**4.2 CGH for PIC applications**

An integrated approach for compression applications implemented in an indium phosphide (InP) optical chip was fabricated to realize a Haar wavelet transform [53]. The HT is a wavelet-based method with promising attributes for compression transformation techniques. Their application in image processing and pattern recognition due to its simple design, fast computation power, and efficiency can be easily realized by optical planar interferometry [53, 56, 57].

The HT operations include low-pass (L) and high-pass (H) filters applied over one dimension at a time. This filtering operation corresponds to the calculation of the average between two neighbors' pixel values (LP) or the difference between them (HP) [57]. The HT is implemented with a two-level network composed by three asymmetric adiabatic couplers (AAC) 2 × 2, reproducing the required operations, i.e., the average (sum) and the difference (subtraction) between the optical input pair [53]. The 2D HT can be decomposed in four sub-bands, LL, LH, HL, and HH [57]. The LL gives the data compressed.

In the optical chip (or PIC), these four sub-bands can be extrapolated from the four output WG at the end of the three AAC network, as depicted in **Figure 8**.

The optical chip is composed of four distributed feedback (DFB) source lasers (L1–L4), three asymmetric adiabatic coupler (AAC1–AAC3), six positive-intrinsicnegative (PIN) photodiodes for network monitoring, six MMI splitters 1 × 2, one MMI splitter 2 × 2, and two spot size converters (SSC), at the correspondent HT network output LL (compression) and HH. Further details about the PIC can be found elsewhere [23, 53].

In the described SLM framework, the hologram is generated in an attempt to create the beam profile in the first order of diffraction when being displayed on the SLM. The CGH is expected to reproduce the four WG outputs of the PIC implementing the HT [23, 53] (see **Figure 8**).

#### **Figure 8.**

*[A] Design architecture of the PIC for data compression based on HT. [B] Measurements of the distance between the four WG at the end of the two-level compression network of the PIC [23].*

**127**

**Figure 9.**

*hologram (right figure).*

*Spatial Light Modulation as a Flexible Platform for Optical Systems*

generated with the initial (I1) and optimized (Iout) CGH [8, 23].

In **Figure 9**, we present the obtained image from the hologram replay field

The analysis of the obtained replay field images can be described by the steps

i.Calculate the intensity integration of the image matrix, i.e., the sum of all

ii.Application of the Savitzky–Golay (SG) filter to smoothen the intensity

iii.Implementation of a first-order Gaussian fit curve to the filtered signal,

iv.Extraction of Gaussian parameters to calculate the distances between the four beams (obtained from the CGH) and compare with the expected results

Results from the integrated intensity profile of the replay field after the CGH

The distance between the four beams was calculated from the center position of each beam profile, given by the Gaussian fit coefficient corresponding to the position of the center of the peak. The coefficients were obtained with 95% confidence bounds [23]. The deviation values (δ) between the generated

output of the optical chip (i.e., *d1*, *d2* and *d3* from **Figure 8**), are presented in

The measured power of the beams obtained by the integration intensity profiles

An improved hologram is achieved with the optimization of the linear phase mask CGH, i.e., with a reduction of up to 11% in the error factor (between

*Hologram replay field obtained by the IR camera with an (i) initial hologram (left figure) and (ii) optimized* 

and optimized *Iout*), when compared with the expected

elements along each line of the image matrix, depicted as *Sraw*.

integration signal obtained in step (1), depicted as *SSG*.

*DOI: http://dx.doi.org/10.5772/intechopen.88216*

depicted as *Gauss fit*.

holograms (i.e., initial *I*<sup>1</sup>

is depicted in **Table 2** [23].

**Table 1** [23].

(*d1*, *d2*, and *d3* from the optical chip).

optimization, i.e., after step (3), are presented in **Figure 10**.

described below:

### *Spatial Light Modulation as a Flexible Platform for Optical Systems DOI: http://dx.doi.org/10.5772/intechopen.88216*

*Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies*

the implemented phase masks [18].

**4.2 CGH for PIC applications**

Future work will be performed in order to optimize the current convergence, namely, improve the optical system components (e.g., lenses and collimator) and

An integrated approach for compression applications implemented in an indium

The HT operations include low-pass (L) and high-pass (H) filters applied over one dimension at a time. This filtering operation corresponds to the calculation of the average between two neighbors' pixel values (LP) or the difference between them (HP) [57]. The HT is implemented with a two-level network composed by three asymmetric adiabatic couplers (AAC) 2 × 2, reproducing the required operations, i.e., the average (sum) and the difference (subtraction) between the optical input pair [53]. The 2D HT can be decomposed in four sub-bands, LL, LH, HL, and

In the optical chip (or PIC), these four sub-bands can be extrapolated from the

In the described SLM framework, the hologram is generated in an attempt to create the beam profile in the first order of diffraction when being displayed on the SLM. The CGH is expected to reproduce the four WG outputs of the PIC imple-

*[A] Design architecture of the PIC for data compression based on HT. [B] Measurements of the distance* 

*between the four WG at the end of the two-level compression network of the PIC [23].*

four output WG at the end of the three AAC network, as depicted in **Figure 8**. The optical chip is composed of four distributed feedback (DFB) source lasers (L1–L4), three asymmetric adiabatic coupler (AAC1–AAC3), six positive-intrinsicnegative (PIN) photodiodes for network monitoring, six MMI splitters 1 × 2, one MMI splitter 2 × 2, and two spot size converters (SSC), at the correspondent HT network output LL (compression) and HH. Further details about the PIC can be

phosphide (InP) optical chip was fabricated to realize a Haar wavelet transform [53]. The HT is a wavelet-based method with promising attributes for compression transformation techniques. Their application in image processing and pattern recognition due to its simple design, fast computation power, and efficiency can be

easily realized by optical planar interferometry [53, 56, 57].

HH [57]. The LL gives the data compressed.

menting the HT [23, 53] (see **Figure 8**).

found elsewhere [23, 53].

**126**

**Figure 8.**

In **Figure 9**, we present the obtained image from the hologram replay field generated with the initial (I1) and optimized (Iout) CGH [8, 23].

The analysis of the obtained replay field images can be described by the steps described below:


Results from the integrated intensity profile of the replay field after the CGH optimization, i.e., after step (3), are presented in **Figure 10**.

The distance between the four beams was calculated from the center position of each beam profile, given by the Gaussian fit coefficient corresponding to the position of the center of the peak. The coefficients were obtained with 95% confidence bounds [23]. The deviation values (δ) between the generated holograms (i.e., initial *I*<sup>1</sup> and optimized *Iout*), when compared with the expected output of the optical chip (i.e., *d1*, *d2* and *d3* from **Figure 8**), are presented in **Table 1** [23].

The measured power of the beams obtained by the integration intensity profiles is depicted in **Table 2** [23].

An improved hologram is achieved with the optimization of the linear phase mask CGH, i.e., with a reduction of up to 11% in the error factor (between

#### **Figure 9.**

*Hologram replay field obtained by the IR camera with an (i) initial hologram (left figure) and (ii) optimized hologram (right figure).*

#### **Figure 10.**

*Gaussian fit (Gauss fit, blue line) of smoothed integrated intensity signal from the replay field image (SSG, red dots) of final optimized CGH [23].*


#### **Table 1.**

*Error factor (δ) values for d1, d2, and d3.*


#### **Table 2.**

*Integration of the intensity profiles for the four beams.*

initial and optimized holograms). Nonetheless, the loss of 1.1 dB identified on the mean beam power for the optimized CGH, an improved equalization between the beams was observed, with a 2% reduction in the standard deviation [23].

Algorithm improvements should be implemented to mitigate the power discrepancies between the four beams and optical artifacts associated with the diffraction of light, with the objective of mitigating the signal loss at the output of the optical chip.

**129**

*Spatial Light Modulation as a Flexible Platform for Optical Systems*

A possible approach to correct some of this artifacts can be the application of the Gerchberg-Saxton [37] or simulated annealing [36] algorithms; nonetheless, due to the power loss (up to 9 dB [26]) associated with these approaches, they were not

The phase mask that replicates the expected output of the PIC optical operation can be used to multiplex/demultiplex the obtained result. Furthermore, a phase mask, which addresses the HT operations, can also be applied to invert the compression induced by the HT (optically implemented in the PIC all-optical network with three AAC). Thus, a proof of concept of the PIC operation through the SLM

LCoS SLM technology implementation has been gaining importance in optical system applications, like telecom with the development of high-capacity optical components in system functionalities as switching (in ROADM), multiplexing and demultiplexing, and optical signal processing. In this chapter, a proof of concept on the implementation of a new SLM-based flexible coupling platform has been provided. We have also explored its implementation for applications in SDM systems and PIC characterization/testing. Furthermore, optimized methodologies to generate the CGH were developed and implemented.

SLM to efficiently excite the different cores of a MCF, and (ii) CGH (δ ≤ 1.5%) to feed/receive the output of an optical chip for data compression based on the HT. The demonstrations pave the way for the potential use of the SLM flexible platform in the development of multidimensional optical systems, by providing a versatile optical method which can overcome impairments introduced by the optical path in a MCF (e.g., by improving the setup alignment and excitation of different cores in MCF) and deliver a more robust optical methodology to assess and test photonic processors (e.g., offering a proof of concept of the PIC HT

This work is funded by Fundação para a Ciência e a Tecnologia (FCT) through national funds under the scholarship PD/BD/105858/2014. It is also supported by FCT/MEC/MCTES and when applicable co-funded by FEDER – PT2020 partnership agreement under the project COMPRESS – PTDC/EEI-TEL/7163/2014 and the project UID/EEA/50008/2019. The authors acknowledge PICadvanced for its

for a SDM system, i.e., the use of the

*DOI: http://dx.doi.org/10.5772/intechopen.88216*

addressed in this implementation [23].

coupling framework is expected [8, 23].

Main results include (i) BER = 1.2 × 10<sup>−</sup><sup>3</sup>

**5. Conclusion**

operation).

collaboration.

**Acknowledgements**

*Spatial Light Modulation as a Flexible Platform for Optical Systems DOI: http://dx.doi.org/10.5772/intechopen.88216*

A possible approach to correct some of this artifacts can be the application of the Gerchberg-Saxton [37] or simulated annealing [36] algorithms; nonetheless, due to the power loss (up to 9 dB [26]) associated with these approaches, they were not addressed in this implementation [23].

The phase mask that replicates the expected output of the PIC optical operation can be used to multiplex/demultiplex the obtained result. Furthermore, a phase mask, which addresses the HT operations, can also be applied to invert the compression induced by the HT (optically implemented in the PIC all-optical network with three AAC). Thus, a proof of concept of the PIC operation through the SLM coupling framework is expected [8, 23].
