# Leveraging AI in Photonics and Beyond

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## Abstract

**:**

## 1. Introduction

## 2. AI for Photonics: Modeling and Simulation

#### 2.1. Neural Networks

#### 2.2. Optical Mode Solving

#### 2.2.1. Modal Classifications

#### 2.2.2. Effective Refractive Indices

#### 2.2.3. Optical Mode Profile

#### 2.3. Inverse Design of Photonic Structures: Deep Generative Models

**x**= G(

**z**) from a random noise vector

**z**, and D classifies the pattern

**x**as synthesized (from G) or real (from training data). G attempts to fool D by producing patterns that cannot be distinguished from the ones in the training data. D is discarded once the networks are trained. Conditional GANs (cGANs) are the most widely used variation of GANs, that are constructed by simply adding conditional vector along with the noise vector. The inverse design of photonics structures requires that G outputs a structure pattern with desired optical response rather than a pattern generated randomely from random sample of noise

**z**. cGANs are the way to do that. By conditioning G on target response

**y**so that G outputs a reconstruction

**$\widehat{x}$**= G(

**y**). An ANN based metamodel was trained to approximate the optical and chromatic response of a hybrid subwavelength grating (HSWG) structure [65]. It can serve as a surrogate model for fast spectral performance prediction in the cGANs for inverse design. Deep Convolutional GANs (DCGANs) are the GANs employing Convolutional Neural Network (CNN) architecture. They are comprised of many convolutional, deconvolutional and fully connected layers.

## 3. Photonics for AI: Using Photonics Computing to Implement AI Algorithms

#### 3.1. Current Developments in Photonics Computing

#### 3.2. Photonic Accelerator

#### 3.3. Coherent Feed-Forward Neural Network

#### 3.4. Continuous-Time Recurrent Neural Network

#### 3.5. Spiking Neural Network with Phase-Change Materials

#### 3.6. Reservoir Computing

#### 3.7. On-Chip Fourier Transform and Convolutions Using Star Couplers

## 4. AI Beyond Photonics

#### 4.1. AI for Computational Electromagnetic Solvers: Forward and Inverse

#### 4.2. AI for Microwave Devices: Design, Optimization, and Applications

#### 4.3. AI for Electromagnetic Compatibility (EMC) and Electromagnetic Interference (EMI) Applications

#### 4.4. AI for Quantum Related Topics

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AI | Artificial Intelligence |

ANN | Artificial Neural Networks |

CEM | Computational Electromagnetics |

CNN | Convolutional Neural Network |

cGAN | Conditional Generative Adversarial Network |

DL | Deep Learning |

DNN | Deep Neural Networks |

DGM | Deep Generative Model |

DCGAN | Deep Convolutional Generative Adversarial Network |

DRL | Deep Reinforcement Learning |

DQN | Deep Q-learning Network |

DDQN | Double Deep Q-learning Network |

DE | Differential Evolution |

EM | Electromagnetics |

EMC | Electromagnetic Compatibility |

EMI | Electromagnetic Interference |

FDTD | Finite-Difference Time-Domain |

FDFD | Finite-Difference Frequency-Domain |

FEM | Finite Element Method |

GAN | Generative Adversarial Network |

GP | Gaussian Process |

ISP | Inverse Scattering Problems |

MOM | Method of Moment |

ML | Machine Learning |

NN | Neural Network |

NLP | Natural Language Processing |

NISQ | Noisy Intermediate-Scale Quantum |

PEEC | Partial Element Equivalent Circuit |

RF | Radiofrequency |

RNN | Recurrent Neural Network |

ReLU | Rectified Linear Unit |

RL | Reinforcement Learning |

SVM | Support Vector Machine |

TLM | Transmission-Line Matrix |

VAE | Variational Autoencoder |

VQA | Variational Quantum-Based Algorithm |

VQE | Variational Quantum Eigensolver |

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**Figure 1.**The trend of the publication on AI and photonics and the network visualization of the highly cited paper from 2021. (Searched by web of science and plotted by VOSviewer).

**Figure 2.**Performance of the deep learning model [58] as a function of number of learning points, NL (

**a**) w-h parameter spaces are shown with random test inputs (crosses), and the learning points (dark yellow circles). The NN predictions for test points are colored as blue for multimode and red for single mode. The green solid line is the predicted B(w,h), and the black solid line is the exact B(w,h). (

**b**) The mean square error between the predicted and exact B(w,h) as a function NL (

**c**) Percentage of misclassifications as a function NL. The purple line shows the average value over ten samples of random 200 test pairs of (w,h). The boxes show the consistencies in the percentage misclassifications (first (Q1), second (median), third (Q3) quartiles, maximum (max) and minimum (min) values; see the insert). Adapted with permission from [58] © Taylor & Francis.

**Figure 3.**Performance of the deep-learning model in [59] as a function of number of learning points (NL). (

**a**) NL = 4, (

**b**) NL = 9, and (

**c**) NL = 16. The diagram on the left in all (

**a**–

**c**) represent the considered w-h parameter space with the learning points indicated in blue circles. The effective refractive indices (exact and predicted) along the dotted lines with specific h and w values (A, B, C, D, E, and F—see the left panel) are shown on right diagrams. Adapted with permission from [59] © IOP Publishing.

**Figure 4.**(

**a**) Training time, and (

**b**) prediction time the best performing neural network (nmax = 21) as a function of data set size, and for varying number of neural network hidden layers (L). Key—Blue: L = 1, Red: L = 2, and Green: L = 3. (

**c**) Comparison of the calculation time and mean squared error for optimized neural networks (trained with Ng = 6), interpolation, and exact methods. Adapted with permission from [36] © The Optical Society.

**Figure 5.**(

**a**) Top panel—Location of learning data points in the input parameter space for three sets of data points. Bottom panel—Number of points used for training, validation, and testing in each data set. (

**b**) An example of neural network prediction of the normalized electric field values, E. Top, middle, and bottom row represent prediction of F = |E|${}^{2}$ when the neural networks are trained with the data sets A, B, and C respectively (the scale of the color code is given by the colorbar in Figure 3). (first column) Image from the exact numerical calculation. (second column) Feedforward neural network (FNN) predicted images (third column) Recurrent neural network (RNN) predicted images. In second and third columns, the one-dimensional plots of F as a function of x are shown for y = 0. Adapted with permission from [38] © Springer Nature.

**Figure 6.**Schematic of a convolution neural network (CNN) architecture and an equivalent implementation of a photonics CNN. A CNN consists of several layers that performs convolution, activation, pooling and the final classification using the fully-connected layers. In the photonics implementation of CNN, the convolution and pooling are performed in the Fourier domain (represented as ‘F’ in the diagram) by using photonics devices, while the fully-connected layers are implemented using photonics devices of Mach–Zehnder interferometer (represented as dark gray boxes) and photonics devices of amplifiers/attenuators (represented as light gray boxes).

**Figure 7.**Schematic of the proposed photonics device of a N × M star coupler to be used for the Fourier transform in the photonics CNN. This device consists of N input waveguides and M output waveguides that are connected by a propagation region that are bounded along the circumference of two confocal circles of radius R.

**Table 1.**The spectrum distribution from RF to optics and the corresponding typical applications/techniques.

Wave | Frequency | Wavelength Photon Energies | Applications Techniques | |
---|---|---|---|---|

RF | a few Hz–1 GHz | up to 300 mm | EMC/EMI [9,10] | |

Microwave | 1 GHz–0.3 THz | 1–300 mm | Antenna/Filters [11,12] | |

THz | 0.3–4 THz | 75 um–1 mm | Non-destructive testing [13] | |

Optics | Far Infrared | 0.3–20 THz | 15 um–1 mm | Human body detection [14] |

Mid Infrared | 20–100 THz | 3–15 um | Composition analysis [15] | |

Near Infrared | 100–384 THz | 780–3000 nm | NIR imaging [16] | |

Visible | 384–750 THz | 390–780 nm | Light field [17,18] | |

Ultraviolet | 750 THz–10 PHz | 320–100 eV | UV-C LED [19] |

Architecture | Description | Reference |
---|---|---|

Photonic Accelerator | Accelerated machine learning inference by speeding up expensive computations using photonics e.g., convolutions | [94,95,96,97,98] |

Coherent Feed-forward Neural Network | Matrix multiplication by coherent interference in multi-port interferometers generally composed of mesh of beam-splitters and phase-shifters | [99,100,101,102] |

Continuous-Time RNN | Summation of weighted WDM signals by photodetector which drives a nonlinear dynamical node producing output to next time step | [103,104] |

Spiking Neural Network with Phase-change Materials | Summation of regular, WDM weighted, pulses using nonvolatile multi-state phase change material embedded in waveguide, emulating spike timing dependent plasticity | [105,106] |

Reservoir Computing | Linear combination of outputs from a nonlinear dynamical system consisting of nodes with randomly weighted connections | [107,108,109,110,111] |

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**MDPI and ACS Style**

Alagappan, G.; Ong, J.R.; Yang, Z.; Ang, T.Y.L.; Zhao, W.; Jiang, Y.; Zhang, W.; Png, C.E.
Leveraging AI in Photonics and Beyond. *Photonics* **2022**, *9*, 75.
https://doi.org/10.3390/photonics9020075

**AMA Style**

Alagappan G, Ong JR, Yang Z, Ang TYL, Zhao W, Jiang Y, Zhang W, Png CE.
Leveraging AI in Photonics and Beyond. *Photonics*. 2022; 9(2):75.
https://doi.org/10.3390/photonics9020075

**Chicago/Turabian Style**

Alagappan, Gandhi, Jun Rong Ong, Zaifeng Yang, Thomas Yong Long Ang, Weijiang Zhao, Yang Jiang, Wenzu Zhang, and Ching Eng Png.
2022. "Leveraging AI in Photonics and Beyond" *Photonics* 9, no. 2: 75.
https://doi.org/10.3390/photonics9020075