**4.2 Loss estimation**

There are three different sources of loss in this holographic device:

a. SLM losses

An FLC-SLM works as a dynamic full π-binary phase fixed grating hologram with a diffraction efficiency *η* = 36.5% (4.38 dB) for the first diffractive order (*m* =1) and a FLC switching angle of 45º.

Another cause of losses is the insertion of the hologram, for a phase SLM, as a result of the light polarization plane and FLC switching angle different to 45º (theoretical optimal angle); at least another 2 dB are lost, assuming a good alignment of the collimated input light and the FLC pixels.

b. Fixed grating losses

The diffraction efficiency for a fixed grating, binary π-phase, is *η* = 36.5% for the first diffractive order (*m*=1). That means a loss of 4.38 dB.

c. Fiber/lens coupling efficiency

A fiber/lens coupling efficiency of 50% is a good approximation; therefore another 3 dB of losses have to be added (2 dB, with very good alignment).

Losses can be improved using multiple-phase or blazed gratings; in this case the efficiency can reach *η* ≈ 80 - 90% and the losses decrease to 1.5 dB (Ahderom, Raisi et al., 2002).

The estimated total losses of the device are: SLM losses + fixed grating losses + fiber/lens coupling losses = (4.38+2) + 4.38 + 3 =13.76 dB and with loss optimization: (1.5+2)+1.5+2= 7 dB can be obtained.

### **5. WDM (wavelength division multiplexing) application**

We can use this device as a 1x M demultiplexer, where *M* is the number of output fibers. For this, a fixed value of *n* is used and the output fibers are located in certain *x* positions. Output fibers (9/125 µm) must be placed in agreement with the diffracted angles *Ф*, according to input wavelengths and they have to be separated at least *Δx* = 125 µm.

From (5), we can calculate the *Δx* taking the value of center to center wavelength channel separation, *Δλ*, into account:

$$
\Delta \approx \lambda \, f\left(\frac{n}{ND} + \frac{1}{d}\right) \Rightarrow \Delta \propto \Delta \lambda \, f\left(\frac{n}{ND} + \frac{1}{d}\right) \tag{9}
$$

In order to design a compatible device with the frequency grid provided in ITU-T G.694.1/G.694.2 Rec. for CWDM/DWDM systems, a 1x4 demultiplexer (*M = 4*) for DWDM **<sup>1</sup>** with *Δx* = 161 µm and a 1x8 demultiplexer (*M = 8*) for CWDM with *Δx* = 321 µm, can be implemented.

<sup>1</sup> In this case, *Δλ's < 20* nm are not feasible due to the physical dimension of the device (i.e. *Δλ = 2* nm and *Δx* = 161 µm *f ,*focal distance of the lens, = 25 cm).

This feature allows the possibility of a multiple pass band filter in the same optical fiber, but with an increment of losses penalty according to the expression 10 log *C* (dB), where *C* is the number of simultaneously tuned channels (Parker et al., 1998). In this case, *C* = 4 and

An FLC-SLM works as a dynamic full π-binary phase fixed grating hologram with a diffraction efficiency *η* = 36.5% (4.38 dB) for the first diffractive order (*m* =1) and a FLC

Another cause of losses is the insertion of the hologram, for a phase SLM, as a result of the light polarization plane and FLC switching angle different to 45º (theoretical optimal angle); at least another 2 dB are lost, assuming a good alignment of the collimated input light and

The diffraction efficiency for a fixed grating, binary π-phase, is *η* = 36.5% for the first

A fiber/lens coupling efficiency of 50% is a good approximation; therefore another 3 dB of

Losses can be improved using multiple-phase or blazed gratings; in this case the efficiency

The estimated total losses of the device are: SLM losses + fixed grating losses + fiber/lens coupling losses = (4.38+2) + 4.38 + 3 =13.76 dB and with loss optimization: (1.5+2)+1.5+2= 7

We can use this device as a 1x M demultiplexer, where *M* is the number of output fibers. For this, a fixed value of *n* is used and the output fibers are located in certain *x* positions. Output fibers (9/125 µm) must be placed in agreement with the diffracted angles *Ф*, according to

From (5), we can calculate the *Δx* taking the value of center to center wavelength channel

*n n* 1 1 *xf x f ND d ND d* 

In order to design a compatible device with the frequency grid provided in ITU-T G.694.1/G.694.2 Rec. for CWDM/DWDM systems, a 1x4 demultiplexer (*M = 4*) for DWDM **<sup>1</sup>** with *Δx* = 161 µm and a 1x8 demultiplexer (*M = 8*) for CWDM with *Δx* = 321 µm, can be

1 In this case, *Δλ's < 20* nm are not feasible due to the physical dimension of the device (i.e. *Δλ = 2* nm

(9)

can reach *η* ≈ 80 - 90% and the losses decrease to 1.5 dB (Ahderom, Raisi et al., 2002).

therefore the increment of losses in the device is: Δ losses = 10 log 4 = 6 dB.

There are three different sources of loss in this holographic device:

diffractive order (*m*=1). That means a loss of 4.38 dB.

losses have to be added (2 dB, with very good alignment).

**5. WDM (wavelength division multiplexing) application** 

input wavelengths and they have to be separated at least *Δx* = 125 µm.

**4.2 Loss estimation** 

switching angle of 45º.

b. Fixed grating losses

dB can be obtained.

separation, *Δλ*, into account:

and *Δx* = 161 µm *f ,*focal distance of the lens, = 25 cm).

implemented.

c. Fiber/lens coupling efficiency

a. SLM losses

the FLC pixels.

Table 6 summarizes the fiber positions in order to demultiplex the wavelengths used in the CWDM/DWDM systems. A CWDM system uses *F1, F2, F3, F4, F5, F6, F8* and F10 and a DWDM uses *F7, F8, F9*, and *F10* output fibers (see Fig. 6). It is necessary to emphasize that a better performance as demultiplexer could be implemented if only this function is required. For example, we could design a demultiplexer device with channel separation smaller than 50 GHz (Parker, Cohen et al., 1997). However, the novel idea is to design a compatible CWDM/DWDM device able to carry out different functions.


Table 6. CWDM/DWDM demultiplexers (n = 180)

#### **6. Wavelength routing application**

Maintaining output fibers in the same place as shown in Table 6, if *n* value (type of hologram) is properly varied, a certain wavelength coming from the input fiber can be routed to any one of the output fibers. As an example, Table 7 highlights the *n* values for routing *λ0* = 1431nm (CWDM) and *λ<sup>0</sup>* = 1551 (DWDM) towards an output fiber; these values have been calculated from (10), considering the variation of *n* according to *Δx*:

$$m \approx \left(\frac{\mathbf{x}}{\lambda f} - \frac{1}{d}\right) \text{ND} \Rightarrow \Delta m \approx \left(\frac{\Delta \mathbf{x}}{\lambda f}\right) \text{ND} \tag{10}$$

For *Δx* = 161 µm, *Δn* was calculated by using (10) resulting in *Δn* = 21 and for *Δx* = 321 µm, *Δn* is 45. Therefore, the device is a 1x8 λ router in case of CWDM and a 1x4 λ router for DWDM systems. It is necessary to highlight that the positions of the fibers are compatible with all applications and that the crosstalk resulting from high-order diffraction beams (*m* = 2, 3,.) are outside of the locations of the output array fibers (*ΔФ* = 4º), (Horche, 2004).

Application of Holograms in WDM Components for Optical Fiber Systems 269

SLM, *N* = 256, have been taken into account. Fig. 9 summarizes the new fiber positions (*F1 to* 

a)

a)

a)

Aperture

Attenuator

Focal plane Image plane

Aperture

lens

SLM control

SLM

CCD camera

lens

Fig. 8. (a) Optical bench diagram; (b) experimental optical bench and c) binary phase SLM

b) c)

characteristics

He-Ne Laser

Aperture

PC - hologram generation



3,84 x 3,84 mm

Active area

Fill factor 87 %

*D* 15 µm

*N* 256

Polarizating beam splitter

*F8*) with a separation of *∆x =* 176.23 μm between them.

Spatial Filter


Table 7. CWDM/DWDM routers

#### **7. Basic experimental results**

In this section two complementary experiments have been made. The first one is related to diffraction patterns measurements for different bars holograms and the second one to a SLM characterization for holographic filters, demultiplexers and routers use with reference to the devices whose design and characteristics have been described in the previous sections. Due to the unavailability of components in the laboratory with the characteristics previously described, the experimental optical bench is somewhat different from the appropriate one, but, the measurements obtained are in agreement with the calculations.

In order to carry out the measurements, the experimental lab bench showed in Fig. 8 was used; it is in agreement with the structure of Fig. 6, but, in this case, we used a reflective SLM instead of a transmissive one; therefore, it is necessary to include a polarizing beam splitter in order to direct the reflected beam to the lens. Due to the "spatial invariability" of the Fourier transform, it is not necessary to illuminate the entire SLM active surface to reproduce the diffraction pattern; taking this into account we can select, by a diaphragm aperture, the SLM zone where the incident light is focused. The characteristics of a commercial binary phase SLM are shown in Fig. 8(c).

As optical sources, a green He-Ne laser and a tunable Argon laser with *λ<sup>g</sup>* = 528.7 nm (green) and *λb* = 462.6 nm (blue) have been used. These wavelengths have been selected because they belong to the visible spectrum and the correct alignment of the system is easier, a critical factor in the experiment. In this case, a detector-array (6.3 × 4.7 mm) of a CCD camera is placed at the "*focal plane*", as an image sensor, to analyze the results.

A single personal computer, PC, is used to generate the CGHs for the design process described previously, and they are loaded onto the SLM by changing its pixels state; the diffracted patterns were stored in the same PC, where they could be observed and processed. To recalculate the new output fibers position, the distance for the diffraction order *(x)* is derived from (5) without the fixed grating:

$$\mathbf{x} = \mathbf{\hat{x}} \cdot \frac{f}{H} \tag{11}$$

where *H*, defined in (4), is the hologram spatial period, but now, the maximum value for *n* = *N/2* = 128, the size of the pixel, *D =15 μm* and the number of pixels in one dimension of the

**DWDM** *n* **value λ0 = 1551 nm** 

**λ0 = 1431 nm** 

*F7* 159 *F8* 315 180 *F9* 201 *F10* 360 222

In this section two complementary experiments have been made. The first one is related to diffraction patterns measurements for different bars holograms and the second one to a SLM characterization for holographic filters, demultiplexers and routers use with reference to the devices whose design and characteristics have been described in the previous sections. Due to the unavailability of components in the laboratory with the characteristics previously described, the experimental optical bench is somewhat different from the appropriate one,

In order to carry out the measurements, the experimental lab bench showed in Fig. 8 was used; it is in agreement with the structure of Fig. 6, but, in this case, we used a reflective SLM instead of a transmissive one; therefore, it is necessary to include a polarizing beam splitter in order to direct the reflected beam to the lens. Due to the "spatial invariability" of the Fourier transform, it is not necessary to illuminate the entire SLM active surface to reproduce the diffraction pattern; taking this into account we can select, by a diaphragm aperture, the SLM zone where the incident light is focused. The characteristics of a

As optical sources, a green He-Ne laser and a tunable Argon laser with *λ<sup>g</sup>* = 528.7 nm (green) and *λb* = 462.6 nm (blue) have been used. These wavelengths have been selected because they belong to the visible spectrum and the correct alignment of the system is easier, a critical factor in the experiment. In this case, a detector-array (6.3 × 4.7 mm) of a CCD

A single personal computer, PC, is used to generate the CGHs for the design process described previously, and they are loaded onto the SLM by changing its pixels state; the diffracted patterns were stored in the same PC, where they could be observed and processed. To recalculate the new output fibers position, the distance for the diffraction

where *H*, defined in (4), is the hologram spatial period, but now, the maximum value for *n* = *N/2* = 128, the size of the pixel, *D =15 μm* and the number of pixels in one dimension of the

*<sup>H</sup>* (11)

camera is placed at the "*focal plane*", as an image sensor, to analyze the results.

but, the measurements obtained are in agreement with the calculations.

commercial binary phase SLM are shown in Fig. 8(c).

order *(x)* is derived from (5) without the fixed grating:

*<sup>f</sup> <sup>x</sup>*

**Output fiber CWDM** *n* **value** 

*F1* 44 *F2* 89 *F3* 135 *F4* 180 *F5* 225 *F6* 270

Table 7. CWDM/DWDM routers

**7. Basic experimental results** 

SLM, *N* = 256, have been taken into account. Fig. 9 summarizes the new fiber positions (*F1 to F8*) with a separation of *∆x =* 176.23 μm between them.

Fig. 8. (a) Optical bench diagram; (b) experimental optical bench and c) binary phase SLM characteristics

b) c)

3,84 x 3,84 mm

Active area

Application of Holograms in WDM Components for Optical Fiber Systems 271

Fig. 10. Diffracted wavelengths with a phase FC-SLM. A tunable Argon laser with λg = 528.7 nm (green) and λb = 462,6 nm (blue) is used. An Δx = 176.25 µm (diffracted wavelengths

The central light spot is due to the zero diffraction order *m* = 0, with the maximum light intensity diffracted (*x* = 0); it can be reduced with a SLM with better performance by

The temporal response of the system was also measured. The SLM optical switching time was estimated to be roughly 250 s, as the sum of the electric storage and FLC material response times (Alarcón, 2004). We also noticed a damped response when low-frequency

**8. Design of equalized holographic ROADMs for application in CWDM metro** 

These type of ROADMs are designed for application in CWDM (Coarse Wavelength Division Multiplexing) networks, where the distance between the different wavelengths allow the use of DML (Direct Modulation Lasers) without cooling, reducing the cost and the tolerances of the network components. Application in METRO networks and its interconnection with some PON (Passive Optical Network), as a part of the access to the

Different technologies have been proposed for the implementation of ROADMs (Ma & Kuo, 2003), (Homa & Bala, 2008). Each of them has its own advantages and drawbacks. The main characteristic of holographic ROADMs is the easy way of changing the tuning and power level of the signal at the output fibers by the dynamic implementation of different

The working principle of the dynamic holographic device is based on the wavelength dispersion produced in a diffraction component (grating, spatial light modulator) as

We use for this application a phase reflective spatial light modulator (SLM) and a fixed transmissive diffraction grating to select the corresponding output wavelength from an set of channels in the input, as shown in Fig 11. The active element of the SLM is a Ferroelectric Liquid Crystal (FLC) with a low switching time (less than 50 μs) that allows a real time

holograms on the SLM according to the requirements of the network management.

switching is carried out; this is probably due to relaxation of the FLC molecules.

separation) is obtained

**networks** 

subscriber, is reviewed.

explained in Section 3.

**8.1 Holographic ROADM structure** 

impacting on the total insertion losses reduction.

Fig. 9. New output fiber positions for the experimental measurements with two different λ's: λg = 5287 nm (green) and λb = 4626 nm (blue)

#### **7.1 SLM characterization for wavelength routers**

When we implement different holograms, according to *n* values, in the SLM and an incident light wavelength is illuminating the pixels, different diffracted angles are obtained; by placing an array of fibers at the output, in the focal plane, a *λ-*router is implemented.

To test the capability of a commercial SLM as a part of a dynamic holographic router, the holographic setup shown in Fig. 8 (a) was implemented; a photo of the experimental optical bench is shown in Fig. 8(b). For this test the optical source was an He-Ne laser at λ = 528.7 nm (green wavelength) and the lens focal length, 8 cm.

In order to route the green wavelength to the *F4* output fiber, according to Fig. 9, it is necessary to load a CGH-(A) with a spatial period *H* corresponding to *n* = 64 in the SLM and for routing the same wavelength to the *F8* output fiber, a CGH-(B) with *n* = 128 was calculated and implemented onto the SLM.

#### **7.2 SLM characterization for filters and demultiplexers**

Other measurements, to test the capability of a commercial SLM as a part of a dynamic holographic device, have been done with the holographic setup shown in Fig. 8 (Alarcón, 2004). According to Fig. 9, if a CGH black & white bars type hologram with *n = 128* is loaded onto the *programmable* SLM, a blue wavelength channel will reach the *F7* output fiber and a green wavelength channel will reach the *F8* output fiber.

The diffracted light spots distance, calculated from (9) without a fixed grating, is:

$$
\Delta \mathfrak{x} \approx \Delta \lambda \, f \left( \frac{n}{ND} \right) \tag{12}
$$

where: *Δλ* = 66.1 nm; *f* = 8 cm; *n* = 128; *N* = 256 and *D* = 15 μm.

In Fig.10 light spots captured by CCD camera, from the CGH with *n* = 128 (black and white bars) are shown. In this case the tunable Argon laser with the blue and green colors has been used. The experimental diffracted light spot distances were *xblue =* 1233.6 µm (*F7*) and *xgreen =*  1409.8 (*F8*) µm, separated by *∆x =* 176.25 µm according to Fig. 9, in good agreement with (12). Therefore, in this way, we can build an optical 1x2 demultiplexer.

*F4* 704.93

*F2* 352.46

*F3* 528.70

0 150 300 450 600 750 900 1050 1200 1350 1500

*Fiber Position, x (µm)*

When we implement different holograms, according to *n* values, in the SLM and an incident light wavelength is illuminating the pixels, different diffracted angles are obtained; by

To test the capability of a commercial SLM as a part of a dynamic holographic router, the holographic setup shown in Fig. 8 (a) was implemented; a photo of the experimental optical bench is shown in Fig. 8(b). For this test the optical source was an He-Ne laser at λ = 528.7

In order to route the green wavelength to the *F4* output fiber, according to Fig. 9, it is necessary to load a CGH-(A) with a spatial period *H* corresponding to *n* = 64 in the SLM and for routing the same wavelength to the *F8* output fiber, a CGH-(B) with *n* = 128 was

Other measurements, to test the capability of a commercial SLM as a part of a dynamic holographic device, have been done with the holographic setup shown in Fig. 8 (Alarcón, 2004). According to Fig. 9, if a CGH black & white bars type hologram with *n = 128* is loaded onto the *programmable* SLM, a blue wavelength channel will reach the *F7* output fiber and a

> *<sup>n</sup> x f ND*

In Fig.10 light spots captured by CCD camera, from the CGH with *n* = 128 (black and white bars) are shown. In this case the tunable Argon laser with the blue and green colors has been used. The experimental diffracted light spot distances were *xblue =* 1233.6 µm (*F7*) and *xgreen =*  1409.8 (*F8*) µm, separated by *∆x =* 176.25 µm according to Fig. 9, in good agreement with

The diffracted light spots distance, calculated from (9) without a fixed grating, is:

placing an array of fibers at the output, in the focal plane, a *λ-*router is implemented.

Fig. 9. New output fiber positions for the experimental measurements with two different

Blue

*F5* 881.16

*F6* 1057.40

*F7* 1233.63

(12)

*F8* 1409.86

Green

0

32

64

*n*

96

128

*F1* 176.23

λ's: λg = 5287 nm (green) and λb = 4626 nm (blue)

**7.1 SLM characterization for wavelength routers** 

nm (green wavelength) and the lens focal length, 8 cm.

**7.2 SLM characterization for filters and demultiplexers** 

green wavelength channel will reach the *F8* output fiber.

where: *Δλ* = 66.1 nm; *f* = 8 cm; *n* = 128; *N* = 256 and *D* = 15 μm.

(12). Therefore, in this way, we can build an optical 1x2 demultiplexer.

calculated and implemented onto the SLM.

Fig. 10. Diffracted wavelengths with a phase FC-SLM. A tunable Argon laser with λg = 528.7 nm (green) and λb = 462,6 nm (blue) is used. An Δx = 176.25 µm (diffracted wavelengths separation) is obtained

The central light spot is due to the zero diffraction order *m* = 0, with the maximum light intensity diffracted (*x* = 0); it can be reduced with a SLM with better performance by impacting on the total insertion losses reduction.

The temporal response of the system was also measured. The SLM optical switching time was estimated to be roughly 250 s, as the sum of the electric storage and FLC material response times (Alarcón, 2004). We also noticed a damped response when low-frequency switching is carried out; this is probably due to relaxation of the FLC molecules.
