53, 56]. The coloration of (a) longhorn beetles, (d) iridophore of tropic fish neon tetra, and (g) hercules beetles can reversibly change their coloration to (b), (e), and (h), which are intrinsically induced by (c) period *d*, (f) tilting angle *θ*, (i)

Besides the well known coloration change strategy via migrations and volumes change of pigment granules such as chameleons, nature develops a second approach which is known as structural coloration change (SCC). By varying photonic structure characterizations, incident light angle, or the refraction index contrast of the color-produced optical system via the environmental stimuli, reversible coloration changes, which are basically passive, are revealed in fishes, beetles, and birds [39–46]. Most structural basis of SCC are attributed to the one-dimensional (1D) reflectors. For example, the damselfish *Chrysiptera cyanea* can change its color from blue to ultraviolet rapidly under stressful conditions, which is triggered by the simultaneous change in the spacing of adjoining reflecting plates made of guanine in the iridophore cell [47–49]. In insect world, the coloration change of longhorn beetles *Tmesisternus isabellae* from golden to red is revealed to originate from the swollen multilayer after water absorption [50] (Fig. 5(a), (b) and (c)). Another origin of structural coloration change is the tilted angle variability of the nanoplates with respect to incident light, which is found in tropic fish neon tetra *Paracheirodon innesi* [51–53] (Fig. 5(d), (e), and (f)). Physically, the underlying mechanism of the coloration change in the mentioned 1D biological photonic structures can

where *d* is the layer thickness, *n* is refraction index, and *θ* is angle of refraction. The subscripts represent the layer index. The angle of refraction at different layers *θ*<sup>1</sup> and *θ*<sup>2</sup> can be obtained from Snell's law *n*1*sinθ*1=*n*1*sinθ*1=*sinθ*0, where *θ*<sup>0</sup> is the incident angle from air. From the equation, it is easy to elucidate that either *n*, *d*, or *θ*<sup>0</sup> is related to the optical path in the

In biological system, high-dimensional photonic structures responsible for the coloration change are also discovered, though they are rare. An intriguing example is hercules beetles

multilayer and thus leads to shifting interference peaks at different wavelengths.

refraction index *n* variation, respectively. Scale bars: (a) and (b) 10 mm, (d) and (e) 20 *μ*m.

**(c)**

**(d) (e)**

**2.2. Color-tunable devices**

be understood according to the given formula

*2.2.1. Prototypes*

**(a) (b)**

**(g) (h) (i)**

*d* **variation**

θ**variation**

*n* **variation**

*λmax* = 2(*n*1*d*1*cosθ*<sup>1</sup> + *n*2*d*2*cosθ*2), (3)

θ1 θ2

Because of relatively simple control by the environmental stimuli and large spectral variation which can be recognized by the naked eye, approaches on the modulation of photonic structure period are always of scientist interests in obtaining tunable color applications.

'M-Ink' is a mixture of colloidal nanocrystal clusters (CNCs), solvent and photocurable resin (Fig. 6(a)). With the superparamagnetic Fe3O4 nanocrystals encapsulated by silica shell, 'M-Ink' can response to external magnetic fields. The role of the resin is to provide repulsive force which balances the attractive force of the CNCs. Without external magnetic fields, CNCs are randomly dispersed (infinite period) in liquid resin. The exhibited coloration is consistent with the magnetite, to be brown. After applying magnetic fields, the CNCs are assembled to form chain-like structures along the magnetic field lines (Fig. 6(b)). The additional magnetic force, the intrinsic force among the CNCs, and the repulsive force by resin

#### 8 Will-be-set-by-IN-TECH 114 Optical Devices in Communication and Computation Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices <sup>9</sup>

establish dynamic balance with variation of the external magnetic fields, tuning the distance between the neighboring CNC (finite period). The switchable period then determines the color of the light diffracted from the CNC chain, leading to a full color show (Fig. 6(c)). The final step is to fix the desired coloration. After exposure to ultraviolet (UV) light at different exerted magnetic fields locations, the chain-like CNCs can be frozen in the solidified resin instantaneously, remaining the periods of the chains undistorted and accomplishing high-resolution color pattern fabrication (Fig. 6(d)) [57].

**(a)**

**(c)**

black line) with the PL peak (grey filled curve).

organic/inorganic vapors.

2.2.2.2. *n* variation

recent reviews [14, 15, 61, 71–74].

**(b)**

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 115

**Figure 7.** (Color online) From color fingerprinting to the control of photoluminescence in EPC films [67]. (a) Schematic diagram of the elastic inverse opal structure fabrication; (b) A captured still image of the EPC film under compression by an index finger; (c) NIR-emitting PL emission of colloidal PbS quantum dots which are incorporated into voids of the EPC can be tuned by overlapping the forbidden gap (solid

closely packed PS and polymer elastomer (colloids and PDMS), the exhibited coloration can be altered reversely by immersing the materials into silicone liquid ('writing process') and an evaporation process ('erasing process'). The spacing between the (111) planes is adjusted by the strength of interaction between PDMS matrix and the contained silicone oligomers with different molecule weight in the liquid. With different solvents ('ink'), the swelling and shrinkage of the matrix show a featured reversible shift of Bragg diffraction peak. A multilayer based on alternating Teflon-like layer and Au nanoparticle/Teflon-like layer composite layer operates not in visible but optical telecommunication wavelength range [70]. When the structure is exposed to different organic solvent vapor (e.g. acetone, ethanol, methanol, water, chloroform, and etc.), the molecules enter the metal/polymer composite inside the holes and microvoids in its structure, resulting in the swelling up, e.g., for acetone vapors at a molar fraction of 0.25, with an relative increase of 12.5% in thickness to an equilibrium state while leaving the Teflon-like layer unchanged due to its inert chemical features. The measured reflectance show a large variation of 0.2 *μ*m, which is advantageous to the detection of the

Other external stimuli such as UV light, heat, or chemical reaction are applied to trigger and fabricate coloration sensitive materials as well by reversely controlling the spacing of the responsible photonic structures. Detailed information can be found in some references and

Besides *d*, the refraction index *n* is another attribute of photonic structures. Different approaches to alter refraction index, in which infiltration is most regular, are revealed in order to achieve novel visual applications. Inspired by beetles *D. hercules*, 3D nanoporous structures are fabricated by so-called dip-coating deposition, achieving humidity sensing [75]. The 3D architecture, which is inverse opal structure, is reported to have its reflective peak

With similar principle, the electric field-driven tunable color sensor is also realized by highly charged polystyrene (PS) colloids which form non-close-packed face-centered cubic (fcc) lattice [58]. Tuning the period along [111] direction by the balance of the exerted electrostatic force and the repulsive force, the exhibited coloration changes as a result of the applied electric field. The so-called 'P-Ink' is an electroactive material which consists of inverse opal inside polyferrocenylsilane (PFS) derivatives matrix. Such ink fabrication includes 3 primary steps: An opal film made of silica spheres is deposited onto glass substrate first by self-assembly; UV light is exposed to the sample in order to solidify the matrix and then form a stable PFS/silica composite; With diluted HF, inverse opal structure are realized in the elastomeric polymer matrix. By applying tunable voltage, macroscopic swelling and shrinking of the polymer matrix and microscopic Bravais lattice change responsible for the reverse coloration occur [59]. Stimulated by electrical forces, quite a few switchable coloration devices or sensors based on other materials or circumstances can be found elsewhere [60–62].

Many pressure-based photonic and even laser devices are reported [63–66]. Using monodispersed PS spheres to form cubic close packing (ccp) structures which are embedded in polydimethylsiloxane (PDMS) matrix, reverse colors are observed simply by stretching and releasing the rubber sheet. Upon mechanical stress, the lattice is elongated along the applied force direction, while the interplanar spacing in the perpendicular direction (i.e. distance between the (111) planes) decreases because of the nearly invariance volume of the rubber. The compressed distance leads to a blue-shift, e.g., from red to green [63]. Such opal rubber is believed to have practical applications such as a color indicator, tension meter or elongation strain sensor. The inverse opal structures (filled by air voids) in elastomer network are also synthesized [64, 67] (Fig. 7(a)). The porous elastomeric photonic crystals (EPCs) show highly reversible optical response to compressive force, e.g., 60 nm spectral blue-shift under a compressive pressure of ∼ 15 kPa in the structures having 350-nm void size. Although the coloration change can be attributed to the Bravais lattice deformability, like the mechanism mentioned before. However, it is especially noteworthy that porous EPCs remain nearly undeformed in orthogonal directions when an external pressure is exerted in one direction, which can be ascribed to the high filling factor of air voids. The air voids enable the distortion of the cross-sectional void spaces from roughly circular to elliptical shape and a reduction of the air volume fraction under pressure. The elastic deformation feature of such structures helps to reduce the redistribution of stress along lateral directions when compressed by a patterned surface, leading to novel biometric applications such as the fingerprint recognition devices, as shown in Fig. 7(b). Additionally, air voids of porous EPCs provide a platform to incorporate with other functional materials for us to explore new applications. For instance, filling PbS quantum dots in the air voids, the photoluminescence (PL) emission, which leads to many potential applications in the near-infrared region, can be modified by overlapping with the forbidden bandgap of the inverse opal structures (Fig. 7(c)).

The chemical solvents are also used to be as stimuli. An interesting example is invention of new type 'photonic paper/ink' system [68, 69]. With novel soft materials consisting of

**Figure 7.** (Color online) From color fingerprinting to the control of photoluminescence in EPC films [67]. (a) Schematic diagram of the elastic inverse opal structure fabrication; (b) A captured still image of the EPC film under compression by an index finger; (c) NIR-emitting PL emission of colloidal PbS quantum dots which are incorporated into voids of the EPC can be tuned by overlapping the forbidden gap (solid black line) with the PL peak (grey filled curve).

closely packed PS and polymer elastomer (colloids and PDMS), the exhibited coloration can be altered reversely by immersing the materials into silicone liquid ('writing process') and an evaporation process ('erasing process'). The spacing between the (111) planes is adjusted by the strength of interaction between PDMS matrix and the contained silicone oligomers with different molecule weight in the liquid. With different solvents ('ink'), the swelling and shrinkage of the matrix show a featured reversible shift of Bragg diffraction peak. A multilayer based on alternating Teflon-like layer and Au nanoparticle/Teflon-like layer composite layer operates not in visible but optical telecommunication wavelength range [70]. When the structure is exposed to different organic solvent vapor (e.g. acetone, ethanol, methanol, water, chloroform, and etc.), the molecules enter the metal/polymer composite inside the holes and microvoids in its structure, resulting in the swelling up, e.g., for acetone vapors at a molar fraction of 0.25, with an relative increase of 12.5% in thickness to an equilibrium state while leaving the Teflon-like layer unchanged due to its inert chemical features. The measured reflectance show a large variation of 0.2 *μ*m, which is advantageous to the detection of the organic/inorganic vapors.

Other external stimuli such as UV light, heat, or chemical reaction are applied to trigger and fabricate coloration sensitive materials as well by reversely controlling the spacing of the responsible photonic structures. Detailed information can be found in some references and recent reviews [14, 15, 61, 71–74].

#### 2.2.2.2. *n* variation

8 Will-be-set-by-IN-TECH

establish dynamic balance with variation of the external magnetic fields, tuning the distance between the neighboring CNC (finite period). The switchable period then determines the color of the light diffracted from the CNC chain, leading to a full color show (Fig. 6(c)). The final step is to fix the desired coloration. After exposure to ultraviolet (UV) light at different exerted magnetic fields locations, the chain-like CNCs can be frozen in the solidified resin instantaneously, remaining the periods of the chains undistorted and accomplishing

With similar principle, the electric field-driven tunable color sensor is also realized by highly charged polystyrene (PS) colloids which form non-close-packed face-centered cubic (fcc) lattice [58]. Tuning the period along [111] direction by the balance of the exerted electrostatic force and the repulsive force, the exhibited coloration changes as a result of the applied electric field. The so-called 'P-Ink' is an electroactive material which consists of inverse opal inside polyferrocenylsilane (PFS) derivatives matrix. Such ink fabrication includes 3 primary steps: An opal film made of silica spheres is deposited onto glass substrate first by self-assembly; UV light is exposed to the sample in order to solidify the matrix and then form a stable PFS/silica composite; With diluted HF, inverse opal structure are realized in the elastomeric polymer matrix. By applying tunable voltage, macroscopic swelling and shrinking of the polymer matrix and microscopic Bravais lattice change responsible for the reverse coloration occur [59]. Stimulated by electrical forces, quite a few switchable coloration devices or sensors based on

Many pressure-based photonic and even laser devices are reported [63–66]. Using monodispersed PS spheres to form cubic close packing (ccp) structures which are embedded in polydimethylsiloxane (PDMS) matrix, reverse colors are observed simply by stretching and releasing the rubber sheet. Upon mechanical stress, the lattice is elongated along the applied force direction, while the interplanar spacing in the perpendicular direction (i.e. distance between the (111) planes) decreases because of the nearly invariance volume of the rubber. The compressed distance leads to a blue-shift, e.g., from red to green [63]. Such opal rubber is believed to have practical applications such as a color indicator, tension meter or elongation strain sensor. The inverse opal structures (filled by air voids) in elastomer network are also synthesized [64, 67] (Fig. 7(a)). The porous elastomeric photonic crystals (EPCs) show highly reversible optical response to compressive force, e.g., 60 nm spectral blue-shift under a compressive pressure of ∼ 15 kPa in the structures having 350-nm void size. Although the coloration change can be attributed to the Bravais lattice deformability, like the mechanism mentioned before. However, it is especially noteworthy that porous EPCs remain nearly undeformed in orthogonal directions when an external pressure is exerted in one direction, which can be ascribed to the high filling factor of air voids. The air voids enable the distortion of the cross-sectional void spaces from roughly circular to elliptical shape and a reduction of the air volume fraction under pressure. The elastic deformation feature of such structures helps to reduce the redistribution of stress along lateral directions when compressed by a patterned surface, leading to novel biometric applications such as the fingerprint recognition devices, as shown in Fig. 7(b). Additionally, air voids of porous EPCs provide a platform to incorporate with other functional materials for us to explore new applications. For instance, filling PbS quantum dots in the air voids, the photoluminescence (PL) emission, which leads to many potential applications in the near-infrared region, can be modified by overlapping

high-resolution color pattern fabrication (Fig. 6(d)) [57].

other materials or circumstances can be found elsewhere [60–62].

with the forbidden bandgap of the inverse opal structures (Fig. 7(c)).

The chemical solvents are also used to be as stimuli. An interesting example is invention of new type 'photonic paper/ink' system [68, 69]. With novel soft materials consisting of Besides *d*, the refraction index *n* is another attribute of photonic structures. Different approaches to alter refraction index, in which infiltration is most regular, are revealed in order to achieve novel visual applications. Inspired by beetles *D. hercules*, 3D nanoporous structures are fabricated by so-called dip-coating deposition, achieving humidity sensing [75]. The 3D architecture, which is inverse opal structure, is reported to have its reflective peak

#### 10 Will-be-set-by-IN-TECH 116 Optical Devices in Communication and Computation Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices <sup>11</sup>

**(a)**

**(c)**

**(d)**

photographs of 'on' and 'off' states are (a), (c), (e), and (b), (d), (f), respectively.

**2.3. Structural color mixing and applications**

*2.3.1. Prototypes*

**Figure 9.** (Color online) Magnetochromatic microspheres switched between 'on' and 'off' states by rotating external fields [84, 85]. Schematic illustrations, optical images, and the corresponding SEM

perceived coloration is changing. Hence, it is feasible to explore novel tunable color devices by tuning orientations of the photonic structures [84–86]. Just like the fish neon tetra *P. innesi*, magnetochromatic microspheres alter their appearance by tilting the inner photonic structures with respect to the incidence (Fig. 9). As mentioned before, with superparamagnetic Fe3O4 particles coated by silica in PEGDA emulsions, the applied magnetic field guides to form photonic chains, in which the interpaticle distances depend on the balance of the attractive and repulsive force. Polymerized by UV light, microspheres are solidified and the inner periodic photonic chains, which give rise to structural coloration, are fixed permanently. Dispersing the microspheres into liquids, various colors are observed in top view due to the random orientations of the photonic chains in the microspheres. By applying external magnetic fields, the microspheres tend to rotate in order to keep the magnetic chains inside in the direction of the magnetic vector, leading to a homogenous coloration of green exhibited. The feature of the switchable coloration 'on' and 'off' status by the external stimuli is believed to have applications in color display, signage, bio- and chemical detection, and magnetic field sensing.

Structural coloration results from the interaction of light and photonic structures with featured size of visible wavelengths. It is even more widespread than pigmentary coloration in animal world. Some literatures have well reviewed the field comprehensively. In the Chapter, we do not plan to pay attention to the overall structural coloration but only focus on a specific subject 'structural color mixing' [87–92]. In tiger beetles *Cicindela oregona*(Fig. 10(a)-(c)) [87, 88], the honeycomb-like pits are found on surfaces of the elytra. Under microscope, the brown morph actually includes blue-green patches in the red background, while the black one consists of magenta patterns surrounded by dull green. The microscopic colors are the results of

**(e)**

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 117

**(f)**

**(b)**

**Figure 8.** (Color online) Silica inverse opal films of 'Watermark-Ink' system [76]. (a) Schematic procedure of chemical encoding; (b) SEM images of the fabricated inverse opal structures in cross-sectional view (left) and top view (right); (c) Optical images of the fabricated film in which the word 'W-INK' is encoded via functional chemical groups on surfaces. (d) Optical images of different encoded patterns under different solvents.

red-shifting 14 nm when the relative humidity changes from 25% to 98%. It is worth noting that after treatments by O2 plasma, the 3D photonic structures exhibit large bandgap shift of 137 nm and dramatic coloration change from bluish green in dry state to red in fully wet state. The modified hydrophilic feature play an important role in water collection in air voids at different level of humidity, leading to larger variation of refraction index contrast. The other clew for the remarkable coloration change can be ascribed to the high filling factor of air voids of inverse opal structures. The high value of ∼ 76% results in a wider modulation of refraction index contrast by the amount of solvent absorption. Tuning hydrophilic features by chemical groups, the inverse opal film can even be used as 'Watermark-Ink' system [76]. In the studies, the inside porous structures are functionalized with chemical group (*R*1, *R*2, *R*3, or *R*4) through vaporizing an alkylchlorosilane. The chemical functionalities of the structures then are erased and the surface is reactivated by *O*<sup>2</sup> plasma exposure, leaving a patterned functionalized region where is masked by a PDMS polymer. With iterations of such kind of functionalization and reactivation, the opal structures are locally patterned by different chemical groups, leading to differentiate hydrophilic feature (Fig. 8(a) and (b)). When immersing the film into specific fluids, regulated infiltration by the wettability occurs spatially in the film and thus surveys different optical responses (i.e. different patterns, Fig. 8(c) and (d)). The fabricated structures are expected to have applications in encryption as well as colorimeter.

Besides infiltration, phase-transition materials can also induce refraction index variation and switchable coloration, providing the transition conditions are satisfied. The best-known phase-transition material maybe is liquid crystals (LCs). Above the phase-transition temperature of 34◦, LCs change their nematic phase which is anisotropic to isotropic phase, leading to a significant change of refraction index and coloration, e.g., in inverse opal structures. By mixing the active material into LCs, sensitive reflection and polarization triggered by UV light are reported by a series of subsequent researches [77–79]. Besides LCs, various sensitive materials, including Ag2Se, W*O*<sup>3</sup> and ferroelectric ceramics, are also found functionally in incorporating with diversified photonic structures to obtain tunable structural coloration materials and thus fabricate thermo- or electro-sensors [80–83].

#### 2.2.2.3. *θ* variation

Iridescence is a characteristic of structural coloration, which is determined by band dispersions of photonic structures. With various incident angle or observation direction, the

**Figure 9.** (Color online) Magnetochromatic microspheres switched between 'on' and 'off' states by rotating external fields [84, 85]. Schematic illustrations, optical images, and the corresponding SEM photographs of 'on' and 'off' states are (a), (c), (e), and (b), (d), (f), respectively.

perceived coloration is changing. Hence, it is feasible to explore novel tunable color devices by tuning orientations of the photonic structures [84–86]. Just like the fish neon tetra *P. innesi*, magnetochromatic microspheres alter their appearance by tilting the inner photonic structures with respect to the incidence (Fig. 9). As mentioned before, with superparamagnetic Fe3O4 particles coated by silica in PEGDA emulsions, the applied magnetic field guides to form photonic chains, in which the interpaticle distances depend on the balance of the attractive and repulsive force. Polymerized by UV light, microspheres are solidified and the inner periodic photonic chains, which give rise to structural coloration, are fixed permanently. Dispersing the microspheres into liquids, various colors are observed in top view due to the random orientations of the photonic chains in the microspheres. By applying external magnetic fields, the microspheres tend to rotate in order to keep the magnetic chains inside in the direction of the magnetic vector, leading to a homogenous coloration of green exhibited. The feature of the switchable coloration 'on' and 'off' status by the external stimuli is believed to have applications in color display, signage, bio- and chemical detection, and magnetic field sensing.

#### **2.3. Structural color mixing and applications**

#### *2.3.1. Prototypes*

10 Will-be-set-by-IN-TECH

**Figure 8.** (Color online) Silica inverse opal films of 'Watermark-Ink' system [76]. (a) Schematic procedure of chemical encoding; (b) SEM images of the fabricated inverse opal structures in cross-sectional view (left) and top view (right); (c) Optical images of the fabricated film in which the word 'W-INK' is encoded via functional chemical groups on surfaces. (d) Optical images of different

red-shifting 14 nm when the relative humidity changes from 25% to 98%. It is worth noting that after treatments by O2 plasma, the 3D photonic structures exhibit large bandgap shift of 137 nm and dramatic coloration change from bluish green in dry state to red in fully wet state. The modified hydrophilic feature play an important role in water collection in air voids at different level of humidity, leading to larger variation of refraction index contrast. The other clew for the remarkable coloration change can be ascribed to the high filling factor of air voids of inverse opal structures. The high value of ∼ 76% results in a wider modulation of refraction index contrast by the amount of solvent absorption. Tuning hydrophilic features by chemical groups, the inverse opal film can even be used as 'Watermark-Ink' system [76]. In the studies, the inside porous structures are functionalized with chemical group (*R*1, *R*2, *R*3, or *R*4) through vaporizing an alkylchlorosilane. The chemical functionalities of the structures then are erased and the surface is reactivated by *O*<sup>2</sup> plasma exposure, leaving a patterned functionalized region where is masked by a PDMS polymer. With iterations of such kind of functionalization and reactivation, the opal structures are locally patterned by different chemical groups, leading to differentiate hydrophilic feature (Fig. 8(a) and (b)). When immersing the film into specific fluids, regulated infiltration by the wettability occurs spatially in the film and thus surveys different optical responses (i.e. different patterns, Fig. 8(c) and (d)). The fabricated structures are expected to have applications in encryption as well

Besides infiltration, phase-transition materials can also induce refraction index variation and switchable coloration, providing the transition conditions are satisfied. The best-known phase-transition material maybe is liquid crystals (LCs). Above the phase-transition temperature of 34◦, LCs change their nematic phase which is anisotropic to isotropic phase, leading to a significant change of refraction index and coloration, e.g., in inverse opal structures. By mixing the active material into LCs, sensitive reflection and polarization triggered by UV light are reported by a series of subsequent researches [77–79]. Besides LCs, various sensitive materials, including Ag2Se, W*O*<sup>3</sup> and ferroelectric ceramics, are also found functionally in incorporating with diversified photonic structures to obtain tunable structural

Iridescence is a characteristic of structural coloration, which is determined by band dispersions of photonic structures. With various incident angle or observation direction, the

coloration materials and thus fabricate thermo- or electro-sensors [80–83].

(c) (d)

(a)

(b)

encoded patterns under different solvents.

as colorimeter.

2.2.2.3. *θ* variation

Structural coloration results from the interaction of light and photonic structures with featured size of visible wavelengths. It is even more widespread than pigmentary coloration in animal world. Some literatures have well reviewed the field comprehensively. In the Chapter, we do not plan to pay attention to the overall structural coloration but only focus on a specific subject 'structural color mixing' [87–92]. In tiger beetles *Cicindela oregona*(Fig. 10(a)-(c)) [87, 88], the honeycomb-like pits are found on surfaces of the elytra. Under microscope, the brown morph actually includes blue-green patches in the red background, while the black one consists of magenta patterns surrounded by dull green. The microscopic colors are the results of

**5** μ**m**

**(a) (b) (c) (d)**

**Figure 11.** (Color online) Mixed structural coloration and applications inspired by nature [95]. (a) Schematic diagram of artificial samples mimicking the scale structures of *P. blumei*; (b) SEM photographs in top view show the concavities on surface of the replica which is (c) green macroscopically but (d) resolved yellow and green microscopically; (e) Modifications of the concavities morphology by melting colloidal spheres embedded in the concavities lead to a striking change in color of the sample from blue to red viewed (f) in direct specular reflection and (g) in retro-reflection. Scales: (a) 2 *μ*m, (c)(f)(g) 5 mm,

orthogonal direction. The nanostructures having different magnitude in size therefore cancel

Structural coloration may be especially crucial for future color and related industry because of the non-fading feature (if the photonic structures are undeformed) [93, 94] and environmental friendliness. Naturally, structural coloration mixing inherits the advantages. Mimicking the nature, mixed structural color and its application can be obtained. For example, PS colloids with a diameter of 5 *μ*m are assembled on a gold-coated silicon substrate. A 2.5-*μ*m-thick layer of platinum or gold is then deposited to fill the interspaces of the colloids by electrochemical approach, creating a negative replica. After removal of the PS colloids by ultrasonic waves and a sputtering thin carbon film, a multilayer of quarter-wave titania and alumina films is grown by ALD (Fig. 11(a)), inheriting the morphology of hexagonally arranged pits of the negative replica (Fig. 11(b)). The sample exhibits similar color mixing with that of butterflies *P. blumei* (Fig. 11(c) and (d)). Moreover, by modifying the surface morphology of the imitation (Fig. 11(e)), even visual information, e.g., a picture, can be encoded into the photonic structures which display a striking appearance change from pale blue in the specular direction to red in retro-reflection (Fig. 11(f) and (g)). The bio-inspired work is expected to find applications in

Inspired by color mixing researches, some novel applications based on polarization conversion are designed [89]. For instance, by etching periodic triangular-like grooves on surfaces of a flat multilayer, the film displays a coloration of green, which is actually a mixed color from yellow in the flat region and blue in the grooves in normal incidence, as shown in Fig. 12(e). Because of the broken symmetry of the 1D structures, the blue color can be suppressed by using a polarizer on light path, leading to the exhibited coloration change to

out the macroscopic polarization effects (Fig. 12(a)-(d)) [89].

security labelling field or color industry such as painting and coating [95].

*2.3.2. Bio-inspired fabrications and applications*

and (e) 5*μ*m.

**(e) (f) (g)**

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 119

**Figure 10.** (Color online) Structural Color Mixing in Nature [87, 90, 91]. Photographs, optical microscopy and SEM images of tiger beetles *C. oregona* ((a), (b), (c)), long-jointed beetles *C. obscuripennis* ((d), (e), (f)), and swallowtail butterflies *P. palinurus* ((g), (h), (i)), respectively.

light interference by the multilayer structures in the cuticle. However, due to the colored patches (40-80 *μ*m across) are too small to be resolved by the unaided eye (the resolution *d* is determined by the Rayleigh criterion *d*=*l*×0.61*λ*/*D*, where *l* is distance of distinct vision, *λ* the wavelength and *D* the average pupil diameter of humankind), the perceived coloration is a mixture of the discrete colors, leading to a totally different exhibition from that equipped with microscope. From the investigations of photonic structures of beetles *Chlorophila obscuripennis* (Fig. 10(d)-(f)), we revealed the color is a juxtaposition in a smaller region (<sup>∼</sup> <sup>10</sup>×<sup>10</sup> *<sup>μ</sup>*m2) by green on the ridges and cyan in centers of the pits. Furthermore, the pits on the elytra surface give rise to diffused light reflected over a wide large of angles, leading to inconspicuous coloration shown [91]. In butterflies *Papilio palinurus* (Fig. 10(g)-(i)), the scanning electronic micrographs show surfaces in the scales comprise a similar two-dimensional (2D) pits (4-6 *μ*m in diameter and 3 *μ*m at the greatest depth). The flat regions between and in pits appear yellow, and the inclined region contributes to blue color. Because of the limitation of human eyes' resolution, the butterfly displays a mixture color of green, i.e. yellow plus blue turns to be green. Due to sufficient depth of the pits, light which normally incidents on the inclined side can experience dual reflection and is back-reflected. The retro-reflection is found to play a key role in the polarization conversion of incident light, which is crucial in some novel optical applications. Thanks to symmetric feature of the pits, no macroscopic polarization effects can be observed [90]. On the cover scale surfaces of butterflies *Suneve coronata*, however, the natural occurring triangular grooves array not symmetric but in 1D way with a period of ∼ 2 *μ*m, giving rise to polarization conversion of the normal incident light in a specific direction. Intriguingly, it is revealed the coloration macroscopically remains unconscious change under different polarized illumination. The reason is the curly scales, which induce polarization conversion between the neighboring rows of scales but in the

**Figure 11.** (Color online) Mixed structural coloration and applications inspired by nature [95]. (a) Schematic diagram of artificial samples mimicking the scale structures of *P. blumei*; (b) SEM photographs in top view show the concavities on surface of the replica which is (c) green macroscopically but (d) resolved yellow and green microscopically; (e) Modifications of the concavities morphology by melting colloidal spheres embedded in the concavities lead to a striking change in color of the sample from blue to red viewed (f) in direct specular reflection and (g) in retro-reflection. Scales: (a) 2 *μ*m, (c)(f)(g) 5 mm, and (e) 5*μ*m.

orthogonal direction. The nanostructures having different magnitude in size therefore cancel out the macroscopic polarization effects (Fig. 12(a)-(d)) [89].

#### *2.3.2. Bio-inspired fabrications and applications*

12 Will-be-set-by-IN-TECH **5** μ**m**

**(a) (b) (c)**

**(d) (e) (f)**

**(g) (h) (i)**

**Figure 10.** (Color online) Structural Color Mixing in Nature [87, 90, 91]. Photographs, optical

((d), (e), (f)), and swallowtail butterflies *P. palinurus* ((g), (h), (i)), respectively.

microscopy and SEM images of tiger beetles *C. oregona* ((a), (b), (c)), long-jointed beetles *C. obscuripennis*

light interference by the multilayer structures in the cuticle. However, due to the colored patches (40-80 *μ*m across) are too small to be resolved by the unaided eye (the resolution *d* is determined by the Rayleigh criterion *d*=*l*×0.61*λ*/*D*, where *l* is distance of distinct vision, *λ* the wavelength and *D* the average pupil diameter of humankind), the perceived coloration is a mixture of the discrete colors, leading to a totally different exhibition from that equipped with microscope. From the investigations of photonic structures of beetles *Chlorophila obscuripennis* (Fig. 10(d)-(f)), we revealed the color is a juxtaposition in a smaller region (<sup>∼</sup> <sup>10</sup>×<sup>10</sup> *<sup>μ</sup>*m2) by green on the ridges and cyan in centers of the pits. Furthermore, the pits on the elytra surface give rise to diffused light reflected over a wide large of angles, leading to inconspicuous coloration shown [91]. In butterflies *Papilio palinurus* (Fig. 10(g)-(i)), the scanning electronic micrographs show surfaces in the scales comprise a similar two-dimensional (2D) pits (4-6 *μ*m in diameter and 3 *μ*m at the greatest depth). The flat regions between and in pits appear yellow, and the inclined region contributes to blue color. Because of the limitation of human eyes' resolution, the butterfly displays a mixture color of green, i.e. yellow plus blue turns to be green. Due to sufficient depth of the pits, light which normally incidents on the inclined side can experience dual reflection and is back-reflected. The retro-reflection is found to play a key role in the polarization conversion of incident light, which is crucial in some novel optical applications. Thanks to symmetric feature of the pits, no macroscopic polarization effects can be observed [90]. On the cover scale surfaces of butterflies *Suneve coronata*, however, the natural occurring triangular grooves array not symmetric but in 1D way with a period of ∼ 2 *μ*m, giving rise to polarization conversion of the normal incident light in a specific direction. Intriguingly, it is revealed the coloration macroscopically remains unconscious change under different polarized illumination. The reason is the curly scales, which induce polarization conversion between the neighboring rows of scales but in the

**100** μ**m**

**10** μ**m**

**10** μ**m**

**12** μ**m**

> Structural coloration may be especially crucial for future color and related industry because of the non-fading feature (if the photonic structures are undeformed) [93, 94] and environmental friendliness. Naturally, structural coloration mixing inherits the advantages. Mimicking the nature, mixed structural color and its application can be obtained. For example, PS colloids with a diameter of 5 *μ*m are assembled on a gold-coated silicon substrate. A 2.5-*μ*m-thick layer of platinum or gold is then deposited to fill the interspaces of the colloids by electrochemical approach, creating a negative replica. After removal of the PS colloids by ultrasonic waves and a sputtering thin carbon film, a multilayer of quarter-wave titania and alumina films is grown by ALD (Fig. 11(a)), inheriting the morphology of hexagonally arranged pits of the negative replica (Fig. 11(b)). The sample exhibits similar color mixing with that of butterflies *P. blumei* (Fig. 11(c) and (d)). Moreover, by modifying the surface morphology of the imitation (Fig. 11(e)), even visual information, e.g., a picture, can be encoded into the photonic structures which display a striking appearance change from pale blue in the specular direction to red in retro-reflection (Fig. 11(f) and (g)). The bio-inspired work is expected to find applications in security labelling field or color industry such as painting and coating [95].

> Inspired by color mixing researches, some novel applications based on polarization conversion are designed [89]. For instance, by etching periodic triangular-like grooves on surfaces of a flat multilayer, the film displays a coloration of green, which is actually a mixed color from yellow in the flat region and blue in the grooves in normal incidence, as shown in Fig. 12(e). Because of the broken symmetry of the 1D structures, the blue color can be suppressed by using a polarizer on light path, leading to the exhibited coloration change to

at the ultra-negative angular dispersion of diffraction and potential novel dispersive optical

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices 121

In the Chapter, several important kinds of bio-inspired photonic applications are reviewed, including antireflection devices, color-tunable sensors, structural color mixing applications and etc. The nature nourishes scientists the functional optical applications either the blueprints of photonic architecture or directly the bio-templates. Due to the higher index of inorganic materials used, the mimicking photonic structures even show better optical performances as well as enhanced mechanical properties of high temperature tolerance, stability and infrangibility. The biomimetic applications are anticipated to help our life better in the near future. However, complicated photonic structures (e.g. those of high-dimensional, hierarchic, amorphous features in nature) still remains hardly reproduced or, if they are fabricated successfully, the efforts involved are so great using the traditional fabrication ways that optical devices can not commercially explored. Thorough physical mechanism understanding as well as better fabrication approach explorations may help to simply the structure fabrications, achieve similar optical functions and realize commercial applications. In addition, adding substances such as functional chemical groups, fluorescence particles, metal, or other active materials, the mimicking photonic structures allow the properties of interest to be augmented, which may open a new window of novel optical device exploration. Although the photonic biomimicry is in its infancy, we believe that the bio-inspired optical

*Laboratory of Opto-electrical Material and Device, Department of Physics, Shanghai Normal*

[1] Yablonovitch, E. (1987). Inhibited Spontaneous Emission in Solid-State Physics and

[2] John, S. (1987). Strong localization of photons in certain disordered dielectric

[3] Joannopoulos, J.D.; Johnson, S.G.; Winn J.N.; & Meade, R.D. (2008). *Photonic Crystals: Molding the Flow of Light*, 2nd Ed. Princeton University Press, Princeton and Oxford,

[4] Fox, D.L. (1976). *Animal Biochromes and Structural Colours*, University of California Press,

[5] Srinivasarao, M. (1999). Nano-Optics in the biological world: beetles, butterflies, birds,

device would surely have profound impacts on our modern society.

*Department of Mechanical Engineering, Northwestern University, Evanston, USA*

*Department of Physics, Fudan University, Shanghai, China*

Electronics. *Phys. Rev. Lett.*, Vol.58: 2059–2062.

superlattices. *Phys. Rev. Lett.*, Vol.58: 2486–2489.

and moths. *Chem. Rev.*, Vol.99: 1935–1961.

elements.

**3. Perspectives**

**Author details**

*University, Shanghai, China*

Feng Liu

Biqin Dong

Xiaohan Liu

**4. References**

USA.

Berkeley, USA.

**Figure 12.** (Color online) (a) Optical image of a male *S. coronata* butterfly in dorsal view; The appearances under (b) TM and (c) TE polarization light show distinguished difference of the blue component, which can be attributed to (d) the broken symmetry of the triangular grooves in the surface plane; Two kinds of anti-fake or encryption designs, which apply (e) colored effect or (f) grey level change linked to the polarization and the broken surface symmetry, are inspired [89].

yellow (i.e. the hue in flat regions). That is, the grooved areas turn the light polarization *π*/2 and thus are shadowed by the inserted polarizer. Following the ideas, an encoded pattern which comprises grooved areas can be distinguished with the background consisting of perpendicular grooves via the luminosity level under different polarized light incidence (Fig. 12(f)). The two imaged examples inspired by the grooved structures of the butterfly show us great prospective in fields such as anti-fake and encryption.

#### **2.4. Other bio-inspired fabrications and applications**

Besides the main categories, some other bio-inspired photonic applications are also reported [96–100]. For examples, the natural scales of *Morpho sulkowskyi* are extremely sensitive to the different environmental vapors, which lead to dramatically improved responses as units of potential sensor applications compared with that of current devices[101]. Using black scales of the butterfly *Papilio paris* and *Thaumantis diores* as templates, hierarchically periodic microstructure titania replica was systhesized by chemical procedures. The high surface area inherited from the natural templates is great advantages to the light harvesting efficiency and dye sorption when the replica is used as photoanode in dye-sensitized solar cell [100]. With *Morpho* as bio-templates, alumina replicas show the potential applications in waveguides and beam-splitters under thin film coating by ALD and sintering [97]. Under thick film coating, the hybrid structure is found not to inherit the 'Christmas-tree' structures but develop a 'Pyramid-like' structures which have potential applications in light trapping [99]. With the complex photonic structures (multilayer plus 2D amorphous structures) of beetles *Trigonophorus rothschildi varians* as 'blueprints', the artificial counterpart which is fabricated by FIB etching holes through a 5×SiO/SiGe multilayer structure show similar optical features like non-specularity and only slightly angle-dependent reflectance [98]. Further bio-inspired work is undergoing which is stimulated by a recent revealed 3D architecture [102], aiming at the ultra-negative angular dispersion of diffraction and potential novel dispersive optical elements.

#### **3. Perspectives**

14 Will-be-set-by-IN-TECH

**(e)**

**(f)**

**Figure 12.** (Color online) (a) Optical image of a male *S. coronata* butterfly in dorsal view; The appearances under (b) TM and (c) TE polarization light show distinguished difference of the blue component, which can be attributed to (d) the broken symmetry of the triangular grooves in the surface plane; Two kinds of anti-fake or encryption designs, which apply (e) colored effect or (f) grey level

yellow (i.e. the hue in flat regions). That is, the grooved areas turn the light polarization *π*/2 and thus are shadowed by the inserted polarizer. Following the ideas, an encoded pattern which comprises grooved areas can be distinguished with the background consisting of perpendicular grooves via the luminosity level under different polarized light incidence (Fig. 12(f)). The two imaged examples inspired by the grooved structures of the butterfly

Besides the main categories, some other bio-inspired photonic applications are also reported [96–100]. For examples, the natural scales of *Morpho sulkowskyi* are extremely sensitive to the different environmental vapors, which lead to dramatically improved responses as units of potential sensor applications compared with that of current devices[101]. Using black scales of the butterfly *Papilio paris* and *Thaumantis diores* as templates, hierarchically periodic microstructure titania replica was systhesized by chemical procedures. The high surface area inherited from the natural templates is great advantages to the light harvesting efficiency and dye sorption when the replica is used as photoanode in dye-sensitized solar cell [100]. With *Morpho* as bio-templates, alumina replicas show the potential applications in waveguides and beam-splitters under thin film coating by ALD and sintering [97]. Under thick film coating, the hybrid structure is found not to inherit the 'Christmas-tree' structures but develop a 'Pyramid-like' structures which have potential applications in light trapping [99]. With the complex photonic structures (multilayer plus 2D amorphous structures) of beetles *Trigonophorus rothschildi varians* as 'blueprints', the artificial counterpart which is fabricated by FIB etching holes through a 5×SiO/SiGe multilayer structure show similar optical features like non-specularity and only slightly angle-dependent reflectance [98]. Further bio-inspired work is undergoing which is stimulated by a recent revealed 3D architecture [102], aiming

change linked to the polarization and the broken surface symmetry, are inspired [89].

show us great prospective in fields such as anti-fake and encryption.

**2.4. Other bio-inspired fabrications and applications**

**(a)**

**(b)**

**(c)**

**(d)**

In the Chapter, several important kinds of bio-inspired photonic applications are reviewed, including antireflection devices, color-tunable sensors, structural color mixing applications and etc. The nature nourishes scientists the functional optical applications either the blueprints of photonic architecture or directly the bio-templates. Due to the higher index of inorganic materials used, the mimicking photonic structures even show better optical performances as well as enhanced mechanical properties of high temperature tolerance, stability and infrangibility. The biomimetic applications are anticipated to help our life better in the near future. However, complicated photonic structures (e.g. those of high-dimensional, hierarchic, amorphous features in nature) still remains hardly reproduced or, if they are fabricated successfully, the efforts involved are so great using the traditional fabrication ways that optical devices can not commercially explored. Thorough physical mechanism understanding as well as better fabrication approach explorations may help to simply the structure fabrications, achieve similar optical functions and realize commercial applications. In addition, adding substances such as functional chemical groups, fluorescence particles, metal, or other active materials, the mimicking photonic structures allow the properties of interest to be augmented, which may open a new window of novel optical device exploration. Although the photonic biomimicry is in its infancy, we believe that the bio-inspired optical device would surely have profound impacts on our modern society.

#### **Author details**

Feng Liu

*Laboratory of Opto-electrical Material and Device, Department of Physics, Shanghai Normal University, Shanghai, China*

Biqin Dong

*Department of Mechanical Engineering, Northwestern University, Evanston, USA*

Xiaohan Liu

*Department of Physics, Fudan University, Shanghai, China*

#### **4. References**


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© 2012 Chen, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Optical Devices Based on** 

Additional information is available at the end of the chapter

Lin Chen

http://dx.doi.org/10.5772/48146

manipulation of optical waves [4].

which are closely related to the UHM in guiding layer.

**1. Introduction** 

**Symmetrical Metal Cladding Waveguides** 

Controlling and guiding light with planar waveguide has a great potential to fabricate attractive optical devices such as modulators [1], filters [2] and sensors [3]. Although many studies use planar waveguide made of dielectric materials or semiconductors, metals also play an important role in this field. Metals have been usually used as mirror in the visible or infrared regions. By constructing the dielectric layer sandwiched by two metal layers and forming the metal-dielectric-metal (MDM) structure, we can obtain the unique optical properties which the dielectric planar waveguides do not have. Recently, Shin *et al*. reported that this structure can function as the negative refraction lens for surface plasmon waves on a metal surface. This structure provides a new way of controlling the propagation of surface plasmons, which are important for nanoscale

This type of MDM can be expected to have the interesting optical features not only in the negative refraction index but also in the mode properties. The above mentioned waveguide structure can commonly accommodate only surface plasmon mode. When the thickness of guiding layer is increased to millimeter-scale, such waveguide can accommodate thousands of guided modes, and ultrahigh-order modes (UHM) can be excited. In this case the MDM is commonly called symmetrical metal-cladding waveguide (SMCW) [5]. To our knowledge, however, there have been few investigations about the UHM properties of the SMCW. In this chapter, we have reported the UHM properties of the SMCW and their applications on optical devices. The UHM of SMCW can be excited by free space coupling [6] in small incident angle. In section 2, we present some details of the UHM properties such as large mode spacing, sensitive to the change of waveguide parameters, and slow wave effect. Section 3 introduces applications on optical devices such as modulators, filters and sensors,

## **Optical Devices Based on Symmetrical Metal Cladding Waveguides**

Lin Chen

20 Will-be-set-by-IN-TECH

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Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48146

### **1. Introduction**

Controlling and guiding light with planar waveguide has a great potential to fabricate attractive optical devices such as modulators [1], filters [2] and sensors [3]. Although many studies use planar waveguide made of dielectric materials or semiconductors, metals also play an important role in this field. Metals have been usually used as mirror in the visible or infrared regions. By constructing the dielectric layer sandwiched by two metal layers and forming the metal-dielectric-metal (MDM) structure, we can obtain the unique optical properties which the dielectric planar waveguides do not have. Recently, Shin *et al*. reported that this structure can function as the negative refraction lens for surface plasmon waves on a metal surface. This structure provides a new way of controlling the propagation of surface plasmons, which are important for nanoscale manipulation of optical waves [4].

This type of MDM can be expected to have the interesting optical features not only in the negative refraction index but also in the mode properties. The above mentioned waveguide structure can commonly accommodate only surface plasmon mode. When the thickness of guiding layer is increased to millimeter-scale, such waveguide can accommodate thousands of guided modes, and ultrahigh-order modes (UHM) can be excited. In this case the MDM is commonly called symmetrical metal-cladding waveguide (SMCW) [5]. To our knowledge, however, there have been few investigations about the UHM properties of the SMCW. In this chapter, we have reported the UHM properties of the SMCW and their applications on optical devices. The UHM of SMCW can be excited by free space coupling [6] in small incident angle. In section 2, we present some details of the UHM properties such as large mode spacing, sensitive to the change of waveguide parameters, and slow wave effect. Section 3 introduces applications on optical devices such as modulators, filters and sensors, which are closely related to the UHM in guiding layer.

© 2012 Chen, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **2. Properties of SMCW**

The SMCWs are the millimeter-scale guiding layers (dielectric constant *ε1*, thickness *d*) sandwiched between two metal films (Fig.1). The upper metal film (dielectric constant ε2, thickness *h*) of several dozens of nanometer acts as coupling layer as well as a metal cladding; and the base metal layer (dielectric constant ε2) acts as a substrate of the waveguide, which is thick enough to prevent the influence of the glass flat on guiding layer. For modulation applications, the upper and base metal films also serve as electrodes of the device. If the light incidents from air to the guiding layer directly, it can meet the coupling condition and couple the mode with effective index less than 1. The allowed range of the effective index in SMCW can be reached from 0 to n1 for the guided modes, where n1= (ε1)1/2 is the refractive index of the guiding slab. This range is much wider than that available to the usual waveguides. The principle model of free-space coupling is shown in Fig.2. When the beam incomes from the air to the metal surface, it will generate evanescent field in the metal. Since the upper metal film is thin (dozens of nanometer), the tail of evanescent field can reach the interface of guided wave layer of the metal. It will generate an opposite evanescent field on the interface. Due to the interaction between two evanescent fields from opposite directions, the incident light can be coupled into waveguide.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 129

*k j* (2)

sin (3)

(1)

**2.1. The attenuated total reflection spectrum** 

the four-layer optical system for TE mode is written as [7]

constant of guided modes are, respectively, expressed as follows:

2

2

*r*

*h*=30nm, and *d*= 0.38mm.

When a laser beam cast on the upper metal layer with resonant conditions, a large part of the light energy is transferred in the guiding layer, resulting in the attenuated total reflection (ATR) spectrum, which describes the relation between reflectivity and incident angle or wavelength of the reflected light. We take TE mode for example. The reflection coefficient of

32 32 21 1 21 2 21 1 2

 

here rij=(κi-κj)/(κi+κj), is the complex Fresnel reflection coefficient for the boundary between media i and j, in which the normal components of the wave vectors and propagation

> 2 2 <sup>0</sup> ,( 1,2,3) *j j*

> > 0 3

here k0=2π/λ is the wavenumber in vacuum; ε3 is the dielectric constant at medium in which the light incident and reflected; *β* is the propagation constant of the guided modes; *θ* and *λ* are the incident angle and wavelength, respectively. As shown in Fig.3, when the energy of the incident light is coupled into the guided modes, the intensity of the reflected light R=|r|2 decreases dramatically, and a series of reflection dips in the ATR spectrum are produced.

**Figure 3.** Simulated ATR curve with the following parameters: *ε2*=-28+i1.8, *ε*1=2.278, *λ*= 859.8nm,

The experimental arrangement for measuring ATR spectrum is shown schematically in Fig.4. The SMCW is fixed on a computer controlled *θ/2θ* goniometer. After passing through the polarizer and mirror, a collimated laser light beam is incident into the structure. Angular scan is carried out by a computer-controlled *θ/2θ* goniometer. As the goniometer rotates, the

 

 

*k*

21 1 32 21 2 32 21 1 2

 

*r i d rr i h rr i d i h*

1 exp(2 ) exp(2 ) exp(2 )exp(2 ) *r rr i d r i h r i d i h*

exp(2 ) exp(2 ) exp(2 )exp(2 )

**Figure 1.** Symmetrical metal-cladding waveguide structure

**Figure 2.** Principle model of free-space coupling

#### **2.1. The attenuated total reflection spectrum**

128 Optical Devices in Communication and Computation

The SMCWs are the millimeter-scale guiding layers (dielectric constant *ε1*, thickness *d*) sandwiched between two metal films (Fig.1). The upper metal film (dielectric constant ε2, thickness *h*) of several dozens of nanometer acts as coupling layer as well as a metal cladding; and the base metal layer (dielectric constant ε2) acts as a substrate of the waveguide, which is thick enough to prevent the influence of the glass flat on guiding layer. For modulation applications, the upper and base metal films also serve as electrodes of the device. If the light incidents from air to the guiding layer directly, it can meet the coupling condition and couple the mode with effective index less than 1. The allowed range of the effective index in SMCW can be reached from 0 to n1 for the guided modes, where n1= (ε1)1/2 is the refractive index of the guiding slab. This range is much wider than that available to the usual waveguides. The principle model of free-space coupling is shown in Fig.2. When the beam incomes from the air to the metal surface, it will generate evanescent field in the metal. Since the upper metal film is thin (dozens of nanometer), the tail of evanescent field can reach the interface of guided wave layer of the metal. It will generate an opposite evanescent field on the interface. Due to the interaction between two evanescent fields from

opposite directions, the incident light can be coupled into waveguide.

**Figure 1.** Symmetrical metal-cladding waveguide structure

**Figure 2.** Principle model of free-space coupling

**2. Properties of SMCW** 

When a laser beam cast on the upper metal layer with resonant conditions, a large part of the light energy is transferred in the guiding layer, resulting in the attenuated total reflection (ATR) spectrum, which describes the relation between reflectivity and incident angle or wavelength of the reflected light. We take TE mode for example. The reflection coefficient of the four-layer optical system for TE mode is written as [7]

$$r = \frac{r\_{32} - r\_{32}r\_{21}^2 \exp(2i\kappa\_1 d) + r\_{21} \exp(2i\kappa\_2 h) - r\_{21} \exp(2i\kappa\_1 d) \exp(2i\kappa\_2 h)}{1 - r\_{21}^2 \exp(2i\kappa\_1 d) + r\_{32}r\_{21} \exp(2i\kappa\_2 h) - r\_{32}r\_{21} \exp(2i\kappa\_1 d) \exp(2i\kappa\_2 h)} \tag{1}$$

here rij=(κi-κj)/(κi+κj), is the complex Fresnel reflection coefficient for the boundary between media i and j, in which the normal components of the wave vectors and propagation constant of guided modes are, respectively, expressed as follows:

$$\kappa\_j = \sqrt{k\_0^2 \varepsilon\_j - \beta^2} \text{ ( $j = 1, 2, 3$ )}\tag{2}$$

$$
\beta = k\_0 \sqrt{\varepsilon\_3} \sin \theta \tag{3}
$$

here k0=2π/λ is the wavenumber in vacuum; ε3 is the dielectric constant at medium in which the light incident and reflected; *β* is the propagation constant of the guided modes; *θ* and *λ* are the incident angle and wavelength, respectively. As shown in Fig.3, when the energy of the incident light is coupled into the guided modes, the intensity of the reflected light R=|r|2 decreases dramatically, and a series of reflection dips in the ATR spectrum are produced.

**Figure 3.** Simulated ATR curve with the following parameters: *ε2*=-28+i1.8, *ε*1=2.278, *λ*= 859.8nm, *h*=30nm, and *d*= 0.38mm.

The experimental arrangement for measuring ATR spectrum is shown schematically in Fig.4. The SMCW is fixed on a computer controlled *θ/2θ* goniometer. After passing through the polarizer and mirror, a collimated laser light beam is incident into the structure. Angular scan is carried out by a computer-controlled *θ/2θ* goniometer. As the goniometer rotates, the

incident angle will change, while the photodiode keeps consistently monitoring the reflected light intensity to scan the reflectance curve. The reflected light intensity is captured by a photodiode fixed on the 2*θ* plate of the goniometer and converted into a voltage signal. At small incident angles, UHM resonance will occur and couple the incident light energy into the SMCW by the free space coupling technique. Then in the reflective curve, a series of resonance dips take place in the angular spectrum, as illustrated in Fig.3.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 131

(8)

(9)

(10)

(11)

(12)

(7)

Furthermore, when d reaches millimeter-scale, the waveguide can accommodate thousands of guided modes. For example, use the parameters: ε2 = −28 + i1.8, ε1 = 2.278, λ= 859.8nm, *h* = 30 nm, and *d* = 0.38 mm, *m* is 1333 for the highest mode. However, the maximum of the absolute value of the second term on the right in Eq. (4) is *π*. It will not generate much error if ignoring it, and the approximate dispersion equation of the UHMs for both TE and TM modes is [5]

<sup>2</sup> *h Nm m*( 0,1,2,......)

where N = *β/k0* is the effective index of the UHM. Eq. (7) implies that when N is close to zero,

Because UHMs have a short retention time in waveguide layer, any tiny change of *λ*, n1 and *d* will cause the sensitive change of *N*. If we define sensitivity *SN* as the derivative of

> *N <sup>N</sup> <sup>S</sup>*

> > 1 *N n n N*

*N*

1

2 2 <sup>1</sup> *N n N*

2 2 <sup>1</sup> *N n N d Nd*

From above mentioned three equations, sensitivity is in inverse proportion to effective index *N*. Therefore, we can obtain high sensitivity when UHM is excited. According to ray optics theory, with the same propagation distance, the small incident angle means that UHM will experience more times reflection and light propagation distance will be longer, resulting in a series of special features different from low-order modes. This property is extremely useful

Finally, according to Eq. (4), tiny change of wavelength can generate great change of effective index, illustrating that UHM has strong dispersion property and consequent slow

> *dN c d n n dn d*

In the equation, group velocity expression is totally different from those conventional slow light schemes, which is composed of two contributions that are shown in Eq. (12): one

11 1

 

light effect. Using Eq. (7), we can also obtain the group velocity of UHM:

*g*

where *ξ* represents *λ*, *n1* or *d.* By the total differential of Eq. (7), we can get:

 

2

1

effective index to certain characteristic parameter, that is

the UHM exhibits polarization insensibility.

to design sensors and modulators.

**Figure 4.** Experimental arrangement for measuring ATR spectrum

#### **2.2. Ultrahigh-order mode**

Disregarding the effects resulting from the limited thickness of the metal film, dispersion equation of the guided modes in SMCW can be written as

$$\kappa\_1 h = m\pi + 2\tan^{-1}(\rho \frac{a\_2}{\kappa\_1}), \quad m = 0, 1, 2, \ldots \tag{4}$$

where attenuated coefficient in the metal α2=iκ2, m is the mode ordinal number of guided mode. The parameters relevant to polarization are given by:

$$\rho = \begin{cases} 1 & \text{TE Polarization} \\ \varepsilon\_1 / \varepsilon\_2 & \text{TM Polarization} \end{cases} \tag{5}$$

According to Eq. (4), we can deduce an approximate formula:

$$
\Delta m \propto \sin 2\theta \Lambda \theta \tag{6}
$$

Since *Δm*=1, when the incident angle is small, a bigger *Δθ* can be obtained. So the mode spacing effect of UHMs is evident. Such property is convenient to comb filter design for optical communication applications.

Furthermore, when d reaches millimeter-scale, the waveguide can accommodate thousands of guided modes. For example, use the parameters: ε2 = −28 + i1.8, ε1 = 2.278, λ= 859.8nm, *h* = 30 nm, and *d* = 0.38 mm, *m* is 1333 for the highest mode. However, the maximum of the absolute value of the second term on the right in Eq. (4) is *π*. It will not generate much error if ignoring it, and the approximate dispersion equation of the UHMs for both TE and TM modes is [5]

130 Optical Devices in Communication and Computation

incident angle will change, while the photodiode keeps consistently monitoring the reflected light intensity to scan the reflectance curve. The reflected light intensity is captured by a photodiode fixed on the 2*θ* plate of the goniometer and converted into a voltage signal. At small incident angles, UHM resonance will occur and couple the incident light energy into the SMCW by the free space coupling technique. Then in the reflective curve, a series of

Disregarding the effects resulting from the limited thickness of the metal film, dispersion

1 2

 

1 *h m* 2tan ( ), 0,1,2,...... *m* 

1 *TEPolarization*

*TM Polarization*

(4)

(5)

(6)

where attenuated coefficient in the metal α2=iκ2, m is the mode ordinal number of guided

*m* sin2 

Since *Δm*=1, when the incident angle is small, a bigger *Δθ* can be obtained. So the mode spacing effect of UHMs is evident. Such property is convenient to comb filter design for

resonance dips take place in the angular spectrum, as illustrated in Fig.3.

**Figure 4.** Experimental arrangement for measuring ATR spectrum

equation of the guided modes in SMCW can be written as

1

mode. The parameters relevant to polarization are given by:

 

According to Eq. (4), we can deduce an approximate formula:

optical communication applications.

1 2

 

**2.2. Ultrahigh-order mode** 

$$\frac{2\pi}{\lambda}h \cdot \sqrt{\varepsilon\_1 - N^2} = m\pi \qquad \text{ (}m = 0, 1, 2, ...\text{)}\tag{7}$$

where N = *β/k0* is the effective index of the UHM. Eq. (7) implies that when N is close to zero, the UHM exhibits polarization insensibility.

Because UHMs have a short retention time in waveguide layer, any tiny change of *λ*, n1 and *d* will cause the sensitive change of *N*. If we define sensitivity *SN* as the derivative of effective index to certain characteristic parameter, that is

$$\mathcal{S}\_N = \frac{\partial \mathcal{N}}{\partial \mathcal{L}}\tag{8}$$

where *ξ* represents *λ*, *n1* or *d.* By the total differential of Eq. (7), we can get:

$$\frac{\partial \mathbf{N}}{\partial n\_1} = \frac{n\_1}{N} \tag{9}$$

$$\frac{\partial \mathbf{N}}{\partial \lambda} = \frac{n\_1^2 - N^2}{N\lambda} \tag{10}$$

$$\frac{\partial \mathbf{N}}{\partial d} = \frac{n\_1^2 - \mathbf{N}^2}{\mathbf{N}d} \tag{11}$$

From above mentioned three equations, sensitivity is in inverse proportion to effective index *N*. Therefore, we can obtain high sensitivity when UHM is excited. According to ray optics theory, with the same propagation distance, the small incident angle means that UHM will experience more times reflection and light propagation distance will be longer, resulting in a series of special features different from low-order modes. This property is extremely useful to design sensors and modulators.

Finally, according to Eq. (4), tiny change of wavelength can generate great change of effective index, illustrating that UHM has strong dispersion property and consequent slow light effect. Using Eq. (7), we can also obtain the group velocity of UHM:

$$\nu\_{\mathcal{g}} = \frac{d\phi}{d\mathcal{\beta}} = \frac{N}{n\_1} \cdot \frac{c}{n\_1 + \alpha d n\_1 / d\phi} \tag{12}$$

In the equation, group velocity expression is totally different from those conventional slow light schemes, which is composed of two contributions that are shown in Eq. (12): one

originates from the first-order dispersion resembling the conventional slow light system, and factor *N/n1* can be called slow light factor which is related to the effective index of the UHMs. The deduced results offer us a new physical mechanism for realizing slow light that may not rely on the existence of a sharp single resonance or multiple resonances, but the effective index of the UHM for the small incident angle (θ→0).

#### **2.3. Propagation loss**

Once SMCW is used to achieving optical devices, the important concern relating to the SMCW is that metallic structures exhibit high losses at optical wavelengths. An issue arising is whether the UHMs could be efficiently confined to the guiding layer over a long distance transmission. To see this clearly, four types of metal cladding waveguides have been considered as shown in Fig.5. Fig.5(a) is a structure of three-layer metal cladding waveguide without considering metal and radiative loss. By using three-layer waveguide theory, for TE mode, propagation constant, *β<sup>a</sup>* , of guided modes for three-layer metal cladding waveguide without considering the metal absorption, can be expressed as:

$$\boldsymbol{\beta}^{a} = \frac{\pi}{\lambda d} \sqrt{4\varepsilon\_{1} d^{2} - \left(\mathbf{m}\_{0}\lambda\right)^{2}} \tag{13}$$

Optical Devices Based on Symmetrical Metal Cladding Waveguides 133

*eff*

(14)

*d*

*k* (15)

(17)

1 

*k* (16)

(18)

is the vertical guiding wave

(19)

*h*

 

 

2 21 3 2 2 22 2 1 23 2

 

2 2 1 01 ( ) *a a*

2 2 <sup>2</sup> 0 2 ( ) *a a*

> 1/2 <sup>2</sup> <sup>2</sup>

> > <sup>2</sup> 2 / *<sup>a</sup>*

*r*

 

*aa a a*

*a a a aa*

 

4 ( ) exp( 2 ) Im( ) (( ) ( ) )(( ) ( ) )

 

> 

 

> *k*

*eff d d*

vector of three-layer metal cladding waveguide without considering the metal absorption, *ε2r* and *ε2i* are real and imaginary parts of dielectric constant (*ε2=ε2r+jε2i*), and *deff* is the effective thickness. Δ*β*rad represents the difference of the eigen-propagation constant between three-layer waveguide and radiative waveguide coupling system. Because the radiative damping is inversely proportional to the exponential function of *h* as shown in Eq.

Fig.5(c) is a structure of three-layer metal cladding waveguide only with considering metal loss. Comparing Fig.5(a) with Fig.5(c) under the condition of |ε2r|>>ε2i at visible and near infrared wavelength, we can obtain that metal loss only affects the imaginary part of propagation constant in three-layer metal cladding waveguide. Then the intrinsic damping,

0 20 1

( ) Im( ) ( ( ))

21 2

where *β<sup>0</sup>* is the eigen-propagation constant of the guided mode for three-layer waveguide with semi-infinite-thick coupling layer. Table1 lists the propagation loss of two kinds of SMCW which thickness of guiding layer *d* is 0.5 mm and 1 mm, corresponding to UHM order *m* is 1421 and 2843, separately. The dielectric constant of Au and Ag at wavelength *λ*= 1053 nm is -40+2.5i and -48+1.6i, respectively. η presents the ratio of the remaining power after the guided mode transmits for *z*= 1 mm to the guided mode initial power and can be expressed as exp(-2*Δβz*). Then the propagation loss ζ can be expressed as -10/*z×lgη*. As shown in table 1, in sub-millimeter scale, the propagation losses of the guided modes are both less than 3 dB/mm, which is benefit for the design of optical devices. In addition, the

*i aa a a*

*k*

 

2 2

 

*a*

2

*eff*

*d*

3 03 *a a*

<sup>2</sup> is the absorption constant of the cladding layer, <sup>a</sup>

(14), the radiative damping can be adjusted by changing the parameter *h*.

propagation loss property has little relation to polarization.

*rad*

with

and

Where <sup>a</sup> 

Im(*β0*), can be written as [8]:

where m0 is mode order.

**Figure 5.** (a) three-layer metal cladding waveguide with ε2=ε2r and h→∞, (b) SMCW with ε2=ε2r and *h* ≠∞, (c) three-layer metal cladding waveguide with ε2=ε2r+iε2i and *h*→∞, (d) SMCW with ε2=ε2r+iε2i and *h*≠∞.

Fig.5(b) is a structure of SMCW only with considering radiative loss. Comparing Fig.5(b) with Fig.5(a) by using weak-coupling condition, which is satisfied with four-layer system [8], the radiative damping, Im(Δ*β*rad), can be expressed as,

#### Optical Devices Based on Symmetrical Metal Cladding Waveguides 133

$$\operatorname{Im}(\Delta \boldsymbol{\beta}^{\mathrm{rad}}) = \frac{4\alpha\_2^a (\kappa\_1^a)^2 \kappa\_3^a \exp(-2\alpha\_2^a \boldsymbol{h})}{((\kappa\_1^a)^2 + (\alpha\_2^a)^2)((\kappa\_3^a)^2 + (\alpha\_2^a)^2)\boldsymbol{\beta}^a d\_{\mathrm{eff}}} \tag{14}$$

with

132 Optical Devices in Communication and Computation

**2.3. Propagation loss** 

mode, propagation constant, *β<sup>a</sup>*

where m0 is mode order.

and *h*≠∞.

effective index of the UHM for the small incident angle (θ→0).

without considering the metal absorption, can be expressed as:

originates from the first-order dispersion resembling the conventional slow light system, and factor *N/n1* can be called slow light factor which is related to the effective index of the UHMs. The deduced results offer us a new physical mechanism for realizing slow light that may not rely on the existence of a sharp single resonance or multiple resonances, but the

Once SMCW is used to achieving optical devices, the important concern relating to the SMCW is that metallic structures exhibit high losses at optical wavelengths. An issue arising is whether the UHMs could be efficiently confined to the guiding layer over a long distance transmission. To see this clearly, four types of metal cladding waveguides have been considered as shown in Fig.5. Fig.5(a) is a structure of three-layer metal cladding waveguide without considering metal and radiative loss. By using three-layer waveguide theory, for TE

1 0 4 (m ) *<sup>a</sup> <sup>d</sup>*

**Figure 5.** (a) three-layer metal cladding waveguide with ε2=ε2r and h→∞, (b) SMCW with ε2=ε2r and *h* ≠∞, (c) three-layer metal cladding waveguide with ε2=ε2r+iε2i and *h*→∞, (d) SMCW with ε2=ε2r+iε2i

Fig.5(b) is a structure of SMCW only with considering radiative loss. Comparing Fig.5(b) with Fig.5(a) by using weak-coupling condition, which is satisfied with four-layer system

[8], the radiative damping, Im(Δ*β*rad), can be expressed as,

*d* 

, of guided modes for three-layer metal cladding waveguide

(13)

2 2

 

$$
\kappa\_1^a = \sqrt{k\_0^2 \varepsilon\_1 - (\mathcal{J}^a)^2} \tag{15}
$$

$$
\alpha\_2^a = \sqrt{(\beta^a)^2 - k\_0^2 \varepsilon\_{2r}} \tag{16}
$$

$$\kappa\_3^a = \left(k\_0^2 \varepsilon\_3 - \left(\mathcal{J}^a\right)^2\right)^{1/2} \tag{17}$$

and

$$d\_{eff} = d + \mathcal{D} / \alpha\_2^a \tag{18}$$

Where <sup>a</sup> <sup>2</sup> is the absorption constant of the cladding layer, <sup>a</sup> 1 is the vertical guiding wave vector of three-layer metal cladding waveguide without considering the metal absorption, *ε2r* and *ε2i* are real and imaginary parts of dielectric constant (*ε2=ε2r+jε2i*), and *deff* is the effective thickness. Δ*β*rad represents the difference of the eigen-propagation constant between three-layer waveguide and radiative waveguide coupling system. Because the radiative damping is inversely proportional to the exponential function of *h* as shown in Eq. (14), the radiative damping can be adjusted by changing the parameter *h*.

Fig.5(c) is a structure of three-layer metal cladding waveguide only with considering metal loss. Comparing Fig.5(a) with Fig.5(c) under the condition of |ε2r|>>ε2i at visible and near infrared wavelength, we can obtain that metal loss only affects the imaginary part of propagation constant in three-layer metal cladding waveguide. Then the intrinsic damping, Im(*β0*), can be written as [8]:

$$\operatorname{Im}(\beta^0) = \frac{\varepsilon\_{2i} k\_0^2 (\kappa\_1^a)^2}{\alpha\_2^a (\kappa\_1^a + (\alpha\_2^a)^2) \beta^a d\_{eff}} \tag{19}$$

where *β<sup>0</sup>* is the eigen-propagation constant of the guided mode for three-layer waveguide with semi-infinite-thick coupling layer. Table1 lists the propagation loss of two kinds of SMCW which thickness of guiding layer *d* is 0.5 mm and 1 mm, corresponding to UHM order *m* is 1421 and 2843, separately. The dielectric constant of Au and Ag at wavelength *λ*= 1053 nm is -40+2.5i and -48+1.6i, respectively. η presents the ratio of the remaining power after the guided mode transmits for *z*= 1 mm to the guided mode initial power and can be expressed as exp(-2*Δβz*). Then the propagation loss ζ can be expressed as -10/*z×lgη*. As shown in table 1, in sub-millimeter scale, the propagation losses of the guided modes are both less than 3 dB/mm, which is benefit for the design of optical devices. In addition, the propagation loss property has little relation to polarization.

134 Optical Devices in Communication and Computation


**Table 1.** Guided-mode propagation loss with different parameters

#### **2.4. The enhanced Goos–Hänchen effect**

When the weak coupling condition |exp(2i*κ2*h)|<<1 is satisfied, Eq. (1) can be rewritten as

$$r = \left| r \right| e^{i\phi} = r\_{32} \frac{\beta - \left[ \text{Re}\left(\boldsymbol{\beta}^{0}\right) + \text{Re}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right] - i \left[ \text{Im}\left(\boldsymbol{\beta}^{0}\right) - \text{Im}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right]}{\beta - \left[ \text{Re}\left(\boldsymbol{\beta}^{0}\right) + \text{Re}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right] - i \left[ \text{Im}\left(\boldsymbol{\beta}^{0}\right) + \text{Im}\left(\boldsymbol{\Delta}\boldsymbol{\beta}^{nd}\right) \right]} \right| \tag{20}$$

where *ϕ* is the phase difference between the reflected and incident waves. Re(β0), Im(β0) and Re(*Δβrad*), Im(*Δβrad*) are the real and imaginary parts of the parameters *β0* and *Δβrad*, respectively.

According to stationary phase method, the Goos-Hänchen (GH) shift L is expressed as:

$$L(\mathcal{A}) = -\frac{\mathcal{A}}{2\pi\sqrt{\varepsilon\_3}} \cdot \left. \frac{d\phi}{d\theta} \right|\_{\theta = \theta\_0} \tag{21}$$

Optical Devices Based on Symmetrical Metal Cladding Waveguides 135

(23)

(24)

(25)

is small, the radiative damping is larger than the intrinsic damping, positive lateral shift is obtained. The negative GH shift corresponds to the reverse case. Larger GH shift can be obtained when intrinsic damping approaches the radiative damping. The critical thickness can

where *n* and *κ* are the refractive index of the metal (*n*+*jκ*=(ε2)1/2). The critical thickness should

<sup>4</sup> *cr <sup>h</sup>*

2 ln

*n*

be determined from Eq. (22) by letting denominator is equal to zero [8]:

**Figure 6.** Reflectivity and lateral beam shift with respect to the incident wavelength

through the photocurrents from the output electrodes x1 and x2 (see Fig.7):

To measure the shift while avoiding small spurious displacement, we use the wavelength interrogation-based method by combining a tunable laser and a one-dimensional position sensitive detector (PSD). The position of the incident light can be determined by the PSD

> 2 *<sup>a</sup> <sup>L</sup>*

12 1 2 12 1 2 *II VV II VV*

here I1 and I2 are the photocurrents of the output electrodes x1 and x2, respectively. V1 and V2 are the voltages converted from I1 and I2 after amplifier circuit. The analog voltages V1 and V2 are further converted into digital signals and collected by the computer (PC). Light

where *ΔL* is the displacement from the center of the PSD, a is the length of the PSD, *δ* is

be about 31nm using the parameters above.

defined as

where *θ0* is the fixed incident angle. Using (20), L at the resonance wavelength of ATR curve can be written as [9]

$$L(\mathcal{A}\_{\rm res}) = -\cos\theta\_0 \cdot \frac{2\operatorname{Im}(\Delta\mathcal{J}^{\rm rad})}{\operatorname{Im}(\mathcal{J}^0)^2 - \operatorname{Im}(\Delta\mathcal{J}^{\rm rad})^2} \tag{22}$$

With the parameters ε3=1, ε1=2.278, ε2=-28+1.8j, *θ*0=8.11, *d*=0.38μm, and *h*=22nm, the calculated GH shifts with respect to wavelength is shown in Fig.6. The reflectivity is also shown in Fig.6 for comparison. It is found from Fig.6 that the enhancement of the lateral shift of reflective light is closely relevant to the coupling of waveguide power. Reflectivity corresponds to the excitation of a guided mode with the change of the incident wavelength. When the incident wavelength gradually meets the condition of resonance, the reflectivity decreased sharply, most of the energy of the incident angle is coupled into waveguide, greatly enhance the reflective GH shift and forms a peak, and this peak of lateral shift corresponds to the minimum of the reflectivity. Moreover, as the radiative damping is inversely proportional to the exponential function of *h* from Eq. (14), we can adjust radiative damping by varying *h*. When h is small, the radiative damping is larger than the intrinsic damping, positive lateral shift is obtained. The negative GH shift corresponds to the reverse case. Larger GH shift can be obtained when intrinsic damping approaches the radiative damping. The critical thickness can be determined from Eq. (22) by letting denominator is equal to zero [8]:

134 Optical Devices in Communication and Computation

**Table 1.** Guided-mode propagation loss with different parameters

When the weak coupling condition |exp(2i*κ2*h)|<<1 is satisfied, Eq. (1) can be rewritten as

 

h/mm λ/nm m mode Δβ η/% ζ/(dB/nm) 0.5 1053 An=-40+2.5i 1421 TE 0.31904 52.8 2.78 0.5 1053 An=-40+2.5i 1421 TM 0.32289 52.4 2.81 0.5 1053 Ag=-48+1.6i 1421 TE 0.15689 73.1 1.36 0.5 1053 Ag=-48+1.6i 1421 TM 0.15834 72.9 1.38 1 1053 An=-40+2.5i 2843 TE 0.15953 72.7 1.38 1 1053 An=-40+2.5i 2843 TM 0.16144 72.4 1.4 1 1053 Ag=-48+1.6i 2843 TE 0.078446 85.4 0.69 1 1053 Ag=-48+1.6i 2843 TM 0.079167 85.3 0.7

 

where *ϕ* is the phase difference between the reflected and incident waves. Re(β0), Im(β0) and Re(*Δβrad*), Im(*Δβrad*) are the real and imaginary parts of the parameters *β0* and *Δβrad*,

where *θ0* is the fixed incident angle. Using (20), L at the resonance wavelength of ATR curve

2Im( ) ( ) cos Im( ) Im( )

With the parameters ε3=1, ε1=2.278, ε2=-28+1.8j, *θ*0=8.11, *d*=0.38μm, and *h*=22nm, the calculated GH shifts with respect to wavelength is shown in Fig.6. The reflectivity is also shown in Fig.6 for comparison. It is found from Fig.6 that the enhancement of the lateral shift of reflective light is closely relevant to the coupling of waveguide power. Reflectivity corresponds to the excitation of a guided mode with the change of the incident wavelength. When the incident wavelength gradually meets the condition of resonance, the reflectivity decreased sharply, most of the energy of the incident angle is coupled into waveguide, greatly enhance the reflective GH shift and forms a peak, and this peak of lateral shift corresponds to the minimum of the reflectivity. Moreover, as the radiative damping is inversely proportional to the exponential function of *h* from Eq. (14), we can adjust radiative damping by varying *h*. When h

*res rad L*

 

<sup>32</sup> 0 0

According to stationary phase method, the Goos-Hänchen (GH) shift L is expressed as:

2 *<sup>d</sup> <sup>L</sup>*

 

( )

*i*

*rad rad*

 

(20)

(22)

 

 

 

*rad rad*

(21)

0 0

Re Re Im Im

Re Re Im Im

*i*

3 <sup>0</sup>

0 0 2 2

*rad*

 

*d* 

 

**2.4. The enhanced Goos–Hänchen effect** 

*i*

*r re r*

respectively.

can be written as [9]

$$h\_{cr} = \frac{\lambda}{4\pi\kappa} \ln\frac{2}{n} \tag{23}$$

where *n* and *κ* are the refractive index of the metal (*n*+*jκ*=(ε2)1/2). The critical thickness should be about 31nm using the parameters above.

**Figure 6.** Reflectivity and lateral beam shift with respect to the incident wavelength

To measure the shift while avoiding small spurious displacement, we use the wavelength interrogation-based method by combining a tunable laser and a one-dimensional position sensitive detector (PSD). The position of the incident light can be determined by the PSD through the photocurrents from the output electrodes x1 and x2 (see Fig.7):

$$
\Delta L = \frac{a}{2}\delta \tag{24}
$$

where *ΔL* is the displacement from the center of the PSD, a is the length of the PSD, *δ* is defined as

$$\delta = \frac{I\_1 - I\_2}{I\_1 + I\_2} = \frac{V\_1 - V\_2}{V\_1 + V\_2} \tag{25}$$

here I1 and I2 are the photocurrents of the output electrodes x1 and x2, respectively. V1 and V2 are the voltages converted from I1 and I2 after amplifier circuit. The analog voltages V1 and V2 are further converted into digital signals and collected by the computer (PC). Light displacement measurement using PSD can achieve high sensitivity and accuracy and will not be affected by the change of the light intensity.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 137

**Figure 8.** Measured analog voltages V1 and V2 and calculated positive value of *δ* as a function of

optical devices based on SMCW have the potential applications in many fields.

The above mentioned properties of UHM in SMCW have been widely used to applications on optical devices. Here, we list several practical application examples, such as filter, sensor, modulator and slow wave device. Due to its excellent performance and simple structure,

As mentioned above, a sub-millimeter SMCW is capable of coupling the incident light with a fixed wavelength from free space into the glass slab directly. As the excitation of the guided modes results in resonant transfer of energy from the incident light, guided modes manifest themselves by a series of resonant dips in the reflectivity when the incident angle is varied. On the other hand, if a polychromatic light is used instead of a single-wavelength light, resonant dips at a fixed incident angle can also be achieved in a spectral plot of the reflectivity. In this way, a comb filter is built [11]. For a better understanding of how it works, we consider the UHMs of the sub-millimeter SMCW in the case of free space

> 1 <sup>2</sup> *nd m* cos

 

where *ν* is the frequency of the light in free space. Without considering the material dispersion of the waveguide, we can express the channel spacing in frequency separated by

> <sup>1</sup> 2 cos *c n d*

It is found that *θ* is a constant as the incident angle of the light is fixed, which means that the channel spacing is equal in frequency for this comb filter. Moreover, according to Eq. (26)

(26)

(27)

*c* 

wavelength with (a) *h*=8nm and (b) *h*=50nm. The incident angle *θ* is 8.11o.

**3. Optical devices based on SMCW** 

**3.1. Tunable comb filters** 

coupling. Eq. (7) can be rewritten as

two neighboring guided modes as

The experimental arrangement for measuring GH shift is shown in Fig.7 [10]. After passing through two apertures (A1, A2) and a splitter (S1), a large part of the Guassian beam from a tunable laser was introduced onto the SMCW. Another part of the beam, which is reflected from S1, irradiated the second splitter (S2) and is detected by a wavemeter connected to a computer. We choose to excite the UHMs, because of the polarization independence of the UHMs, TE and TM incidences have nearly the same characteristics. The reflected light from the SMCW was first detected by a photodiode (PD). Angular scan was performed by rotating the goniometer and the ATR spectrum was generated. We selected the operation angle to be located at the maximum reflectivity near a certain dip of the spectrum (Position 1). The GH effect is not remarkable at this position due to the deviation of the resonance condition. The position of the reflected beam was set as the reference at this point. Then we moved the PD out of the light path (Position 2) without changing any position of the incident beam and let the reflected light beam cast onto the center of the PSD perpendicularly. Then by changing the wavelength through temperature tuning, the variation of *δ* can be measured obviously on the computer screen. To gain better understanding of GH shift measurement using PSD, Fig.8(a) and (b) show the two sets of measurement results when the wavelength of the incident light is changed artificially. The values of V1 and V2 are also measured and plotted in the two figures for comparison. Since the preliminarily setting of the light is at the center of PSD under the case of unresonance, which means the reference values of *δ* is equal to zero, the change of the value *δ* shown on the computer were the actual relative enhanced positive and negative lateral beam displacement under the case of resonance. Then the actual position *ΔL* can be obtained by using Eq. (24).

**Figure 7.** Experimental setup (A1 and A2, aperture; PD:photodiode; S1 and S2: splitter; 1-D PSD: onedimensional position sensitive detector and PC: computer).

**Figure 8.** Measured analog voltages V1 and V2 and calculated positive value of *δ* as a function of wavelength with (a) *h*=8nm and (b) *h*=50nm. The incident angle *θ* is 8.11o.

#### **3. Optical devices based on SMCW**

The above mentioned properties of UHM in SMCW have been widely used to applications on optical devices. Here, we list several practical application examples, such as filter, sensor, modulator and slow wave device. Due to its excellent performance and simple structure, optical devices based on SMCW have the potential applications in many fields.

#### **3.1. Tunable comb filters**

136 Optical Devices in Communication and Computation

by using Eq. (24).

not be affected by the change of the light intensity.

displacement measurement using PSD can achieve high sensitivity and accuracy and will

The experimental arrangement for measuring GH shift is shown in Fig.7 [10]. After passing through two apertures (A1, A2) and a splitter (S1), a large part of the Guassian beam from a tunable laser was introduced onto the SMCW. Another part of the beam, which is reflected from S1, irradiated the second splitter (S2) and is detected by a wavemeter connected to a computer. We choose to excite the UHMs, because of the polarization independence of the UHMs, TE and TM incidences have nearly the same characteristics. The reflected light from the SMCW was first detected by a photodiode (PD). Angular scan was performed by rotating the goniometer and the ATR spectrum was generated. We selected the operation angle to be located at the maximum reflectivity near a certain dip of the spectrum (Position 1). The GH effect is not remarkable at this position due to the deviation of the resonance condition. The position of the reflected beam was set as the reference at this point. Then we moved the PD out of the light path (Position 2) without changing any position of the incident beam and let the reflected light beam cast onto the center of the PSD perpendicularly. Then by changing the wavelength through temperature tuning, the variation of *δ* can be measured obviously on the computer screen. To gain better understanding of GH shift measurement using PSD, Fig.8(a) and (b) show the two sets of measurement results when the wavelength of the incident light is changed artificially. The values of V1 and V2 are also measured and plotted in the two figures for comparison. Since the preliminarily setting of the light is at the center of PSD under the case of unresonance, which means the reference values of *δ* is equal to zero, the change of the value *δ* shown on the computer were the actual relative enhanced positive and negative lateral beam displacement under the case of resonance. Then the actual position *ΔL* can be obtained

**Figure 7.** Experimental setup (A1 and A2, aperture; PD:photodiode; S1 and S2: splitter; 1-D PSD: one-

dimensional position sensitive detector and PC: computer).

As mentioned above, a sub-millimeter SMCW is capable of coupling the incident light with a fixed wavelength from free space into the glass slab directly. As the excitation of the guided modes results in resonant transfer of energy from the incident light, guided modes manifest themselves by a series of resonant dips in the reflectivity when the incident angle is varied. On the other hand, if a polychromatic light is used instead of a single-wavelength light, resonant dips at a fixed incident angle can also be achieved in a spectral plot of the reflectivity. In this way, a comb filter is built [11]. For a better understanding of how it works, we consider the UHMs of the sub-millimeter SMCW in the case of free space coupling. Eq. (7) can be rewritten as

$$\frac{2\pi\nu}{c}n\_1d\cos\theta = m\pi\tag{26}$$

where *ν* is the frequency of the light in free space. Without considering the material dispersion of the waveguide, we can express the channel spacing in frequency separated by two neighboring guided modes as

$$
\Delta\nu = \frac{c}{2n\_1 d\cos\theta} \tag{27}
$$

It is found that *θ* is a constant as the incident angle of the light is fixed, which means that the channel spacing is equal in frequency for this comb filter. Moreover, according to Eq. (26)

and (27), both the center wavelength and the channel spacing can be tuned by simply changing the incident angle. The parameters of SMCW that achieve comb filter are as follows: a glass (ZF7) slab (*d*=900μm); the thickness of the upper film *h*=20 nm. Fig.9 shows the output spectrum from the SMCW.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 139

(29)

(32)

(33)

(34)

(28)

 

*I*

Combined (28) with (29), the sensitivity *S*I can be written by

*N* 

 

*R*

dip, and *α* is the divergence half-angle of the laser beam.

 

index N can be expressed as

expressed as

with

*dR R N <sup>S</sup> d N*

Using the phase matching condition of resonance energy transfer, the effective refractive

*I R N R N R N <sup>S</sup> S S*

where SN is defined as the rate of change of the effective refractive index N with respect to certain characteristic parameter and determined by Eq.(9)-(11). As described in section 2.2, optical waveguide oscillating field sensor exhibits the substantial improvement: the UHMs of the SMCW with millimeter scale is selected to act the sensing probe, so *N*→0 and SN enhancement has been achieved. SR represents the slope of the dip at the operation angle θ0, which was usually set at the fall-off side. The absolute maximum values of the slopes are related to the width of the ATR reflection dips and the mode number. The larger the mode number, the wider the corresponding ATR dip, and the smaller the steepest slope. So the divergence angle of the incident light should be taken into consideration. To calculate the maximum value of sensitivity SI, Lorentzian function is used to approximate the reflection dip in the ATR spectrum. The FWHM is assumed to be larger than the divergence of the incident light in order to prevent profile distortion. According to Ref [12], SR can be

<sup>3</sup> *N* sin

 

3 3

2 0 2 2 2

(31)

0 4( ) <sup>2</sup> exp( ) <sup>2</sup> ( )2

*S x x dx*

*xx Q*

*Q W* /

2( )/ *<sup>i</sup> x* 

<sup>0</sup> 2( )/ *i sp x* 

where *Rm* and *R0* are the values of the reflectivity when guided mode is and is not excited, respectively. θsp is the angle for exciting the guided mode, *W* is the half of the FWHM of the

Taking wavelength sensing for example [13], use the parameters: ε2 = −28 + i1.8, *ε1* = 2.278 at 859.8 nm*, h* = 30 nm, *α* = 0.4 mrad and *d* = 0.38 mm. The sensitivity *SI* with respect to the

*m*

*R Q R R*

  1 1 cos cos

(30)

 

**Figure 9.** Experimental and theoretical reflective spectrum of SMCW, with parameters ε2 = −132+ i12.56, *n1* = 1.765, *h* = 21 nm, *d* = 0.85 mm and *θ* = 6.1o

From Fig.9, we can see equally spaced loss peaks with a 3 dB line-width of 0.1 nm appear in the spectral plot from 1551 to 1556 nm. The wavelength spacing of these peaks is just 0.8 nm. The channel isolation, which is closely related to the thickness of the upper gold film of the waveguide, has been found to be 12 dB. Insertion loss is characterized by the maximum reflectivity, which is greater than 95% (~0.2 dB). The tunability of the filter can be obtained simply by slightly rotating the waveguide with respect to the incident light. Tuning of the center wavelength in the range of channel spacing can be easily obtained by changing several degrees of the incident angle according to Eq. (26).

#### **3.2. Optical sensors**

In this section, we propose oscillating wave sensors using SMCW structure. The thickness of guiding layer can be expanded to millimeter scale, which it can contain very sensitive UHM. The high sensitivity can be detected by measuring the intensity variation of the reflected light due to the movement of the corresponding synchronous angle by an optical sensor. In addition, an alternative approach is presented via measuring the enhanced GH shifts at excitement of UHM. This approach enables the possibility to obtain a higher resolution and prevent the disturbance caused by the power fluctuation of the light source.

#### *3.2.1. Sensitivity analysis*

If we using the intensity measurement interrogation to observe the response of the sensor, the sensitivity in SMCW can be defined as the rate of change of the reflectivity to center characteristics parameters which is expressed as:

Optical Devices Based on Symmetrical Metal Cladding Waveguides 139

$$S\_I = \frac{d\mathcal{R}}{d\xi} = \left(\frac{\partial\mathcal{R}}{\partial\theta}\right)\left(\frac{\partial\theta}{\partial\mathcal{N}}\right)\left(\frac{\partial\mathcal{N}}{\partial\xi}\right) \tag{28}$$

Using the phase matching condition of resonance energy transfer, the effective refractive index N can be expressed as

$$N = \sqrt{\varepsilon\_3} \sin \theta \tag{29}$$

Combined (28) with (29), the sensitivity *S*I can be written by

$$\mathbf{S}\_{I} = \left(\frac{\partial \mathbf{R}}{\partial \theta}\right) \left(\frac{\partial \theta}{\partial \mathbf{N}}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) = \frac{1}{\sqrt{\varepsilon\_{3} \cos \theta}} \left(\frac{\partial \mathbf{R}}{\partial \theta}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) \equiv \frac{1}{\sqrt{\varepsilon\_{3} \cos \theta}} \mathbf{S}\_{R} \mathbf{S}\_{N} \tag{30}$$

where SN is defined as the rate of change of the effective refractive index N with respect to certain characteristic parameter and determined by Eq.(9)-(11). As described in section 2.2, optical waveguide oscillating field sensor exhibits the substantial improvement: the UHMs of the SMCW with millimeter scale is selected to act the sensing probe, so *N*→0 and SN enhancement has been achieved. SR represents the slope of the dip at the operation angle θ0, which was usually set at the fall-off side. The absolute maximum values of the slopes are related to the width of the ATR reflection dips and the mode number. The larger the mode number, the wider the corresponding ATR dip, and the smaller the steepest slope. So the divergence angle of the incident light should be taken into consideration. To calculate the maximum value of sensitivity SI, Lorentzian function is used to approximate the reflection dip in the ATR spectrum. The FWHM is assumed to be larger than the divergence of the incident light in order to prevent profile distortion. According to Ref [12], SR can be expressed as

$$S\_R = \frac{\partial R}{\partial \theta} = \frac{4(R\_0 - R\_m)}{a\sqrt{2\pi}} \int\_{-\infty}^{\infty} \left| \frac{2Q^2}{\left(\mathbf{x} - \mathbf{x}\_0\right)^2 + 2Q^2} \right| \cdot \mathbf{x} \exp(-\mathbf{x}^2) d\mathbf{x} \tag{31}$$

with

138 Optical Devices in Communication and Computation

the output spectrum from the SMCW.

*n1* = 1.765, *h* = 21 nm, *d* = 0.85 mm and *θ* = 6.1o

**3.2. Optical sensors** 

*3.2.1. Sensitivity analysis* 

characteristics parameters which is expressed as:

several degrees of the incident angle according to Eq. (26).

and (27), both the center wavelength and the channel spacing can be tuned by simply changing the incident angle. The parameters of SMCW that achieve comb filter are as follows: a glass (ZF7) slab (*d*=900μm); the thickness of the upper film *h*=20 nm. Fig.9 shows

**Figure 9.** Experimental and theoretical reflective spectrum of SMCW, with parameters ε2 = −132+ i12.56,

From Fig.9, we can see equally spaced loss peaks with a 3 dB line-width of 0.1 nm appear in the spectral plot from 1551 to 1556 nm. The wavelength spacing of these peaks is just 0.8 nm. The channel isolation, which is closely related to the thickness of the upper gold film of the waveguide, has been found to be 12 dB. Insertion loss is characterized by the maximum reflectivity, which is greater than 95% (~0.2 dB). The tunability of the filter can be obtained simply by slightly rotating the waveguide with respect to the incident light. Tuning of the center wavelength in the range of channel spacing can be easily obtained by changing

In this section, we propose oscillating wave sensors using SMCW structure. The thickness of guiding layer can be expanded to millimeter scale, which it can contain very sensitive UHM. The high sensitivity can be detected by measuring the intensity variation of the reflected light due to the movement of the corresponding synchronous angle by an optical sensor. In addition, an alternative approach is presented via measuring the enhanced GH shifts at excitement of UHM. This approach enables the possibility to obtain a higher resolution and

If we using the intensity measurement interrogation to observe the response of the sensor, the sensitivity in SMCW can be defined as the rate of change of the reflectivity to center

prevent the disturbance caused by the power fluctuation of the light source.

$$Q = W / \alpha \tag{32}$$

$$\propto = \sqrt{2} \left( \theta\_i - \theta \right) / a \tag{33}$$

$$\propto\_0 = \sqrt{2}(\theta\_i - \theta\_{sp}) / a \tag{34}$$

where *Rm* and *R0* are the values of the reflectivity when guided mode is and is not excited, respectively. θsp is the angle for exciting the guided mode, *W* is the half of the FWHM of the dip, and *α* is the divergence half-angle of the laser beam.

Taking wavelength sensing for example [13], use the parameters: ε2 = −28 + i1.8, *ε1* = 2.278 at 859.8 nm*, h* = 30 nm, *α* = 0.4 mrad and *d* = 0.38 mm. The sensitivity *SI* with respect to the angle of incidence is shown in Fig.10. The UHMs are more sensitive than the low-order modes and are more applicable for sensing.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 141

In the intensity interrogation (as illustrated in Fig. 11(a)), the sample is sealed by an O-ring sandwiched between two gold films that deposited on glass substrates. The two gold films and the sample cell form the SMCW structure. The upper gold film (35 nm in thickness) is deposited on a thin glass slide. The glass slide is 0.178 mm in thickness, with a RI of 1.50. The lower gold film (300 nm) is deposited on a glass plate. The lower glass plate's thickness is 2 mm with an RI of 1.50. The dielectric constants of the gold films are −11.4+i1.50 at the wavelength of 650 nm. The sample cell serves as the guiding layer of the waveguide sensor, and the thickness of the sample cell is governed by the thickness of the O-ring of about 1.99 mm. The aqueous sample could be pumped in and out of the sample cell by a peristaltic pump through the inlet and outlet on the lower substrate. The water sample with an RI of 1.333 can be used as the guiding layer of the waveguide. The guided wave concentrates and propagates in the sample layer as the oscillating field and hence a magnification in

*3.2.2. Refractive index sensing* 

sensitivity is expected. Fig.11(b) is the sensor sample [14].

**Figure 11.** RI sensor of intensity interrogation (a) structural sketch; (b) actual picture

1

3 1

 

*R N S n <sup>S</sup>*

*n*

Then we can see that the use of a smaller incident angle (1.69° in the experiment) as a sensing probe can achieve higher sensitivity. The experimental results are shown in Fig.12. In this case, a 20 ppm NaCl concentration change (corresponding to 2.6×10−6 RIU) can cause a reflectance change of around 3%.With a standard error of 0.2% for the measurement of the optical intensity[15], its resolution with 1% noise level can reach up to 0.88×10-6 RIU for the

cos cos sin

1

  (36)

*R*

Based on sensitivity analysis, SI can be cast in the form of

*I*

ideal case.

**Figure 10.** *S*I versus incident angle *θ*

Similarly, in the GH shift interrogation, the sensitivity of the sensor is defined by the change rate of the GH shift (L) with respect to center characteristics parameters and it can be written as

$$\mathbf{S}\_{\rm GH} = \left(\frac{\partial L}{\partial \theta}\right) \left(\frac{\partial \theta}{\partial \mathbf{N}}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left(\frac{\partial L}{\partial \theta}\right) \left(\frac{\partial \mathbf{N}}{\partial \xi}\right) \equiv \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \mathbf{S}\_L \mathbf{S}\_N \tag{35}$$

Compared with the intensity interrogation, the only difference is the replacement of SR by SL. According to Eq. (22), if the intrinsic damping of the UHM is close to the radiative damping, a large GH shift can be observed [10]. The dependence of the GH shift on the effective index for a selected mode forms a resonance peak. High sensitivity *S*GH can be reached at the up and down sides of the peak. In addition, since the magnitude of the GH shift is irrelevant to the incident light intensity, a power fluctuation of the laser brings no disturbance to the resolution of the optical sensor.

Moreover, the thickness of the upper metal cladding is also an important factor that must be considered when analyzing the sensitivity. The thicknesses of upper and bottom metal films are essential parameters in the determination of the sensitivity. If thickness *h* is excessively thick, it is difficult for the incident light power to be coupled into the planar waveguide structure. However, if thickness *h* is too thin, it is easy for the incident energy to be coupled into the waveguide. On the other hand, it is also easy for the light energy to be coupled out of the waveguide. As a consequence, there is an optimum solution to thickness *h* by which the highest sensitivity is obtained. Theoretical and experimental results show that the optimal thickness for the upper metal layer is within the range of about 31–33 nm if the maximum sensitivity is to be achieved. In the following section, refractive index (RI), displacement and light wavelength sensing with extremely high sensitivity are introduced.

#### *3.2.2. Refractive index sensing*

140 Optical Devices in Communication and Computation

**Figure 10.** *S*I versus incident angle *θ*

modes and are more applicable for sensing.

angle of incidence is shown in Fig.10. The UHMs are more sensitive than the low-order

Similarly, in the GH shift interrogation, the sensitivity of the sensor is defined by the change rate of the GH shift (L) with respect to center characteristics parameters and it can be written as

> *GH L N L N L N <sup>S</sup> S S*

Compared with the intensity interrogation, the only difference is the replacement of SR by SL. According to Eq. (22), if the intrinsic damping of the UHM is close to the radiative damping, a large GH shift can be observed [10]. The dependence of the GH shift on the effective index for a selected mode forms a resonance peak. High sensitivity *S*GH can be reached at the up and down sides of the peak. In addition, since the magnitude of the GH shift is irrelevant to the incident light intensity, a power fluctuation of the laser brings no

Moreover, the thickness of the upper metal cladding is also an important factor that must be considered when analyzing the sensitivity. The thicknesses of upper and bottom metal films are essential parameters in the determination of the sensitivity. If thickness *h* is excessively thick, it is difficult for the incident light power to be coupled into the planar waveguide structure. However, if thickness *h* is too thin, it is easy for the incident energy to be coupled into the waveguide. On the other hand, it is also easy for the light energy to be coupled out of the waveguide. As a consequence, there is an optimum solution to thickness *h* by which the highest sensitivity is obtained. Theoretical and experimental results show that the optimal thickness for the upper metal layer is within the range of about 31–33 nm if the maximum sensitivity is to be achieved. In the following section, refractive index (RI), displacement and light wavelength sensing with extremely high sensitivity are introduced.

*N* 

 

disturbance to the resolution of the optical sensor.

3 3

1 1 cos cos

(35)

 

  In the intensity interrogation (as illustrated in Fig. 11(a)), the sample is sealed by an O-ring sandwiched between two gold films that deposited on glass substrates. The two gold films and the sample cell form the SMCW structure. The upper gold film (35 nm in thickness) is deposited on a thin glass slide. The glass slide is 0.178 mm in thickness, with a RI of 1.50. The lower gold film (300 nm) is deposited on a glass plate. The lower glass plate's thickness is 2 mm with an RI of 1.50. The dielectric constants of the gold films are −11.4+i1.50 at the wavelength of 650 nm. The sample cell serves as the guiding layer of the waveguide sensor, and the thickness of the sample cell is governed by the thickness of the O-ring of about 1.99 mm. The aqueous sample could be pumped in and out of the sample cell by a peristaltic pump through the inlet and outlet on the lower substrate. The water sample with an RI of 1.333 can be used as the guiding layer of the waveguide. The guided wave concentrates and propagates in the sample layer as the oscillating field and hence a magnification in sensitivity is expected. Fig.11(b) is the sensor sample [14].

**Figure 11.** RI sensor of intensity interrogation (a) structural sketch; (b) actual picture

Based on sensitivity analysis, SI can be cast in the form of

$$S\_I = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left(\frac{\partial R}{\partial \theta}\right) \left(\frac{\partial N}{\partial n\_1}\right) \equiv \frac{S\_R n\_1}{\cos \theta \cdot \sin \theta} \tag{36}$$

Then we can see that the use of a smaller incident angle (1.69° in the experiment) as a sensing probe can achieve higher sensitivity. The experimental results are shown in Fig.12. In this case, a 20 ppm NaCl concentration change (corresponding to 2.6×10−6 RIU) can cause a reflectance change of around 3%.With a standard error of 0.2% for the measurement of the optical intensity[15], its resolution with 1% noise level can reach up to 0.88×10-6 RIU for the ideal case.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 143

Fig.14. The step change of 20 ppm NaCl solution in concentration, which corresponds to a variation of 2.64 ×10−6 RIU, induces a GH shift change of at least 20 μm. Considering the noise level in the experiment, the probing sensitivity of 2.0×10−7 RIU is resolved since the measurement variation of the GH shift is confined within 1.5 μm for each sample [16].

In the experimental setup, we propose to use a variable air gap produced by a calibrated piezoelectric translator (PZT) to act as the guiding layer of the optical waveguide. As shown in Fig.15, the sample for minute displacement measurement is composed of two parts: one is a glass prism on its base precoated with a thin gold film; the other is a 500 μm thick LiNbO3 slab sandwiched between two 400 nm thick gold films and serves as a PZT. The two components, separated by an air gap with a thickness of 100 mm, are rigidly mounted on a heavy platform. The gold films deposited on the prism and the upper surface of LiNbO3

**Figure 14.** The GH shifts with respect to solutions of different concentrations in the sample cell: (a) pure water, (b) 20ppm NaCl solution, (c) 40 ppm NaCl solution, (d) 60 ppm NaCl solution, and (e) 80 ppm

As soon as applying a dc voltage on the pair electrodes of the PZT, the air gap changes its thickness due to the piezoelectric effect of the LiNbO3 slab. As a result, the reflection dip shifts its peak position and result in a change of the reflectivity. According to the resolution of the reflectivity variation, displacement can be evaluated from the applied voltage and the piezoelectric coefficient of the LiNbO3 slab. In the intensity interrogation, SI can be cast in

> 1 sin cos cos sin *I R R N S S*

We can also use UHM as the sensing probe to achieve higher sensitivity. Test experiment has been performed with the waveguide parameters as follows: *ε1*=1.0, *ε2*=−11+i1.0, *ε3*=3.0, *d*=108 μm, *h*=40 nm, and *λ*=650 nm. Displacement sensitivity of proposed configuration is

 

3 3

  2

(37)

 

1 3

*d d* 

 

*3.2.3. Displacement sensing* 

NaCl solution

the form of

slab, together with the air gap form an SMCW.

**Figure 12.** Sensor response for NaCl water solution in the experiment. The left side of the curve is the scanned reflectance curve of the three highest guiding modes. The scan motor stopped at the fall-off of the fourth resonance dip. 20 ppm NaCl water solution is filled in the sample cell and the first measurement starts at A and is then paused. After pure water is pumped in the sample cell and the signal stabilized, measurement starts at B and then back to the 20 ppm NaCl sample measurement at C. The sensor response is enlarged in the inset.

**Figure 13.** RI sensor of GH shift interrogation (a) structural sketch; (b) actual picture

In the GH shift interrogation (as illustrated in Fig. 13), a glass prism is coated with a 20 nm thick gold film to serve as the coupling layer. A 300 nm thick gold film is sputtered on a glass slab to act as the substrate. The air gap of 0.7 mm sandwiched between two gold films works as the guiding layer, where a gasket is used to form a sealed sample cell. With the help of a peristaltic pump, sample liquids to be detected flow into the cell through the inlet and the outlet tubes embedded in the substrate glass plate.

The expression of sensitivity SGH is similar to Eq. (36) by replacing SR with SL. So UHM is also selected as a sensing probe. Experiments are carried out with the waveguide parameters as follows: *θ*=4.60°, *ε3*=2.25, *ε2*=−28+1.8i, *h*=20 nm, and *d*=0.7 mm, for pure water (solid curve), *n1*=1.333 RIU. A series of NaCl solutions with the change step of 20 ppm in concentration is used as sample analyte to be probed. The experimental result is shown in Fig.14. The step change of 20 ppm NaCl solution in concentration, which corresponds to a variation of 2.64 ×10−6 RIU, induces a GH shift change of at least 20 μm. Considering the noise level in the experiment, the probing sensitivity of 2.0×10−7 RIU is resolved since the measurement variation of the GH shift is confined within 1.5 μm for each sample [16].

#### *3.2.3. Displacement sensing*

142 Optical Devices in Communication and Computation

The sensor response is enlarged in the inset.

**Figure 12.** Sensor response for NaCl water solution in the experiment. The left side of the curve is the scanned reflectance curve of the three highest guiding modes. The scan motor stopped at the fall-off of

the fourth resonance dip. 20 ppm NaCl water solution is filled in the sample cell and the first measurement starts at A and is then paused. After pure water is pumped in the sample cell and the signal stabilized, measurement starts at B and then back to the 20 ppm NaCl sample measurement at C.

**Figure 13.** RI sensor of GH shift interrogation (a) structural sketch; (b) actual picture

and the outlet tubes embedded in the substrate glass plate.

In the GH shift interrogation (as illustrated in Fig. 13), a glass prism is coated with a 20 nm thick gold film to serve as the coupling layer. A 300 nm thick gold film is sputtered on a glass slab to act as the substrate. The air gap of 0.7 mm sandwiched between two gold films works as the guiding layer, where a gasket is used to form a sealed sample cell. With the help of a peristaltic pump, sample liquids to be detected flow into the cell through the inlet

The expression of sensitivity SGH is similar to Eq. (36) by replacing SR with SL. So UHM is also selected as a sensing probe. Experiments are carried out with the waveguide parameters as follows: *θ*=4.60°, *ε3*=2.25, *ε2*=−28+1.8i, *h*=20 nm, and *d*=0.7 mm, for pure water (solid curve), *n1*=1.333 RIU. A series of NaCl solutions with the change step of 20 ppm in concentration is used as sample analyte to be probed. The experimental result is shown in In the experimental setup, we propose to use a variable air gap produced by a calibrated piezoelectric translator (PZT) to act as the guiding layer of the optical waveguide. As shown in Fig.15, the sample for minute displacement measurement is composed of two parts: one is a glass prism on its base precoated with a thin gold film; the other is a 500 μm thick LiNbO3 slab sandwiched between two 400 nm thick gold films and serves as a PZT. The two components, separated by an air gap with a thickness of 100 mm, are rigidly mounted on a heavy platform. The gold films deposited on the prism and the upper surface of LiNbO3 slab, together with the air gap form an SMCW.

**Figure 14.** The GH shifts with respect to solutions of different concentrations in the sample cell: (a) pure water, (b) 20ppm NaCl solution, (c) 40 ppm NaCl solution, (d) 60 ppm NaCl solution, and (e) 80 ppm NaCl solution

As soon as applying a dc voltage on the pair electrodes of the PZT, the air gap changes its thickness due to the piezoelectric effect of the LiNbO3 slab. As a result, the reflection dip shifts its peak position and result in a change of the reflectivity. According to the resolution of the reflectivity variation, displacement can be evaluated from the applied voltage and the piezoelectric coefficient of the LiNbO3 slab. In the intensity interrogation, SI can be cast in the form of

$$S\_I = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left(\frac{\partial \mathcal{R}}{\partial \theta}\right) \left(\frac{\partial \mathcal{N}}{\partial d}\right) \equiv \frac{\varepsilon\_1 - \varepsilon\_3 \sin^2 \theta}{\varepsilon\_3 \cos \theta \cdot \sin \theta \cdot d} \cdot S\_R \tag{37}$$

We can also use UHM as the sensing probe to achieve higher sensitivity. Test experiment has been performed with the waveguide parameters as follows: *ε1*=1.0, *ε2*=−11+i1.0, *ε3*=3.0, *d*=108 μm, *h*=40 nm, and *λ*=650 nm. Displacement sensitivity of proposed configuration is

shown in Fig.16. The waveguide thickness *d* is increased and decreased in steps by increasing and reducing the voltages applied on the electrodes of the PZT. The step-style change of voltage is 50 V. According to the piezoelectric coefficient of a Z-cut LiNbO3 slab, d33=33.45 pm/V, the value of the displacement resolution for the proposed configuration is determined as SI =50×33.45×10-3=1.7 nm, which corresponds to the reflectivity change of R=1%[17].

Optical Devices Based on Symmetrical Metal Cladding Waveguides 145

2

 

(38)

 

1 3

 

coefficient of the z-cut LiNbO3 is d33=8 ×10−12 m/v. Thus, the thickness change per step is determined as *Δd*=8×10−12×10 m=8×10−11 m, which leads to a GH shift change of 2 μm. The experimental ripple of each step is confined to 0.5 μm. With this noise level, the sensing

> 1 sin cos cos sin *I R R N S S*

It is found that the effective index is extremely sensitive to *λ* in the case of *N* → 0. The waveguide parameters are given as follows: *d* = 0.38 mm, ε2 = −28 + i1.8, ε1 = 2.278, and *h*= 31 nm. The initial wavelength was set to 859.800 nm. Once this value was stabilized, the reference wavelength was changed subsequently to 859.8005, 859.8010, 859.8015, and 859.8020 nm and decreased back to 859.8000 nm in steps. The step-style change of wavelength is 0.5 pm, with the average 2.5% change in the reflectivity *ΔR*. Considering a noise level of about 0.05% in Fig.18, a resolution of 0.2pm is finally obtained for the

**Figure 17.** Experimental sensitivity of the proposed configuration. Voltage applied on the PZT between

each step is 10 V, which leads to an 8×10−11 m change of the air gap thickness.

 

In the intensity interrogation, the wavelength sensitivity SI can be written as

 

3 3

resolution is evaluated to be 40 pm[18].

*3.2.4. Wavelength sensing* 

reflectivity change of R=1%[13].

**Figure 15.** Displacement sensor of intensity interrogation (a) structural sketch; (b) actual picture

**Figure 16.** Experimental result of displacement measurement: (a) m-line obtained by angular scanning and displacement experimental result; (b) intensity export by applying step-styled voltages.

In the GH shift interrogation, the sensor structure is the same as Fig. 15. The experiment was performed with the following parameters: ε2=−28+1.8i, ε1=1, ε3=2.25, *d*=500 μm, and *h* =18 nm. The incident wavelength is adjusted to be 859.00 nm. The experimental result is shown in Fig.17. The voltage applied on the PZT between each step is 10 V, and the piezoelectric coefficient of the z-cut LiNbO3 is d33=8 ×10−12 m/v. Thus, the thickness change per step is determined as *Δd*=8×10−12×10 m=8×10−11 m, which leads to a GH shift change of 2 μm. The experimental ripple of each step is confined to 0.5 μm. With this noise level, the sensing resolution is evaluated to be 40 pm[18].

#### *3.2.4. Wavelength sensing*

144 Optical Devices in Communication and Computation

R=1%[17].

shown in Fig.16. The waveguide thickness *d* is increased and decreased in steps by increasing and reducing the voltages applied on the electrodes of the PZT. The step-style change of voltage is 50 V. According to the piezoelectric coefficient of a Z-cut LiNbO3 slab, d33=33.45 pm/V, the value of the displacement resolution for the proposed configuration is determined as SI =50×33.45×10-3=1.7 nm, which corresponds to the reflectivity change of

**Figure 15.** Displacement sensor of intensity interrogation (a) structural sketch; (b) actual picture

**Figure 16.** Experimental result of displacement measurement: (a) m-line obtained by angular scanning

In the GH shift interrogation, the sensor structure is the same as Fig. 15. The experiment was performed with the following parameters: ε2=−28+1.8i, ε1=1, ε3=2.25, *d*=500 μm, and *h* =18 nm. The incident wavelength is adjusted to be 859.00 nm. The experimental result is shown in Fig.17. The voltage applied on the PZT between each step is 10 V, and the piezoelectric

and displacement experimental result; (b) intensity export by applying step-styled voltages.

In the intensity interrogation, the wavelength sensitivity SI can be written as

$$\boldsymbol{S}\_{I} = \frac{1}{\sqrt{\varepsilon\_{3}} \cos \theta} \left( \frac{\partial \mathcal{R}}{\partial \theta} \right) \left( \frac{\partial \mathcal{N}}{\partial \mathcal{L}} \right) \equiv \frac{\varepsilon\_{1} - \varepsilon\_{3} \sin^{2} \theta}{\varepsilon\_{3} \cos \theta \cdot \sin \theta \cdot \mathcal{L}} \cdot \mathcal{S}\_{R} \tag{38}$$

It is found that the effective index is extremely sensitive to *λ* in the case of *N* → 0. The waveguide parameters are given as follows: *d* = 0.38 mm, ε2 = −28 + i1.8, ε1 = 2.278, and *h*= 31 nm. The initial wavelength was set to 859.800 nm. Once this value was stabilized, the reference wavelength was changed subsequently to 859.8005, 859.8010, 859.8015, and 859.8020 nm and decreased back to 859.8000 nm in steps. The step-style change of wavelength is 0.5 pm, with the average 2.5% change in the reflectivity *ΔR*. Considering a noise level of about 0.05% in Fig.18, a resolution of 0.2pm is finally obtained for the reflectivity change of R=1%[13].

**Figure 17.** Experimental sensitivity of the proposed configuration. Voltage applied on the PZT between each step is 10 V, which leads to an 8×10−11 m change of the air gap thickness.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 147

4 1 33

 

1

(39)

(40)

electric field modulates refractive index of the EO polymer, resulting in the change of the effective refractive index for the guided modes, shifting the resonance dips along the angular direction in ATR spectrum. If we define γ33 as the EO coefficient of the polymer and E is the applied electric field across the EO polymer film. The refractive index change of

> 3 1 1 33 1 2 *n nE*

cos sin 2 *<sup>R</sup> R N S n*

*R n E n*

Therefore the reflected light is modulated by the applied electric field. Higher sensitivity is obtained at the midst of the fall-off of the resonance dip excited at smaller resonance angle with thicker guiding layer, so that enhanced modulation is realized by enabling the device

In the experiment, the gold film about 300nm was sputtered onto the surface of the K9 glass flat to serve as substrate and one electrode. A PMMA-based second-order nonlinear optical (NLO) side-chain material containing the disperse red chromophore was synthesized through copolymerization for electro-optic device. The polymer was dissolved in toluene, 25% polymer to 75% toluene by weight. A 12-thick polymer film was spin coated onto the gold film substrate, and then was tempered at 40o in a vacuum for 12 hours to remove the residual solvent. The refractive index of polymer is 1.52 at wavelength 832nm. In order to remove the centrosymmetric structure of the chromophores, the film was corona-poled in the air by an applied electric voltage of 4000V at 110o for 25 min with inter-electrode distance being 20mm, and cooled down to room temperature with the field still applied. Finally, the upper gold film about 30nm thick was deposited on the polymer film by sputtering technique to serve as the coupling layer and another electrode. The complex dielectric constant of the gold film is *ε2* = −28 + i1.6. The EO coefficient γ33 of polymer measured at 832 nm using improved ATR method is 11.9 pmV. A collimated TM-polarized beam with 832nm wavelength is used. The modulation working angle was chosen at the midst of the fall-off of the resonance dip excited at resonance angle 9.7o. A sinusoidal electrical field was applied across the two electrodes with 10 Vp-p driving voltage at 1MHz, the electro-optic modulation process was obtained. The oscilloscope traces of modulating voltage and reflected intensity versus time are shown, respectively, in Fig.20. The modulation depth was measured to be 8.7%. However, under the same electrical field the modulation depth was only 5.6% when the resonance dip at 28.9o was used, which is attributed to lower sensitivity at larger

At the midst of the fall-offs of resonance dip, where a considerably good linearity is

*R*

3 1

 

1

to operate with stronger modulation depth and lower driving voltage.

resonance angle. The total insertion loss of the sample was 1.08 dB[20].

guiding layer Δn1 is written as [19]:

observed, the change of the light reflectivity is:

**Figure 18.** Wavelength sensitivity of the proposed configuration. The shift in the ATR curve was measured by changing the wavelength in steps of 0.5 pm. The angle of incidence is 3.82°.

For the GH shift measurement, the waveguide parameters are given as follows: *d* = 0.5 mm, *ε<sup>2</sup>* = −28 + i1.8, *ε1* = 1, *ε3* =2.25, *h* = 19.8 nm, and *θ*=4.263°. We first fix the wavelength (*λ*=859.003 nm). As shown in Fig.19, the change of wavelength 1 pm will cause the average variation of reflective light lateral shift about 10 μm.

**Figure 19.** Experiment result using GH shift measurement

#### **3.3. Optical modulators**

The configuration of electro-optic (EO) modulator is a SMCW on a glass (K9) flat. The cover and the substrate are both gold film, and the waveguide is EO polymer film. An applied electric field modulates refractive index of the EO polymer, resulting in the change of the effective refractive index for the guided modes, shifting the resonance dips along the angular direction in ATR spectrum. If we define γ33 as the EO coefficient of the polymer and E is the applied electric field across the EO polymer film. The refractive index change of guiding layer Δn1 is written as [19]:

146 Optical Devices in Communication and Computation

**Figure 18.** Wavelength sensitivity of the proposed configuration. The shift in the ATR curve was measured by changing the wavelength in steps of 0.5 pm. The angle of incidence is 3.82°.

variation of reflective light lateral shift about 10 μm.

**Figure 19.** Experiment result using GH shift measurement

**3.3. Optical modulators** 

For the GH shift measurement, the waveguide parameters are given as follows: *d* = 0.5 mm, *ε<sup>2</sup>* = −28 + i1.8, *ε1* = 1, *ε3* =2.25, *h* = 19.8 nm, and *θ*=4.263°. We first fix the wavelength (*λ*=859.003 nm). As shown in Fig.19, the change of wavelength 1 pm will cause the average

The configuration of electro-optic (EO) modulator is a SMCW on a glass (K9) flat. The cover and the substrate are both gold film, and the waveguide is EO polymer film. An applied

$$
\Delta \mathfrak{m}\_1 = -\frac{1}{2} \mathfrak{m}\_1^3 \mathcal{V}\_{33} E \tag{39}
$$

At the midst of the fall-offs of resonance dip, where a considerably good linearity is observed, the change of the light reflectivity is: *R*

$$
\Delta R = \frac{1}{\sqrt{\varepsilon\_3} \cos \theta} \left( \frac{\partial R}{\partial \theta} \right) \left( \frac{\partial N}{\partial n\_1} \right)
\Delta n\_1 = \frac{S\_R n\_1^4 \gamma\_{33}}{\sin 2\theta} E \tag{40}
$$

Therefore the reflected light is modulated by the applied electric field. Higher sensitivity is obtained at the midst of the fall-off of the resonance dip excited at smaller resonance angle with thicker guiding layer, so that enhanced modulation is realized by enabling the device to operate with stronger modulation depth and lower driving voltage.

In the experiment, the gold film about 300nm was sputtered onto the surface of the K9 glass flat to serve as substrate and one electrode. A PMMA-based second-order nonlinear optical (NLO) side-chain material containing the disperse red chromophore was synthesized through copolymerization for electro-optic device. The polymer was dissolved in toluene, 25% polymer to 75% toluene by weight. A 12-thick polymer film was spin coated onto the gold film substrate, and then was tempered at 40o in a vacuum for 12 hours to remove the residual solvent. The refractive index of polymer is 1.52 at wavelength 832nm. In order to remove the centrosymmetric structure of the chromophores, the film was corona-poled in the air by an applied electric voltage of 4000V at 110o for 25 min with inter-electrode distance being 20mm, and cooled down to room temperature with the field still applied. Finally, the upper gold film about 30nm thick was deposited on the polymer film by sputtering technique to serve as the coupling layer and another electrode. The complex dielectric constant of the gold film is *ε2* = −28 + i1.6. The EO coefficient γ33 of polymer measured at 832 nm using improved ATR method is 11.9 pmV. A collimated TM-polarized beam with 832nm wavelength is used. The modulation working angle was chosen at the midst of the fall-off of the resonance dip excited at resonance angle 9.7o. A sinusoidal electrical field was applied across the two electrodes with 10 Vp-p driving voltage at 1MHz, the electro-optic modulation process was obtained. The oscilloscope traces of modulating voltage and reflected intensity versus time are shown, respectively, in Fig.20. The modulation depth was measured to be 8.7%. However, under the same electrical field the modulation depth was only 5.6% when the resonance dip at 28.9o was used, which is attributed to lower sensitivity at larger resonance angle. The total insertion loss of the sample was 1.08 dB[20].

Optical Devices Based on Symmetrical Metal Cladding Waveguides 149

**Figure 21.** Schematic layout of the SMCW for verifying slow light effect

delay [22].

*ε2* =−19 + 0.5i , *ε1* = 2.89, and *d* = 2 mm.

In the experimental arrangement, the source is a collimated light beam at a wavelength of 650 nm, which is modulated by an EO modulator to produce a signal of 1.0 GHz sinusoidal pulse train. Two photodiodes are setup to detect the light intensity. The first photodiode (PD1) takes in the reflected light beam, which serves as the reference beam. The second photodiode (PD2) is used to measure the time delay of the slowed light beam. The tunable delay is measured by an oscilloscope with the bandwidth of 2 GHz. We measure the delay times *Δt* at different fixed incident angles, which become larger as the incident angle *θ* becomes smaller. The experimental results are illustrated in Fig.23. After propagating through a 1.1-cm-long active region, a delay of 2.165 ns was achieved, that corresponds to group velocities less than 0.017c. Further decreasing the incident angle could generate more

**Figure 22.** Dispersion curves and group index characteristics of ultrahigh-order modes with parameters

**Figure 20.** Oscilloscope traces of modulating voltage versus time (upside) and the reflected intensity versus time (downside).

#### **3.4. Slow light devices**

The scheme diagram of the SMCW for verifying slow light effect is illustrated in Fig. 21. The advantages of this geometry are that the slow light properties can be tailored to the desired wavelength and the delay is tunable by varying the incident angle and the parameters of the guiding layer. This is important because the applications of slow light require a degree of tunability. These make the proposed slow light scheme useful and practical.

Test experiment has been performed with the waveguide parameters as follows: *ε1* = 2.89, *ε<sup>2</sup>* = −19 + 0.5i (silver lms), *ε3*=1.0, *d*=2mm (glass slab), *h*=30 nm, *λ*=632.8 nm, and *θ*=3°. An additional silver stripe (about 500nm thick and 1.1 cm wide) is fabricated in the middle of this layer to prevent light leakage. According to Eq.(19), one finds that Im(*β0*)=0.1158526mm−1, which shows that the signal power is about 10% after propagating along the guiding layer for about 1 cm. The proposed structure is completely different from the conventional Fabry-Perot cavity, and those similar folded optical delay lines where the incident ray of light bounces in the cavity between the two interfaces (mirrors) before it exits [21]. From Eq. (12), the slow light effect can be observed only when a specific UHM that propagates along the guiding layer is excited, thus the proposed slow light scheme does not rely on obtaining long optical paths. This proposed slow light mechanism can also be interpreted in terms of the anomalous dispersion of the UHMs, which is depicted in Fig.22. It is demonstrated in Fig.22 that anomalous dispersion curves of the proposed structure exhibit an extremely flattened region (slow light region) in the vicinity of zero wave number (N→0).

**Figure 21.** Schematic layout of the SMCW for verifying slow light effect

versus time (downside).

practical.

(N→0).

**3.4. Slow light devices** 

**Figure 20.** Oscilloscope traces of modulating voltage versus time (upside) and the reflected intensity

The scheme diagram of the SMCW for verifying slow light effect is illustrated in Fig. 21. The advantages of this geometry are that the slow light properties can be tailored to the desired wavelength and the delay is tunable by varying the incident angle and the parameters of the guiding layer. This is important because the applications of slow light require a degree of tunability. These make the proposed slow light scheme useful and

Test experiment has been performed with the waveguide parameters as follows: *ε1* = 2.89, *ε<sup>2</sup>* = −19 + 0.5i (silver lms), *ε3*=1.0, *d*=2mm (glass slab), *h*=30 nm, *λ*=632.8 nm, and *θ*=3°. An additional silver stripe (about 500nm thick and 1.1 cm wide) is fabricated in the middle of this layer to prevent light leakage. According to Eq.(19), one finds that Im(*β0*)=0.1158526mm−1, which shows that the signal power is about 10% after propagating along the guiding layer for about 1 cm. The proposed structure is completely different from the conventional Fabry-Perot cavity, and those similar folded optical delay lines where the incident ray of light bounces in the cavity between the two interfaces (mirrors) before it exits [21]. From Eq. (12), the slow light effect can be observed only when a specific UHM that propagates along the guiding layer is excited, thus the proposed slow light scheme does not rely on obtaining long optical paths. This proposed slow light mechanism can also be interpreted in terms of the anomalous dispersion of the UHMs, which is depicted in Fig.22. It is demonstrated in Fig.22 that anomalous dispersion curves of the proposed structure exhibit an extremely flattened region (slow light region) in the vicinity of zero wave number In the experimental arrangement, the source is a collimated light beam at a wavelength of 650 nm, which is modulated by an EO modulator to produce a signal of 1.0 GHz sinusoidal pulse train. Two photodiodes are setup to detect the light intensity. The first photodiode (PD1) takes in the reflected light beam, which serves as the reference beam. The second photodiode (PD2) is used to measure the time delay of the slowed light beam. The tunable delay is measured by an oscilloscope with the bandwidth of 2 GHz. We measure the delay times *Δt* at different fixed incident angles, which become larger as the incident angle *θ* becomes smaller. The experimental results are illustrated in Fig.23. After propagating through a 1.1-cm-long active region, a delay of 2.165 ns was achieved, that corresponds to group velocities less than 0.017c. Further decreasing the incident angle could generate more delay [22].

**Figure 22.** Dispersion curves and group index characteristics of ultrahigh-order modes with parameters *ε2* =−19 + 0.5i , *ε1* = 2.89, and *d* = 2 mm.

Optical Devices Based on Symmetrical Metal Cladding Waveguides 151

*Engineering Research Center of Optical Instrument and System, Ministry of Education,* 

The author thanks Ning Yang and YinQi Bao, students from the University of Shanghai for Science and Technology, for editing the manuscript of this chapter. This work is partly supported by the Leading Academic Discipline Project of Shanghai Municipal Government (S30502), "Chen Guang" Research Fund from Shanghai Municipal Education Commission and Shanghai Education Development Foundation (09CG49), and the Basic Research Program of Shanghai from Shanghai Committee of Science and Technology

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[2] B. Yu, G. Pickrell, and A. Wang, Thermally tunable extrinsic Fabry-Perot filter, *IEEE* 

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**Author details** 

**Acknowledgement** 

(11ZR1425000).

**5. References** 

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*Shanghai Key Lab of Modern Optical System,* 

*University of Shanghai for Science and Technology, China* 

Lin Chen

**Figure 23.** Delay tuning of slow light in an SMCW structure by adjusting the incident angle.

#### **4. Conclusion**

The properties of UHM in a SMCW and its applications on optical devices have been demonstrated in this chapter. It is found that the effective refractive index of UHM is sensitive to the refractive index, the thickness of the waveguide layer and the incident wavelength. UHM has also shown strong dispersion and polarization independent effects. Then, a polarization independent and tunable comb filter based on SMCW has been introduced, which has greater than 12 dB channel isolation, less than 0.2 dB insertion loss, and accurate 0.8 nm channel spacing in optical communication range. Taking the reflectivity and GH shift as the sensing probe, a new oscillating wave sensor is investigated to measure minute changes in various parameters such as the refractive index of the guiding layer, the thickness of the waveguide layer and the incident wavelength. It is demonstrated both theoretically and experimentally that its sensitivity is enhanced by one order of magnitude than that of evanescent wave sensor. Furthermore, an EO polymer modulator employing an SMCW is presented. The fabricated modulator achieves an 8.2% modulation depth with 10Vp-p driving voltage at 1 MHz. Finally, a new mechanism for slow light assisted by UHMs excited in the SMCW is introduced. A delay bandwidth product greater than 2 is demonstrated in the experiment with a signal of 1.0 GHz sinusoidal pulse train. Without use of any coherent or material resonance, this scheme is not subject to limitations of the delay bandwidth product and can generate arbitrarily small group velocities over an unusually large frequency bandwidth. We think such SMCWs possess unique and advantageous properties over the state-of-the-art and may have great potential for next generation optical devices.

#### **Author details**

150 Optical Devices in Communication and Computation

**4. Conclusion** 

devices.

**Figure 23.** Delay tuning of slow light in an SMCW structure by adjusting the incident angle.

The properties of UHM in a SMCW and its applications on optical devices have been demonstrated in this chapter. It is found that the effective refractive index of UHM is sensitive to the refractive index, the thickness of the waveguide layer and the incident wavelength. UHM has also shown strong dispersion and polarization independent effects. Then, a polarization independent and tunable comb filter based on SMCW has been introduced, which has greater than 12 dB channel isolation, less than 0.2 dB insertion loss, and accurate 0.8 nm channel spacing in optical communication range. Taking the reflectivity and GH shift as the sensing probe, a new oscillating wave sensor is investigated to measure minute changes in various parameters such as the refractive index of the guiding layer, the thickness of the waveguide layer and the incident wavelength. It is demonstrated both theoretically and experimentally that its sensitivity is enhanced by one order of magnitude than that of evanescent wave sensor. Furthermore, an EO polymer modulator employing an SMCW is presented. The fabricated modulator achieves an 8.2% modulation depth with 10Vp-p driving voltage at 1 MHz. Finally, a new mechanism for slow light assisted by UHMs excited in the SMCW is introduced. A delay bandwidth product greater than 2 is demonstrated in the experiment with a signal of 1.0 GHz sinusoidal pulse train. Without use of any coherent or material resonance, this scheme is not subject to limitations of the delay bandwidth product and can generate arbitrarily small group velocities over an unusually large frequency bandwidth. We think such SMCWs possess unique and advantageous properties over the state-of-the-art and may have great potential for next generation optical Lin Chen *Engineering Research Center of Optical Instrument and System, Ministry of Education, Shanghai Key Lab of Modern Optical System, University of Shanghai for Science and Technology, China* 

### **Acknowledgement**

The author thanks Ning Yang and YinQi Bao, students from the University of Shanghai for Science and Technology, for editing the manuscript of this chapter. This work is partly supported by the Leading Academic Discipline Project of Shanghai Municipal Government (S30502), "Chen Guang" Research Fund from Shanghai Municipal Education Commission and Shanghai Education Development Foundation (09CG49), and the Basic Research Program of Shanghai from Shanghai Committee of Science and Technology (11ZR1425000).

#### **5. References**


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**Chapter 8** 

© 2012 Huang and Tao, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

Surface Plasmon polaritons (SPPs) are electromagnetic waves that propagate along the interface of metal and dielectric. In recent years, plasmonics is called the area of

and reproduction in any medium, provided the original work is properly cited.

**Nano-Plasmonic Filters Based on** 

Xu Guang Huang and Jin Tao

nano-scale optical elements integration.

http://dx.doi.org/10.5772/75765

**1. Introduction** 

Additional information is available at the end of the chapter

**Tooth-Shaped Waveguide Structures** 

Along with development of human society and technology, it becomes more dependable on the miniaturization and integration of semiconductor components, circuits and devices. The performance of integrated circuits, such as micro-processor, is in accordance with the famous Moore's law that the number of transistors placed inexpensively on an integrated circuit doubles approximately every two years. However, the integration of modern electronic components and devices for information communication and processing have been approaching its fundamental speed and bandwidth limitation, because the ultra-intensive electrical interconnects have an increased effective resistor-capacitor (RC) time constant that increases the time of charging and discharging [1, 2]. This has caused an increasing serious problem that hinders further development in many fields of modern science and technology. Using light signals instead of electronic is one of the most promising solutions. The speed of optical signal is on the order of 108 m/s, which is about 3 orders of the saturation velocity of electrons in a semiconductor such as silicon [3]. However, a major problem with using light as information carrier in conventional optical devices is the poor performance of integration and miniaturization. Dielectric waveguides are basic components and cannot allow the localization of electromagnetic waves into subwavelength-scale regions because of diffraction limit λ0/2*n*, here λ0 is the wavelength of the light in the free space and *n* is the refractive index of the dielectric. Photonic crystal (PC) structures and devices have been studied by many researchers since E. Yablonovitch and S. John ' s two milestone published papers in 1987 [4, 5], which confirmed that the light can be confined in the nanoscale. However, the dimensions of the PC system are on the order of the wavelength or even larger, making them less appropriate for


## **Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures**

Xu Guang Huang and Jin Tao

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/75765

#### **1. Introduction**

152 Optical Devices in Communication and Computation

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[18] T. Y. Yu, H. G. Li, Z. Q. Cao, Y. Wang, Q. S. Shen, and Y. He, Oscillating wave displacement sensor using the enhanced Goos–Hänchen effect in a symmetrical metal-

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[20] X. X. Deng, P. P. Xiao, X. Zheng, Z. Q. Cao, Q. S. Shen, K. Zhu, H. G. Li, W. Wei, S. X. Xie, and Z. J. Zhang, An electro-optic polymer modulator based on the free-space

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polymers, *J. Opt. Soc. Am. B*, Vol. 17, No. 5, pp. 805-808 (2000).

waveguides, *Opt. lett.*, Vol. 32, No.11, pp. 1432-1434 (2007).

Along with development of human society and technology, it becomes more dependable on the miniaturization and integration of semiconductor components, circuits and devices. The performance of integrated circuits, such as micro-processor, is in accordance with the famous Moore's law that the number of transistors placed inexpensively on an integrated circuit doubles approximately every two years. However, the integration of modern electronic components and devices for information communication and processing have been approaching its fundamental speed and bandwidth limitation, because the ultra-intensive electrical interconnects have an increased effective resistor-capacitor (RC) time constant that increases the time of charging and discharging [1, 2]. This has caused an increasing serious problem that hinders further development in many fields of modern science and technology. Using light signals instead of electronic is one of the most promising solutions. The speed of optical signal is on the order of 108 m/s, which is about 3 orders of the saturation velocity of electrons in a semiconductor such as silicon [3]. However, a major problem with using light as information carrier in conventional optical devices is the poor performance of integration and miniaturization. Dielectric waveguides are basic components and cannot allow the localization of electromagnetic waves into subwavelength-scale regions because of diffraction limit λ0/2*n*, here λ0 is the wavelength of the light in the free space and *n* is the refractive index of the dielectric. Photonic crystal (PC) structures and devices have been studied by many researchers since E. Yablonovitch and S. John ' s two milestone published papers in 1987 [4, 5], which confirmed that the light can be confined in the nanoscale. However, the dimensions of the PC system are on the order of the wavelength or even larger, making them less appropriate for nano-scale optical elements integration.

Surface Plasmon polaritons (SPPs) are electromagnetic waves that propagate along the interface of metal and dielectric. In recent years, plasmonics is called the area of

© 2012 Huang and Tao, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

nanophotonics under the light diffraction limit that studies the transmission characteristics, localization, guiding of the SPP mode using metallic nanosturctures. The plasmonic waveguides are the most basic components and have been given much attention. Various kinds of metallic nanostructures have been proposed for SPP guiding. Generally these structures could be classified into three big categories: 1) chains of metal nanoparticles [6] and cylindrical metallic nanorods with various geometries [7]. 2) Metaldielectirc-metal (MDM) or Metal-insulator-metal (MIM) plasmonic waveguides, including groove channel structures in metallic substrates [8], slot waveguide [9]. 3) Dielectricmetal-dielectric (DMD)/ Insulator-metal-Insulator (IMI) waveguide [10]. It should be noted that not all these plasmonic structures can be used for guiding SPP mode to achieve subwavelength localization. Among them, MDM/MIM plasmonic waveguide can propagate SPP mode in the subwavelength scale with relatively low dissipation and large propagation distance. Our following proposed structures are mainly based on the MDM/MIM structures.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 155

(2)

*<sup>p</sup> Hz* is the bulk plasma

stands for the dielectric constant at

),

is the angular

with *k*z1 and *k*z2 defined by momentum conservations:

Drude model: <sup>2</sup> ( ) / ( ). *m p <sup>i</sup>* Here <sup>16</sup> 1.38 10

frequency of the incident electromagnetic radiation,

infinite angular frequency with the value of 3.7 [16]

electrons. <sup>13</sup> 

Where *in* and *<sup>m</sup>*

2 22 2 22 10 20 , . *z in z m kk kk*

*k0*=2π/*λ0* is the free-space wave vector. The propagation constant *β* is represented as the effective index *neff* =*β/k0* of the waveguide for SPPs. The real part of *neff* of the slit waveguide as a function of the slit width at different wavelengths is shown in Fig. 1. It should be noted that the dependence of *neff* on waveguide width is also suitable to the region of the tooth waveguide with the tooth width of *wt* shown in Fig. 2. The imaginary part of *neff* is referred to the propagation length which is defined as the length over which the power carried by the wave decays to 1/e of its initial value: *Lspps*=*λ0*/[4π·Im(*neff*)]. In the calculation above and the following simulations, the insulator in all of the structures is assumed to be air ( 1 *in*

and the frequency-dependent complex relative permittivity of silver is characterized by

frequency, which represents the natural frequency of the oscillations of free conduction

**Figure 1.** Real part of the effective of refraction index versus the width of a MIM slit waveguide structure.

The tooth-shaped waveguide filter is shown in Fig. 2. In the following FDTD simulations, the grid sizes in the *x* and *z* directions are chosen to be 5nm×5nm. Since the width of the waveguide is much smaller than the operating wavelength in the structure, only fundamental waveguide mode is supported. Two power monitors are respectively set at the

2.73 10 *Hz* is the damping frequency of the oscillations,

 

are respectively dielectric constants of the insulator and the metal,

Wavelength selection is one of key technologies in fields of optical communication and computing. To achieve wavelength filtering characteristics, plasmonic Bragg reflectors and nanocavities have been proposed. They include the metal hetero-structures constructed with several periodic slots vertically along a metal-dielectric-metal (MDM) waveguide [11], the Bragg grating fabricated by periodic modulating the thickness of thin metal stripes embedded in an insulator [12] and the periodic structure formed by changing alternately two kinds of the insulators [13,14]. Lately, a high-order plasmonic Bragg reflector with a periodic modulation of the core index of the insulators [15], and a structure with periodic variation of the width of the dielectric in MDM waveguide [16] have been proposed. Most of the periodic structures mentioned above, however, have total length of micrometers and relatively high propagation loss of several decibels.

In this chapter, we present our recent work on compact nano-plasmonic waveguide filters based on T-series and nano-capillary structures. In section 2, we introduce the novel nanometeric plasmonic filter in a tooth-shaped MIM waveguide and give an analytic model based on the scattering matrix method. In section 3, we investigate the characteristics of double-side teeth-shaped nano-plasmonic waveguide. In section 4 and section 5, we introduce the multiple multiple-teeth-shaped plasmonic filters and asymmetrical multiple teeth-shaped narrow pass band subwavelength filter. In section 6, we introduce a wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nanocapillary resonators. Finally, we make a conclusion.

#### **2. Single-tooth shaped plasmonic waveguide filter [17]**

To begin with the dispersion relation of the fundamental TM mode in a MIM waveguide (shown in the inset of Fig. 1) is given by [18]:

$$
\varepsilon\_{in} k\_{z2} + \varepsilon\_m k\_{z1} \coth(-\frac{ik\_{z1}}{2}w) = 0,\tag{1}
$$

with *k*z1 and *k*z2 defined by momentum conservations:

154 Optical Devices in Communication and Computation

MDM/MIM structures.

relatively high propagation loss of several decibels.

capillary resonators. Finally, we make a conclusion.

(shown in the inset of Fig. 1) is given by [18]:

**2. Single-tooth shaped plasmonic waveguide filter [17]** 

*in z m z*

 

nanophotonics under the light diffraction limit that studies the transmission characteristics, localization, guiding of the SPP mode using metallic nanosturctures. The plasmonic waveguides are the most basic components and have been given much attention. Various kinds of metallic nanostructures have been proposed for SPP guiding. Generally these structures could be classified into three big categories: 1) chains of metal nanoparticles [6] and cylindrical metallic nanorods with various geometries [7]. 2) Metaldielectirc-metal (MDM) or Metal-insulator-metal (MIM) plasmonic waveguides, including groove channel structures in metallic substrates [8], slot waveguide [9]. 3) Dielectricmetal-dielectric (DMD)/ Insulator-metal-Insulator (IMI) waveguide [10]. It should be noted that not all these plasmonic structures can be used for guiding SPP mode to achieve subwavelength localization. Among them, MDM/MIM plasmonic waveguide can propagate SPP mode in the subwavelength scale with relatively low dissipation and large propagation distance. Our following proposed structures are mainly based on the

Wavelength selection is one of key technologies in fields of optical communication and computing. To achieve wavelength filtering characteristics, plasmonic Bragg reflectors and nanocavities have been proposed. They include the metal hetero-structures constructed with several periodic slots vertically along a metal-dielectric-metal (MDM) waveguide [11], the Bragg grating fabricated by periodic modulating the thickness of thin metal stripes embedded in an insulator [12] and the periodic structure formed by changing alternately two kinds of the insulators [13,14]. Lately, a high-order plasmonic Bragg reflector with a periodic modulation of the core index of the insulators [15], and a structure with periodic variation of the width of the dielectric in MDM waveguide [16] have been proposed. Most of the periodic structures mentioned above, however, have total length of micrometers and

In this chapter, we present our recent work on compact nano-plasmonic waveguide filters based on T-series and nano-capillary structures. In section 2, we introduce the novel nanometeric plasmonic filter in a tooth-shaped MIM waveguide and give an analytic model based on the scattering matrix method. In section 3, we investigate the characteristics of double-side teeth-shaped nano-plasmonic waveguide. In section 4 and section 5, we introduce the multiple multiple-teeth-shaped plasmonic filters and asymmetrical multiple teeth-shaped narrow pass band subwavelength filter. In section 6, we introduce a wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-

To begin with the dispersion relation of the fundamental TM mode in a MIM waveguide

2 1 coth( ) 0, <sup>2</sup>

1

*kk w* (1)

*z*

*ik*

$$k\_{z1}^2 = \varepsilon\_{in} k\_0^2 - \beta^2 \quad , \quad k\_{z2}^2 = \varepsilon\_m k\_0^2 - \beta^2 \,. \tag{2}$$

Where *in* and *<sup>m</sup>* are respectively dielectric constants of the insulator and the metal, *k0*=2π/*λ0* is the free-space wave vector. The propagation constant *β* is represented as the effective index *neff* =*β/k0* of the waveguide for SPPs. The real part of *neff* of the slit waveguide as a function of the slit width at different wavelengths is shown in Fig. 1. It should be noted that the dependence of *neff* on waveguide width is also suitable to the region of the tooth waveguide with the tooth width of *wt* shown in Fig. 2. The imaginary part of *neff* is referred to the propagation length which is defined as the length over which the power carried by the wave decays to 1/e of its initial value: *Lspps*=*λ0*/[4π·Im(*neff*)]. In the calculation above and the following simulations, the insulator in all of the structures is assumed to be air ( 1 *in* ), and the frequency-dependent complex relative permittivity of silver is characterized by Drude model: <sup>2</sup> ( ) / ( ). *m p <sup>i</sup>* Here <sup>16</sup> 1.38 10 *<sup>p</sup> Hz* is the bulk plasma frequency, which represents the natural frequency of the oscillations of free conduction electrons. <sup>13</sup> 2.73 10 *Hz* is the damping frequency of the oscillations, is the angular frequency of the incident electromagnetic radiation, stands for the dielectric constant at infinite angular frequency with the value of 3.7 [16]

**Figure 1.** Real part of the effective of refraction index versus the width of a MIM slit waveguide structure.

The tooth-shaped waveguide filter is shown in Fig. 2. In the following FDTD simulations, the grid sizes in the *x* and *z* directions are chosen to be 5nm×5nm. Since the width of the waveguide is much smaller than the operating wavelength in the structure, only fundamental waveguide mode is supported. Two power monitors are respectively set at the

positions of *P* and *Q* to detect the incident and transmission fields for calculating the incident power of *Pin* and the transmitted power of *Pout*. The transmittance is defined to be *T*=*Pout/Pin*. The length of *L* is fixed to be 300nm, while the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The tabulation of the optical constants of silver [19] is used in the simulation. As shown in Fig. 3(a), the tooth-shaped waveguide is of a filtering function: A transmission dip occurs at the free space wavelength nearly 784nm with the transmittance of ~0%. The maximum transmittance at the wavelengths longer than 1700nm is over 90%. The contour profiles of the field distributions around the tooth-shaped area at different wavelengths are shown in Figs. 3(b)-3(d). The filtering structure is distinguished from the Bragg reflectors based on periodical heterostructure.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 157

, (3)

<sup>i</sup> *E* and

The phenomenon above can be physically explained in the scattering matrix theory [20] as

out in 1 1 out in 2 2 out in 3 3

splitting coefficients of a incident beam from Port *i* (*i*=1,2,3), caused by the structure. in

2 2

in in 2 1 1

out in 13 1

2 1 3

*E s s T t i E r i*

2 11

Therefore, the transmittance *T* from Port 1 to Port 2 is given by:

It can be seen from Eq. (8) that, if the phase satisfies

in 1 1 3

*s E E sE i r i r i <sup>i</sup>*

 

3

*ssE E tE <sup>i</sup> r i*

reflection on the air-silver surface. Combined Eq. (5) and Eq. (6), the output field at Port 2 is

in

 

<sup>2</sup> <sup>2</sup> out

terms inside the absolute value sign on the right of the equation will cancel each other (as it

exp( ( )) 1 exp( ( ))

exp( ( )) 1 exp( ( ))

 

, and

<sup>i</sup> *E* stand for the fields of incident and output beams at Port *i*, respectively. Using the fact

out in in

exp( ( ))(1 exp( ( )) exp(2 ( )) ...) exp( ( )) 1 exp( ( ))

( ) 

> 

, (7)

 

( ) (2 1) 

 

*m* (*m=*0,1,2…), the two

. (8)

 

, (6)

, *ri, ti* and *si* (*i*=1,2,3) are respectively the reflection, transmission and

3

1 3 113 113 1 *r r tss rss t r* 22 1 . (4)

2 11 33 *E tE sE* , (5)

3

*r i*

in

 

is the phase-shift caused by the

 

*E E E SE E E*

follows:

where

out

113 11 3 113

*rts S trs ssr* 

that *S* 1 , one can obtain:

<sup>2</sup> *E* 0 , one has

<sup>3</sup> *E* is given as follows:

 

3 11 3 3

where the phase delay <sup>4</sup> ( ) ( ) *eff n d*

 

For the case of in

in which in

derived as:

**Figure 2.** The structure schematic of a single tooth-shaped waveguide filter, with the slit width of *w*, the tooth width of *wt*, and the tooth depth of *d*.

**Figure 3.** (a) Transmission of the single tooth-shaped MIM waveguide compared with a straight MIM slit waveguide. The width of the waveguide is *w*=50nm, and the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The contour profiles of field *Hy* of the tooth-shaped waveguide at different wavelengths of (b) λ=510nm, (c) λ=783nm, and (d) λ=1550nm.

The phenomenon above can be physically explained in the scattering matrix theory [20] as follows:

$$
\begin{pmatrix} E\_1^{\text{out}} \\ E\_2^{\text{out}} \\ E\_3^{\text{out}} \end{pmatrix} = \mathbf{S} \cdot \begin{pmatrix} E\_1^{\text{in}} \\ E\_2^{\text{in}} \\ E\_3^{\text{in}} \end{pmatrix}' \tag{3}
$$

where 113 11 3 113 *rts S trs ssr* , *ri, ti* and *si* (*i*=1,2,3) are respectively the reflection, transmission and

splitting coefficients of a incident beam from Port *i* (*i*=1,2,3), caused by the structure. in <sup>i</sup> *E* and out <sup>i</sup> *E* stand for the fields of incident and output beams at Port *i*, respectively. Using the fact that *S* 1 , one can obtain:

$$2r\_1^2r\_3 + 2t\_1s\_1s\_3 - 2r\_1s\_1s\_3 - t\_1^2r\_{\phantom{e}3} = 1\,\text{.}\tag{4}$$

For the case of in <sup>2</sup> *E* 0 , one has

156 Optical Devices in Communication and Computation

tooth width of *wt*, and the tooth depth of *d*.

from the Bragg reflectors based on periodical heterostructure.

positions of *P* and *Q* to detect the incident and transmission fields for calculating the incident power of *Pin* and the transmitted power of *Pout*. The transmittance is defined to be *T*=*Pout/Pin*. The length of *L* is fixed to be 300nm, while the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The tabulation of the optical constants of silver [19] is used in the simulation. As shown in Fig. 3(a), the tooth-shaped waveguide is of a filtering function: A transmission dip occurs at the free space wavelength nearly 784nm with the transmittance of ~0%. The maximum transmittance at the wavelengths longer than 1700nm is over 90%. The contour profiles of the field distributions around the tooth-shaped area at different wavelengths are shown in Figs. 3(b)-3(d). The filtering structure is distinguished

**Figure 2.** The structure schematic of a single tooth-shaped waveguide filter, with the slit width of *w*, the

**Figure 3.** (a) Transmission of the single tooth-shaped MIM waveguide compared with a straight MIM slit waveguide. The width of the waveguide is *w*=50nm, and the tooth width and depth are respectively *wt*=50nm and *d*=100nm. The contour profiles of field *Hy* of the tooth-shaped waveguide at different

wavelengths of (b) λ=510nm, (c) λ=783nm, and (d) λ=1550nm.

$$E\_2^{\text{out}} = t\_1 E\_1^{\text{in}} + s\_3 E\_3^{\text{in}} \, \text{ \, \, \tag{5}$$

in which in <sup>3</sup> *E* is given as follows:

$$E\_3^{\text{in}} = \text{s}\_1 E\_1^{\text{in}} \exp(i\phi(\lambda))(1 + r\_3 \exp(i\phi(\lambda)) + r\_3^2 \exp(2i\phi(\lambda)) + \dots) = \frac{\text{s}\_1 E\_1^{\text{in}}}{1 - r\_3 \exp(i\phi(\lambda))} \exp(i\phi(\lambda)) \tag{6}$$

where the phase delay <sup>4</sup> ( ) ( ) *eff n d* , and ( ) is the phase-shift caused by the reflection on the air-silver surface. Combined Eq. (5) and Eq. (6), the output field at Port 2 is derived as:

$$E\_2^{\text{out}} = t\_1 E\_1^{\text{in}} + \frac{s\_1 s\_3 E\_1^{\text{in}}}{1 - r\_3 \exp(i \phi(\mathcal{A}))} \exp(i \phi(\mathcal{A})) \,, \tag{7}$$

Therefore, the transmittance *T* from Port 1 to Port 2 is given by:

$$T = \left| \frac{E\_2^{\text{out}}}{E\_1^{\text{in}}} \right|^2 = \left| t\_1 + \frac{s\_1 s\_3}{1 - r\_3 \exp(i\phi(\mathcal{L}))} \exp(i\phi(\mathcal{L})) \right|^2. \tag{8}$$

It can be seen from Eq. (8) that, if the phase satisfies ( ) (2 1) *m* (*m=*0,1,2…), the two terms inside the absolute value sign on the right of the equation will cancel each other (as it can be seen in Fig. 3(c)), so that the transmittance *T* will become minimum. Therefore, the wavelength *λm* of the transmission dip is determined as follows:

$$\lambda\_m = \frac{4 \cdot n\_{eff} \cdot d}{(2m+1) - \frac{\Delta \rho(\lambda)}{\pi}} \cdot \tag{9}$$

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 159

**Figure 5.** (a) Transmission spectra of the waveguide filters with different tooth depths of *d*, and with a given tooth width of *wt*=50nm and the slit width of *w*=50nm. (b) The wavelength of the transmission dip

Figure 6(a) shows the structure of a proposed double-side teeth-shaped waveguide filter. The waveguide width *w* and the distance *L* are fixed to be 50nm and 300 nm. *d*1 and *d*2 are the depths of the teeth on each side of a MIM waveguide. The transmission spectra of the double-side teeth-shaped waveguide filter and the single-side tooth-shaped waveguide filter are shown in Fig. 6(b), which is obtained with the FDTD method. One can see that there is one dip at the free-space wavelength of nearly 1550nm with the transmittance of ~0%. An analytic model to explain the filtering function of single-side tooth-shaped waveguide structure based on multiple-beam-interference and scattering matrix has been

It can be seen that the wavelength λm is linear to the tooth depth *d* and depends on tooth width *w* through the somewhat inverse-proportionlike relationship between *n*eff and *w* shown in Fig. 1. The dip width of the double-side structure is wider compared with that of the single-side tooth-shaped structure. For better understanding the characteristics of double-side teeth structure, we next discuss the dependence of its filtering spectrum on the

Figure 7 shows the transmission spectra of the double-side teeth-shaped waveguide filters with different teeth depths of *d*1 and *d*2. From Fig. 7(a), one can see that there are two transmission dips at the free-space wavelengths of nearly 790nm and 1230nm with *d*1=100nm and *d*2=180nm. It is found that the wavelength of the second dip shifts to a long wavelength with the increasing of *d*2 while the first trough keeps unchanged due to a fixed value of *d*1=100nm. From Fig. 7(b), we can see that the first dip shifts to a long wavelength with the increasing of *d*1 while the position of the second dip is fixed due to a given

**3. Double-side teeth-shaped nano-plasmonic waveguide filters [21]** 

vs. the tooth depth of *d* with *wt*=15nm, *wt*=30nm and *wt*=50nm.

given in the section 1

symmetry of teeth depth.

*d*2=180nm.

It can be seen that the wavelength *λm* is linear to the tooth depth *d*, and depends on tooth width *wt*, through the somewhat inverse-proportion-like relationship between *neff* and *wt* shown in Fig. 1.

Figure 4(a) shows the transmission spectra of the waveguide filters with various tooth widths of *wt*. The maximum transmittance can reach 97%. Figure 4(b) shows the wavelength of the trough vs. the tooth width of *wt*. The primary dip of the transmission moves very significantly to short wavelength (blue-shift) with the increase of *wt* for *wt<*20nm. The shift rate rapidly becomes small after *wt>*20nm, and tends to be saturated when *wt>*200nm. As revealed in the Eq. (9), the above relationship between the dip position and *wt* mainly results from the contribution of the inverse-proportion-like dependence of *neff* on *wt*. The change rate of Δ*neff /*Δ*wt* within the tooth width of 20nm is much higher than that of Δ*neff /*Δ*wt* after *wt>*20nm, as shown in Fig. 1, and becomes finally saturated after *wt>*200nm. Obviously, tooth width *wt* should be chosen within the range of 20-200nm to avoid the critical behavior and the difficulty in fabrication process.

**Figure 4.** (a) Transmission spectra of the waveguide filters with various tooth widths of *wt*, at a fixed tooth depth of *d*=100nm and the slit width of *w*=50nm. (b) The wavelength of the trough versus the tooth width of *wt.* 

Figure 5(a) shows the transmission spectra of the filters with different tooth depths of *d*. It is found that the wavelength of the transmission dip shifts to long wavelength with the increasing of *d*. Figure 5(b) reveals that the wavelength of the transmission dip has a linear relationship with the tooth depth, as our expectation in Eq. (9). Therefore, one can realize the filter function in various required wavelength with high performance by changing the width or/and the depth of the tooth. For example, to obtain a filter with a transmission dip at the wavelength of 1550nm, the structural parameters of *wt*=*w*=50nm and *d*=237.5nm can be chosen.

the difficulty in fabrication process.

shown in Fig. 1.

tooth width of *wt.* 

wavelength *λm* of the transmission dip is determined as follows:

*m*

can be seen in Fig. 3(c)), so that the transmittance *T* will become minimum. Therefore, the

4

 

*m*

( ) (2 1) *eff*

It can be seen that the wavelength *λm* is linear to the tooth depth *d*, and depends on tooth width *wt*, through the somewhat inverse-proportion-like relationship between *neff* and *wt*

Figure 4(a) shows the transmission spectra of the waveguide filters with various tooth widths of *wt*. The maximum transmittance can reach 97%. Figure 4(b) shows the wavelength of the trough vs. the tooth width of *wt*. The primary dip of the transmission moves very significantly to short wavelength (blue-shift) with the increase of *wt* for *wt<*20nm. The shift rate rapidly becomes small after *wt>*20nm, and tends to be saturated when *wt>*200nm. As revealed in the Eq. (9), the above relationship between the dip position and *wt* mainly results from the contribution of the inverse-proportion-like dependence of *neff* on *wt*. The change rate of Δ*neff /*Δ*wt* within the tooth width of 20nm is much higher than that of Δ*neff /*Δ*wt* after *wt>*20nm, as shown in Fig. 1, and becomes finally saturated after *wt>*200nm. Obviously, tooth width *wt* should be chosen within the range of 20-200nm to avoid the critical behavior and

**Figure 4.** (a) Transmission spectra of the waveguide filters with various tooth widths of *wt*, at a fixed tooth depth of *d*=100nm and the slit width of *w*=50nm. (b) The wavelength of the trough versus the

Figure 5(a) shows the transmission spectra of the filters with different tooth depths of *d*. It is found that the wavelength of the transmission dip shifts to long wavelength with the increasing of *d*. Figure 5(b) reveals that the wavelength of the transmission dip has a linear relationship with the tooth depth, as our expectation in Eq. (9). Therefore, one can realize the filter function in various required wavelength with high performance by changing the width or/and the depth of the tooth. For example, to obtain a filter with a transmission dip at the wavelength of 1550nm, the structural parameters of *wt*=*w*=50nm and *d*=237.5nm can be chosen.

*n d*

 

. (9)

**Figure 5.** (a) Transmission spectra of the waveguide filters with different tooth depths of *d*, and with a given tooth width of *wt*=50nm and the slit width of *w*=50nm. (b) The wavelength of the transmission dip vs. the tooth depth of *d* with *wt*=15nm, *wt*=30nm and *wt*=50nm.

#### **3. Double-side teeth-shaped nano-plasmonic waveguide filters [21]**

Figure 6(a) shows the structure of a proposed double-side teeth-shaped waveguide filter. The waveguide width *w* and the distance *L* are fixed to be 50nm and 300 nm. *d*1 and *d*2 are the depths of the teeth on each side of a MIM waveguide. The transmission spectra of the double-side teeth-shaped waveguide filter and the single-side tooth-shaped waveguide filter are shown in Fig. 6(b), which is obtained with the FDTD method. One can see that there is one dip at the free-space wavelength of nearly 1550nm with the transmittance of ~0%. An analytic model to explain the filtering function of single-side tooth-shaped waveguide structure based on multiple-beam-interference and scattering matrix has been given in the section 1

It can be seen that the wavelength λm is linear to the tooth depth *d* and depends on tooth width *w* through the somewhat inverse-proportionlike relationship between *n*eff and *w* shown in Fig. 1. The dip width of the double-side structure is wider compared with that of the single-side tooth-shaped structure. For better understanding the characteristics of double-side teeth structure, we next discuss the dependence of its filtering spectrum on the symmetry of teeth depth.

Figure 7 shows the transmission spectra of the double-side teeth-shaped waveguide filters with different teeth depths of *d*1 and *d*2. From Fig. 7(a), one can see that there are two transmission dips at the free-space wavelengths of nearly 790nm and 1230nm with *d*1=100nm and *d*2=180nm. It is found that the wavelength of the second dip shifts to a long wavelength with the increasing of *d*2 while the first trough keeps unchanged due to a fixed value of *d*1=100nm. From Fig. 7(b), we can see that the first dip shifts to a long wavelength with the increasing of *d*1 while the position of the second dip is fixed due to a given *d*2=180nm.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 161

**Figure 8.** Transmission spectra of the two single-tooth waveguide filters and an asymmetrical double-

It is also interest to address a staggered double-side teeth-shaped MIM waveguide structure (shown in Fig. 9(a)). *Ls* stands for the shift length between two single teeth. A typical transmittance of the staggered double-side teeth-shaped waveguide filter with *wt*=50nm, *d*1=*d*2=260.5nm, and *Ls* =250nm is shown in Fig. 9(b). A wide bandgap occurs

wavelengths at of which the transmittance is equal to 1%) is 660nm, and the transmittance of passband is over 85%. The filter's feature can be attributed to the interference superposition of the reflected and transmitted fields from each tooth of the double-side

**Figure 9.** (a) Schematic of a staggered double-side teeth-shaped nano-plasmonic waveguide with a shift length of *Ls.* (b) The transmittance of the staggered double-side teeth-shaped waveguide filter with

Figure 10 shows the central wavelength of the bandgap as a function of the double-side teeth depth of *d*. During the simulation, we set *d*=*d*1=*d*2. The FDTD simulation results reveal

=1700nm with the bandgap width (defined as the difference between the two

side teeth-shaped structure with a given tooth width of *wt*=50nm and a slit width of *w*=50nm.

around

structure.

*w*t=50nm, *d*1=*d*2=260.5nm, *Ls*=250nm.

**Figure 6.** (a) Schematic of a double-side teeth-shaped nano-plasmonic waveguide. The double-side teeth-shaped structure can be asymmetrical, if *d*1*d*2. (b) The transmission spectra of a symmetrical double-side teeth-shaped waveguide filter with *w*t=50nm, *d*1=*d*2=245nm and a single-side tooth-shaped waveguide filter with *w*t=50nm, *d*1= 245nm.

**Figure 7.** (a)Transmission spectra of the asymmetrical double-side teeth-shaped waveguide filters for different tooth depths of *d*2 with a fixed *d*1=100nm and *w*t=50nm. (b) Transmission spectra of the asymmetrical double-side teeth-shaped waveguide filters for different tooth depths of *d*1 with a fixed *d*2=180nm and *w*t=50nm.

To better understand the origin of the two dips, the transmission spectra of an asymmetrical double-side teeth-shaped waveguide filter with *d*1=100nm and *d*2=180nm and two single tooth shaped structures with the tooth depths of 100nm and 180nm are all shown in Fig. 8. From it, one can see that the trough positions of the two single tooth waveguide filters with the tooth depths *d*1=100nm and *d*2=0 as well as *d*1=0 and *d*2=180nm overlap with the positions of the dips of the asymmetrical double-side teeth-shaped structure, which means the positions of the two dips of the double-side teeth-shaped structure are almost respectively determined by its two different single-tooth parts. Therefore, one can realize the filter function in various required wavelengths by respectively changing the depths of *d*1 and *d*2 of the two single teeth.

waveguide filter with *w*t=50nm, *d*1= 245nm.

*d*2=180nm and *w*t=50nm.

the two single teeth.

**Figure 6.** (a) Schematic of a double-side teeth-shaped nano-plasmonic waveguide. The double-side teeth-shaped structure can be asymmetrical, if *d*1*d*2. (b) The transmission spectra of a symmetrical double-side teeth-shaped waveguide filter with *w*t=50nm, *d*1=*d*2=245nm and a single-side tooth-shaped

**Figure 7.** (a)Transmission spectra of the asymmetrical double-side teeth-shaped waveguide filters for different tooth depths of *d*2 with a fixed *d*1=100nm and *w*t=50nm. (b) Transmission spectra of the asymmetrical double-side teeth-shaped waveguide filters for different tooth depths of *d*1 with a fixed

To better understand the origin of the two dips, the transmission spectra of an asymmetrical double-side teeth-shaped waveguide filter with *d*1=100nm and *d*2=180nm and two single tooth shaped structures with the tooth depths of 100nm and 180nm are all shown in Fig. 8. From it, one can see that the trough positions of the two single tooth waveguide filters with the tooth depths *d*1=100nm and *d*2=0 as well as *d*1=0 and *d*2=180nm overlap with the positions of the dips of the asymmetrical double-side teeth-shaped structure, which means the positions of the two dips of the double-side teeth-shaped structure are almost respectively determined by its two different single-tooth parts. Therefore, one can realize the filter function in various required wavelengths by respectively changing the depths of *d*1 and *d*2 of

**Figure 8.** Transmission spectra of the two single-tooth waveguide filters and an asymmetrical doubleside teeth-shaped structure with a given tooth width of *wt*=50nm and a slit width of *w*=50nm.

It is also interest to address a staggered double-side teeth-shaped MIM waveguide structure (shown in Fig. 9(a)). *Ls* stands for the shift length between two single teeth. A typical transmittance of the staggered double-side teeth-shaped waveguide filter with *wt*=50nm, *d*1=*d*2=260.5nm, and *Ls* =250nm is shown in Fig. 9(b). A wide bandgap occurs around =1700nm with the bandgap width (defined as the difference between the two wavelengths at of which the transmittance is equal to 1%) is 660nm, and the transmittance of passband is over 85%. The filter's feature can be attributed to the interference superposition of the reflected and transmitted fields from each tooth of the double-side structure.

**Figure 9.** (a) Schematic of a staggered double-side teeth-shaped nano-plasmonic waveguide with a shift length of *Ls.* (b) The transmittance of the staggered double-side teeth-shaped waveguide filter with *w*t=50nm, *d*1=*d*2=260.5nm, *Ls*=250nm.

Figure 10 shows the central wavelength of the bandgap as a function of the double-side teeth depth of *d*. During the simulation, we set *d*=*d*1=*d*2. The FDTD simulation results reveal

that the relationship between the central wavelength of the bandgap and the double-side teeth depth of *d* is a linear function. It reveals that the central wavelength of the bandgap shifts toward long wavelength with the increasing of the teeth depth of *d*.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 163

=1.55μm with the bandgap width

when

**4. A multiple-teeth-shaped waveguide bandgap filter [22]** 

with FDTD method. A wide bandgap occurs around

50-100nm with a slope of / 5 *center t d dw*

*w w t gap*

teeth.

It is straight forward and basic interest to expand a single tooth structure to multipleteeth structure (shown in Fig. 12(a)), and check the difference between them. For the sake of comparison, the waveguide width *w* and the distance *L* are fixed to be 50nm and 300nm. *Λ* and *N* are the period and the number of rectangular teeth, respectively. *wgap* stands for the width of the gap that between any two adjacent teeth, and one has

*wt*=50nm, *Λ*=150nm, *d*=260.5nm and *N*=5 is shown in the Fig. 12(b), which is obtained

590nm, and the transmittance of passband is over 90%. The filter's feature can be attributed to the superposition of the reflected and transmitted fields from each of the five single tooth-shaped components. Figure 13(a) shows the central wavelength of the transmittance bandgap, while the right y-axis displays the bandgap width of the waveguide filter as a function of teeth depth *d* at various *wt* with the same *Λ*=150nm and *N*=5. The FDTD simulation results reveal that the relationship between the central wavelength of the bandgap and the teeth depth *d* is a linear function for any *wt*, which is indeed the one of expectations in Eq. (9). Figure 13(b) shows the central wavelength of the bandgap and the bandgap width as a function of teeth width of *wt* at various teeth depths. As revealed in the Eq. (9), the relationship between the bandgap position and *wt* mainly results from the contribution of the inverse-proportion-like dependence of *neff* on *wt* as shown in Fig. 1(a). Obviously, teeth width *wt* should be chosen within the range of

*wt* <45nm in Fig. 13(b), and to reduce the sensitivity of the central wavelength of bandgap in fabrication process. Therefore, one can realize the filter function at various required wavelengths with high performance, by choosing the width or/and the depth of the

**Figure 12.** (a) Schematic of a multiple-teeth-shaped MIM waveguide structure. (b) The transmittance of

the multiple-teeth-shaped waveguide filter with *wt*=50nm, *Λ*=150nm, *d*=260.5nm and *N*=5.

. A typical transmittance of the multiple-teeth-shaped waveguide filter with

to avoid a large value of / 20 *center t d dw*

**Figure 10.** The central wavelength of the bandgap as a function of the double-side teeth depth of d at teeth width of 50nm.

Figure 11 shows how the shift length of the teeth influences or modifies the filtering spectrum of the structure. One can see that central bandgap shifts left and becomes wider with increasing the shift length of *Ls*. It reveals the filtering characteristics of the structure depend on the phase difference between the plasmon waves passing through the tooth. The optimized filtering response with a sharp left band-edge and high passband-transmittances over 85% can be achieved when the shift length is around 200nm.

**Figure 11.** The transmittance of the two-sided staggered teeth-shaped waveguide filter for different shift lengths with *w*t=50nm, *d*1=*d*2=260.5nm.

#### **4. A multiple-teeth-shaped waveguide bandgap filter [22]**

162 Optical Devices in Communication and Computation

teeth width of 50nm.

shift lengths with *w*t=50nm, *d*1=*d*2=260.5nm.

200nm.

that the relationship between the central wavelength of the bandgap and the double-side teeth depth of *d* is a linear function. It reveals that the central wavelength of the bandgap

**Figure 10.** The central wavelength of the bandgap as a function of the double-side teeth depth of d at

Figure 11 shows how the shift length of the teeth influences or modifies the filtering spectrum of the structure. One can see that central bandgap shifts left and becomes wider with increasing the shift length of *Ls*. It reveals the filtering characteristics of the structure depend on the phase difference between the plasmon waves passing through the tooth. The optimized filtering response with a sharp left band-edge and high passband-transmittances over 85% can be achieved when the shift length is around

**Figure 11.** The transmittance of the two-sided staggered teeth-shaped waveguide filter for different

shifts toward long wavelength with the increasing of the teeth depth of *d*.

It is straight forward and basic interest to expand a single tooth structure to multipleteeth structure (shown in Fig. 12(a)), and check the difference between them. For the sake of comparison, the waveguide width *w* and the distance *L* are fixed to be 50nm and 300nm. *Λ* and *N* are the period and the number of rectangular teeth, respectively. *wgap* stands for the width of the gap that between any two adjacent teeth, and one has *w w t gap* . A typical transmittance of the multiple-teeth-shaped waveguide filter with *wt*=50nm, *Λ*=150nm, *d*=260.5nm and *N*=5 is shown in the Fig. 12(b), which is obtained with FDTD method. A wide bandgap occurs around =1.55μm with the bandgap width 590nm, and the transmittance of passband is over 90%. The filter's feature can be attributed to the superposition of the reflected and transmitted fields from each of the five single tooth-shaped components. Figure 13(a) shows the central wavelength of the transmittance bandgap, while the right y-axis displays the bandgap width of the waveguide filter as a function of teeth depth *d* at various *wt* with the same *Λ*=150nm and *N*=5. The FDTD simulation results reveal that the relationship between the central wavelength of the bandgap and the teeth depth *d* is a linear function for any *wt*, which is indeed the one of expectations in Eq. (9). Figure 13(b) shows the central wavelength of the bandgap and the bandgap width as a function of teeth width of *wt* at various teeth depths. As revealed in the Eq. (9), the relationship between the bandgap position and *wt* mainly results from the contribution of the inverse-proportion-like dependence of *neff* on *wt* as shown in Fig. 1(a). Obviously, teeth width *wt* should be chosen within the range of 50-100nm with a slope of / 5 *center t d dw* to avoid a large value of / 20 *center t d dw* when *wt* <45nm in Fig. 13(b), and to reduce the sensitivity of the central wavelength of bandgap in fabrication process. Therefore, one can realize the filter function at various required wavelengths with high performance, by choosing the width or/and the depth of the teeth.

**Figure 12.** (a) Schematic of a multiple-teeth-shaped MIM waveguide structure. (b) The transmittance of the multiple-teeth-shaped waveguide filter with *wt*=50nm, *Λ*=150nm, *d*=260.5nm and *N*=5.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 165

. The separation

**5. A narrow band subwavelength plasmonic waveguide filter with** 

The asymmetrical multiple-teeth-shaped structure is shown in Fig. 15(a), which is composed of two sets of multiple-teeth with two different teeth depths. The short set has three teeth, and the long set has four teeth. *Λ*, *N*1 and *N*2, are the period, the numbers of short rectangular teeth and long teeth, respectively. *wgap* stands for the width of the gap between

between the 3rd short tooth and 1st long tooth is *ws*. The length of *L* and the waveguide width *w* are, respectively, fixed to be 150nm and 50nm. In Fig. 15(a) we set *d*1=148nm, *d*2=340nm, *wt*=50nm, *wgap*= *ws* =84nm. Figure 15(b) shows a typical transmission spectrum of

**Figure 15.** (a) Schematic of an asymmetrical multiple-teeth structure consisted of two sets with different teeth depth. (b) The transmittance of the asymmetrical multiple-teeth-shaped waveguide filter with

One can see the maximum transmittance at the wavelength of 1287nm is nearly 90%, and the full-width at half-maximum (FWHM) is nearly 70nm which is much smaller than the bandgap width of 1300nm. The FWHM of the asymmetrical multiple-teeth-shaped structure

In order to understand the origin of the narrow passband of the structure, the spectra of the transmission of a single-set of short three-teeth structure and a single-set of long four-teeth structure are calculated, and shown in Fig. 16. The parameters of the two structures are respectively equal to the parameters of the short teeth part and the long teeth part of the asymmetrical multiple-teeth-shaped structure (shown in Fig. 15(a)). One can see that the passband (or the bandgap) of the long teeth structure and the bandgap (or the passband) of the short teeth are overlapped from 800nm to 1200nm (or from 1450 to 1800nm), and then the transmission of the cascade of the two structure is very low within the two regions. Only the overlapping between the right edge of the passband of the long teeth structure and the

is also smaller than our previous coupler-type MIM optical filter [24].

**asymmetrical multiple teeth-shaped structure [23]** 

any two adjacent teeth in multiple-teeth structure, and one has *w w t gap*

the asymmetrical multiple-teeth-shaped structure using FDTD method.

*d*1=148nm, *d*2=340nm. *wgap= ws =84*nm, *N*1=3, and *N*2=4.

**Figure 13.** (a) The central wavelength of the bandgap and the bandgap width as a function of the teeth depth of *d* at various teeth widths. (b) The central wavelength of the bandgap and the bandgap width as a function of teeth widths of *wt* at various teeth depths.

For the multiple-teeth-shaped structure with the parameters of , 1.070 *eff teeth n* for the width of *D*=*d*+*w*=(260.5+50)nm, , 1.375 *eff wg n* for *w*=50nm, and the teeth period of *w w t gap* 150nm in z-axis direction, one can see *wn w n t eff teeth gap eff wg* Re( ) Re( ) , , 401.1nm 1550nm / 2 . Thus the structure does not follow the Bragg condition in z-axis direction.

Figure 14(a) and (b) show the transmission spectra of a multiple-teeth-shaped waveguide filter at different periods *Λ* and period numbers *N*. As one can see from Fig. 14(a), when *Λ*=100nm is chosen, the coupling of the SPPs waves between two adjacent teeth is strong which causes the central bandgap wavelength to shift left and the bandgap to be wider. When the period equals to *Λ*=200nm, the coupling between any two adjacent teeth becomes very weak. One can see in Fig. 14(b) that, the forbidden bandwidth increases little with the changing of the period number from *N*=3 to 7, while the transmittance of the passband decreases from 93% to 86%. The reason for the decreasing in transmittance can be attributed to the increasing of the propagation loss of the lengthened structure with a large period number. From the simulation results, a tradeoff period number *N*=4 is the optimized number with the transverse filter length of 4×150nm, which is ~5 times shorter than the previous grating-like filter structures.

**Figure 14.** (a) Transmittance spectra of multi-teeth filters with different periods and a fixed *N*=5, (b) Transmittance spectra of multi-teeth filters consisting of 3-7 periods with a fixed *Λ*=150nm.

#### **5. A narrow band subwavelength plasmonic waveguide filter with asymmetrical multiple teeth-shaped structure [23]**

164 Optical Devices in Communication and Computation

a function of teeth widths of *wt* at various teeth depths.

direction.

**Figure 13.** (a) The central wavelength of the bandgap and the bandgap width as a function of the teeth depth of *d* at various teeth widths. (b) The central wavelength of the bandgap and the bandgap width as

For the multiple-teeth-shaped structure with the parameters of , 1.070 *eff teeth n* for the width of *D*=*d*+*w*=(260.5+50)nm, , 1.375 *eff wg n* for *w*=50nm, and the teeth period of *w w t gap* 150nm in z-axis direction, one can see *wn w n t eff teeth gap eff wg* Re( ) Re( ) , , 401.1nm 1550nm / 2 . Thus the structure does not follow the Bragg condition in z-axis

Figure 14(a) and (b) show the transmission spectra of a multiple-teeth-shaped waveguide filter at different periods *Λ* and period numbers *N*. As one can see from Fig. 14(a), when *Λ*=100nm is chosen, the coupling of the SPPs waves between two adjacent teeth is strong which causes the central bandgap wavelength to shift left and the bandgap to be wider. When the period equals to *Λ*=200nm, the coupling between any two adjacent teeth becomes very weak. One can see in Fig. 14(b) that, the forbidden bandwidth increases little with the changing of the period number from *N*=3 to 7, while the transmittance of the passband decreases from 93% to 86%. The reason for the decreasing in transmittance can be attributed to the increasing of the propagation loss of the lengthened structure with a large period number. From the simulation results, a tradeoff period number *N*=4 is the optimized number with the transverse filter length

of 4×150nm, which is ~5 times shorter than the previous grating-like filter structures.

**Figure 14.** (a) Transmittance spectra of multi-teeth filters with different periods and a fixed *N*=5, (b)

Transmittance spectra of multi-teeth filters consisting of 3-7 periods with a fixed *Λ*=150nm.

The asymmetrical multiple-teeth-shaped structure is shown in Fig. 15(a), which is composed of two sets of multiple-teeth with two different teeth depths. The short set has three teeth, and the long set has four teeth. *Λ*, *N*1 and *N*2, are the period, the numbers of short rectangular teeth and long teeth, respectively. *wgap* stands for the width of the gap between any two adjacent teeth in multiple-teeth structure, and one has *w w t gap* . The separation

between the 3rd short tooth and 1st long tooth is *ws*. The length of *L* and the waveguide width *w* are, respectively, fixed to be 150nm and 50nm. In Fig. 15(a) we set *d*1=148nm, *d*2=340nm, *wt*=50nm, *wgap*= *ws* =84nm. Figure 15(b) shows a typical transmission spectrum of the asymmetrical multiple-teeth-shaped structure using FDTD method.

**Figure 15.** (a) Schematic of an asymmetrical multiple-teeth structure consisted of two sets with different teeth depth. (b) The transmittance of the asymmetrical multiple-teeth-shaped waveguide filter with *d*1=148nm, *d*2=340nm. *wgap= ws =84*nm, *N*1=3, and *N*2=4.

One can see the maximum transmittance at the wavelength of 1287nm is nearly 90%, and the full-width at half-maximum (FWHM) is nearly 70nm which is much smaller than the bandgap width of 1300nm. The FWHM of the asymmetrical multiple-teeth-shaped structure is also smaller than our previous coupler-type MIM optical filter [24].

In order to understand the origin of the narrow passband of the structure, the spectra of the transmission of a single-set of short three-teeth structure and a single-set of long four-teeth structure are calculated, and shown in Fig. 16. The parameters of the two structures are respectively equal to the parameters of the short teeth part and the long teeth part of the asymmetrical multiple-teeth-shaped structure (shown in Fig. 15(a)). One can see that the passband (or the bandgap) of the long teeth structure and the bandgap (or the passband) of the short teeth are overlapped from 800nm to 1200nm (or from 1450 to 1800nm), and then the transmission of the cascade of the two structure is very low within the two regions. Only the overlapping between the right edge of the passband of the long teeth structure and the left passband of the short teeth is non-zero. This is the reason why the wavelengths around 1300nm have a transmission peak in Fig. 15 (b).

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 167

**Figure 18.** Dependence of transmission characteristic on separation between the 3rd short tooth and the

The inset of Fig. 19 shows the nano-capillary resonators composed of two parallel metal plates with a dielectric core. Obviously, the structure can be treated as two MDM waveguides with different widths. Because the width of the lower MDM waveguide is much smaller than that of the upper part, here we call the lower (narrower) part as a nanocapillary. When the gap width *w* of the MDM waveguide is reduced below the diffraction limit, only a single propagation mode TM0 can exist. The dielectric in the core of the

To fully understand how the width of the nano-capillary structure influences the SPPs propagation, the dependences of the effective index of SPPs on the width *w* at various wavelengths of the incident light are calculated and shown in Fig. 19. From the figure 19, one can see that the effective index of the waveguide decreases with increasing of *w* at the same wavelength. The effective index at short wavelength is larger than that at long wavelength, for a given width *w*. The effective index *neff*2 of the nano-capillary can be larger than *neff*3 of upper MDM part and *n*1 of air. As shown in inset of Fig. 19, the waves will flow into the nano-capillary due to its higher effective index, when SPP waves propagate along the interface between metal and air. The wave transmitted into the capillary will be partly reflected at two ends of nano-capillary, because of index differences between *neff2* and *neff*3 as well as *n*1. One can expect the nano-capillary operates as a resonator. Resonance waves can

**6. A wavelength demultiplexing structure based on metal-dielectric-**

1st long tooth with *d*1=148nm, *N*1=3, *d*2=340nm, *N*2=4, respectively.

**metal plasmonic nano-capillary resonators [25].** 

structure is assumed to be air with a permittivity *εd* =1.

**Figure 16.** The transmission spectra of the single-set of multiple-teeth structure with *d*1=148nm, *N*1=3 and the single set of multiple-teeth structure with *d*2=340nm, *N*2=4, respectively.

Figure 17 shows the central wavelength of the narrow-band as a function of the variation of △*d*=△*d*1=△*d*2. △*d* is the increment of *d*1 and *d*2. The initial values of *d*1 and *d*2 are respectively, 128nm and 320nm. From the Fig. 17 can see that the central wavelength of the narrow-band linearly increases with the simultaneous increasing of *d*1 and *d*2. Figure 18 shows the dependence of transmission characteristic on separation *ws*. It is found that the transmission at the wavelength of 1287nm reaches the peak value when the separation of *ws* equals the gap of *wt.* Therefore, one can realize the narrow-bandwidth filter function at different required wavelengths by means of properly choosing the parameters of the device, such as the teeth-depth, the period or the separation of *ws*.

**Figure 17.** Central wavelength of the narrow-band as a function of the variation of △*d*=△*d*1=△*d*2, △*d*1and △*d*2 are respectively the increment of *d*1 and *d*2.

1300nm have a transmission peak in Fig. 15 (b).

left passband of the short teeth is non-zero. This is the reason why the wavelengths around

**Figure 16.** The transmission spectra of the single-set of multiple-teeth structure with *d*1=148nm, *N*1=3

Figure 17 shows the central wavelength of the narrow-band as a function of the variation of △*d*=△*d*1=△*d*2. △*d* is the increment of *d*1 and *d*2. The initial values of *d*1 and *d*2 are respectively, 128nm and 320nm. From the Fig. 17 can see that the central wavelength of the narrow-band linearly increases with the simultaneous increasing of *d*1 and *d*2. Figure 18 shows the dependence of transmission characteristic on separation *ws*. It is found that the transmission at the wavelength of 1287nm reaches the peak value when the separation of *ws* equals the gap of *wt.* Therefore, one can realize the narrow-bandwidth filter function at different required wavelengths by means of properly choosing the parameters of the device, such as

**Figure 17.** Central wavelength of the narrow-band as a function of the variation of △*d*=△*d*1=△*d*2, △*d*1and

and the single set of multiple-teeth structure with *d*2=340nm, *N*2=4, respectively.

the teeth-depth, the period or the separation of *ws*.

△*d*2 are respectively the increment of *d*1 and *d*2.

**Figure 18.** Dependence of transmission characteristic on separation between the 3rd short tooth and the 1st long tooth with *d*1=148nm, *N*1=3, *d*2=340nm, *N*2=4, respectively.

### **6. A wavelength demultiplexing structure based on metal-dielectricmetal plasmonic nano-capillary resonators [25].**

The inset of Fig. 19 shows the nano-capillary resonators composed of two parallel metal plates with a dielectric core. Obviously, the structure can be treated as two MDM waveguides with different widths. Because the width of the lower MDM waveguide is much smaller than that of the upper part, here we call the lower (narrower) part as a nanocapillary. When the gap width *w* of the MDM waveguide is reduced below the diffraction limit, only a single propagation mode TM0 can exist. The dielectric in the core of the structure is assumed to be air with a permittivity *εd* =1.

To fully understand how the width of the nano-capillary structure influences the SPPs propagation, the dependences of the effective index of SPPs on the width *w* at various wavelengths of the incident light are calculated and shown in Fig. 19. From the figure 19, one can see that the effective index of the waveguide decreases with increasing of *w* at the same wavelength. The effective index at short wavelength is larger than that at long wavelength, for a given width *w*. The effective index *neff*2 of the nano-capillary can be larger than *neff*3 of upper MDM part and *n*1 of air. As shown in inset of Fig. 19, the waves will flow into the nano-capillary due to its higher effective index, when SPP waves propagate along the interface between metal and air. The wave transmitted into the capillary will be partly reflected at two ends of nano-capillary, because of index differences between *neff2* and *neff*3 as well as *n*1. One can expect the nano-capillary operates as a resonator. Resonance waves can be formed only in some appropriate conditions within nano-capillary segment. Defining to be the phase delay per round-trip in the nano-capillary, one has 4/, *eff r n d* where 1 2 , *<sup>r</sup>* 1 and 2 are respectively the phase shifts of a beam reflected on the entrance of the capillary and the junction connecting the nano-capillary and the upper MDM waveguide, and *d* is the length of the capillary. The waves propagating through the structure will be trapped within the nano-capillary when the following resonant condition is satisfied: *m* 2 . Here, positive integer *m* is the number of antinodes of the standing SPP wave. The resonant wavelengths can be obtained as follows:

$$\lambda\_m = \text{Tr}\_{\text{eff}} d \mid (m - \phi\_r / \pi). \tag{10}$$

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 169

travel back and forth within a capillary, similar

traveling in a bulk medium with

Fig. 20(a) shows a typical schematic of a 1×3 wavelength demultiplexing structure based on MDM nano-capillary resonators. The wavelength demultiplexing structure consists of three nano-capillary resonators perpendicularly connected to a bus waveguide. *w*1 and *d*<sup>1</sup> stand for the width and the length of the first nano-capillary, respectively. Since the width of the bus waveguide is much smaller than the operating wavelength in the structure, only the excitation of the fundamental waveguide mode is considered. The incident light used to excite SPP wave is a TM-polarized (the magnetic field is parallel to y axis) fundamental mode. In the following FDTD simulation, the grid sizes in the x and the z directions are chosen to be Δ*x =* 5 nm, Δ*z =* 1.5 nm. Power monitors are respectively set at the positions of *P* and *Q* to detect the incident power of *Pin* and the transmitted power of *Pout*. The transmittance is defined to be / . *out in TP P* The width *w*΄ of the bus waveguide is set to be 250 nm while the length of *L*1 and *L*2 are fixed to be 50 nm and 500 nm. As an example, three nano-capillaries have been designed to split the first, the second and third optical transmission windows, although more nano-capillaries can be added. The parameters of the structure are set to be *w* = 15 nm, *w*1 = 250 nm, *d*1 = 202 nm, *d*2 = 290 nm, and *d*3 = 347 nm in calculation. Fig. 20(b) shows the transmission spectra at the outputs of the three channels, and inset of fig. 20(b) shows transmittance and reflectance of the bus waveguide. From it, one can see channels l-3 can select 980 nm, 1310 nm, 1550 nm bands, respectively, and the maximum transmittance in three bands can exceed 30% (-5.2 dB). And there is also another high transmission in channel 3 around 820 nm wavelength for *m* = 2. Given the total phase shift *φr*, one can estimate the resonance wavelength from Eq. (10). Submitting *λm =* 1310 nm into Eq. (10) gives *φr* = 0.35 for *d* = 290 nm and *neff =* 2.01. Other resonance wavelengths can be approximately calculated with the formula. For the lengths of the nano-capillaries of 347 nm and 202 nm, resonance wavelengths are simply estimated to be 1559 nm and 926 nm. The deviation between FDTD simulation and the result from Eq. (10) could be partly attributed to the neglecting of wavelength dependence of *φr*. And it is partly due to the fact that Eq. (10) is derived based on the effective index approximation that SPP waves

with the phase factor of exp(i2 / ) *eff*

refractive index *n*.

*n x* 

The FWHM of channel 1-3 are 75 nm, 130 nm, 160 nm, respectively. Obviously, the FWHM of the channel 2 and channel 3 are larger than that of channel 1. The reason is that, from the calculation in Fig. 19, the effective index at short wavelength with a fixed width of nanocapillary is higher compared with the one at long wavelength, thus the waves at short wavelength have a higher reflectivity at two ends of nano-capillary and its Q factor is higher. Cross-talk is defined as the ratio between the power of the undesired and desired bands at the outputs. The cross-talk between channel 1 and channel 2 is around -19.7 dB for the 980 nm branch, and the cross-talk between them is -13.1 dB for the 1310 nm branch. The cross-talk between channel 1 and the whole channel 3 is around -19.2 dB for the 980 nm branch, and is -16.6 dB for the 1550 nm branch, although there is also another high

to a 3-dimentional plane wave with exp( 2 / ) *i nx*

It can be seen that the wavelength *λm* is linear to the length and the effective index of the nano-capillary, respectively. Obviously, only the waves with the wavelength *λm* can stably exist in the nano-capillary, and thus partly transmit or drop into the output end of the nano-capillary. When wideband SPP waves incident into the structure, only the resonance waves with the wavelength *λm* can be selected and dropped by the nanocapillary. In other words, a transmission peak with the wavelength *λm* will be formed in the output section.

**Figure 19.** Dependence of real part of the effective index of SPPs in a plasmonic MDM waveguide on wavelength of the incident light and width *w*. Inset: schematic picture of a MDM nano-capillary resonator.

Fig. 20(a) shows a typical schematic of a 1×3 wavelength demultiplexing structure based on MDM nano-capillary resonators. The wavelength demultiplexing structure consists of three nano-capillary resonators perpendicularly connected to a bus waveguide. *w*1 and *d*<sup>1</sup> stand for the width and the length of the first nano-capillary, respectively. Since the width of the bus waveguide is much smaller than the operating wavelength in the structure, only the excitation of the fundamental waveguide mode is considered. The incident light used to excite SPP wave is a TM-polarized (the magnetic field is parallel to y axis) fundamental mode. In the following FDTD simulation, the grid sizes in the x and the z directions are chosen to be Δ*x =* 5 nm, Δ*z =* 1.5 nm. Power monitors are respectively set at the positions of *P* and *Q* to detect the incident power of *Pin* and the transmitted power of *Pout*. The transmittance is defined to be / . *out in TP P* The width *w*΄ of the bus waveguide is set to be 250 nm while the length of *L*1 and *L*2 are fixed to be 50 nm and 500 nm. As an example, three nano-capillaries have been designed to split the first, the second and third optical transmission windows, although more nano-capillaries can be added. The parameters of the structure are set to be *w* = 15 nm, *w*1 = 250 nm, *d*1 = 202 nm, *d*2 = 290 nm, and *d*3 = 347 nm in calculation. Fig. 20(b) shows the transmission spectra at the outputs of the three channels, and inset of fig. 20(b) shows transmittance and reflectance of the bus waveguide. From it, one can see channels l-3 can select 980 nm, 1310 nm, 1550 nm bands, respectively, and the maximum transmittance in three bands can exceed 30% (-5.2 dB). And there is also another high transmission in channel 3 around 820 nm wavelength for *m* = 2. Given the total phase shift *φr*, one can estimate the resonance wavelength from Eq. (10). Submitting *λm =* 1310 nm into Eq. (10) gives *φr* = 0.35 for *d* = 290 nm and *neff =* 2.01. Other resonance wavelengths can be approximately calculated with the formula. For the lengths of the nano-capillaries of 347 nm and 202 nm, resonance wavelengths are simply estimated to be 1559 nm and 926 nm. The deviation between FDTD simulation and the result from Eq. (10) could be partly attributed to the neglecting of wavelength dependence of *φr*. And it is partly due to the fact that Eq. (10) is derived based on the effective index approximation that SPP waves with the phase factor of exp(i2 / ) *eff n x* travel back and forth within a capillary, similar to a 3-dimentional plane wave with exp( 2 / ) *i nx* traveling in a bulk medium with

168 Optical Devices in Communication and Computation

where 1 2 , *<sup>r</sup>* 1 and 2 

satisfied: *m* 2 . 

the output section.

resonator.

be formed only in some appropriate conditions within nano-capillary segment. Defining

to be the phase delay per round-trip in the nano-capillary, one has 4/, *eff r*

entrance of the capillary and the junction connecting the nano-capillary and the upper MDM waveguide, and *d* is the length of the capillary. The waves propagating through the structure will be trapped within the nano-capillary when the following resonant condition is

*nd m*

It can be seen that the wavelength *λm* is linear to the length and the effective index of the nano-capillary, respectively. Obviously, only the waves with the wavelength *λm* can stably exist in the nano-capillary, and thus partly transmit or drop into the output end of the nano-capillary. When wideband SPP waves incident into the structure, only the resonance waves with the wavelength *λm* can be selected and dropped by the nanocapillary. In other words, a transmission peak with the wavelength *λm* will be formed in

**Figure 19.** Dependence of real part of the effective index of SPPs in a plasmonic MDM waveguide on wavelength of the incident light and width *w*. Inset: schematic picture of a MDM nano-capillary

SPP wave. The resonant wavelengths can be obtained as follows:

2 / ( / ). *m eff <sup>r</sup>*

 *n d*

(10)

are respectively the phase shifts of a beam reflected on the

Here, positive integer *m* is the number of antinodes of the standing

  refractive index *n*.

The FWHM of channel 1-3 are 75 nm, 130 nm, 160 nm, respectively. Obviously, the FWHM of the channel 2 and channel 3 are larger than that of channel 1. The reason is that, from the calculation in Fig. 19, the effective index at short wavelength with a fixed width of nanocapillary is higher compared with the one at long wavelength, thus the waves at short wavelength have a higher reflectivity at two ends of nano-capillary and its Q factor is higher. Cross-talk is defined as the ratio between the power of the undesired and desired bands at the outputs. The cross-talk between channel 1 and channel 2 is around -19.7 dB for the 980 nm branch, and the cross-talk between them is -13.1 dB for the 1310 nm branch. The cross-talk between channel 1 and the whole channel 3 is around -19.2 dB for the 980 nm branch, and is -16.6 dB for the 1550 nm branch, although there is also another high transmission in channel 3 around 820nm wavelength for *m*=2. Therefore, this structure is suitable for wideband wavelengths demultiplexing.

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 171

**Figure 21.** The central wavelength of nano-capillary resonator as a function of nano-capillary length *d*.

Finally, Figure 22 shows the propagation of field *H*y for two monochromatic waves with different wavelengths of 980 nm and 1550 nm launched into nano-capillary resonator demultiplexing structure. The demultiplexing effect is clearly observed. From the figure, one can see the wave with wavelength of 980 nm passing through the first nano-capillary and the wavelength of 1550 nm wave transmitting from the third nano-capillary. This is in good

**Figure 22.** The contour profiles of field *H*y of the 1×3 wavelength demultiplexing structure at different wavelengths, (a) λ = 980 nm, (b) λ = 1310 nm. All parameters of the structure are same as in Fig. 2(b).

agreement with the transmission spectra shown in Fig. 20(b).

Equation (10) indicates that the transmission behavior of each nano-capillary (channel of the demultiplexing structure) mainly depends on two parameters: the length of the nanocapillary, and the effective index of SPPs in the nano-capillary, which is determined by its width. Figure 21 shows the central wavelength of the nano-capillary resonator as a function of nano-capillary length *d*. One can see that the central wavelength of nano-capillary shifts toward longer wavelengths with the increasing of nano-capillary length *d*, as expected from equation (10). Therefore, one can realize the demultiplexing function at arbitrary wavelengths through the nano-capillary resonator by means of properly choosing the parameters of the structure, such as nano-capillary length and width.

**Figure 20.** (a) Schematic of a 1×3 wavelength demultiplexing structure based on MDM plasmonic nanocapillary resonators. (b) Transmission spectra of the three channels of the demultiplexing structure with *w* = 15 nm, *w*1 = 250 nm, *d*1 = 202 nm, *d*2 = 290 nm and *d*3 = 347 nm. Inset: Transmittance and reflectance of the bus waveguide.

the bus waveguide.

suitable for wideband wavelengths demultiplexing.

parameters of the structure, such as nano-capillary length and width.

transmission in channel 3 around 820nm wavelength for *m*=2. Therefore, this structure is

Equation (10) indicates that the transmission behavior of each nano-capillary (channel of the demultiplexing structure) mainly depends on two parameters: the length of the nanocapillary, and the effective index of SPPs in the nano-capillary, which is determined by its width. Figure 21 shows the central wavelength of the nano-capillary resonator as a function of nano-capillary length *d*. One can see that the central wavelength of nano-capillary shifts toward longer wavelengths with the increasing of nano-capillary length *d*, as expected from equation (10). Therefore, one can realize the demultiplexing function at arbitrary wavelengths through the nano-capillary resonator by means of properly choosing the

**Figure 20.** (a) Schematic of a 1×3 wavelength demultiplexing structure based on MDM plasmonic nanocapillary resonators. (b) Transmission spectra of the three channels of the demultiplexing structure with *w* = 15 nm, *w*1 = 250 nm, *d*1 = 202 nm, *d*2 = 290 nm and *d*3 = 347 nm. Inset: Transmittance and reflectance of

**Figure 21.** The central wavelength of nano-capillary resonator as a function of nano-capillary length *d*.

Finally, Figure 22 shows the propagation of field *H*y for two monochromatic waves with different wavelengths of 980 nm and 1550 nm launched into nano-capillary resonator demultiplexing structure. The demultiplexing effect is clearly observed. From the figure, one can see the wave with wavelength of 980 nm passing through the first nano-capillary and the wavelength of 1550 nm wave transmitting from the third nano-capillary. This is in good agreement with the transmission spectra shown in Fig. 20(b).

**Figure 22.** The contour profiles of field *H*y of the 1×3 wavelength demultiplexing structure at different wavelengths, (a) λ = 980 nm, (b) λ = 1310 nm. All parameters of the structure are same as in Fig. 2(b).

### **7. Conclusion**

In this chapter, we present our work on nano-plasmonic waveguide filters based on tooth/teeth-shaped and nano-capillary structures. We firstly investigated a novel plasmonic waveguide filter constructed with a MDM structure engraved single rectangular tooth. The filter is of an ultra-compact size with a few hundreds of nanometers in length, with reducing fabrication difficulties, compared with previous grating-like heterostructures with a few micrometers in length. We then extended it to symmetric/asymmetric multiple-teeth, capillary structures. The asymmetrical multiple-teeth structure and the capillary structure can achieve selective narrow-band filtering and wavelength demultiplexing functions, respectively. The plasmonic filters might become a choice for the design of all-optical high-integrated architectures for optical computing and communication in nanoscale. In the future, it will be very interesting and usefully to find some solutions to improve the performance of the MIM/MDM plasmonic components. Such as to combine surface plasmons with electrically and optically pumped gain media such as semiconductor quantum dots, semiconductor quantum well, and organic dyes embedded to the dielectric part. Electrically and optically pumped semiconductor gain media and the emerging technology of graphene are also expected to provide loss compensation from visible to terahertz spectra range [26].

Nano-Plasmonic Filters Based on Tooth-Shaped Waveguide Structures 173

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[9] K. Tanaka, M. Tanaka, and T. Sugiyama, "Simulation of practical nanometric optical circuits based on surface plasmon polariton gap waveguides," Opt. Express, Vol. 13,

[10] J. R. Krenn et al. "Non-diffraction-limited light transport by gold nanowires," Europhys

[11] B. Wang and G. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic

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[13] A. Hossieni and Y. Massoud, "A low-loss metal-insulator-metal plasmonic bragg

[14] A. Hosseini, H. Nejati, and Y. Massoud, "Modeling and design methodology for metalinsulator-metal plasmonic Bragg reflectors," Opt. Express, Vol. 16, 1475-1480, 2008. [15] J. Park, H. Kim, and B. Lee, "High order plasmonic Bragg reflection in the metalinsulator-metal waveguide Bragg grating," Opt. Express*,* Vol. 16, 413-425, 2008. [16] Z. Han, E. Forsberg, and S. He, "Surface plasmon Bragg gratings formed in metalinsulator-metal waveguides," IEEE Photon.Technol. Lett, Vol. 19, 91-93, 2007. [17] Xian Shi Lin and Xu Guang Huang, "Tooth-shaped plasmonic waveguide filters with

[18] J. A. Dionne, L. A. Sweatlock, and H. A. Atwater, "Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B., Vol 73,

[19] E. D. Palik, Handbook of optical constants of *solids* (Academic Press, New York, NY

[20] H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ,

[21] J. Tao, Xu Guang Huang, X. S. Lin, et al, "Systematical research on characteristics of double-sided teeth-shaped nanoplasmonic waveguide filters," J. Opt. Soc. Am. B, Vol.

[22] X. S. Lin and X. G. Huang, "Numerical modeling of a teeth-shaped nanoplasmonic

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### **Author details**

Xu Guang Huang\* and Jin Tao *Key Laboratory of Photonic Information Technology of Guangdong Higher Education Institutes, South China Normal University, Guangzhou, China* 

### **Acknowledgement**

The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 11977866).

#### **8. References**


<sup>\*</sup> Corresponding Author

[5] S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett, Vol. 58 , 2486–2489 ,1987.

172 Optical Devices in Communication and Computation

In this chapter, we present our work on nano-plasmonic waveguide filters based on tooth/teeth-shaped and nano-capillary structures. We firstly investigated a novel plasmonic waveguide filter constructed with a MDM structure engraved single rectangular tooth. The filter is of an ultra-compact size with a few hundreds of nanometers in length, with reducing fabrication difficulties, compared with previous grating-like heterostructures with a few micrometers in length. We then extended it to symmetric/asymmetric multiple-teeth, capillary structures. The asymmetrical multiple-teeth structure and the capillary structure can achieve selective narrow-band filtering and wavelength demultiplexing functions, respectively. The plasmonic filters might become a choice for the design of all-optical high-integrated architectures for optical computing and communication in nanoscale. In the future, it will be very interesting and usefully to find some solutions to improve the performance of the MIM/MDM plasmonic components. Such as to combine surface plasmons with electrically and optically pumped gain media such as semiconductor quantum dots, semiconductor quantum well, and organic dyes embedded to the dielectric part. Electrically and optically pumped semiconductor gain media and the emerging technology of graphene are also expected to

provide loss compensation from visible to terahertz spectra range [26].

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Prentice-Hall of India, New Dehli – 110 001. pg. 102.

Electronics," Phys. Rev. Lett 58, Vol. 20, 2059–2062 ,1987.

*Guangdong Higher Education Institutes, South China Normal University, Guangzhou, China* 

The authors acknowledge the financial support from the National Natural Science

[1] J. Davis, R. Venkatesam, A. Kaloyeros, M.Meylansky, S. Souri, K. Banerjee, K. Saraswat, A. Rahman, R. Reif, J. Meidl, "Interconnect Limits on Gigascale Integration (GSI) in the

[2] J. A. Conway, S. Sahni, and T. Szkopek, "Plasmonic interconnects versus conventional interconnects: a comparison of latency, crosstalk and energy costs," Opt. Express, Vol.

[3] P. Bhattacharya. Semiconductor Optoelectronic Devices. Second Edition. © 2005

[4] E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and

 and Jin Tao *Key Laboratory of Photonic Information Technology of* 

Foundation of China (Grant No. 11977866).

**7. Conclusion** 

**Author details** 

Xu Guang Huang\*

**8. References** 

 \*

**Acknowledgement** 

15, 4474-4484 (2007).

Corresponding Author

	- [23] J. Tao, X. G. Huang, X. S. Lin, Q. Zhang, X. P, Jin, "A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure," Opt. Express*,* Vol. 17, 13989-13994, 2009.

**Section 3** 

**Functional Optical Materials** 


**Section 3** 

**Functional Optical Materials** 

174 Optical Devices in Communication and Computation

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[24] Qin Zhang, Xu-Guang Huang, Xian-Shi Lin, Jin Tao, and Xiao-Ping Jin, "A subwavelength coupler-type MIM optical filter," Opt. Express, Vol. 17, 7549-7555, 2009. [25] Jin Tao, Xu Guang Huang, and Jia Hu Zhu, "A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators," Opt. Express,

[26] A. A Dubinov, V. Y. Aleshkin, V. Mitin, T. Otsuji and V. Ryzhii, "Terahertz surface plasmons in optically pumped graphene structures," J. Phys.Condens. Matter, Vol. 23,

**Chapter 9** 

© 2012 Hong and Kazuyoshi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**Fluidic Optical Devices Based** 

Additional information is available at the end of the chapter

Gordon et al. [1] reported that the beam shape of incident laser light expands after passing through a liquid medium. This phenomenon was termed "the thermal lens effect," and it has become a well-known photo-thermal phenomenon. Phenomenological, optical, and spectroscopic studies of the thermal lens effect have been carried out to describe nonlinear defocusing effect [2-8]. Recent progress in laser technology has revealed the various aspects of the thermal lens effect. Based on these efforts, other mechanisms, such as liquid density, electronic population, and molecular orientation, have been found to play important role as well as thermal lens effect. Recent studies term these effects as "the transient lens effect" [9,10]. The main advantage of using the transient lens effect in Photo-Thermal-Spectroscopy is that the sensitivity is 100 to 1000 greater than a traditional

In this research, a new idea of applying the thermal lens effect in order to develop fluidic optical device is proposed. A schematic of the concept is shown in Fig. 1. A rectangular solid region shown in Fig. 1a represents the liquid medium, which has a temperature field generated by a heater-heat sink system or laser-induced absorption. By controlling the temperature field as well as the refractive index distribution of the liquid medium, the refractive angle of each light ray passing through the liquid medium can be controlled in order to develop fluidic optical devices such as: an optical switching in Fig. 1a to change the direction of the input laser beam, a laser beam shaper in Fig. 1b to transform a Gaussian beam to a flat-top beam and a fluidic divergent lens in Fig. 1c. Merits of these devices include flexibility of optical parameters, versatility

and reproduction in any medium, provided the original work is properly cited.

**on Thermal Lens Effect** 

Duc Doan Hong

**1. Introduction** 

absorptiometry [11].

and low cost.

and Fushinobu Kazuyoshi

http://dx.doi.org/10.5772/48072

**Chapter 9** 

## **Fluidic Optical Devices Based on Thermal Lens Effect**

Duc Doan Hong and Fushinobu Kazuyoshi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48072

#### **1. Introduction**

Gordon et al. [1] reported that the beam shape of incident laser light expands after passing through a liquid medium. This phenomenon was termed "the thermal lens effect," and it has become a well-known photo-thermal phenomenon. Phenomenological, optical, and spectroscopic studies of the thermal lens effect have been carried out to describe nonlinear defocusing effect [2-8]. Recent progress in laser technology has revealed the various aspects of the thermal lens effect. Based on these efforts, other mechanisms, such as liquid density, electronic population, and molecular orientation, have been found to play important role as well as thermal lens effect. Recent studies term these effects as "the transient lens effect" [9,10]. The main advantage of using the transient lens effect in Photo-Thermal-Spectroscopy is that the sensitivity is 100 to 1000 greater than a traditional absorptiometry [11].

In this research, a new idea of applying the thermal lens effect in order to develop fluidic optical device is proposed. A schematic of the concept is shown in Fig. 1. A rectangular solid region shown in Fig. 1a represents the liquid medium, which has a temperature field generated by a heater-heat sink system or laser-induced absorption. By controlling the temperature field as well as the refractive index distribution of the liquid medium, the refractive angle of each light ray passing through the liquid medium can be controlled in order to develop fluidic optical devices such as: an optical switching in Fig. 1a to change the direction of the input laser beam, a laser beam shaper in Fig. 1b to transform a Gaussian beam to a flat-top beam and a fluidic divergent lens in Fig. 1c. Merits of these devices include flexibility of optical parameters, versatility and low cost.

© 2012 Hong and Kazuyoshi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fluidic Optical Devices Based on Thermal Lens Effect 179

The light ray is modeled in the domain shown in Fig. 2 in order to calculate the refractive angle of the probe beam, which is transmitted in a one-dimensional temperature distribution in the liquid medium. The light ray direction transmitted in a medium having a refractive index dependent only on the *y*-axis, is described by the following

> 0 0 2 22 0

> 0 0 2 22 0

*<sup>y</sup> n*

*<sup>y</sup> n*

**Figure 2.** Schematic diagram of computational domain

sin cos ( ) sin

sin sin ( ) sin

  (1)

(2)

 

*x dy ny n*

*z dy ny n*

In which, the light ray passes through the medium at coordinate center, *θ* and *φ* are the incident angle with *y* and *x*-axis respectively, *n*0 is the refractive index of the medium at the

Figure 2 shows a schematic diagram of the model set up. The rectangular solid medium in the figure represents the domain considered in the calculation which consists of ethylene glycol. In the medium, ethylene glycol has linear temperature distribution in only *y*-axis direction and the probe beam propagate along *z*-axis direction. Therefore, *θ* = *φ* = π/2, and

0 *x* (3)

*<sup>y</sup> n z dy ny n*

variable *y* and temperature *T* at point *y* is calculated following:

0 0 2 2 <sup>0</sup> ( )

The temperature distribution of the liquid medium is modeled with a linear function of the

(4)

**2.1. Theoretical background** 

form [12]

coordinate center.

Eq. (1), (2) become:

**Figure 1.** Schematic of the concept of the fluidic optical devices

#### **2. Fundamental light ray transmitted in one-dimensional refractive index medium**

In this section, as a first step to develop fluidic optical device, the refractive characteristics of a probe beam, which is transmitted in one-dimensional temperature distribution in a liquid medium is presented.

#### **2.1. Theoretical background**

178 Optical Devices in Communication and Computation

**Figure 1.** Schematic of the concept of the fluidic optical devices

**index medium** 

medium is presented.

**2. Fundamental light ray transmitted in one-dimensional refractive** 

In this section, as a first step to develop fluidic optical device, the refractive characteristics of a probe beam, which is transmitted in one-dimensional temperature distribution in a liquid The light ray is modeled in the domain shown in Fig. 2 in order to calculate the refractive angle of the probe beam, which is transmitted in a one-dimensional temperature distribution in the liquid medium. The light ray direction transmitted in a medium having a refractive index dependent only on the *y*-axis, is described by the following form [12]

$$\propto = \int\_0^y \frac{n\_0 \sin \theta \cos \phi}{\sqrt{n^2(y) - n\_0^2 \sin^2 \theta}} dy \tag{1}$$

$$z = \int\_0^y \frac{n\_0 \sin \theta \sin \phi}{\sqrt{n^2(y) - n\_0^2 \sin^2 \theta}} dy \tag{2}$$

In which, the light ray passes through the medium at coordinate center, *θ* and *φ* are the incident angle with *y* and *x*-axis respectively, *n*0 is the refractive index of the medium at the coordinate center.

**Figure 2.** Schematic diagram of computational domain

Figure 2 shows a schematic diagram of the model set up. The rectangular solid medium in the figure represents the domain considered in the calculation which consists of ethylene glycol. In the medium, ethylene glycol has linear temperature distribution in only *y*-axis direction and the probe beam propagate along *z*-axis direction. Therefore, *θ* = *φ* = π/2, and Eq. (1), (2) become:

$$\mathbf{x} = \mathbf{0} \tag{3}$$

$$z = \int\_0^y \frac{n\_0}{\sqrt{n^2(y) - n\_0^2}} dy\tag{4}$$

The temperature distribution of the liquid medium is modeled with a linear function of the variable *y* and temperature *T* at point *y* is calculated following:

$$T(y) = T\_0 + \frac{dT}{dy}y\tag{5}$$

Fluidic Optical Devices Based on Thermal Lens Effect 181

*L* = 4.5 mm

*L* = 3.0 mm

*L* = 1.5 mm

**Figure 3.** Relationship between the refractive angle and temperature gradient

Refractive angle, , mrad

Temperature gradient, d*T*/d*y*, K/mm

**Figure 4.** Refractive angle measurement system

**Figure 5.** Schematic diagram of sample

In which, *T*0 is the temperature of the liquid medium at coordinate origin and d*T*/d*y* is constant.

Furthermore, between 0°C and 100°C refractive index of ethylene glycol is a linear function of temperature with refractive index change d*n/*d*T* = -2.6×10-4 1/K [13]. Therefore, the relationship between refractive index and the variable *y* can be rewriten as follows:

$$y = \frac{n(y) - n\_0}{dn \; / \; dy} \tag{6}$$

And

$$
\Delta dy = dn \times \frac{dy}{dm} = dn \times \frac{dy}{dT} \times \frac{dT}{dm} = \frac{dn}{k} \tag{7}
$$

Where,

$$k = -2.6 \times 10^{-4} \times \frac{dT}{dy} \tag{8}$$

By substituting Eq. (7) into Eq. (4) and solving the differential equation, we can obtain the relationship between *y* and *z* as:

$$y = \frac{n\_0[\exp(kz/n\_0) - 1]^2}{2k \exp(kz/n\_0)}\tag{9}$$

And refractive angle (RA) can be obtained as:

$$\alpha = \frac{dy}{dz} = \frac{1}{2} \exp(\frac{kz}{n\_0}) - \frac{1}{2} \exp(-\frac{kz}{n\_0}) \tag{10}$$

Equation (10) shows the expression of the refractive angle as a function of the temperature gradient and the thickness of the liquid medium (optical path length). Figure 3 shows the relationship between refractive angle and temperature gradient at points where the thickness of sample, *L*, is 1.5, 3.0 and 4.5 mm respectively. As shown in Fig. 3 the relationship between the refractive angle and temperature gradient can be well approximated as linear at a small temperature gradient.

#### **2.2. Experimental set-up**

Figure 4 shows the experimental set-up to measure the refractive angle. Fluidic optical device in Fig. 4 is a pyrex vessel (internal size: 21×10×*L* [mm], thickness of the liquid medium, *L*, can be varied) filled with ethylene glycol. The vessel is held in an adiabatic material (Mica glass-ceramics (Photoveel®) as shown in Fig. 5. The temperature on both sides of the vessel was controlled by a heater-heat sink system to create a one-dimensional temperature distribution in the liquid medium.

**Figure 3.** Relationship between the refractive angle and temperature gradient

**Figure 4.** Refractive angle measurement system

And

Where,

relationship between *y* and *z* as:

**2.2. Experimental set-up** 

And refractive angle (RA) can be obtained as:

approximated as linear at a small temperature gradient.

temperature distribution in the liquid medium.

<sup>0</sup> ( ) *dT Ty T y dy*

In which, *T*0 is the temperature of the liquid medium at coordinate origin and d*T*/d*y* is constant. Furthermore, between 0°C and 100°C refractive index of ethylene glycol is a linear function of temperature with refractive index change d*n/*d*T* = -2.6×10-4 1/K [13]. Therefore, the

> <sup>0</sup> ( ) / *ny n <sup>y</sup> dn dy*

<sup>4</sup> 2.6 10 *dT <sup>k</sup>*

By substituting Eq. (7) into Eq. (4) and solving the differential equation, we can obtain the

0 0

2 2 *dy kz kz dz n n*

Equation (10) shows the expression of the refractive angle as a function of the temperature gradient and the thickness of the liquid medium (optical path length). Figure 3 shows the relationship between refractive angle and temperature gradient at points where the thickness of sample, *L*, is 1.5, 3.0 and 4.5 mm respectively. As shown in Fig. 3 the relationship between the refractive angle and temperature gradient can be well

Figure 4 shows the experimental set-up to measure the refractive angle. Fluidic optical device in Fig. 4 is a pyrex vessel (internal size: 21×10×*L* [mm], thickness of the liquid medium, *L*, can be varied) filled with ethylene glycol. The vessel is held in an adiabatic material (Mica glass-ceramics (Photoveel®) as shown in Fig. 5. The temperature on both sides of the vessel was controlled by a heater-heat sink system to create a one-dimensional

[exp( / ) 1] 2 exp( / ) *n kz n <sup>y</sup> k kz n*

*dy*

0

0 0 1 1 exp( ) exp( )

2

relationship between refractive index and the variable *y* can be rewriten as follows:

(5)

(6)

*dy dy dT dn dy dn dn dn dT dn k* (7)

(8)

(9)

(10)

**Figure 5.** Schematic diagram of sample

**Figure 6.** Temperature gradient measurement system

The temperature distribution in the liquid medium is confirmed by measuring the temperatures at 5 points with 2 mm pitch in the vessel using 5 thermocouples as shown in Fig. 6. The temperature gradient in the experiment is given as:

$$\frac{dT}{dy} = \frac{T\_4 - T\_5}{\Delta y} \tag{11}$$

Fluidic Optical Devices Based on Thermal Lens Effect 183

**Figure 7.** The comparison of theoretical and experimental results

Flat-top laser are well known to present significant advantages for laser technology, such as holographic recording system, Z-scan measurement, laser heat treatment and surface annealing in microelectronics and various nonlinear optical processes [15-19]. For CW beams, several approaches to spatially shape Gaussian beams have been developed, such as the use of aspheric lenses, implement beam shaping or the use of diffractive optical devices [20]. However, these methods have some disadvantages: a refractive beam shaping system lead to large aberration [21] and implemental beam shaping has low energy efficiency and lacks of flexibility [22]; and the use of refractive optical devices requires complex configuration design and high cost [23]. In practice, a low-cost and flexible method to convert a Gaussian beam into a flat-top beam is required. In this section, a novel method to convert a Gaussian beam into a flat-top beam is discussed. The concept is based on the control of the pump power and propagation distance of the probe beam in the thermal

(b) *L* = 3 mm

(a) *L* = 1.5 mm

**3. Fluidic laser beam shaper** 

lens system.

In which, Δ*y* is the distance between two thermocouples to obtain the temperature gradient, Δ*y* = 4 mm.

A CW laser (*P* = 0.6 mW, *λ* = 632 nm, *Φ* = 0.8 mm, TEM00) is used as a probe beam. A CCD camera (OPHIR, BeamStar-FX 50) is used as a detector. Based on probe beam position, the refractive angle is estimated with:

$$a = \frac{r}{d} \tag{12}$$

Where *d* is the distance from the sample to the detector of the camera = 286 mm; *r* is the beam position.

#### **2.3. Results and discussions**

Figure 7(a) and (b) show the comparison of theoretical and experimental results at points where the thickness of sample, *L*, is 1.5 and 3.0 mm respectively. The temperature gradient in the theoretical results is based on the measurement as described above. As shown in this figure, theoretical and experimental results agree well with each other. The experimental data includes the error corresponding to the difference between the actual temperature gradient at the laser incidence which is calculated by using Eq. (11). The discrepancy at higher d*T*/d*y* may correspond to the error where the measured temperature gives higher d*T*/d*y* and therefore higher a prediction by using Eq. (10). This discrepancy should increase with increasing sample thickness and the temperature gradient as a consequence of the effect of natural convection and the temperature gradient in the *z*-axis [14].

**Figure 7.** The comparison of theoretical and experimental results

#### **3. Fluidic laser beam shaper**

182 Optical Devices in Communication and Computation

**Figure 6.** Temperature gradient measurement system

*z*

3

Δ*y* = 4 mm.

beam position.

in the *z*-axis [14].

refractive angle is estimated with:

**2.3. Results and discussions** 

Fig. 6. The temperature gradient in the experiment is given as:

*y*

5

*x*

The temperature distribution in the liquid medium is confirmed by measuring the temperatures at 5 points with 2 mm pitch in the vessel using 5 thermocouples as shown in

1 2

Thermocouples

4 5 *dT T T dy y*

In which, Δ*y* is the distance between two thermocouples to obtain the temperature gradient,

A CW laser (*P* = 0.6 mW, *λ* = 632 nm, *Φ* = 0.8 mm, TEM00) is used as a probe beam. A CCD camera (OPHIR, BeamStar-FX 50) is used as a detector. Based on probe beam position, the

> *r d*

Where *d* is the distance from the sample to the detector of the camera = 286 mm; *r* is the

Figure 7(a) and (b) show the comparison of theoretical and experimental results at points where the thickness of sample, *L*, is 1.5 and 3.0 mm respectively. The temperature gradient in the theoretical results is based on the measurement as described above. As shown in this figure, theoretical and experimental results agree well with each other. The experimental data includes the error corresponding to the difference between the actual temperature gradient at the laser incidence which is calculated by using Eq. (11). The discrepancy at higher d*T*/d*y* may correspond to the error where the measured temperature gives higher d*T*/d*y* and therefore higher a prediction by using Eq. (10). This discrepancy should increase with increasing sample thickness and the temperature gradient as a consequence of the effect of natural convection and the temperature gradient

(11)

4

(12)

Flat-top laser are well known to present significant advantages for laser technology, such as holographic recording system, Z-scan measurement, laser heat treatment and surface annealing in microelectronics and various nonlinear optical processes [15-19]. For CW beams, several approaches to spatially shape Gaussian beams have been developed, such as the use of aspheric lenses, implement beam shaping or the use of diffractive optical devices [20]. However, these methods have some disadvantages: a refractive beam shaping system lead to large aberration [21] and implemental beam shaping has low energy efficiency and lacks of flexibility [22]; and the use of refractive optical devices requires complex configuration design and high cost [23]. In practice, a low-cost and flexible method to convert a Gaussian beam into a flat-top beam is required. In this section, a novel method to convert a Gaussian beam into a flat-top beam is discussed. The concept is based on the control of the pump power and propagation distance of the probe beam in the thermal lens system.

#### **3.1. Principle of thermal lens effect**

The principle of the transient lens effect is schematically illustrated in Fig.8. A CW diode pumped blue laser is used as pump-beam (BCL-473-030, *λ* = 473 nm, *Φ* = 0.8 mm, TEM00) with maximum output power of 30mW. The laser beam intensity was adjusted by using ND-filter. A CW infrared DPSS laser is used as probe-beam (MIL, *λ* = 1064 nm, *Φ* = 3.0 mm, TEM00) with maximum output power of 10 mW. A CCD camera is used as a detector to measure the intensity distribution of the laser beam. A cuvette, which is a three-layer structure with a sheet copper is sandwiched between 2 pieces of fused silica. The height of the fused silica is 1 mm. The sheet copper has doughnut shape. The liquid that is contained inside the doughnut hole has the same height with the sheet copper. By varying the thickness of the sheet copper, the liquid height can be changed. The ethanol solution dissolved dye termed as Sunset-yellow is filled in the cuvette. The chemical formula of the Sunset-yellow is shown in Ref. 24.

Fluidic Optical Devices Based on Thermal Lens Effect 185

(13)

(14)

(15)

2 0

(16)

2

 

Theoretical analysis of laser beam profile change in thermal lens effect is done with a model that includes continuity equation, Navier-Stokes equation, energy conservation equation and Helmholtz equation in 2D cylindrical symmetry coordinate. It is assumed that the change of refractive index is caused only by the temperature change of the liquid medium and the thermal coefficient of the refractive index, d*n*/d*T*. The concentration is supposed to be constant over the range of the temperature rise induced by the pump beam. When the liquid medium is irradiated, temperature distribution perpendicular to the optical axis is formed due to intensity distribution of laser beam and heat transport. To consider the natural convection effect, the temperature distribution of liquid sample in steady state is

> <sup>1</sup> <sup>0</sup> *<sup>z</sup> r z*

*v v rv a*

 

 

 

*v v r g TT b*

1

*TT TT vva r S r z rr r z*

 

Here, *I*0(*r*) is the intensity distribution of the pump laser. The spot sizes of the laser beams are assumed to be constant through the interaction volume within the liquid medium.

The temperature distribution is calculated numerically based on the finite difference method. The 1st order upwind scheme and a 2nd order center differencing are applied to discretize the advection term and the diffusion term respectively. The thermal properties of

To model the propagation of laser through an inhomogeneous medium, the wave equation which includes an absorption term and an inhomogeneous refractive index term is applied

> 2 0 0 0 0 00 1 () <sup>1</sup> <sup>2</sup>

Here, *E* is the envelope of the oscillating electric field, *z* is the axis of propagation, *r* is transverse coordinates, *k*0 is the free space wave number and *α* is the absorption coefficient. The variable *n* is the refractive index profile depending on medium temperature following:

*E E rE ik n k n n E ik n E*

<sup>2</sup>

 

 

*z z rr r*

   

0 p e () C *z I r <sup>S</sup>* 

 

*rv v rr z*

*r r r*

 

*v v p v*

*r z r rr r z v v p v v*

*z z z z*

*r z z rr r z*

 

> 

*v*

 

2 2

2 2

 

22 2

(17)

2

1 1 ( )

1 1 ( )

 

 

calculated numerically following these governing equations [24]:

*r z r*

 

 

*r z*

*r z*

liquid medium can be found in Ref. 24.

[24]:

 

> 

 

> 

**Figure 8.** Schematic diagram of a dual-beam thermal lens system

**Figure 9.** Experiment result: the difference of intensity profile of the probe beam after passing through the thermal lens (left side) and a quart divergent lens (right side)

In this experiment, the absorbance of the pump-beam is 2.776 and that of the probe-beam is negligible small. Figure 9 shows the laser beam profile of the probe beam after propagating through a divergent lens and a thermal lens. It is clear that, the probe beam change its profile from Gaussian to doughnut beam with a hollow center is created.

Theoretical analysis of laser beam profile change in thermal lens effect is done with a model that includes continuity equation, Navier-Stokes equation, energy conservation equation and Helmholtz equation in 2D cylindrical symmetry coordinate. It is assumed that the change of refractive index is caused only by the temperature change of the liquid medium and the thermal coefficient of the refractive index, d*n*/d*T*. The concentration is supposed to be constant over the range of the temperature rise induced by the pump beam. When the liquid medium is irradiated, temperature distribution perpendicular to the optical axis is formed due to intensity distribution of laser beam and heat transport. To consider the natural convection effect, the temperature distribution of liquid sample in steady state is calculated numerically following these governing equations [24]:

184 Optical Devices in Communication and Computation

**3.1. Principle of thermal lens effect** 

Sunset-yellow is shown in Ref. 24.

**Figure 8.** Schematic diagram of a dual-beam thermal lens system

the thermal lens (left side) and a quart divergent lens (right side)

profile from Gaussian to doughnut beam with a hollow center is created.

The principle of the transient lens effect is schematically illustrated in Fig.8. A CW diode pumped blue laser is used as pump-beam (BCL-473-030, *λ* = 473 nm, *Φ* = 0.8 mm, TEM00) with maximum output power of 30mW. The laser beam intensity was adjusted by using ND-filter. A CW infrared DPSS laser is used as probe-beam (MIL, *λ* = 1064 nm, *Φ* = 3.0 mm, TEM00) with maximum output power of 10 mW. A CCD camera is used as a detector to measure the intensity distribution of the laser beam. A cuvette, which is a three-layer structure with a sheet copper is sandwiched between 2 pieces of fused silica. The height of the fused silica is 1 mm. The sheet copper has doughnut shape. The liquid that is contained inside the doughnut hole has the same height with the sheet copper. By varying the thickness of the sheet copper, the liquid height can be changed. The ethanol solution dissolved dye termed as Sunset-yellow is filled in the cuvette. The chemical formula of the

**Figure 9.** Experiment result: the difference of intensity profile of the probe beam after passing through

In this experiment, the absorbance of the pump-beam is 2.776 and that of the probe-beam is negligible small. Figure 9 shows the laser beam profile of the probe beam after propagating through a divergent lens and a thermal lens. It is clear that, the probe beam change its

$$\frac{1}{r}\frac{\partial}{\partial r}(rv\_r) + v\_z \frac{\partial v\_z}{\partial z} = 0 \tag{13}$$

$$\left(v\_r \frac{\partial v\_r}{\partial r} + v\_z \frac{\partial v\_r}{\partial z} = -\frac{1}{\rho} \frac{\partial p}{\partial r} + \nu \left(\frac{\partial}{\partial r} \left(\frac{1}{r} \frac{\partial}{\partial r} (rv\_r)\right) + \frac{\partial^2 v\_r}{\partial z^2}\right) \tag{a}$$

$$\nabla \cdot \frac{\partial \mathbf{v}\_z}{\partial r} + \mathbf{v}\_z \frac{\partial \mathbf{v}\_z}{\partial z} = -\frac{1}{\rho} \frac{\partial p}{\partial z} + \nu \left( \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial \mathbf{v}\_z}{\partial r} \right) + \frac{\partial^2 \mathbf{v}\_z}{\partial z^2} \right) + \mathbf{g} \mathcal{J} \{T - T\_0\} \tag{b}$$

$$v\_r \frac{\partial T}{\partial r} + v\_z \frac{\partial T}{\partial z} = a \left( \frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right) + \frac{\partial^2 T}{\partial z^2} \right) + S \tag{15}$$

$$S = \frac{\alpha \mathbf{e}^{-\alpha z} I\_0(r)}{\rho \mathbf{C}\_p} \tag{16}$$

Here, *I*0(*r*) is the intensity distribution of the pump laser. The spot sizes of the laser beams are assumed to be constant through the interaction volume within the liquid medium.

The temperature distribution is calculated numerically based on the finite difference method. The 1st order upwind scheme and a 2nd order center differencing are applied to discretize the advection term and the diffusion term respectively. The thermal properties of liquid medium can be found in Ref. 24.

To model the propagation of laser through an inhomogeneous medium, the wave equation which includes an absorption term and an inhomogeneous refractive index term is applied [24]:

$$-\frac{\partial^2 E}{\partial z^2} + 2ik\_0 n\_0 \frac{\partial E}{\partial z} = \frac{1}{r} \frac{\partial}{\partial r} \left(\frac{\partial (rE)}{\partial r}\right) + k\_0^2 \left(n^2 - n\_0^2\right) E - \frac{1}{2} ik\_0 n\_0 a E \tag{17}$$

Here, *E* is the envelope of the oscillating electric field, *z* is the axis of propagation, *r* is transverse coordinates, *k*0 is the free space wave number and *α* is the absorption coefficient. The variable *n* is the refractive index profile depending on medium temperature following:

$$m(T) = n\_0 + \frac{dn}{dT}(T - T\_0) \tag{18}$$

Fluidic Optical Devices Based on Thermal Lens Effect 187

distance is 200 mm the probe beam is converted to the flat-top profile approximately. Therefore, by controlling the pump power and the propagation distance the Gaussian beam

(a) Influence of the propagation distance

**Figure 10.** Influence of the propagation distance and the pump power to the probe beam profile

In order to confirm the role of the fluidic laser beam shaper, a single-beam experiment is set up as shown in Fig. 11. A CW diode blue laser is used as pump and probe-beam (*P* = 10 mW, *λ* = 488 nm, *Φ* = 0.69 mm, TEM00). In this experiment, the height of the liquid medium is 0.5 mm, the dye concentration is 0.1 g/l and the absorption coefficient is 2.92 cm-1 (measured value) respectively. The propagation distance to obtain the flat-top beam profile is measured by changing the distance from the cuvette to the CCD camera. At the propagation distance

(b) Influence of the pump power

Figure 12(b) shows the beam profile change from the Gaussian to the flat-top beam. The vertical and horizontal axes show the intensity and distance from the laser axis respectively. The o-line shows the profile of the Gaussian input beam by fitting the laser beam profile measured at the surface of the cuvette. The strange-line shows the profile of the flat-top beam calculated by beam propagation method. The solid-line shows the profile of the flat-

**3.3. Experimental set-up to shape spatial profile** 

of 150 mm, the flat-top beam is confirmed as shown in Fig. 12(a).

can be converted into the flat-top beam.

Here, *n*0 = 1.359 is the refractive index of the liquid medium at reference temperature *T*0 = 298.15 K, d*n*/d*T* is the temperature coefficient of the refractive index. The propagation of laser is calculated based on Pade method. The optical properties parameter can be found in Ref. 24.

#### **3.2. Influences of the pump power and the propagation distance on the change of probe beam profile**

Influences of the pump power and the propagation distance to the probe beam profile were investigated numerically using the calculation parameters in Table. 1. In this calculation, both of the pump beam and the probe beam are written as follows.

$$E = E\_0 \exp\left(\frac{-r^2}{r\_0^2}\right) \exp\left(\frac{-ik\_0 n\_0 r^2}{2R}\right) \tag{19}$$

$$E\_0 = \sqrt{\frac{2P}{\pi r\_0^2}}\tag{20}$$

Here *P* is the power of laser, *R* is the radius of curvature of the wave front, *r* and *r0* are distance from laser axis and beam radius respectively.


**Table 1.** Calculation conditions

Effects of the pump power and the propagation distance to the probe beam profile are shown in Fig. 10(a) and (b) respectively. The vertical axis and horizontal axis show intensity and distance from laser axis respectively. Plots of '*P* = 0 mW' and '*d* = 0 mm' represent intensity distribution of the probe beam without thermal lens effect. As shown in Fig. 10(a), the further the propagation distance, the lower intensity at the probe beam center, and higher intensity at the wing. With increasing of the propagation distance, the laser beam profile changes from Gaussian to flat-top and the doughnut beam profile respectively. The profile of the probe beam changes with the same tendency as the increasing of pump power as shown in Fig. 10(b). In particular, when the pump power is 3 mW and propagation distance is 200 mm the probe beam is converted to the flat-top profile approximately. Therefore, by controlling the pump power and the propagation distance the Gaussian beam can be converted into the flat-top beam.

(a) Influence of the propagation distance

**Figure 10.** Influence of the propagation distance and the pump power to the probe beam profile

#### **3.3. Experimental set-up to shape spatial profile**

186 Optical Devices in Communication and Computation

Ref. 24.

**of probe beam profile** 

**Table 1.** Calculation conditions

 0 0 ( ) *dn nT n T T dT*

Here, *n*0 = 1.359 is the refractive index of the liquid medium at reference temperature *T*0 = 298.15 K, d*n*/d*T* is the temperature coefficient of the refractive index. The propagation of laser is calculated based on Pade method. The optical properties parameter can be found in

**3.2. Influences of the pump power and the propagation distance on the change** 

Influences of the pump power and the propagation distance to the probe beam profile were investigated numerically using the calculation parameters in Table. 1. In this calculation,

> 0 2 0

Here *P* is the power of laser, *R* is the radius of curvature of the wave front, *r* and *r0* are

Effects of the pump power and the propagation distance to the probe beam profile are shown in Fig. 10(a) and (b) respectively. The vertical axis and horizontal axis show intensity and distance from laser axis respectively. Plots of '*P* = 0 mW' and '*d* = 0 mm' represent intensity distribution of the probe beam without thermal lens effect. As shown in Fig. 10(a), the further the propagation distance, the lower intensity at the probe beam center, and higher intensity at the wing. With increasing of the propagation distance, the laser beam profile changes from Gaussian to flat-top and the doughnut beam profile respectively. The profile of the probe beam changes with the same tendency as the increasing of pump power as shown in Fig. 10(b). In particular, when the pump power is 3 mW and propagation

Parameter (a) (b) Pump power, mW 3 0 ~ 7 Pump beam diameter, mm 0.8 0.8 Probe power, mW 10 10 Probe beam diameter, mm 0.8 0.8 Absorption coefficient, cm-1 2.0 2.0 Distance from experimental section to CCD camera, mm 0 ~ 500 200 Phase front curvature radius, *R*, mm ∞ ∞

<sup>2</sup>*<sup>P</sup> <sup>E</sup>* 

2 2 0 0

*r R* 

both of the pump beam and the probe beam are written as follows.

distance from laser axis and beam radius respectively.

0 2 0 exp exp <sup>2</sup> *<sup>r</sup> ik n r E E*

(18)

(19)

*<sup>r</sup>* (20)

In order to confirm the role of the fluidic laser beam shaper, a single-beam experiment is set up as shown in Fig. 11. A CW diode blue laser is used as pump and probe-beam (*P* = 10 mW, *λ* = 488 nm, *Φ* = 0.69 mm, TEM00). In this experiment, the height of the liquid medium is 0.5 mm, the dye concentration is 0.1 g/l and the absorption coefficient is 2.92 cm-1 (measured value) respectively. The propagation distance to obtain the flat-top beam profile is measured by changing the distance from the cuvette to the CCD camera. At the propagation distance of 150 mm, the flat-top beam is confirmed as shown in Fig. 12(a).

Figure 12(b) shows the beam profile change from the Gaussian to the flat-top beam. The vertical and horizontal axes show the intensity and distance from the laser axis respectively. The o-line shows the profile of the Gaussian input beam by fitting the laser beam profile measured at the surface of the cuvette. The strange-line shows the profile of the flat-top beam calculated by beam propagation method. The solid-line shows the profile of the flattop beam measured by CCD camera at propagation distance of 150 mm from the cuvette. Both experimental and calculated results agree well with each other.

Fluidic Optical Devices Based on Thermal Lens Effect 189

**Figure 13.** Temperature distribution inside the liquid medium [K]. The calibration shows the difference

In order to explain in more detail about the mechanism of this fluidic beam shaper, the temperature distribution of liquid medium is calculated. As shown in Fig. 13, local heating near the beam axis produces a radially dependent temperature variation, which changes the liquid refractive index in which the lower refractive index is in the region near to the beam center. As a consequence, the radius of curvature of the wave front at the region near the beam center is shorter than one at the beam wing. Therefore the sample liquid locally acts as a micro divergent lens with shorter focal length at beam center. As shown in Fig. 1b, the beam center that passes through shorter focal length is spread out more rapidly than the beam wing. As the probe beam propagates to increasing distance, the intensity in the center region drops rapidly than one in the wing region. At a certain value of propagation distance,

It is noted that, in the case of single-beam shaper, one part of laser beam energy (about 15% in this experiment) is converted into thermal energy in order to change temperature distribution or in other words to change refractive index distribution in the liquid medium. Therefore, in the case of single-beam shaper, the beam shaper has another role, which is as an attenuator. This laser beam shaper/attenuator can be applied in practical laser drilling technology. In the case of applying on only laser beam shaper, the double-beam system is recommended. In this case, it is needed to select dye whose absorbance of the probe-beam is

**3.4. Relationship between pump power and distance to shape spatial profile** 

As shown in previous section, the flat-top beam can be obtained only at a fixed distance. In order to control this distance, the influence of pump power is investigated theoretically and experimentally. The calculation parameters are shown in Table. 2. The pump power is changed from 1 to 8 mW. The distance to obtain the flat-top beam is obtained numerically. The relationship between the pump power and the distance to shape spatial profile is shown in Fig. 14(a). The horizontal and vertical axes show pump power and distance to obtain the flat-top beam respectively. As shown in Fig. 14(a), the distance to obtain a flat-top beam is in

between temperature inside the liquid medium with the ambient temperature.

the Gaussian beam can be converted into the flat-top beam.

negligible small.

inverse proportion to the pump power.

**Figure 11.** Experimental set up for a single-beam thermal lens system to transfer a Gaussian beam to flat-top beam

(a) Flat-top beam profile measured by CCD camera

(b) Beam profile change from Gaussian to flat-top

flat-top beam

**Figure 12.** Experimental results

top beam measured by CCD camera at propagation distance of 150 mm from the cuvette.

**Figure 11.** Experimental set up for a single-beam thermal lens system to transfer a Gaussian beam to

(a) Flat-top beam profile measured by CCD camera

(b) Beam profile change from Gaussian to flat-top

Both experimental and calculated results agree well with each other.

**Figure 13.** Temperature distribution inside the liquid medium [K]. The calibration shows the difference between temperature inside the liquid medium with the ambient temperature.

In order to explain in more detail about the mechanism of this fluidic beam shaper, the temperature distribution of liquid medium is calculated. As shown in Fig. 13, local heating near the beam axis produces a radially dependent temperature variation, which changes the liquid refractive index in which the lower refractive index is in the region near to the beam center. As a consequence, the radius of curvature of the wave front at the region near the beam center is shorter than one at the beam wing. Therefore the sample liquid locally acts as a micro divergent lens with shorter focal length at beam center. As shown in Fig. 1b, the beam center that passes through shorter focal length is spread out more rapidly than the beam wing. As the probe beam propagates to increasing distance, the intensity in the center region drops rapidly than one in the wing region. At a certain value of propagation distance, the Gaussian beam can be converted into the flat-top beam.

It is noted that, in the case of single-beam shaper, one part of laser beam energy (about 15% in this experiment) is converted into thermal energy in order to change temperature distribution or in other words to change refractive index distribution in the liquid medium. Therefore, in the case of single-beam shaper, the beam shaper has another role, which is as an attenuator. This laser beam shaper/attenuator can be applied in practical laser drilling technology. In the case of applying on only laser beam shaper, the double-beam system is recommended. In this case, it is needed to select dye whose absorbance of the probe-beam is negligible small.

#### **3.4. Relationship between pump power and distance to shape spatial profile**

As shown in previous section, the flat-top beam can be obtained only at a fixed distance. In order to control this distance, the influence of pump power is investigated theoretically and experimentally. The calculation parameters are shown in Table. 2. The pump power is changed from 1 to 8 mW. The distance to obtain the flat-top beam is obtained numerically. The relationship between the pump power and the distance to shape spatial profile is shown in Fig. 14(a). The horizontal and vertical axes show pump power and distance to obtain the flat-top beam respectively. As shown in Fig. 14(a), the distance to obtain a flat-top beam is in inverse proportion to the pump power.

In order to validate the numerical prediction, a single beam experiment was carried out. The pump power is changed from 1 to 6 mW and the distance to obtain the flat-top beam was measured. The experimental result shown in Fig. 14(b), shows excellent agreement with calculation prediction. The relationship between pump power and distance to obtain the flat-top beam can be explained by the interaction between energy absorption of liquid medium with the focal length of local micro lens. As the pump power increase, the absorption energy increases. As a consequence, the rate of decreasing of *R* is enhanced. This can be thought as the reason why the distance to obtain a flat-top beam decreases. In other words, the distance to obtain the flat-top beam profile also decreases with the increasing of absorption coefficient. Therefore, by changing the absorption coefficient or the pump power, the distance to obtain a flat-top beam can be controlled.

Fluidic Optical Devices Based on Thermal Lens Effect 191

Fluidic lenses are well known to present significant advantages for wide range of applications from mobile phone to laboratory on a chip. Fluidic lenses have a number of apparent advantages such as tunable refractive index and reconfigurable geometry. Several approaches to design the liquid lens have been developed based on the microfluidic techniques to modify the liquid lens shape by using: out-of-plane micro-optofluidic [25-26], in-plane micro-optofluidic [27-28], electron wetting [29], dielectrophoresis [30] and hydrodynamic force [31]. Other approach bases on turning the refractive index of the liquid by different means such as pressure control, optical

When the liquid medium is irradiated, local heating near the beam axis produces a radially dependent temperature variation, which changes the liquid refractive index in which the lower refractive index is in the region near to the beam center. As a consequence, the radius of curvature of the wave front at the region near the beam center is shorter than one at the beam wing. The liquid medium behaviors as a convergence GRIN-L with focal length depends on the radial position of the incident ray relative to the optical axis of the cuvette. The ray equation that

> grad( ) *d dR n n ds ds*

Where, d*s* and *R* are the differential element of the path length and the positional vector of the ray respectively. The variable *n* is the refractive index of the liquid sample. The variable *n* is the refractive index profile depending on medium temperature following equation (13-16, 18).

Influences of the pump beam profile to the focal length of the GRIN-L were investigated numerically with the calculation conditions in Table. 3. The intensity profile of the pump is applied with the Gaussian beam and the quasi-flat-top beam (a super-Gaussian distribution

Gaussian 2 2

2/

*F k Pk <sup>r</sup> <sup>I</sup>*

exp 2 (2 / )

Here Γ is the Gamma function, *r* and *r0* are distance from laser axis and beam radius, respectively. In this calculation, quasi-flat-top beam is the 10 order of the super-Gaussian

lat-top 2

distribution, two types of the pump intensity profile are shown in Fig.15.

0 0 2 2 exp *P r <sup>I</sup>* 

> 0 0 2 2

*rk r* 

*k k*

*r r* 

2

(21)

(22)

(23)

is calculated numerically to obtain the path of an incident beam, which is given by:

control, magnetic control, thermo-optic control, and electro-optic control.

**4. Tunable fluidic lens** 

**4.1. Principle of fluidic lens** 

**4.2. Influences of the pump beam profile** 

of order *k*) using Eq. 22 and Eq. 23 respectively.


**Table 2.** Calculation conditions

**Figure 14.** Relationship between the pump power and the distance to obtain the flat-top beam profile. The horizontal and vertical axes show the pump power and the distance to obtain the flat-top beam profile respectively.

#### **4. Tunable fluidic lens**

190 Optical Devices in Communication and Computation

**Table 2.** Calculation conditions

profile respectively.

the distance to obtain a flat-top beam can be controlled.

In order to validate the numerical prediction, a single beam experiment was carried out. The pump power is changed from 1 to 6 mW and the distance to obtain the flat-top beam was measured. The experimental result shown in Fig. 14(b), shows excellent agreement with calculation prediction. The relationship between pump power and distance to obtain the flat-top beam can be explained by the interaction between energy absorption of liquid medium with the focal length of local micro lens. As the pump power increase, the absorption energy increases. As a consequence, the rate of decreasing of *R* is enhanced. This can be thought as the reason why the distance to obtain a flat-top beam decreases. In other words, the distance to obtain the flat-top beam profile also decreases with the increasing of absorption coefficient. Therefore, by changing the absorption coefficient or the pump power,

> Pump power, mW 1 ~ 8 Pump beam diameter, mm 0.8 Probe power, mW 10 Probe beam diameter, mm 0.8 Absorption coefficient, cm-1 2.0 Phase front curvature radius, *R*, mm 320

**Figure 14.** Relationship between the pump power and the distance to obtain the flat-top beam profile. The horizontal and vertical axes show the pump power and the distance to obtain the flat-top beam

(b) Experimental result

(a) Calculation result

Fluidic lenses are well known to present significant advantages for wide range of applications from mobile phone to laboratory on a chip. Fluidic lenses have a number of apparent advantages such as tunable refractive index and reconfigurable geometry. Several approaches to design the liquid lens have been developed based on the microfluidic techniques to modify the liquid lens shape by using: out-of-plane micro-optofluidic [25-26], in-plane micro-optofluidic [27-28], electron wetting [29], dielectrophoresis [30] and hydrodynamic force [31]. Other approach bases on turning the refractive index of the liquid by different means such as pressure control, optical control, magnetic control, thermo-optic control, and electro-optic control.

#### **4.1. Principle of fluidic lens**

When the liquid medium is irradiated, local heating near the beam axis produces a radially dependent temperature variation, which changes the liquid refractive index in which the lower refractive index is in the region near to the beam center. As a consequence, the radius of curvature of the wave front at the region near the beam center is shorter than one at the beam wing. The liquid medium behaviors as a convergence GRIN-L with focal length depends on the radial position of the incident ray relative to the optical axis of the cuvette. The ray equation that is calculated numerically to obtain the path of an incident beam, which is given by:

$$\frac{d}{ds}\left(n\frac{dR}{ds}\right) = \text{grad}(n)\tag{21}$$

Where, d*s* and *R* are the differential element of the path length and the positional vector of the ray respectively. The variable *n* is the refractive index of the liquid sample. The variable *n* is the refractive index profile depending on medium temperature following equation (13-16, 18).

#### **4.2. Influences of the pump beam profile**

Influences of the pump beam profile to the focal length of the GRIN-L were investigated numerically with the calculation conditions in Table. 3. The intensity profile of the pump is applied with the Gaussian beam and the quasi-flat-top beam (a super-Gaussian distribution of order *k*) using Eq. 22 and Eq. 23 respectively.

$$I\_{\text{Gaussian}} = \frac{2P}{\pi r\_0^2} \exp\left(\frac{-2r^2}{r\_0^2}\right) \tag{22}$$

$$I\_{\text{Flat-top}} = \frac{Pk 2^{2/k}}{2\pi r\_0^2 \Gamma(2/k)} \exp\left(\frac{-2r^k}{r\_0^k}\right) \tag{23}$$

Here Γ is the Gamma function, *r* and *r0* are distance from laser axis and beam radius, respectively. In this calculation, quasi-flat-top beam is the 10 order of the super-Gaussian distribution, two types of the pump intensity profile are shown in Fig.15.


Fluidic Optical Devices Based on Thermal Lens Effect 193

In order to confirm the qualities of the GRIN-L, an experiment with the quasi flat-top pump beam is carried out as shown in Fig. 17. A CW diode blue laser is used as pump laser (*P* = 10 mW, *λ*= 488 nm, *Φ* = 0.69 mm, TEM00). In cuvette 1, the height of liquid is 0.5 mm, and the absorption coefficient is 2.92 cm-1 (at wavelength of 488 nm). In the cuvette 2, the height of liquid is 1 mm, and the absorption coefficient is 55 cm-1 (at wavelength of 488 nm). A CW He-Ne laser is used as probe laser (*P* = 0.6 mW, *λ* = 632 nm, *Φ* = 0.8 mm, TEM00). It is noted that, the absorption of ethanol solution can be ignored at the wavelength of the probe laser. First, the pump beam passes through cuvette1, then the beam profile of pump beam was converted from Gaussian to flat-top during its transmission to cuvette 2 as shown in Fig. 18. Then, the probe laser was adjusted to overlap with pump laser. After propagating through

**Figure 18.** The intensity profile of the pump beam during its transmission to cuvette 2. Dotted and solid

Distance from laser axis, *r*, mm

lines show the measured result and fitting by super-Gaussian distribution respectively.

**4.3. Experimental set-up** 

**Figure 17.** Experimental set-up for the fluidic divergent lens

Intensity, *I*, W/cm2

**Table 3.** Calculation conditions

**Figure 15.** Two types of the pump beam profile

**Figure 16.** Effect of the pump beam profile to the focal length of the GRIN-L lens

The effect of the pump beam profile to the focal length of the GRIN-L lens is shown in Fig. 16. The vertical and horizontal axes show focal length and distance from laser axis respectively. The solid and dashed lines represent the plot of the focal length again the radial position of the incident ray relative to the optical axis of the cuvette in the case of Gaussian pump beam and quasi flat-top pump beam respectively. As shown in Fig. 16, for the Gaussian pump beam the focal length of the GRIN-L increases sharply with increasing of the distance from laser axis, which means larger spherical aberration. It means that, the beam center which passes through shorter focal length is spread out more rapidly than the beam wing. As a consequence, the further the propagation distance of the probe beam, the laser beam profile changes from Gaussian to the doughnut beam profile [24], which should cause some undesirable results in laser processing [32]. In contrast, with the quasi flat-top pump beam, the focal length of the GRIN-L varies lightly with increasing of the distance from laser axis smaller than beam waist of the flat-top pump beam. The area smaller than the beam waist of the flat-top pump beam acts as a divergent lens with small spherical aberration. Therefore, for the purpose of designing the GRIN-L lens the uniform pump beam shows the advance in reducing the spherical aberration.

#### **4.3. Experimental set-up**

192 Optical Devices in Communication and Computation

**Figure 15.** Two types of the pump beam profile

Intensity, *I*, W/cm2

Focal length , *f*, mm

**Figure 16.** Effect of the pump beam profile to the focal length of the GRIN-L lens

The effect of the pump beam profile to the focal length of the GRIN-L lens is shown in Fig. 16. The vertical and horizontal axes show focal length and distance from laser axis respectively. The solid and dashed lines represent the plot of the focal length again the radial position of the incident ray relative to the optical axis of the cuvette in the case of Gaussian pump beam and quasi flat-top pump beam respectively. As shown in Fig. 16, for the Gaussian pump beam the focal length of the GRIN-L increases sharply with increasing of the distance from laser axis, which means larger spherical aberration. It means that, the beam center which passes through shorter focal length is spread out more rapidly than the beam wing. As a consequence, the further the propagation distance of the probe beam, the laser beam profile changes from Gaussian to the doughnut beam profile [24], which should cause some undesirable results in laser processing [32]. In contrast, with the quasi flat-top pump beam, the focal length of the GRIN-L varies lightly with increasing of the distance from laser axis smaller than beam waist of the flat-top pump beam. The area smaller than the beam waist of the flat-top pump beam acts as a divergent lens with small spherical aberration. Therefore, for the purpose of designing the GRIN-L lens the uniform pump beam shows the advance in reducing the spherical aberration.

Distance from laser axis, *r*, mm

Distance from laser axis, *r*, mm

**Table 3.** Calculation conditions

Pump power, mW 10 Pump beam diameter, mm 1.5 Absorption coefficient, cm-1 2.0

In order to confirm the qualities of the GRIN-L, an experiment with the quasi flat-top pump beam is carried out as shown in Fig. 17. A CW diode blue laser is used as pump laser (*P* = 10 mW, *λ*= 488 nm, *Φ* = 0.69 mm, TEM00). In cuvette 1, the height of liquid is 0.5 mm, and the absorption coefficient is 2.92 cm-1 (at wavelength of 488 nm). In the cuvette 2, the height of liquid is 1 mm, and the absorption coefficient is 55 cm-1 (at wavelength of 488 nm). A CW He-Ne laser is used as probe laser (*P* = 0.6 mW, *λ* = 632 nm, *Φ* = 0.8 mm, TEM00). It is noted that, the absorption of ethanol solution can be ignored at the wavelength of the probe laser. First, the pump beam passes through cuvette1, then the beam profile of pump beam was converted from Gaussian to flat-top during its transmission to cuvette 2 as shown in Fig. 18. Then, the probe laser was adjusted to overlap with pump laser. After propagating through

**Figure 17.** Experimental set-up for the fluidic divergent lens

**Figure 18.** The intensity profile of the pump beam during its transmission to cuvette 2. Dotted and solid lines show the measured result and fitting by super-Gaussian distribution respectively.

the sample the probe laser is directed towards the CCD camera and the pump laser is blocked using filters located at the detection plane. The distance between cuvette 2 and the CCD camera is varied, and the 1/e2 diameter of probe laser is measured.

Fluidic Optical Devices Based on Thermal Lens Effect 195

**Figure 20.** Relationship between the pump power and focal length

Focal length , *f*, mm

whose absorbance of the probe-beam is negligible small.

will be promising tools in many fields of laser application.

Hong Duc Doan and Kazuyoshi Fushinobu *Department of Mechanical and Control Engineering,* 

by adjusting the pump power, the focal length can be controlled

In this research, a novel idea of fluidic optical devices which includes laser beam shaper and fluidic divergent lens are demonstrated. The fluidic optical devices are based on controlling some parameters in the thermal lens system. The interaction among the intensity distribution, power of the pump beam, the absorption coefficient, the propagation distance and the intensity profile of the probe beam have been investigated experimentally and theoretically. It

Pump power, *P*, mW

 By controlling the pump power and the absorption coefficient, the input Gaussian beam can be converted into a flat-top beam profile. The distance to get the flat-top beam profile can be controlled easily by adjusting the pump power and the absorption coefficient. In actual applications, single-beam shaper has another role, which is as an attenuator. This laser beam shaper/attenuator can be applied in practical laser drilling technology. In the case of applying on only laser beam shaper, the double-beam system is recommended. In this case, it is needed to select a dye

The uniform pump beam shows the advance in reducing the spherical aberration. And

With some merits such as flexiblility, versatility and low cost, these fluidic optical devices

**5. Conclusion** 

is found that

**Author details** 

*Meguro-ku, Tokyo,* 

*Japan* 

*Tokyo Institute of Technology,* 

Figure 19(a) shows the change along the propagation direction in the beam profile. The vertical and horizontal axes show the intensity and distance from the laser axis respectively. By using the quasi flat-top pump beam, the beam profile of probe laser can remain in Gaussian distribution during its propagation. Figure 19(b) shows the plot of probe beam waist again propagation distance. As shown in Fig. 19(b), the beam waist of probe laser varies linearly with propagation distance. In other words, cuvette 2 acts as a divergence lens with focal length of f = -424 mm (this value has been calculated by considering the divergence angle of probe laser *θ* = 1.2 mrad).

Next, the pump power is changed from *P*0 = 7.7 mW to *P*0/2, *P*0/3 and *P*0/4 respectively. Figure 20 shows the plots of focal length against the pump power. Square and circle plots show the calculation and experimental result, respectively. As shown in Fig. 20, the focal length increases with increasing of the pump power. This means that, by adjusting the pump power, the focal length can be controlled.

**Figure 19.** Probe beam changes along the propagation direction

**Figure 20.** Relationship between the pump power and focal length

#### **5. Conclusion**

194 Optical Devices in Communication and Computation

divergence angle of probe laser *θ* = 1.2 mrad).

pump power, the focal length can be controlled.

**Figure 19.** Probe beam changes along the propagation direction

Beam waist, *Φ*, mm

the sample the probe laser is directed towards the CCD camera and the pump laser is blocked using filters located at the detection plane. The distance between cuvette 2 and the

Figure 19(a) shows the change along the propagation direction in the beam profile. The vertical and horizontal axes show the intensity and distance from the laser axis respectively. By using the quasi flat-top pump beam, the beam profile of probe laser can remain in Gaussian distribution during its propagation. Figure 19(b) shows the plot of probe beam waist again propagation distance. As shown in Fig. 19(b), the beam waist of probe laser varies linearly with propagation distance. In other words, cuvette 2 acts as a divergence lens with focal length of f = -424 mm (this value has been calculated by considering the

Next, the pump power is changed from *P*0 = 7.7 mW to *P*0/2, *P*0/3 and *P*0/4 respectively. Figure 20 shows the plots of focal length against the pump power. Square and circle plots show the calculation and experimental result, respectively. As shown in Fig. 20, the focal length increases with increasing of the pump power. This means that, by adjusting the

(a) Beam profile

(b) Beam waist Distance from cuvette 2 to camera, *d*, mm

CCD camera is varied, and the 1/e2 diameter of probe laser is measured.

In this research, a novel idea of fluidic optical devices which includes laser beam shaper and fluidic divergent lens are demonstrated. The fluidic optical devices are based on controlling some parameters in the thermal lens system. The interaction among the intensity distribution, power of the pump beam, the absorption coefficient, the propagation distance and the intensity profile of the probe beam have been investigated experimentally and theoretically. It is found that


With some merits such as flexiblility, versatility and low cost, these fluidic optical devices will be promising tools in many fields of laser application.

#### **Author details**

Hong Duc Doan and Kazuyoshi Fushinobu *Department of Mechanical and Control Engineering, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan* 

#### **Acknowledgement**

Part of this work has been supported by the Grant-in-Aid for JSPS Fellows and Grant-in-Aid for Scientific Research of MEXT/JSPS. The authors also would like to acknowledge Mr. Akamine Yoshihiko.

Fluidic Optical Devices Based on Thermal Lens Effect 197

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[19] M. T. Eismann, A. M. Tai and J. N. Cederquist, Iterative design of a holographic beam

[20] F. M. Dickey and S. C. Holswade, Laser beam shaping: Theory and Techniques, Marcel

[21] P. Scott, Reflective optics for irradiance redistribution of laser beam design, Appl. Opt.

[22] S. Zhang, Q. Zhang and G. Lupke, Spatial beam shaping of ultrashort laser pulse:

[23] B. Mercier, J.P. Rousseau, A. Jullien, L. Antonucci, Nonlinear beam shaper for femtosecond laser pulses, from Gaussian to at-top prole, Optics Communications 283

[24] H. D. Doan, Y. Akamine, K. Fushinobu, Fluidic laser beam shaper by using thermal lens

[25] S. H. Ahn, Y. K. Kim, Proposal of human eye's crystalline lens-like variable focusing

[26] D. Y. Zhang, V. Lien, Y. Berdichevsky, J. H. Choi, Y. H. Lo, Fluidic adaptive lens with

[27] S. K. Hsiung, C. H. Lee, and G. B. Lee, Microcapillary electrophoresis chips utilizing controllable micro-lens structures and buried optical fibers for on-line optical detection,

[28] V. Lien, Y. Berdichevsky, Y. H. Lo, Microspherical surfaces with predefined focal lengths fabricated using microfluidic capillaries, Appl. Phys. Lett. (2003) 83,

[29] C. B. Gorman, H. A. Biebuyck, G. M. Whitesides, Control of the Shape of Liquid Lenses on a Modified Gold Surface Using an Applied Electrical Potential across a Self-

[30] C. C. Cheng, C. A. Chang, H. A. Yeh, Variable focus dielectric liquid droplet lens, Opt.

[31] S. K. Y. Tang, C. A. Stan, G. M. Whitesides, Dynamically reconfigurable liquid-core

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#### **6. References**


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**Acknowledgement** 

Akamine Yoshihiko.

**6. References** 

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	- [32] D.H. Doan, Y. Yin, N. Iwatani, K. Fushinobu, Laser processing by using fluidic laser beam shaper, Proc. National Heat Transfer Symposium 2012, Inpress

**Chapter 10** 

© 2012 Choi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

Silicate glass has been widely used for optical device materials due to its excellent optical transparency. To satisfy our multiple demands in advanced optical device materials, organic/inorganic hybrid composites have been widely prepared by a bulk mixing

However, conventional glassy materials have shown limitations to modify their physicochemical properties by inserting desired components into glassy hosts. In addition, a significant phase separation occurs during a mixing process of multiple components,

To overcome those limitations, there are growing interests in doping organic components or semiconductor particles into glassy hosts without any phase separation to combine beneficial

Hybrid materials lie at the interface of the organic and inorganic material regimes, where versatility in molecular tailoring approach offers novel molecular modifications in design of new chemical structures. Hybrid materials can also range, depending on the method of formation and domain size, from physical mixtures of inorganic oxides and organics (blends, composites) to nanocomposites and molecular composites that utilize formal chemical linkages between the organic and inorganic domains on the molecular scale.

Hybrid materials are ranged from the bulk-scales to molecular scales as shown in Figure 2 to

Usually, hybrid materials mixed at the bulk scales retain the original properties of the individual organic and inorganic components. In other words, their final properties are significantly influenced by the characteristics and their domain sizes of individual

and reproduction in any medium, provided the original work is properly cited.

properties at the molecular scales, and thus to bring desired properties (Figure 1). [1]

technique, which is physically mixing multiple components at the bulk scales.

**Novel Optical Device Materials** 

**– Molecular-Level Hybridization** 

Additional information is available at the end of the chapter

Kyung M. Choi

**1. Introduction** 

http://dx.doi.org/10.5772/50032

especially immiscible phases.

mix up multiple components. [1-10]

components after the mixing process at the bulk scales.

## **Novel Optical Device Materials – Molecular-Level Hybridization**

Kyung M. Choi

198 Optical Devices in Communication and Computation

[32] D.H. Doan, Y. Yin, N. Iwatani, K. Fushinobu, Laser processing by using fluidic laser

beam shaper, Proc. National Heat Transfer Symposium 2012, Inpress

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50032

### **1. Introduction**

Silicate glass has been widely used for optical device materials due to its excellent optical transparency. To satisfy our multiple demands in advanced optical device materials, organic/inorganic hybrid composites have been widely prepared by a bulk mixing technique, which is physically mixing multiple components at the bulk scales.

However, conventional glassy materials have shown limitations to modify their physicochemical properties by inserting desired components into glassy hosts. In addition, a significant phase separation occurs during a mixing process of multiple components, especially immiscible phases.

To overcome those limitations, there are growing interests in doping organic components or semiconductor particles into glassy hosts without any phase separation to combine beneficial properties at the molecular scales, and thus to bring desired properties (Figure 1). [1]

Hybrid materials lie at the interface of the organic and inorganic material regimes, where versatility in molecular tailoring approach offers novel molecular modifications in design of new chemical structures. Hybrid materials can also range, depending on the method of formation and domain size, from physical mixtures of inorganic oxides and organics (blends, composites) to nanocomposites and molecular composites that utilize formal chemical linkages between the organic and inorganic domains on the molecular scale.

Hybrid materials are ranged from the bulk-scales to molecular scales as shown in Figure 2 to mix up multiple components. [1-10]

Usually, hybrid materials mixed at the bulk scales retain the original properties of the individual organic and inorganic components. In other words, their final properties are significantly influenced by the characteristics and their domain sizes of individual components after the mixing process at the bulk scales.

© 2012 Choi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Novel Optical Device Materials – Molecular-Level Hybridization 201

To overcome those limitations of the bulk-scale mixing technique, *molecular-level hybridization technique* has been actively investigated. [1-10] This technique results in molecular-level composites, which are their domain sizes in the nanometer scale often create new properties, which would not be expected from those individuals by the loss of individuals' identities after the molecular-level mixing process thereby creating new

Especially for optical device materials, desired properties of hybrid glasses can be chemically designed and then prepared by incorporating functional organic fragments

With this strategy, novel optical device materials with beneficial properties can be obtained by embedding organic spacers into silicate network to create organically modified hybrid glasses as demonstrated in earlier publications (Figure 3). [1-10] Furthermore, the molecularlevel mixing technique doesn't show any significant phase separation; because, *the molecularlevel hybridization* is based on a microscopically homogeneous mixing and thus the uniform distribution of organic and inorganic moieties in a domain size at the molecular level is

Those organically modified glasses mixed at the molecular scale, were provided by a molecular modification, which inserts desired organic fragments between two inorganic oxides to create entirely new optical properties. Figure 3 shows *the molecular-level* 

**Figure 3.** Molecular-level hybridization technique to produce polysilsesquioxanes. [6]

properties.

provided.

between inorganic oxides.

*hybridization* to produce polysilsesquioxanes.

**Figure 1.** Organic/inorganic hybrid materials. [1]

In addition, a phase separation problem also limits to achieve a uniform mixing of multiple components during the bulk-mixing process.

**Figure 2.** Relative size scale of mixing domains for different types of hybrid materials. [1-10]

To overcome those limitations of the bulk-scale mixing technique, *molecular-level hybridization technique* has been actively investigated. [1-10] This technique results in molecular-level composites, which are their domain sizes in the nanometer scale often create new properties, which would not be expected from those individuals by the loss of individuals' identities after the molecular-level mixing process thereby creating new properties.

200 Optical Devices in Communication and Computation

**Figure 1.** Organic/inorganic hybrid materials. [1]

components during the bulk-mixing process.

In addition, a phase separation problem also limits to achieve a uniform mixing of multiple

**Figure 2.** Relative size scale of mixing domains for different types of hybrid materials. [1-10]

Especially for optical device materials, desired properties of hybrid glasses can be chemically designed and then prepared by incorporating functional organic fragments between inorganic oxides.

With this strategy, novel optical device materials with beneficial properties can be obtained by embedding organic spacers into silicate network to create organically modified hybrid glasses as demonstrated in earlier publications (Figure 3). [1-10] Furthermore, the molecularlevel mixing technique doesn't show any significant phase separation; because, *the molecularlevel hybridization* is based on a microscopically homogeneous mixing and thus the uniform distribution of organic and inorganic moieties in a domain size at the molecular level is provided.

Those organically modified glasses mixed at the molecular scale, were provided by a molecular modification, which inserts desired organic fragments between two inorganic oxides to create entirely new optical properties. Figure 3 shows *the molecular-level hybridization* to produce polysilsesquioxanes.

**Figure 3.** Molecular-level hybridization technique to produce polysilsesquioxanes. [6]

Bridged polysilsesquioxanes are a new family of molecular-level composites, which also a new version of hybrid glasses; these are prepared from hybrid sol–gel processable monomers through a sol-gel polymerization. These are microscopically homogeneous with uniform distribution of the organic spacers and thus also show an excellent optical transparency. There are many publications of novel optical device materials based on organic/inorganic hybrid glasses. [11-17]

Novel Optical Device Materials – Molecular-Level Hybridization 203

**Figure 4.** A variety of sol-gel processable monomers prepared by *the molecular-level hybridization*.

We have developed novel laser devices based on those organic/inorganic hybrid glasses

Silicate-based optical fibers and planar waveguide amplifiers are widely studied for optoelectronic applications because of the superior chemical resistance and compatibility

Transparent silica doped with rare-earth metal ions has been used for laser amplifiers, such as photonic fiber amplifiers, solid-state lasers, compact laser amplifiers, ultra short pulse

Planar waveguides and fibers doped with rare-earth metal ions are a key challenge; thus, an enormous amount of publications in rare-earth metal ion doped optical devices has been found. [29-37] Fabrication of optical devices with high resolution offers an efficient approach

High gain laser amplifiers can be achieved by improving several relative factors, such as optical losses, phonon energies, pumping powers and distances, fluorescence life times, and refractive indices of optical medium. The lasing efficiency can be also improved by changing

**2. Novel optical device materials for laser amplifier [25]** 

prepared by *the molecular-level hybridization.* 

lasers, high-power lasers, so on. [29-39]

**2.1. Rare-earth ion doped laser amplifier** 

with other optical devices based on polymeric materials.

to minimize the cost and size of optical amplifiers.

the chemical environment of rare-earth metal ions.

In optical device materials, organically modified silicate glasses/transparent polymers have been actively pursued to develop novel optical devices, such as lasers, optical switches, optical fibers, waveguides, laser amplifiers, optical displays, and data storage devices.

[11-17]

In addition, we can also control the porosity of those organically modified silica, polysilsesquioxanes, by inserting different molecules or sizes of organic spacers as shown the void space in Figure 3 (right); due to the insertion of organic spacers, the porosity of the resulting hybrid glass significantly increased. [18-26]

The expanded pores allow us to dope semiconductor or metal particles without any significant mechanical cracks. *The molecular-level hybridization* also solves the phase separation problem during molecular-level mixing process.

The pore size of organically modified silicate materials can be controlled by both choices of organic spacers and sol-gel conditions. Those molecularly designed hybrid glasses have shown high surface areas and a relatively narrow distribution of pore sizes that range from the high micropore to the low mesopore domain (15-100 Å).

Several organic/inorganic hybrid sol-gel monomers have been molecularly designed and then synthesized for developing novel hybrid glasses. A variety of bridged polysilsesquioxanes, organically modified hybrid silica, have been designed by *the molecular-level hybridization*  (Figure 4). [18-26]

Those functional organic spacers inserted in the silicate networks (Figures 3 and 4) can serve as dopant precursors to growth particles in the porous glassy hosts. Those void volumes in the glassy hosts can be a matrix for the growth of quantum dots, such as semiconductor or metal particles. No phase separation occurs during the corporations of those dopants.

In Figure 5, those sol-gel processable monomers contain functional groups, which are sol-gel polymerized under either acidic or base condition, and then produce highly porous xerogels. [4]

Due to the highly porous silicate matrices, we doped various dopants without any phase separation; for example, we prepared highly nano-porous polysilsesquioxane systems, and then controlled sol-gel conditions to dope nano-sized transition metal particles or semiconductor particles, such as CdS [18, 19, 21], chromium [20, 21], iron [22], cobalt [27], and platinum [28] into the silicate hosts.

**Figure 4.** A variety of sol-gel processable monomers prepared by *the molecular-level hybridization*.

### **2. Novel optical device materials for laser amplifier [25]**

We have developed novel laser devices based on those organic/inorganic hybrid glasses prepared by *the molecular-level hybridization.* 

#### **2.1. Rare-earth ion doped laser amplifier**

202 Optical Devices in Communication and Computation

organic/inorganic hybrid glasses. [11-17]

resulting hybrid glass significantly increased. [18-26]

separation problem during molecular-level mixing process.

the high micropore to the low mesopore domain (15-100 Å).

[11-17]

(Figure 4). [18-26]

and platinum [28] into the silicate hosts.

[4]

Bridged polysilsesquioxanes are a new family of molecular-level composites, which also a new version of hybrid glasses; these are prepared from hybrid sol–gel processable monomers through a sol-gel polymerization. These are microscopically homogeneous with uniform distribution of the organic spacers and thus also show an excellent optical transparency. There are many publications of novel optical device materials based on

In optical device materials, organically modified silicate glasses/transparent polymers have been actively pursued to develop novel optical devices, such as lasers, optical switches, optical fibers, waveguides, laser amplifiers, optical displays, and data storage devices.

In addition, we can also control the porosity of those organically modified silica, polysilsesquioxanes, by inserting different molecules or sizes of organic spacers as shown the void space in Figure 3 (right); due to the insertion of organic spacers, the porosity of the

The expanded pores allow us to dope semiconductor or metal particles without any significant mechanical cracks. *The molecular-level hybridization* also solves the phase

The pore size of organically modified silicate materials can be controlled by both choices of organic spacers and sol-gel conditions. Those molecularly designed hybrid glasses have shown high surface areas and a relatively narrow distribution of pore sizes that range from

Several organic/inorganic hybrid sol-gel monomers have been molecularly designed and then synthesized for developing novel hybrid glasses. A variety of bridged polysilsesquioxanes, organically modified hybrid silica, have been designed by *the molecular-level hybridization* 

Those functional organic spacers inserted in the silicate networks (Figures 3 and 4) can serve as dopant precursors to growth particles in the porous glassy hosts. Those void volumes in the glassy hosts can be a matrix for the growth of quantum dots, such as semiconductor or metal

In Figure 5, those sol-gel processable monomers contain functional groups, which are sol-gel polymerized under either acidic or base condition, and then produce highly porous xerogels.

Due to the highly porous silicate matrices, we doped various dopants without any phase separation; for example, we prepared highly nano-porous polysilsesquioxane systems, and then controlled sol-gel conditions to dope nano-sized transition metal particles or semiconductor particles, such as CdS [18, 19, 21], chromium [20, 21], iron [22], cobalt [27],

particles. No phase separation occurs during the corporations of those dopants.

Silicate-based optical fibers and planar waveguide amplifiers are widely studied for optoelectronic applications because of the superior chemical resistance and compatibility with other optical devices based on polymeric materials.

Transparent silica doped with rare-earth metal ions has been used for laser amplifiers, such as photonic fiber amplifiers, solid-state lasers, compact laser amplifiers, ultra short pulse lasers, high-power lasers, so on. [29-39]

Planar waveguides and fibers doped with rare-earth metal ions are a key challenge; thus, an enormous amount of publications in rare-earth metal ion doped optical devices has been found. [29-37] Fabrication of optical devices with high resolution offers an efficient approach to minimize the cost and size of optical amplifiers.

High gain laser amplifiers can be achieved by improving several relative factors, such as optical losses, phonon energies, pumping powers and distances, fluorescence life times, and refractive indices of optical medium. The lasing efficiency can be also improved by changing the chemical environment of rare-earth metal ions.

Novel Optical Device Materials – Molecular-Level Hybridization 205

Organic/inorganic hybrid glasses have been actively pursued as an alternative to conventional silicate glass for fabricating laser devices due to low temperature process and the promise of

Furthermore, organic/inorganic hybrid silica is a good candidate to adjust the fluorescence environment of rare-earth metal ions by incorporating desired organic precursors into glassy hosts without any phase separation; usually, in inorganic silicate hosts, rare-earth ions tend to aggregate due to the absence of non-bridging oxygens, which cause a significant deduction of lasing efficiency. The synthesis of chemically modified silica with homogeneous doping of rare-earth ions is a key contributor to improve the performance of

Optical device materials are required good optical transparency, controllable porosity, chemical purity, tunable refractive index, so on. Our goal for achieving those desired properties is to improve the fluorescence environment of Er3+ -ions in glassy hosts. For that, we devoted our attention to achieve an excellent chemical homogeneity of Er3+-ion

To demonstrate enhanced performance in laser amplifiers, we designed fluoroalkylenebridged polysilsesquioxanes doped with Er3+/CdSe nano-particles. [25] The fluoroalkylenebridged silica was initially designed to reduce the phonon energy of the glassy host. Furthermore, CdSe nano-particles were also provided for further manipulation of the

Use of organic silanes incorporates an organic fragment as an internal component of the silicate network. Sol–gel polymerization involves the hydrolysis of ethoxysilyl groups to yield silanols follows by subsequent condensation to form siloxane (Si–O–Si) linkages. In the solstate, the condensation is insufficient to form a network, and the solution remains processable. When sufficient cross-linking occurs, a network is formed and the transition from the solstate to the gel state occurs. The presence of organic fragments within the 3-D structure imparts organic character to the hybrid glass that changes the microenvironment of

In this study, fluorocarbon-linkages were designed to achieve high hydrophobicity within the hybrid glassy matrix. Erbium isopropoxide was also employed as the source for the Er3+ ions. Furthermore, CdSe nano-particles were also prepared and incorporated into the fluorinated glassy matrix to reduce the phonon energy of the glassy host (the phonon energy of CdSe =

In principle, when rare-earth metal ions are excited in transparent glassy matrices, they can behave as a laser, which enables amplification of the incident light intensity. The lasing performance significantly relies on rare-earth metal ion doping level, host materials'

**2.2. Design of fluoroalkylene-bridged xerogel doped with Er 3+/CdSe** 

photochemical environment of erbium-ions in the matrix.

physicochemical property, and chemical homogeneity.

additional fluorescence rare-earth ions incorporated in the glassy host.

bringing new optical properties that are not possible from inorganic silica. [1, 40-42]

laser amplifications.

200 cm−1). [43]

environment in glassy hosts.

**Figure 5.** Highly porous polysilsesquioxanes. [4]

In a laser amplification based on rare-earth metal ions, erbium (Er) has been widely used as a gain medium due to its strong fluorescence at 1540 nm, which is a useful wavelength in optical amplifications. Especially, erbium-doped fiber amplifiers (EDFA) dominate this object of high gain optical amplifications. [32-35]

Since the performance of laser amplifiers is significantly influenced by optical media, scientists have been investigating organic/inorganic hybrid silicate hosts doped with Er3+ ions, in order to achieve high NIR efficiency and low phonon energy of the matrix to shorten the pumping distance and thus to obtain proper gain/life time. [32-35, 38, 39]

However, inorganic based optical media have shown a limitation to adjust the chemical environment of doped metal ions. For example, conventional silicate-based laser amplifiers often fail to produce high lasing performance because of a strong absorption raised from the OH-group at 1540 nm. The low concentration of erbium-ions in silicate host and the small absorption cross-section of the erbium-ions also limit the performance of normal silicatebased laser amplifiers since the doping level of rare-earth ions in glassy hosts significantly depends upon lasing efficiency.

Organic/inorganic hybrid glasses have been actively pursued as an alternative to conventional silicate glass for fabricating laser devices due to low temperature process and the promise of bringing new optical properties that are not possible from inorganic silica. [1, 40-42]

204 Optical Devices in Communication and Computation

**Figure 5.** Highly porous polysilsesquioxanes. [4]

object of high gain optical amplifications. [32-35]

depends upon lasing efficiency.

In a laser amplification based on rare-earth metal ions, erbium (Er) has been widely used as a gain medium due to its strong fluorescence at 1540 nm, which is a useful wavelength in optical amplifications. Especially, erbium-doped fiber amplifiers (EDFA) dominate this

Since the performance of laser amplifiers is significantly influenced by optical media, scientists have been investigating organic/inorganic hybrid silicate hosts doped with Er3+ ions, in order to achieve high NIR efficiency and low phonon energy of the matrix to shorten

However, inorganic based optical media have shown a limitation to adjust the chemical environment of doped metal ions. For example, conventional silicate-based laser amplifiers often fail to produce high lasing performance because of a strong absorption raised from the OH-group at 1540 nm. The low concentration of erbium-ions in silicate host and the small absorption cross-section of the erbium-ions also limit the performance of normal silicatebased laser amplifiers since the doping level of rare-earth ions in glassy hosts significantly

the pumping distance and thus to obtain proper gain/life time. [32-35, 38, 39]

Furthermore, organic/inorganic hybrid silica is a good candidate to adjust the fluorescence environment of rare-earth metal ions by incorporating desired organic precursors into glassy hosts without any phase separation; usually, in inorganic silicate hosts, rare-earth ions tend to aggregate due to the absence of non-bridging oxygens, which cause a significant deduction of lasing efficiency. The synthesis of chemically modified silica with homogeneous doping of rare-earth ions is a key contributor to improve the performance of laser amplifications.

Optical device materials are required good optical transparency, controllable porosity, chemical purity, tunable refractive index, so on. Our goal for achieving those desired properties is to improve the fluorescence environment of Er3+ -ions in glassy hosts. For that, we devoted our attention to achieve an excellent chemical homogeneity of Er3+-ion environment in glassy hosts.

#### **2.2. Design of fluoroalkylene-bridged xerogel doped with Er 3+/CdSe**

To demonstrate enhanced performance in laser amplifiers, we designed fluoroalkylenebridged polysilsesquioxanes doped with Er3+/CdSe nano-particles. [25] The fluoroalkylenebridged silica was initially designed to reduce the phonon energy of the glassy host. Furthermore, CdSe nano-particles were also provided for further manipulation of the photochemical environment of erbium-ions in the matrix.

Use of organic silanes incorporates an organic fragment as an internal component of the silicate network. Sol–gel polymerization involves the hydrolysis of ethoxysilyl groups to yield silanols follows by subsequent condensation to form siloxane (Si–O–Si) linkages. In the solstate, the condensation is insufficient to form a network, and the solution remains processable.

When sufficient cross-linking occurs, a network is formed and the transition from the solstate to the gel state occurs. The presence of organic fragments within the 3-D structure imparts organic character to the hybrid glass that changes the microenvironment of additional fluorescence rare-earth ions incorporated in the glassy host.

In this study, fluorocarbon-linkages were designed to achieve high hydrophobicity within the hybrid glassy matrix. Erbium isopropoxide was also employed as the source for the Er3+ ions. Furthermore, CdSe nano-particles were also prepared and incorporated into the fluorinated glassy matrix to reduce the phonon energy of the glassy host (the phonon energy of CdSe = 200 cm−1). [43]

In principle, when rare-earth metal ions are excited in transparent glassy matrices, they can behave as a laser, which enables amplification of the incident light intensity. The lasing performance significantly relies on rare-earth metal ion doping level, host materials' physicochemical property, and chemical homogeneity.

#### **2.3. Experimental**

A set of three different sol–gel processable monomers were prepared; tetraethoxy-silane (TEOS), 1,6-bis (triethoxysilyl)hexane, and 2,2,3,3,4,4,5,5-octafluoro-1,6-hexanediol bis(3 triethoxysilyl)propyl carbamate.

Novel Optical Device Materials – Molecular-Level Hybridization 207

We also examined the homogeneity of three sol–gel mixtures (Figure 6). Ethanol was used as a solvent. A visual inspection was carried out to determine the comparative homogeneity of those sol–gel mixtures containing erbium isopropoxide (Figure 6-1) or both of erbium isopropoxide/CdSe nano-particles (Figure 6-2). In a mixing test (Figure 6), erbium isopropoxide was indicated as a bright pink color in the photographs. The CdSe nano-

particles also show a characteristic bright orange-color in those mixtures.

**Table 1.** List of xerogels doped with different components.

**Figure 6.** Mixing test.

#### *2.3.1. Tetraethoxysilane (TEOS)*

TEOS was purified by drying over 4 Å molecular sieves followed by a vacuum distillation.

#### *2.3.2. Synthesis of 1,6-bis(triethoxysilyl)hexane*

1,6-Bis(triethoxysilyl)hexane was synthesized by a 'hydrosilylation' of the corresponding α, ω-alkyldienes with triethoxysilane employing chloroplatinic acid (H2PtCl6) as a catalyst. 1,5- Hexadiene (12.3 g, 0.15 mol), triethoxysilane (54.1 g, 0.33 mol), and chloroplatinic acid (1mL of 7.5×10−5 mol in isopropanol) were placed in a round bottle flask. After 10 hours of simple stirring process at a room temperature, the reaction mixture darkened.

The reaction was monitored by GC. The crude product was purified by a vacuum distillation with a resulting purity of 99.87 % by GC analysis: bp 130 ◦C/0.1 mmHg. The final product was verified by NMR analysis and mass spectroscopic analysis and was consistent with data previously report*.* [11]

#### *2.3.3. Synthesis of 2,2,3,3,4,4,5,5-octafluoro-1,6-hexanediol bis(3-triethoxysilyl)propyl carbamate*

2,2,3,3,4,4,5,5-Octafluoro-1,6-hexanediol (1g, 3.8 mmol) and 3-isocyanatopropyl triethoxysilane (1.9 g, 4.3 mmol) were placed in a round bottom flask with a magnetic stirrer. The flask was sealed, purged with nitrogen, and 10 mg of dibutyl-tin-dilaurate was injected into the vial using a syringe as a catalyst.

The reaction was kept at room temperature under a nitrogen flow for several hours and monitored for the disappearance of the isocyanate peak at 2270 cm−1 (CN) in FT-IR. As the isocyanate group was converted to urethane group, identical peaks of 3400 cm−1 (NH) and 1720 cm−1 (CO) were observed. The product was dissolved in methanol and the tin catalyst was completely removed using a separated funnel. Methanol was then removed by a rotary evaporator. The product was used without further purification.

#### *2.3.4. Er3+-ion/CdSe doping procedure*

A sol-gel processible monomer, erbium isopropoxide (Chemat Technology), was used as a source of Er3+-ions. CdSe nano-particles were synthesized by a previously reported procedure. [44, 45] Those dopants were incorporated by mixing with the appropriate sol–gel mixtures (Table 1); xerogels-a5 and -a10 denote higher erbium concentrations (5 and 10 times higher) than that of xerogel-a system.

We also examined the homogeneity of three sol–gel mixtures (Figure 6). Ethanol was used as a solvent. A visual inspection was carried out to determine the comparative homogeneity of those sol–gel mixtures containing erbium isopropoxide (Figure 6-1) or both of erbium isopropoxide/CdSe nano-particles (Figure 6-2). In a mixing test (Figure 6), erbium isopropoxide was indicated as a bright pink color in the photographs. The CdSe nanoparticles also show a characteristic bright orange-color in those mixtures.


**Table 1.** List of xerogels doped with different components.

**Figure 6.** Mixing test.

206 Optical Devices in Communication and Computation

triethoxysilyl)propyl carbamate.

*2.3.1. Tetraethoxysilane (TEOS)* 

with data previously report*.* [11]

the vial using a syringe as a catalyst.

*2.3.4. Er3+-ion/CdSe doping procedure* 

times higher) than that of xerogel-a system.

*carbamate* 

*2.3.2. Synthesis of 1,6-bis(triethoxysilyl)hexane* 

A set of three different sol–gel processable monomers were prepared; tetraethoxy-silane (TEOS), 1,6-bis (triethoxysilyl)hexane, and 2,2,3,3,4,4,5,5-octafluoro-1,6-hexanediol bis(3-

TEOS was purified by drying over 4 Å molecular sieves followed by a vacuum distillation.

1,6-Bis(triethoxysilyl)hexane was synthesized by a 'hydrosilylation' of the corresponding α, ω-alkyldienes with triethoxysilane employing chloroplatinic acid (H2PtCl6) as a catalyst. 1,5- Hexadiene (12.3 g, 0.15 mol), triethoxysilane (54.1 g, 0.33 mol), and chloroplatinic acid (1mL of 7.5×10−5 mol in isopropanol) were placed in a round bottle flask. After 10 hours of simple

The reaction was monitored by GC. The crude product was purified by a vacuum distillation with a resulting purity of 99.87 % by GC analysis: bp 130 ◦C/0.1 mmHg. The final product was verified by NMR analysis and mass spectroscopic analysis and was consistent

*2.3.3. Synthesis of 2,2,3,3,4,4,5,5-octafluoro-1,6-hexanediol bis(3-triethoxysilyl)propyl* 

2,2,3,3,4,4,5,5-Octafluoro-1,6-hexanediol (1g, 3.8 mmol) and 3-isocyanatopropyl triethoxysilane (1.9 g, 4.3 mmol) were placed in a round bottom flask with a magnetic stirrer. The flask was sealed, purged with nitrogen, and 10 mg of dibutyl-tin-dilaurate was injected into

The reaction was kept at room temperature under a nitrogen flow for several hours and monitored for the disappearance of the isocyanate peak at 2270 cm−1 (CN) in FT-IR. As the isocyanate group was converted to urethane group, identical peaks of 3400 cm−1 (NH) and 1720 cm−1 (CO) were observed. The product was dissolved in methanol and the tin catalyst was completely removed using a separated funnel. Methanol was then removed by a rotary

A sol-gel processible monomer, erbium isopropoxide (Chemat Technology), was used as a source of Er3+-ions. CdSe nano-particles were synthesized by a previously reported procedure. [44, 45] Those dopants were incorporated by mixing with the appropriate sol–gel mixtures (Table 1); xerogels-a5 and -a10 denote higher erbium concentrations (5 and 10

stirring process at a room temperature, the reaction mixture darkened.

evaporator. The product was used without further purification.

**2.3. Experimental** 

#### *2.3.5. Sol–gel procedures*

Those sol–gel mixtures were then polymerized to produce the condensed xerogels under acidic condition using HCl as a sol-gel catalyst. Those xerogels were kept in a vacuum oven for 1–2 days to remove the remaining solvent and complete condensation.

Novel Optical Device Materials – Molecular-Level Hybridization 209

Si O

Si

O Si

Si

O O

Si

**Degree of condensation (78.8%)**

In contrast, a hybrid sol-gel monomer system (H-xerogel-b) shown in Figure 6-2, the CdSe nano-particles mixed better than the T-xerogel-b. In the H-xerogel-b mixture, most of CdSe particles were dissolved, except some of undissolved orange-colored CdSe residues toward the middle of the container. In fluorinated mixture (F-xerogel-b) shown in Figure 6-2, CdSe nano-particles were incorporated without phase separation. This result demonstrates that the fluoroalkelene-bridged sol-gel monomer has the capability of uniformly incorporating

The chemical composition and the degree of condensation for those condensed xerogels can be determined by solid state nuclear magnetic resonance, infrared, and Raman

We employed a solid state NMR analysis to determine the degree of condensation of hybrid glassy hosts. 29 Si solid state NMR was used to identify the Si–O–Si bonds in variety states of condensation for three matrices. Single pulse magic angle spinning NMR methods were employed for the characterization of T-xerogel, H-xerogel, and F-xerogel to calculate the

**Q3**

**Q4**

**Q2**

**-140**

**-60 -70 -80 -90 -100 -110 -120 -130**

both types of dopants without any phase separation.

**Figure 7.** 29 Si solid state NMR spectrum for undoped T-xerogel.

**-100.40**

**-91.14**

**-60 -60 -80 -100 -**

**-107.60 -109.26**

> **12 0**

*2.4.2. Solid state NMR analysis* 

spectroscopies. [1]

degree of condensation.

**29Si (SP/MAS) NMR**

#### *2.3.6. Solid state NMR experiments*

The 29Si solid state NMR analysis of condensed xerogels was performed using a Varian Unity 400 solid state NMR spectrometer. The degree of condensation of undoped xerogels was computed from the single pulse magic angle spinning (SP/MAS) technique. A line fitting routine was also used in the analysis of the 29Si NMR resonance in each spectrum to establish the siloxane ratio in the different structures.

#### *2.3.7. Fluorescence measurements*

Fluorescence study of Er3+-ions doped into those glassy matrices was carried out by using the Ar+ ion laser (488 nm). Laser power densities ranging from 1.5 to 3 Wcm−2 were used for the measurements.

#### **2.4. Results and discussions**

#### *2.4.1. Mixing test*

During the mixing test (Figure 6), we observed that the TEOS-based mixtures revealed a substantial degree of undesirable phase separations after doping with the Er+3-ion sources or Er+3/CdSe nano-particles. For example, in Figure 6-1, the T-xerogel-a mixture shows a significant phase separation even at the lower erbium concentration.

In contrast, hybrid sol–gel monomer mixtures showed significantly less phase separations (Figure 6). Hybrid sol–gel monomer mixtures accommodate and homogeneously distribute the Er3+/CdSe source without any significant phase separation. In mixing test with hybrid sol-gel monomer mixtures, we observed no momentous phase separation, especially in the highly fluorinated sol-gel mixtures.

It is apparent that the TEOS-based sol–gel mixture has a rather limited solubility of erbium-ions, and hence a limited capability for fluorescence enhancement.

Subsequently, we provided CdSe nano-particles by following the earlier method [44, 45], and then added CdSe nano-particles into those sol–gel monomer mixtures containing the the Er3+/CdSe source. Usually, CdSe nano-particles synthesized in colloidal configuration are suitable for incorporation into a variety of hosts including sol–gel mixtures. The comparative homogeneity of the three sol-gel monomer mixtures containing both of the erbium isopropoxide and CdSe nano-particles is also shown in Figure 6-2.

In Figure 6-2, TEOS-based mixture (T-xerogel-b) shows the CdSe nano-particles segregated in the mixture; the orange-colored CdSe nano-particles are observed to phase separate within the mixture.

In contrast, a hybrid sol-gel monomer system (H-xerogel-b) shown in Figure 6-2, the CdSe nano-particles mixed better than the T-xerogel-b. In the H-xerogel-b mixture, most of CdSe particles were dissolved, except some of undissolved orange-colored CdSe residues toward the middle of the container. In fluorinated mixture (F-xerogel-b) shown in Figure 6-2, CdSe nano-particles were incorporated without phase separation. This result demonstrates that the fluoroalkelene-bridged sol-gel monomer has the capability of uniformly incorporating both types of dopants without any phase separation.

#### *2.4.2. Solid state NMR analysis*

208 Optical Devices in Communication and Computation

*2.3.6. Solid state NMR experiments* 

*2.3.7. Fluorescence measurements* 

**2.4. Results and discussions** 

highly fluorinated sol-gel mixtures.

the measurements.

*2.4.1. Mixing test* 

within the mixture.

establish the siloxane ratio in the different structures.

Those sol–gel mixtures were then polymerized to produce the condensed xerogels under acidic condition using HCl as a sol-gel catalyst. Those xerogels were kept in a vacuum oven

The 29Si solid state NMR analysis of condensed xerogels was performed using a Varian Unity 400 solid state NMR spectrometer. The degree of condensation of undoped xerogels was computed from the single pulse magic angle spinning (SP/MAS) technique. A line fitting routine was also used in the analysis of the 29Si NMR resonance in each spectrum to

Fluorescence study of Er3+-ions doped into those glassy matrices was carried out by using the Ar+ ion laser (488 nm). Laser power densities ranging from 1.5 to 3 Wcm−2 were used for

During the mixing test (Figure 6), we observed that the TEOS-based mixtures revealed a substantial degree of undesirable phase separations after doping with the Er+3-ion sources or Er+3/CdSe nano-particles. For example, in Figure 6-1, the T-xerogel-a mixture shows a

In contrast, hybrid sol–gel monomer mixtures showed significantly less phase separations (Figure 6). Hybrid sol–gel monomer mixtures accommodate and homogeneously distribute the Er3+/CdSe source without any significant phase separation. In mixing test with hybrid sol-gel monomer mixtures, we observed no momentous phase separation, especially in the

It is apparent that the TEOS-based sol–gel mixture has a rather limited solubility of

Subsequently, we provided CdSe nano-particles by following the earlier method [44, 45], and then added CdSe nano-particles into those sol–gel monomer mixtures containing the the Er3+/CdSe source. Usually, CdSe nano-particles synthesized in colloidal configuration are suitable for incorporation into a variety of hosts including sol–gel mixtures. The comparative homogeneity of the three sol-gel monomer mixtures containing both of the

In Figure 6-2, TEOS-based mixture (T-xerogel-b) shows the CdSe nano-particles segregated in the mixture; the orange-colored CdSe nano-particles are observed to phase separate

erbium-ions, and hence a limited capability for fluorescence enhancement.

erbium isopropoxide and CdSe nano-particles is also shown in Figure 6-2.

significant phase separation even at the lower erbium concentration.

for 1–2 days to remove the remaining solvent and complete condensation.

*2.3.5. Sol–gel procedures* 

The chemical composition and the degree of condensation for those condensed xerogels can be determined by solid state nuclear magnetic resonance, infrared, and Raman spectroscopies. [1]

We employed a solid state NMR analysis to determine the degree of condensation of hybrid glassy hosts. 29 Si solid state NMR was used to identify the Si–O–Si bonds in variety states of condensation for three matrices. Single pulse magic angle spinning NMR methods were employed for the characterization of T-xerogel, H-xerogel, and F-xerogel to calculate the degree of condensation.

**Figure 7.** 29 Si solid state NMR spectrum for undoped T-xerogel.

Novel Optical Device Materials – Molecular-Level Hybridization 211

Figures 7-9 show the result of 29Si SP/MAS solid state NMR analyses and peak

Figure 7 shows the 29Si SP/MAS solid state NMR spectrum of the undoped T-xerogel. As shown in Figure 7, it reveals three peaks, which correspond to the Q2, Q3, and Q4. The degree

Figure 8 shows the 29Si SP/MAS solid state NMR spectrum of the undoped H-xerogel. Three peaks shown in spectrum correspond to the T1, T2, and T3. The degree of condensation of the

The 29Si SP/MAS solid state NMR spectrum of the undoped F-xerogel is given in Figure 9. The T1 peak is not observed in this system. Also, the T3 peak intensity in Figure 9 is higher than that of T2. We found that the degree of condensation was dramatically increased to

The high degree of condensation in the undoped F-xerogel can be explained as a result of the electron-withdrawing effect of the fluorine, which causes a partial positive charge at the silicon facilitating nucleophilic attack in the sol–gel process thus accelerating hydrolysis and

The high degree of condensation, disappearance of T1 peak, and enhanced T3 peak in the Fxerogel indicate a low level of hydroxyl group content and a greater degree of condensation

The reduction in hydroxyl content in the F-xerogel matrix decreases the phonon energy of the matrix. The exclusion of moisture from the high hydrophobicity of the fluoro-alkylene groups in the F-xerogel matrix may also contribute to reduce the absorption at 1540 nm with

All these effects contribute to the increased fluorescence from erbium-ions in the fluorinated

We also employed a XPS study to determine the chemical composition of F-xerogel-a. [46]

A full XPS scan was obtained in the 0–1100 eV range. Detail scan was also recorded for the Er (4d) region. Figure 10 shows a full spectrum for F-xerogel-a. The XPS spectrum of Fxerogel-a shows an erbium peak at ~169 eV, which corresponds to the presence of Er2O3.

The atomic compositions were evaluated in this study. The concentration of each element (atomic %) was calculated; O(1s)—22.74 atomic %, C(1s)—53.29 atomic %, Er(4d)—1.49 atomic %, F(1s)—9.02 atomic %, Si(2p)—10.91 atomic %, N(1s)—2.55 atomic %. From the

XPS analysis, it was estimated that the F-xerogel-a contains ~1.49 atomic % of erbium.

deconvolution lines of both normal and modified silicate systems.

of condensation for the T-xerogel was calculated to be 78.8%.

when fluorinated alkylene groups are present in the glassy hosts.

a concomitant increase the fluorescence intensity of Er3+-ions.

Si–OH groups show a high phonon energy (3000–3500 cm−1) at 1540 nm. [43]

H-xerogel was also computed to be 79.1%.

91.1% in this case.

condensation.

hybrid glassy matrix.

*2.4.3. XPS analysis* 

**Figure 8.** 29 Si solid state NMR spectrum for undoped H-xerogel.

**Figure 9.** 29 Si solid state NMR spectrum for undoped F-xerogel.

Figures 7-9 show the result of 29Si SP/MAS solid state NMR analyses and peak deconvolution lines of both normal and modified silicate systems.

Figure 7 shows the 29Si SP/MAS solid state NMR spectrum of the undoped T-xerogel. As shown in Figure 7, it reveals three peaks, which correspond to the Q2, Q3, and Q4. The degree of condensation for the T-xerogel was calculated to be 78.8%.

Figure 8 shows the 29Si SP/MAS solid state NMR spectrum of the undoped H-xerogel. Three peaks shown in spectrum correspond to the T1, T2, and T3. The degree of condensation of the H-xerogel was also computed to be 79.1%.

The 29Si SP/MAS solid state NMR spectrum of the undoped F-xerogel is given in Figure 9. The T1 peak is not observed in this system. Also, the T3 peak intensity in Figure 9 is higher than that of T2. We found that the degree of condensation was dramatically increased to 91.1% in this case.

The high degree of condensation in the undoped F-xerogel can be explained as a result of the electron-withdrawing effect of the fluorine, which causes a partial positive charge at the silicon facilitating nucleophilic attack in the sol–gel process thus accelerating hydrolysis and condensation.

The high degree of condensation, disappearance of T1 peak, and enhanced T3 peak in the Fxerogel indicate a low level of hydroxyl group content and a greater degree of condensation when fluorinated alkylene groups are present in the glassy hosts.

Si–OH groups show a high phonon energy (3000–3500 cm−1) at 1540 nm. [43]

The reduction in hydroxyl content in the F-xerogel matrix decreases the phonon energy of the matrix. The exclusion of moisture from the high hydrophobicity of the fluoro-alkylene groups in the F-xerogel matrix may also contribute to reduce the absorption at 1540 nm with a concomitant increase the fluorescence intensity of Er3+-ions.

All these effects contribute to the increased fluorescence from erbium-ions in the fluorinated hybrid glassy matrix.

#### *2.4.3. XPS analysis*

210 Optical Devices in Communication and Computation

**-57.90**

**-66.48**

**-20 -40 -60 -80 -100**

**29Si (SP/MAS) NMR**

**29Si (SP/MAS) NMR**

O O Si O

O Si O

Si <sup>O</sup> <sup>O</sup>

Si O O

O Si O

O Si <sup>O</sup> <sup>O</sup>

O Si O O

Si <sup>O</sup> <sup>O</sup> <sup>O</sup>

**Degree of condensation (79.1%)**

> **Degree of condensation (91.1 %)**

**Figure 8.** 29 Si solid state NMR spectrum for undoped H-xerogel.

**-65.65**

**-65.65**

**-57.49**

**T1**

**T2**

**T3**

**-30 -40 -50 -60 -70 -80 -90 ppm-100 ppm**

**T3**

**-30 -40 -50 -60 -70 -80 -90 -100 ppm**

**T2**

**Figure 9.** 29 Si solid state NMR spectrum for undoped F-xerogel.

**-40 -60 -80 -100**

We also employed a XPS study to determine the chemical composition of F-xerogel-a. [46]

A full XPS scan was obtained in the 0–1100 eV range. Detail scan was also recorded for the Er (4d) region. Figure 10 shows a full spectrum for F-xerogel-a. The XPS spectrum of Fxerogel-a shows an erbium peak at ~169 eV, which corresponds to the presence of Er2O3.

The atomic compositions were evaluated in this study. The concentration of each element (atomic %) was calculated; O(1s)—22.74 atomic %, C(1s)—53.29 atomic %, Er(4d)—1.49 atomic %, F(1s)—9.02 atomic %, Si(2p)—10.91 atomic %, N(1s)—2.55 atomic %. From the XPS analysis, it was estimated that the F-xerogel-a contains ~1.49 atomic % of erbium.

#### *2.4.4. Fluorescence measurements*

Erbium-ions incorporated into glassy matrices exhibit well defined energy level transitions in 4f-shell electronic configurations.

Novel Optical Device Materials – Molecular-Level Hybridization 213

In Figure 11, fluorescence intensity of erbium-ions increased significantly more in F-xerogel-

**Figure 11.** Photoluminescence of erbium-ions; different silicate matrices. Comparative fluorescence intensities of two different hybrid xerogels doped with Er+3 ions using a low power of 1.5 Wcm−2.

The explanation of Figure 11 is that the enhanced fluorescence intensity of the fluorinated matrix is attributed to mainly its high hydrophobicity combined with the lower OH-group contents, which revealed in NMR study in Figure 9. Solid state silicon NMR analysis indicates an enhanced condensation in fluorinated xerogel compared to that of alkylenebridged xerogel. The fluorinated hosts also showed an excellent chemical homogeneity in

Further investigations in fluorescence studies have been carried out. Since it is important to consider the erbium-ion concentration effect, fluoroalkylene-based glasses doped with two different levels of erbium concentrations were prepared for the determination of erbium-

Intensity of those xerogels (F-xerogel-a and F-xerogel-a5) was measured at a power density of 3 Wcm−2. As shown in Figure 12, the fluorescence intensity increases (the upper curve) in the case of F-xerogel-a. It can be explained that the higher erbium concentration of F-

Fluoroalkylene-bridged xerogel containing Er3+-ions shows significantly reduced absorptions

The presence of CdSe nano-particles also significantly influences the fluorescence environment of Er3+-ions in different glassy hosts, resulting in the increased fluorescence intensity. [43]

mixing test (Figure 6), which significantly affects the lasing performance.

xerogel-a5 caused a low lasing efficiency due to the "self-quenching effect."

at the 1540 nm by reducing amounts of uncondensed hydroxyl groups.

concentration effect (Figure 12).

a than the other hybrid system of H-xerogel-a.

**Figure 10.** XPS Analysis of F-xerogel-a.

For erbium-ions, the 4I13/2 to 4I15/2 transition is important in optical communications; because, it results in fluorescence at 1540 nm, which is the most important wavelength regime for optical communication applications, especially in long-distance telecommunication networks. [47]

We examined how the fluorescence intensity of erbium-ions was dependent upon the matrix environment when fluorine and CdSe nano-particles were incorporated into hybrid glassy hosts. We carried out fluorescence analysis of erbium-ions around 1540 nm. The results are shown in Figures 11-13.

A comparison of fluorescence intensities from erbium-ions doped into different glassy hosts is shown in Figure 11 (H-xerogel-a and F-xerogel-a).

In Figure 11, fluorescence intensity of erbium-ions increased significantly more in F-xerogela than the other hybrid system of H-xerogel-a.

212 Optical Devices in Communication and Computation

Erbium-ions incorporated into glassy matrices exhibit well defined energy level transitions

For erbium-ions, the 4I13/2 to 4I15/2 transition is important in optical communications; because, it results in fluorescence at 1540 nm, which is the most important wavelength regime for optical communication applications, especially in long-distance telecommunication networks. [47]

We examined how the fluorescence intensity of erbium-ions was dependent upon the matrix environment when fluorine and CdSe nano-particles were incorporated into hybrid glassy hosts. We carried out fluorescence analysis of erbium-ions around 1540 nm. The results are

A comparison of fluorescence intensities from erbium-ions doped into different glassy hosts

*2.4.4. Fluorescence measurements* 

in 4f-shell electronic configurations.

**Figure 10.** XPS Analysis of F-xerogel-a.

is shown in Figure 11 (H-xerogel-a and F-xerogel-a).

shown in Figures 11-13.

**Figure 11.** Photoluminescence of erbium-ions; different silicate matrices. Comparative fluorescence intensities of two different hybrid xerogels doped with Er+3 ions using a low power of 1.5 Wcm−2.

The explanation of Figure 11 is that the enhanced fluorescence intensity of the fluorinated matrix is attributed to mainly its high hydrophobicity combined with the lower OH-group contents, which revealed in NMR study in Figure 9. Solid state silicon NMR analysis indicates an enhanced condensation in fluorinated xerogel compared to that of alkylenebridged xerogel. The fluorinated hosts also showed an excellent chemical homogeneity in mixing test (Figure 6), which significantly affects the lasing performance.

Further investigations in fluorescence studies have been carried out. Since it is important to consider the erbium-ion concentration effect, fluoroalkylene-based glasses doped with two different levels of erbium concentrations were prepared for the determination of erbiumconcentration effect (Figure 12).

Intensity of those xerogels (F-xerogel-a and F-xerogel-a5) was measured at a power density of 3 Wcm−2. As shown in Figure 12, the fluorescence intensity increases (the upper curve) in the case of F-xerogel-a. It can be explained that the higher erbium concentration of Fxerogel-a5 caused a low lasing efficiency due to the "self-quenching effect."

Fluoroalkylene-bridged xerogel containing Er3+-ions shows significantly reduced absorptions at the 1540 nm by reducing amounts of uncondensed hydroxyl groups.

The presence of CdSe nano-particles also significantly influences the fluorescence environment of Er3+-ions in different glassy hosts, resulting in the increased fluorescence intensity. [43]

Novel Optical Device Materials – Molecular-Level Hybridization 215

**Figure 13.** Photoluminescence of erbium-ions; CdSe nanoparticle effect. Comparative fluorescence intensities of fluoroalkylene-bridged xerogels doped without and with the CdSe nano-particles (F-

To avoid the high phonon energy raised from OH-groups (3000–5300 cm−1) at 1540 nm [43], we designed highly fluorinated hybrid glasses to shorten the fluorescence-level life times of

The presence of CdSe nano-particles, by virtue of its lowering of phonon energy, also appears to significantly influence the nature of the surrounding photochemical environment

From those study, we found that the control of such optical materials' properties affect the performance of optical devices via molecular tailoring strategy, which is molecular-level

The preparation of semiconductors, metals, and ions in a variety of transparent materials has been actively pursued for optical devices. Scientists have taken a great attention to incorporate metal particles/ions in glassy hosts to develop high performance optical devices. Chemists also have taken intensive challenges on how to achieve homogeneous incorporations of semiconductors or metal particles in glassy hosts, which are significantly influenced by diffusion of reagents, the number of nucleation sites, stabilization of growing particles by surface functionality, the boundary constraints of the growth matrix, and the opportunity for equilibration or "ripening" of particles formed under kinetic growth conditions. [2, 21, 48, 49] Organically modified hybrid glasses, which were prepared by '*molecular-level hybridization'*  (Figure 3), are a good candidate to develop laser device materials due to their easy

xerogels-a5 and -b5), respectively, using a high power of 3Wcm−2.

dopants, which adversely affect optical device performance.

**3. Novel optical device materials for acoustic wave [26]** 

**3.1. Novel optical device materials based on polysilsesquioxanes** 

of Er3+-ions in the fluorescence study.

processability and chemical modification.

hybridization technique.

**Figure 12.** Photoluminescence of erbium-ions; different erbium concentrations. Comparative fluorescence intensities of xerogels with different Er3+-ion concentrations (F-xerogels-a and -a5) using a power of 3.0 Wcm−2.

CdSe nano-particles were used to modify the photochemical environments of erbium-ions in glassy hosts by taking advantage of a low phonon energy of CdSe phase (200 cm−1) [43], since the incorporation of semiconductor nano-particles resulted in an enhancement of the semiconductor-to-erbium transfer when the quantum well and erbium-ion transition energies became close.

We thus examined the fluorescence of erbium-ions surrounded by CdSe nano-particles since it was anticipated that the presence of CdSe in the modified glassy hosts would affect the fluorescence performance (Figure 13). In order to test this, we prepared fluoroalkylenebridged hybrid glasses doped without and with the CdSe nano-particles, F-xerogels-a5 and F-xerogel-b5, respectively.

As shown in Figure 13, the fluorescence intensity of F-xerogel-b5 is dramatically increased, which indicates an improvement in lasing efficiency by modifying photochemical environments of erbium-ions.

By taking advantage of the structural features and uniform doping capability in modified glassy matrices, we successfully demonstrate that the fluorescence environments of erbiumions can be a key to improving the performances of optical devices like laser amplifiers to overcome the limitations in inorganic silica.

In conclusion, we have demonstrated here a promising result in laser amplifications by employing bridged polysilsesquioxanes doped with Er3+-ions/CdSe nanoparticles.

using a power of 3.0 Wcm−2.

energies became close.

F-xerogel-b5, respectively.

environments of erbium-ions.

overcome the limitations in inorganic silica.

**Figure 12.** Photoluminescence of erbium-ions; different erbium concentrations. Comparative fluorescence intensities of xerogels with different Er3+-ion concentrations (F-xerogels-a and -a5)

CdSe nano-particles were used to modify the photochemical environments of erbium-ions in glassy hosts by taking advantage of a low phonon energy of CdSe phase (200 cm−1) [43], since the incorporation of semiconductor nano-particles resulted in an enhancement of the semiconductor-to-erbium transfer when the quantum well and erbium-ion transition

We thus examined the fluorescence of erbium-ions surrounded by CdSe nano-particles since it was anticipated that the presence of CdSe in the modified glassy hosts would affect the fluorescence performance (Figure 13). In order to test this, we prepared fluoroalkylenebridged hybrid glasses doped without and with the CdSe nano-particles, F-xerogels-a5 and

As shown in Figure 13, the fluorescence intensity of F-xerogel-b5 is dramatically increased, which indicates an improvement in lasing efficiency by modifying photochemical

By taking advantage of the structural features and uniform doping capability in modified glassy matrices, we successfully demonstrate that the fluorescence environments of erbiumions can be a key to improving the performances of optical devices like laser amplifiers to

In conclusion, we have demonstrated here a promising result in laser amplifications by

employing bridged polysilsesquioxanes doped with Er3+-ions/CdSe nanoparticles.

**Figure 13.** Photoluminescence of erbium-ions; CdSe nanoparticle effect. Comparative fluorescence intensities of fluoroalkylene-bridged xerogels doped without and with the CdSe nano-particles (Fxerogels-a5 and -b5), respectively, using a high power of 3Wcm−2.

To avoid the high phonon energy raised from OH-groups (3000–5300 cm−1) at 1540 nm [43], we designed highly fluorinated hybrid glasses to shorten the fluorescence-level life times of dopants, which adversely affect optical device performance.

The presence of CdSe nano-particles, by virtue of its lowering of phonon energy, also appears to significantly influence the nature of the surrounding photochemical environment of Er3+-ions in the fluorescence study.

From those study, we found that the control of such optical materials' properties affect the performance of optical devices via molecular tailoring strategy, which is molecular-level hybridization technique.

#### **3. Novel optical device materials for acoustic wave [26]**

#### **3.1. Novel optical device materials based on polysilsesquioxanes**

The preparation of semiconductors, metals, and ions in a variety of transparent materials has been actively pursued for optical devices. Scientists have taken a great attention to incorporate metal particles/ions in glassy hosts to develop high performance optical devices.

Chemists also have taken intensive challenges on how to achieve homogeneous incorporations of semiconductors or metal particles in glassy hosts, which are significantly influenced by diffusion of reagents, the number of nucleation sites, stabilization of growing particles by surface functionality, the boundary constraints of the growth matrix, and the opportunity for equilibration or "ripening" of particles formed under kinetic growth conditions. [2, 21, 48, 49]

Organically modified hybrid glasses, which were prepared by '*molecular-level hybridization'*  (Figure 3), are a good candidate to develop laser device materials due to their easy processability and chemical modification.

Polysilsesquioxanes can be prepared by '*molecular-level hybridization'*, which inserts different types and sizes of organic spacers between two inorganic oxides. The sol-gel chemistry was employed to covalently incorporate semiconductors/metals in various oxidation states as an integral component of hybrid silicate matrices.

Novel Optical Device Materials – Molecular-Level Hybridization 217

**Figure 15.** Periodic alignment of alkyl-chains to create "optical grating" at the molecular scales.

wave. This is a new optical phenomenon, which hitherto hasn't been discovered.

because, in solid media, heat doesn't decay through the solid medium effectively.

with Cro/CrOx phases showed a strong 'acoustic response' as much as a liquid.

conductivity of the doped xerogel, is FIVE times less than that of normal glass.

polysilsesquioxanes.

Figure 15 illustrates a light that passes through 'optical grating at the molecular-scales' designed in the hybrid silicate host. As you can see, the periodic alkylene-spacers create 'effective diffraction grating at the molecular scales' and thus produces a huge acoustic

In addition, the distance between those alkyl-spacers can be also "controlled" by both choices of different organic spacers and sizes of sol-gel monomers. This is an effective method of developing new laser device materials based on organically modified silica,

Usually, when the laser beam goes through a solid medium, the density wave is linear;

Interestingly, the highly compressed xerogel, hexylene-bridged polysilsesquioxane doped

In our laser experiments, we calculated physical parameters of hexylene-bridged xerogel doped with Cro/CrOx phases. The coefficient of phonon diffraction (D) of the doped xerogel was FIVE times smaller than that of normal glass. Which means that the thermal

The 'molecular-level corporation techniques' also can be employed for the incorporation of semiconductors or transition metals/ions dispersed in optically transparent silica to prepare novel optical devices.

Especially, polysilsesquioxanes are microscopically homogeneous due to uniform distribution of organic and inorganic moieties in a domain size at the molecular level. Hence, these hybrid glasses can be used for optical device materials since the molecularscale mixing process significantly reduces phase separation and thus produces high quality of optical clearance.

In this work, we molecularly designed a novel hybrid glass to develop alkylene-bridged polysilsesquioxanes doped with Cro/CrOx phases (Figure 14). The doped xerogel film effectively generates a HUGE ACOUSTIC WAVE.

#### **3.2. Periodic alignment of alkylene-spacers to create molecular-scale optical grating for acoustic wave**

Usually, scientists prepare 'periodic metal frames' to create 'diffraction grating' at the bulk-scales. For example, in a spectroscopic monochromator, 'optical grating effect' is used to split, and then diffract the light into several beams traveling in different directions.

In 'grating equation', the directions of these beams rely on the spacing/distances of the grating, which has a periodic structure of the media, and the wavelength of the light. Gratings, which modulate the phase rather than the amplitude of the incident light, can be also produced. A key idea of the periodic alignment of alkylene-spacers is to create 'a molecular-scale diffraction grating effect' and thus to generate a huge acoustic wave.

**Figure 14.** Hexylene-bridged polysilsesquioxane doped with Cro/CrOx.

novel optical devices.

of optical clearance.

directions.

**grating for acoustic wave** 

integral component of hybrid silicate matrices.

effectively generates a HUGE ACOUSTIC WAVE.

Polysilsesquioxanes can be prepared by '*molecular-level hybridization'*, which inserts different types and sizes of organic spacers between two inorganic oxides. The sol-gel chemistry was employed to covalently incorporate semiconductors/metals in various oxidation states as an

The 'molecular-level corporation techniques' also can be employed for the incorporation of semiconductors or transition metals/ions dispersed in optically transparent silica to prepare

Especially, polysilsesquioxanes are microscopically homogeneous due to uniform distribution of organic and inorganic moieties in a domain size at the molecular level. Hence, these hybrid glasses can be used for optical device materials since the molecularscale mixing process significantly reduces phase separation and thus produces high quality

In this work, we molecularly designed a novel hybrid glass to develop alkylene-bridged polysilsesquioxanes doped with Cro/CrOx phases (Figure 14). The doped xerogel film

Usually, scientists prepare 'periodic metal frames' to create 'diffraction grating' at the bulk-scales. For example, in a spectroscopic monochromator, 'optical grating effect' is used to split, and then diffract the light into several beams traveling in different

In 'grating equation', the directions of these beams rely on the spacing/distances of the grating, which has a periodic structure of the media, and the wavelength of the light. Gratings, which modulate the phase rather than the amplitude of the incident light, can be also produced. A key idea of the periodic alignment of alkylene-spacers is to create 'a

molecular-scale diffraction grating effect' and thus to generate a huge acoustic wave.

**Figure 14.** Hexylene-bridged polysilsesquioxane doped with Cro/CrOx.

**3.2. Periodic alignment of alkylene-spacers to create molecular-scale optical** 

**Figure 15.** Periodic alignment of alkyl-chains to create "optical grating" at the molecular scales.

Figure 15 illustrates a light that passes through 'optical grating at the molecular-scales' designed in the hybrid silicate host. As you can see, the periodic alkylene-spacers create 'effective diffraction grating at the molecular scales' and thus produces a huge acoustic wave. This is a new optical phenomenon, which hitherto hasn't been discovered.

In addition, the distance between those alkyl-spacers can be also "controlled" by both choices of different organic spacers and sizes of sol-gel monomers. This is an effective method of developing new laser device materials based on organically modified silica, polysilsesquioxanes.

Usually, when the laser beam goes through a solid medium, the density wave is linear; because, in solid media, heat doesn't decay through the solid medium effectively.

Interestingly, the highly compressed xerogel, hexylene-bridged polysilsesquioxane doped with Cro/CrOx phases showed a strong 'acoustic response' as much as a liquid.

In our laser experiments, we calculated physical parameters of hexylene-bridged xerogel doped with Cro/CrOx phases. The coefficient of phonon diffraction (D) of the doped xerogel was FIVE times smaller than that of normal glass. Which means that the thermal conductivity of the doped xerogel, is FIVE times less than that of normal glass.

In addition, the diffraction efficiency, absorption light efficiency, (45%) of the doped xerogel is higher than that of methanol (25%), which means the COMPRESSIBILITY of the doped xerogel is as effective as liquid. The acoustic refractive intensity and acoustic response generated from the doped xerogel was as strong as liquid. Therefore, the doped xerogel serves as a 'heat generator,' and thus the heat gets transferred into expansion or compression wave (acoustic waves) effectively.

Novel Optical Device Materials – Molecular-Level Hybridization 219

**Figure 16.** A comparative photos of undoped- (top left) and the Cro/CrOx doped- (top right and bottom) xerogels based on hexylene-bridged polysilsesquioxane under an acidic condition.

Syntheses of sol-gel monomers, 1,6-bis(triethoxsilyl)hexane and chromium precursor, η6 chromium tricarbonyl(triethoxysilyl)benzene, were carried out by following the earlier

Subsequently, hexylene-bridged xerogel doped with Cro/CrOx phases was prepared by a copolymerization of η6-chromium tri-carbonyl(triethoxysilyl)benzene and 1,6-bis(triethoxsilyl)hexane under an acidic condition (Figure 17). A green glass was provided after the sol-

**3.4. Experiments** 

*3.4.1. Preparation of doped xerogels* 

procedures, respectively. [11, 20]

gel polymerization (Figure 16).

There were a lot of efforts to develop novel laser device materials based on organic and inorganic hybrid silica. [50-54] Especially, this is a unique approach to create an effective optical grating, which brings a HUGE ACOUSTIC RESPONSE by setting up a molecularscale optical grating effect. By building up the periodic structure of long alkyl-chains in the hybrid glassy hosts, we obtained a HUGE ACOUSTIC WAVE, which hasn't been found. This is a new optical phenomenon.

#### **3.3. Novel sol-gel condition to produce thin films of alkylene-bridged xerogel doped with Cro/CrOx**

The new optical property partially rose from a new sol-gel mixing condition, which effectively produces HIGHLY COMPRESSED, THIN xerogel films. Conventional sol-gel conditions often result in poor optical transparency/mechanical property. For example, xerogels obtained from the conventional sol-gel conditions are thick and brittle materials. Those thick xerogels are difficult to handle, especially for optical applications.

The limitation motivated us to find a novel sol-gel mixing condition, which produces a highly compressed, thin sol-gel film with a smooth surface and excellent optical clarity.

We discovered a novel sol-gel mixing condition, which results in such a thin xerogel film of alkylene-bridged polysilsesquioxanes doped with Cro/CrOx with a low thermal conductivity and high compressibility (Figure 16). [26]

During the sol-gel polymerization, a volume of the sol-gel mixture was dramatically reduced, and then left a green sol-gel film with an excellent optical clarity (Figure 16).

For a source of chromium, we have synthesized a sol-gel processable chromium precursor [20, 26]; we prepared a green sol-gel film based on hexylene-bridged polysilsesquioxanes doped with Cro/CrOx phases using the chromium precursor. [20, 26]

In Figure 16 (top left), it shows a undoped hexylene-bridged polysilsesquioxane prepared from our novel sol-gel mixing condition; it was plastic-like a xerogel monolith. As you see in Figure 16 (top, left), it shows an excellent optical transparency.

Doped xerogels were also prepared in Figure 16 (top, Right and bottom). Those green xerogels were obtained as "plastic-like thin films" with an excellent optical compressibility and low thermal conductivity. It was prepared without any mechanical damage/cracking problem.

**Figure 16.** A comparative photos of undoped- (top left) and the Cro/CrOx doped- (top right and bottom) xerogels based on hexylene-bridged polysilsesquioxane under an acidic condition.

#### **3.4. Experiments**

218 Optical Devices in Communication and Computation

compression wave (acoustic waves) effectively.

This is a new optical phenomenon.

and high compressibility (Figure 16). [26]

**doped with Cro/CrOx** 

problem.

In addition, the diffraction efficiency, absorption light efficiency, (45%) of the doped xerogel is higher than that of methanol (25%), which means the COMPRESSIBILITY of the doped xerogel is as effective as liquid. The acoustic refractive intensity and acoustic response generated from the doped xerogel was as strong as liquid. Therefore, the doped xerogel serves as a 'heat generator,' and thus the heat gets transferred into expansion or

There were a lot of efforts to develop novel laser device materials based on organic and inorganic hybrid silica. [50-54] Especially, this is a unique approach to create an effective optical grating, which brings a HUGE ACOUSTIC RESPONSE by setting up a molecularscale optical grating effect. By building up the periodic structure of long alkyl-chains in the hybrid glassy hosts, we obtained a HUGE ACOUSTIC WAVE, which hasn't been found.

**3.3. Novel sol-gel condition to produce thin films of alkylene-bridged xerogel** 

Those thick xerogels are difficult to handle, especially for optical applications.

The new optical property partially rose from a new sol-gel mixing condition, which effectively produces HIGHLY COMPRESSED, THIN xerogel films. Conventional sol-gel conditions often result in poor optical transparency/mechanical property. For example, xerogels obtained from the conventional sol-gel conditions are thick and brittle materials.

The limitation motivated us to find a novel sol-gel mixing condition, which produces a highly compressed, thin sol-gel film with a smooth surface and excellent optical clarity.

We discovered a novel sol-gel mixing condition, which results in such a thin xerogel film of alkylene-bridged polysilsesquioxanes doped with Cro/CrOx with a low thermal conductivity

During the sol-gel polymerization, a volume of the sol-gel mixture was dramatically

For a source of chromium, we have synthesized a sol-gel processable chromium precursor [20, 26]; we prepared a green sol-gel film based on hexylene-bridged polysilsesquioxanes

In Figure 16 (top left), it shows a undoped hexylene-bridged polysilsesquioxane prepared from our novel sol-gel mixing condition; it was plastic-like a xerogel monolith. As you see in

Doped xerogels were also prepared in Figure 16 (top, Right and bottom). Those green xerogels were obtained as "plastic-like thin films" with an excellent optical compressibility and low thermal conductivity. It was prepared without any mechanical damage/cracking

reduced, and then left a green sol-gel film with an excellent optical clarity (Figure 16).

doped with Cro/CrOx phases using the chromium precursor. [20, 26]

Figure 16 (top, left), it shows an excellent optical transparency.

#### *3.4.1. Preparation of doped xerogels*

Syntheses of sol-gel monomers, 1,6-bis(triethoxsilyl)hexane and chromium precursor, η6 chromium tricarbonyl(triethoxysilyl)benzene, were carried out by following the earlier procedures, respectively. [11, 20]

Subsequently, hexylene-bridged xerogel doped with Cro/CrOx phases was prepared by a copolymerization of η6-chromium tri-carbonyl(triethoxysilyl)benzene and 1,6-bis(triethoxsilyl)hexane under an acidic condition (Figure 17). A green glass was provided after the solgel polymerization (Figure 16).

Density of the doped xerogel was measured to be 1.2696 g/cm3 using a He-gas pycnometer. From AAS analysis, the chromium amount was also analyzed to be 1.4% by weight.

Novel Optical Device Materials – Molecular-Level Hybridization 221

**Figure 17.** Synthesis of hexylene-bridged xerogel attached with the Cro precursors.

In contrast, the acid-catalyzed system produced thinner sol-gel films than those of glasses obtained under base condition (Figure 16). Under the acidic sol-gel condition, decomposition of the M-1 competes with sol-gel copolymerization. The product of acid

In Figure 18, TEM images of alkylene-bridged silica doped with Cro/CrOx phases reveal unusual nano-fringe patterns, which rose from the lattice fringes of the aligned alkyl-spacers in the silicate matrix. The novel molecular design results in 'a molecular level grating

Based on those nano-fringe patterns, an effective optical grating was created in the hybrid silicate matrix. The TEM images of the doped hybrid glass reveal nano-fringe patterns, which are highly organized nano-periodicity (pointed with arrows in Figure 18). The nano-periodic patterns are sustained over substantial domains and appear to arise from lattice fringes.

In short, the formation mechanism of these nanoperiodic features observed in the TEM images arises from the highly arranged alkylene-spacers in the sol-gel monomer (Figure 15). EDAX and electron diffraction analyses of these dark regions shown in the TEM images were also performed. In the EDAX spectrum, a Cr (Kα) peak was observed; thus, the dark contrast shown in the TEM images (Figure 18) was identified as a chromium phase spread

catalyzed decomposition reaction is "chromium oxides" and H2 (Figure 17). [56-58]

characteristic' when laser light passes by those periodic carbon-chains (Figure 15).

over the hybrid glassy host by both of EDAX/electron diffraction analyses.

#### *3.4.2. TEM, EDAX, and electron diffraction analysis*

A novel periodic alignment of alkylene-spacers in hybrid glass was specifically designed for creating 'a molecular-scale diffraction grating.' We employed TEM analysis to identify the molecular alignment built up in the hybrid silicate matrix.

The doped hybrid glass under an acidic condition (Figure 17) was ground to powders with a particle size (<150 µm), and deposited on a plasma-etched carbon substrate supported copper grid. TEM dark-field images were obtained using a Philips transmission electron microscope (TEM: CM 20/STEM, PW 6060).

The energy-dispersive X-ray diffraction (EDAX) pattern of the glassy particles was also obtained by an EDAX analyzer (Philips TEM-EDAX, PV 9800). For the electron diffraction, the camera length was calibrated experimentally with a gold standard, and an X-ray spectrum analyzer at 200 kV was used.

#### *3.4.3. Laser analysis*

To establish the optical properties of doped xerogels, we prepared a sample (<1mm thickness) fabricated with η6-chromium tricarbonyl(triethoxysilyl)benzene loading of 2.4 % under an acidic sol-gel condition. The thin xerogel film exhibited a nonlinear property. The nonlinear optical (NLO) properties of doped xerogel films were measured by the degenerated into four wave mixing (DFWM) technique. [55] A quartz sample was used as a reference.

We used two types of lasers, a YAG laser with 50 ps pulse-width at 532 nm and a dye laser with 150 fs pulse-width at 640 nm. The output of either of lasers is split into two strong pump beams and a weak probe. The delay between two pump pulses is set to zero to create interference patterns in the doped sol-gel film. Variable delay line on the probe beam allows to measure the decay time of the diffracted beam.

#### **3.5. Results and discussions**

Figure 17 describes a sol-gel procedure for the preparations of hexylene-bridged polysilsesquioxanes doped with Cro/ CrOx.

The sol-gel process was carried out by a copolymerization of two sol-gel monomers, η6 chromium tricarbonyl(tri-ethoxysilyl)benzene (M-1) and 1,6-bis(triethoxsilyl)hexane (M-2) (Figure 14).

Those sol-gel monomers can be produced bridged Si-O-Si network under either acidic or basic condition, and thus processed into transparent glasses, glassy films, fibers, xerogels, and aerogels, and monoliths. [1,6] From the basic condition, it produced hybrid glasses containing chromium metal particles; because, the M-1 was stable under the basic sol-gel condition.

**Figure 17.** Synthesis of hexylene-bridged xerogel attached with the Cro precursors.

*3.4.2. TEM, EDAX, and electron diffraction analysis* 

molecular alignment built up in the hybrid silicate matrix.

microscope (TEM: CM 20/STEM, PW 6060).

spectrum analyzer at 200 kV was used.

to measure the decay time of the diffracted beam.

polysilsesquioxanes doped with Cro/ CrOx.

**3.5. Results and discussions** 

(Figure 14).

*3.4.3. Laser analysis* 

Density of the doped xerogel was measured to be 1.2696 g/cm3 using a He-gas pycnometer.

A novel periodic alignment of alkylene-spacers in hybrid glass was specifically designed for creating 'a molecular-scale diffraction grating.' We employed TEM analysis to identify the

The doped hybrid glass under an acidic condition (Figure 17) was ground to powders with a particle size (<150 µm), and deposited on a plasma-etched carbon substrate supported copper grid. TEM dark-field images were obtained using a Philips transmission electron

The energy-dispersive X-ray diffraction (EDAX) pattern of the glassy particles was also obtained by an EDAX analyzer (Philips TEM-EDAX, PV 9800). For the electron diffraction, the camera length was calibrated experimentally with a gold standard, and an X-ray

To establish the optical properties of doped xerogels, we prepared a sample (<1mm thickness) fabricated with η6-chromium tricarbonyl(triethoxysilyl)benzene loading of 2.4 % under an acidic sol-gel condition. The thin xerogel film exhibited a nonlinear property. The nonlinear optical (NLO) properties of doped xerogel films were measured by the degenerated into four

We used two types of lasers, a YAG laser with 50 ps pulse-width at 532 nm and a dye laser with 150 fs pulse-width at 640 nm. The output of either of lasers is split into two strong pump beams and a weak probe. The delay between two pump pulses is set to zero to create interference patterns in the doped sol-gel film. Variable delay line on the probe beam allows

Figure 17 describes a sol-gel procedure for the preparations of hexylene-bridged

The sol-gel process was carried out by a copolymerization of two sol-gel monomers, η6 chromium tricarbonyl(tri-ethoxysilyl)benzene (M-1) and 1,6-bis(triethoxsilyl)hexane (M-2)

Those sol-gel monomers can be produced bridged Si-O-Si network under either acidic or basic condition, and thus processed into transparent glasses, glassy films, fibers, xerogels, and aerogels, and monoliths. [1,6] From the basic condition, it produced hybrid glasses containing chromium metal particles; because, the M-1 was stable under the basic sol-gel condition.

wave mixing (DFWM) technique. [55] A quartz sample was used as a reference.

From AAS analysis, the chromium amount was also analyzed to be 1.4% by weight.

In contrast, the acid-catalyzed system produced thinner sol-gel films than those of glasses obtained under base condition (Figure 16). Under the acidic sol-gel condition, decomposition of the M-1 competes with sol-gel copolymerization. The product of acid catalyzed decomposition reaction is "chromium oxides" and H2 (Figure 17). [56-58]

In Figure 18, TEM images of alkylene-bridged silica doped with Cro/CrOx phases reveal unusual nano-fringe patterns, which rose from the lattice fringes of the aligned alkyl-spacers in the silicate matrix. The novel molecular design results in 'a molecular level grating characteristic' when laser light passes by those periodic carbon-chains (Figure 15).

Based on those nano-fringe patterns, an effective optical grating was created in the hybrid silicate matrix. The TEM images of the doped hybrid glass reveal nano-fringe patterns, which are highly organized nano-periodicity (pointed with arrows in Figure 18). The nano-periodic patterns are sustained over substantial domains and appear to arise from lattice fringes.

In short, the formation mechanism of these nanoperiodic features observed in the TEM images arises from the highly arranged alkylene-spacers in the sol-gel monomer (Figure 15).

EDAX and electron diffraction analyses of these dark regions shown in the TEM images were also performed. In the EDAX spectrum, a Cr (Kα) peak was observed; thus, the dark contrast shown in the TEM images (Figure 18) was identified as a chromium phase spread over the hybrid glassy host by both of EDAX/electron diffraction analyses.

Novel Optical Device Materials – Molecular-Level Hybridization 223

(b) **Figure 18. A and b.** TEM Image of Cro/CrOx-doped hexylene-bridged polysilsesquioxane under acidic condition; it reveals unusual nano-fringe patterns with alternating features of a lattice spacing of about

50 Å in different areas.

(a)

(a)

(b)

**Figure 18. A and b.** TEM Image of Cro/CrOx-doped hexylene-bridged polysilsesquioxane under acidic condition; it reveals unusual nano-fringe patterns with alternating features of a lattice spacing of about 50 Å in different areas.

The Cro/CrOx phases were produced by a chemical reaction, which is a simultaneous sol-gel copolymerization then decomposition of the chromium precursor under the acidic condition. The electron diffraction pattern of the dark areas in TEM images was also identified as a mixture of Cro/ CrOx phases.

Novel Optical Device Materials – Molecular-Level Hybridization 225

In order to calculate a lattice space of those highly organized nano-fringe patterns shown in the TEM images, we also carried out electron diffraction analysis of the doped sol-gel film. The result is shown in Figure 19. The nano-periodicity gives rise to features in the electron

Figure 19 shows the circled diffraction patterns that a rise from crystalline chromium metal and a set of diffractions near the center of the beam corresponded to the nanofringes

From the diffraction pattern corresponded to the nano-fringes, a lattice space of the nanostriped patterns observed in TEM images was calculated about 50 Å from a distance between two diffraction spots in two sets of diffraction patterns, which are pointed with

The distance between alkyl-spacers significantly relies on the optical grating efficiency, and

As shown in Figure 14, the reactions occurring during the formation of the sol-gel xerogels are complex and include simultaneous sol-gel copolymerization and decomposition of M-1 under the acidic condition. At present, the mechanism of formation of these nanoperiodic features observed in the TEM images may arise from the highly arranged alkyl-spacers in

In this study, the nonlinear optical (NLO) properties of the doped xerogel film were

In femto- and pico-second experiments, "electronic χ3" and "population χ3" of the doped xerogel film have been measured (Figure 20). The DFWM signals for both "pure electronic and population χ3" are shown in Figure 20 as a small spike around t = 0. It is asymmetric and longer than the laser pulse. The trailing edge of the peak has decay, which is probably

In thermal nonlinearity, the coefficient of phonon diffraction, which is proportional to the coefficient of thermal conductivity, has been calculated from the DFWM experiments as 1.9x10-3 cm2 /sec using an equation, D = Λ2/4πτ (where, Λ is the period of the diffraction

This number is about FIVE times lower than that of a normal glass. In other words, the thermal conductivity of the doped xerogel is FIVE times less than that of a normal glass. In acoustic study, the doped xerogel also shows an interesting new optical property*, an effective* 

When the temperature of the doped xerogel at the maximum of the interference pattern goes up, the material expands then a counter propagating wave of expansion and compression start traveling inside the glassy host. Since the index of refraction depends on density of the material, on top of slow decaying thermal grating, we will have *a dynamic diffraction grating* 

thus it can be "controlled" by inserting different types and sizes of organic spacers.

measured by the degenerated four wave mixing (DFWM) technique. [12, 13, 55]

diffraction pattern.

observed in TEM images (Figure 18).

the sol-gel monomer (M-2).

connected with population relaxation.

*generation of a large acoustic wave.* 

*propagating with the sound velocity.* 

grating and τ is the decay time of the thermal signal).

arrows in Figure 19; each set consists of two diffraction spots.

**Figure 19.** Electron diffraction pattern of doped hybrid glass; circled diffraction patterns correspond to the d-spacings of chromium metal. Highlighted features (arrows) correspond to the nanoperiodicity in the TEM images in Figure 18. From a distance between two diffraction spots point out each arrow a lattice spacing of the nanoscale fringes was calculated to be ~50 Å.

In order to calculate a lattice space of those highly organized nano-fringe patterns shown in the TEM images, we also carried out electron diffraction analysis of the doped sol-gel film. The result is shown in Figure 19. The nano-periodicity gives rise to features in the electron diffraction pattern.

224 Optical Devices in Communication and Computation

identified as a mixture of Cro/ CrOx phases.

The Cro/CrOx phases were produced by a chemical reaction, which is a simultaneous sol-gel copolymerization then decomposition of the chromium precursor under the acidic condition. The electron diffraction pattern of the dark areas in TEM images was also

**Figure 19.** Electron diffraction pattern of doped hybrid glass; circled diffraction patterns correspond to the d-spacings of chromium metal. Highlighted features (arrows) correspond to the nanoperiodicity in the TEM images in Figure 18. From a distance between two diffraction spots point out each arrow a

lattice spacing of the nanoscale fringes was calculated to be ~50 Å.

Figure 19 shows the circled diffraction patterns that a rise from crystalline chromium metal and a set of diffractions near the center of the beam corresponded to the nanofringes observed in TEM images (Figure 18).

From the diffraction pattern corresponded to the nano-fringes, a lattice space of the nanostriped patterns observed in TEM images was calculated about 50 Å from a distance between two diffraction spots in two sets of diffraction patterns, which are pointed with arrows in Figure 19; each set consists of two diffraction spots.

The distance between alkyl-spacers significantly relies on the optical grating efficiency, and thus it can be "controlled" by inserting different types and sizes of organic spacers.

As shown in Figure 14, the reactions occurring during the formation of the sol-gel xerogels are complex and include simultaneous sol-gel copolymerization and decomposition of M-1 under the acidic condition. At present, the mechanism of formation of these nanoperiodic features observed in the TEM images may arise from the highly arranged alkyl-spacers in the sol-gel monomer (M-2).

In this study, the nonlinear optical (NLO) properties of the doped xerogel film were measured by the degenerated four wave mixing (DFWM) technique. [12, 13, 55]

In femto- and pico-second experiments, "electronic χ3" and "population χ3" of the doped xerogel film have been measured (Figure 20). The DFWM signals for both "pure electronic and population χ3" are shown in Figure 20 as a small spike around t = 0. It is asymmetric and longer than the laser pulse. The trailing edge of the peak has decay, which is probably connected with population relaxation.

In thermal nonlinearity, the coefficient of phonon diffraction, which is proportional to the coefficient of thermal conductivity, has been calculated from the DFWM experiments as 1.9x10-3 cm2 /sec using an equation, D = Λ2/4πτ (where, Λ is the period of the diffraction grating and τ is the decay time of the thermal signal).

This number is about FIVE times lower than that of a normal glass. In other words, the thermal conductivity of the doped xerogel is FIVE times less than that of a normal glass. In acoustic study, the doped xerogel also shows an interesting new optical property*, an effective generation of a large acoustic wave.* 

When the temperature of the doped xerogel at the maximum of the interference pattern goes up, the material expands then a counter propagating wave of expansion and compression start traveling inside the glassy host. Since the index of refraction depends on density of the material, on top of slow decaying thermal grating, we will have *a dynamic diffraction grating propagating with the sound velocity.* 

By changing the delay on the laser probe beam, we measured *the period of acoustic grating and extract the sound velocity of the material* (Figure 20). We used YAG laser at 532 nm and 50 ps pulse-width for a laser analysis for the doped xerogel obtained by the novel sol-gel condition, which produces thin xerogel films with unusually high compressibility (higher density).

Novel Optical Device Materials – Molecular-Level Hybridization 227

The amplitude of the acoustic signal will depend upon how effectively the laser pulse energy is transferred to an expansion wave, which in turn depends on compressibility of the host materials. For a comparison we did the same measurement for a dye solution in methanol with the same optical density and the same energy density. The diffraction efficiency of methanol was 25 %, which means the compressibility of the doped xerogel film is as effective as liquid.

In a conclusion from the laser experiments, the doped xerogel film has a lower thermal conductivity than that of a normal glass. The compressibility of the doped xerogel is sufficiently high so the density grating formed in the doped xerogel could be effective to

**Figure 21.** The decay of thermal signal for the doped xerogel measured in CW probe experiment.

We also believe that the nano-fringe patterns revealed in the TEM images (Figure 18), which rose from the lattice fringes of alkylene-bridged silicate matrix may result in an effective grating characteristics when the light passes by those long carbon-chains of alkylene-based

The characteristics observed from the novel doped xerogel are new photonic properties, which hitherto have not been possible from simple physical mixing process of individual components at the bulk scale. In other words, those new optical properties are created by *the* 

Based on these experiments, the (Cro/CrOx)-doped polysilsesquioxane with low thermal conductivity and high compressibility are suggested as a new type of optical device

materials for optical applications, for example diffraction beam modulators.

create high diffraction beam in the sound velocity.

polymeric networks.

*molecular-level hybridization*.

Small spike around t= 0 corresponds to the signal due to electronic nonlinearlity (Figure 20). The time required for the acoustic wave to travel from one interference maximum to another is twice the time between t=0 and the peak of the acoustic signal. The sound velocity (C) in the thin doped xerogel was calculated from the distance between two acoustic waves (Δτ) as C = 3.2 x 10 5 cm/sec.

**Figure 20.** DFWM signals obtained from the doped xerogel measured in femto-second experiment (in a box) and pico-second experiment.

The signal decay time raised from the doped xerogel film was evaluated by the continuous wave (CW) probe experiment (Figure 21); it was obtained as 17 µsec.

Therefore, the doped xerogel serves as a heat generator in the slow nonlinearities due to the low thermal conductivity and high compressibility of the hybrid glass, thus the heat is transferred into expansion or compression wave (acoustic wave) very efficiently.

We also measured the diffraction efficiency of the probe beam at the delay time, corresponding to the peak of acoustic signal. At energy level about P = 0.47 J/cm2, which is close to the optical damage threshold, the diffraction efficiency was 45 %.

The amplitude of the acoustic signal will depend upon how effectively the laser pulse energy is transferred to an expansion wave, which in turn depends on compressibility of the host materials. For a comparison we did the same measurement for a dye solution in methanol with the same optical density and the same energy density. The diffraction efficiency of methanol was 25 %, which means the compressibility of the doped xerogel film is as effective as liquid.

226 Optical Devices in Communication and Computation

density).

C = 3.2 x 10 5 cm/sec.

box) and pico-second experiment.

By changing the delay on the laser probe beam, we measured *the period of acoustic grating and extract the sound velocity of the material* (Figure 20). We used YAG laser at 532 nm and 50 ps pulse-width for a laser analysis for the doped xerogel obtained by the novel sol-gel condition, which produces thin xerogel films with unusually high compressibility (higher

Small spike around t= 0 corresponds to the signal due to electronic nonlinearlity (Figure 20). The time required for the acoustic wave to travel from one interference maximum to another is twice the time between t=0 and the peak of the acoustic signal. The sound velocity (C) in the thin doped xerogel was calculated from the distance between two acoustic waves (Δτ) as

**Figure 20.** DFWM signals obtained from the doped xerogel measured in femto-second experiment (in a

The signal decay time raised from the doped xerogel film was evaluated by the continuous

Therefore, the doped xerogel serves as a heat generator in the slow nonlinearities due to the low thermal conductivity and high compressibility of the hybrid glass, thus the heat is

We also measured the diffraction efficiency of the probe beam at the delay time, corresponding to the peak of acoustic signal. At energy level about P = 0.47 J/cm2, which is

transferred into expansion or compression wave (acoustic wave) very efficiently.

close to the optical damage threshold, the diffraction efficiency was 45 %.

wave (CW) probe experiment (Figure 21); it was obtained as 17 µsec.

In a conclusion from the laser experiments, the doped xerogel film has a lower thermal conductivity than that of a normal glass. The compressibility of the doped xerogel is sufficiently high so the density grating formed in the doped xerogel could be effective to create high diffraction beam in the sound velocity.

**Figure 21.** The decay of thermal signal for the doped xerogel measured in CW probe experiment.

We also believe that the nano-fringe patterns revealed in the TEM images (Figure 18), which rose from the lattice fringes of alkylene-bridged silicate matrix may result in an effective grating characteristics when the light passes by those long carbon-chains of alkylene-based polymeric networks.

The characteristics observed from the novel doped xerogel are new photonic properties, which hitherto have not been possible from simple physical mixing process of individual components at the bulk scale. In other words, those new optical properties are created by *the molecular-level hybridization*.

Based on these experiments, the (Cro/CrOx)-doped polysilsesquioxane with low thermal conductivity and high compressibility are suggested as a new type of optical device materials for optical applications, for example diffraction beam modulators.

We demonstrated here some examples of creating new optical properties by designing novel molecular building blocks at the molecular-scales via *the molecular-level hybridization.* 

Novel Optical Device Materials – Molecular-Level Hybridization 229

Copper, T. M., Gresser, J. D., Trantolo, D. J., & Wnek, G. E., (World Scientific,

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#### **4. Conclusions**

We introduce the *molecular-level hybridization* for the preparation of polysilsesquioxanes, which are hybrids of inorganic oxides and organic network polymers.

Optically transparent hybrid glasses are prepared by a molecular tailoring technique, which produces sol-gel processible monomers.

The resulting hybrid glasses show novel optical properties, which would not be expected from those individuals by the loss of individuals' identities after the molecular-level mixing process, thereby creating entirely new properties.

### **Author details**

Kyung M. Choi *University of California at Irvine, USA* 

#### **5. References**


Copper, T. M., Gresser, J. D., Trantolo, D. J., & Wnek, G. E., (World Scientific, Singapore) Chapter 18.


228 Optical Devices in Communication and Computation

produces sol-gel processible monomers.

*University of California at Irvine, USA* 

Laboratory, Hitachi Ltd.

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**4. Conclusions** 

**Author details** 

Kyung M. Choi

**5. References** 

We demonstrated here some examples of creating new optical properties by designing novel

We introduce the *molecular-level hybridization* for the preparation of polysilsesquioxanes,

Optically transparent hybrid glasses are prepared by a molecular tailoring technique, which

The resulting hybrid glasses show novel optical properties, which would not be expected from those individuals by the loss of individuals' identities after the molecular-level mixing

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## *Edited by Peng Xi*

Optical devices in communication and computation have a significant impact on our daily life, although we may not even be aware of their existence, as in case of inter-continent fiber cables that connect people around the world, making it a global village. Novel nanoscale structures have demonstrated a wide range of unique features; therefore have became a hot research topic. Not only that the novel structural materials are used in biomedical therapy, but also the nature inspires the design of innovative optical structures. In this book, we focus on recent developments of theoretical analysis, designs of novel nano-photonic structures and functional materials for optical instrumentation. This book is constituted of 10 chapters contributed by renowned researchers from all over the world who work in the forefront of this field.

Optical Devices in Communication and Computation

Optical Devices in

Communication and

Computation

*Edited by Peng Xi*