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# Inverse design in photonics

Stefanie Kroker, Stéphane Lanteri, Owen Miller, Jens Niegemann, Lora Ramunno

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Stefanie Kroker, Stéphane Lanteri, Owen Miller, Jens Niegemann, Lora Ramunno. Inverse design in photonics. Journal of the Optical Society of America B, 41 (2), pp.IDP1, 2024, Inverse design in photonics, 10.1364/josab.520193. hal-04848994

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Submitted on 19 Dec 2024

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# Inverse design in photonics: introduction

STEFANIE KROKER,<fnref n="1" /> STÉPHANE LANTERI,<fnref n="2" />,\* OWEN MILLER,<fnref n="3" /> JENS NIEGEMANN,<fnref n="4" /> AND LORA RAMUNNO<fnref n="5" />

Received 26 January 2024; posted 26 January 2024; published 31 January 2024

In this introduction, we provide an overview of the papers that were accepted for publication in the feature issue on inverse design in photonics. This feature issue presents cutting-edge research on methodological contributions and applications of inverse design in photonics.

© 2024 Optica Publishing Group

https://doi.org/10.1364/JOSAB.520193

Over the past two decades, nanoscale photonic devices have garnered significant attention due to their compactness and remarkable functionality. Computational design of these devices is considered a challenging task, and fabrication uncertainties can make them even more so. When designing complex nanophotonic devices with many parameters, inverse design methodologies are preferable to iterative brute-force approaches that exhaustively sweep over the design space. These inverse design approaches leverage numerical optimization algorithms to explore the design space of possible solutions efficiently, ideally capturing the desired result in a shorter design time. An inverse design method begins with the definition of a suitable figure of merit (FOM), or equivalently a cost function whose minimum defines the structural definition of a nanophotonic device. The cost function is progressively optimized through intelligent exploration of its landscape.

Two main classes of optimization methods have been used in the inverse design of photonic devices: gradient-based algorithms and gradient-free approaches. Gradient-based methods are efficient in finding local optima, even for a large number of design parameters, but require knowledge of the derivatives of the cost function with respect to design parameters, which can be evaluated analytically or approximated numerically in most cases. These methods have a lengthy history in nanoscale photonic device design, and several descent methods, ranging from steepest-descent to quasi-Newton methods for both constrained and unconstrained problems, have been applied. The most common methods from recent literature include the objective-first and topology optimization algorithms, which have proven to be efficient and rigorous design methodologies.

Gradient-free approaches are capable of capturing global optima, albeit for a limited number of parameters, thereby overcoming the local minimum trapping issue of gradient-based

algorithms. In other words, with gradient-free global optimization techniques, the final optimized results are not influenced by the initialization of the optimizer. In addition, some of these algorithms can deal with discrete optimization parameters and non-differentiable objective functions, which are conditions that are generally not handled by gradient-based algorithms. Without gradients to help guide the optimization, convergence with global optimization algorithms is often considerably slower than convergence with gradient-based algorithms. To date, several global optimization techniques have been proposed in the context of nanophotonic device design. To deal with the existence of several local optima, global-optimization techniques for nanophotonic device design are typically stochastic, including genetic algorithms and evolutionary strategies. In addition to the methods discussed above, emergent approaches, including methods based on artificial neural networks and Bayesian optimization methods, have recently been utilized to uncover surprising new designs.

This feature issue reviews state-of-the-art inverse design methodologies for large-scale nanoscale photonic devices and also presents some applications of these methodologies to the design of photonics in general and specific related topics including wave guiding and confinement, optical materials, ultra-fast optics, metamaterials, light sources, and amplifiers.

First of all, this feature issue includes two tutorials to get the reader started: on one hand an illustrated tutorial on global optimization by Bennet et al.; on the other hand, a tutorial on a Python software for computing the optical properties of multi-layered structures by Langevin et al. These tutorials should make readers aware of two important topics: modern optimization techniques and easily usable software for a first appreciation of the possibilities offered by inverse design methodologies.

<footnote n="1">¹TU Braunschweig, Institut für Halbleitertechnik, Hans-Sommer-Str. 66, 38106 Braunschweig and Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany</footnote>

<footnote n="2">²Atlantis project-team, Université Côte d'Azur, Inria, CNRS, LJAD, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis, France</footnote>

<footnote n="3">³Department of Applied Physics and Energy Sciences Institute, Yale University, New Haven, Connecticut 06511, USA</footnote>

<footnote n="4">⁴Ansys Canada Ltd, 1700 - 1095 West Pender Street, Vancouver, BC V6E 2M6, Canada</footnote>

<footnote n="5">⁵Department of Physics and Nexus for Quantum Technologies, University of Ottawa, Ottawa, ON K1R 5M5, Canada</footnote>

<footnote>\*opex@optica.org</footnote>
In the same spirit, the paper from Chen *et al.* introduces a reproducible suite of test problems for large-scale topology optimization, which should make it much easier to develop, validate, and gain trust in inverse design approaches and software. The paper by Lipan and De Sabata differs from the other papers in this issue as it is based on closed-form exact analytical solutions. While it focusses on the optimization of very specific bi-layered periodic structures, the presented results potentially also serve as reference results for validating more general optimization approaches.

As alluded to above, the topic of artificial intelligence and machine learning (AI/ML) is an increasingly important topic in the field of nanophotonics. The paper from Sanchez *et al.* reviews recent results regarding the development of in numerical

optimization based on a variety of AI/ML approaches including Bayesian optimization and deep neural networks in the context of new application in photonics and quantum nanophotonics. The work by Schulte *et al.* discusses the acceleration of the inverse design process by generating suitable initial guesses from an artificial neural network.

Apart from these general contributions, most of the works presented in this feature issue are concerned with practical applications of inverse design using different approaches that are tailored to the particular context considered, such as the paper of de Aguirre Jokisch *et al.*, which discusses the use of topology optimization for thermo-optical phase shifters of silicon photonics platforms, or the paper of Shi *et al.*, who apply a genetic algorithm to the optimization of a MIM waveguide.