Numerical optimization for the inverse design of photonic structures is a tool that is providing increasingly convincing results—even though the wave nature of problems in photonics makes them particularly complex. In the meantime, the field of global optimization is rapidly evolving but is prone to reproducibility problems, making it harder to identify the right algorithms to use. This paper is thought as a tutorial on global optimization for photonics problems. We provide a general background on global optimization algorithms and a rigorous methodology for a physicist interested in using these tools—especially in the context of inverse design. We suggest algorithms and provide explanations for their efficiency. We provide codes and examples as an illustration that can be run online, integrating quick simulation code and Nevergrad, a state-of-the-art benchmarking library. Finally, we show how physical intuition can be used to discuss optimization results and to determine whether the solutions are satisfactory or not.
The development and optimization of photonic devices and various other nanostructure electromagnetic devices present a computationally intensive task. Much optimization relies on finite-difference time-domain or finite element analysis simulations, which can become very computationally demanding for finely detailed structures and dramatically reduce the available optimization space. In recent years, various inverse design machine learning (ML) techniques have been successfully applied to realize previously unexplored optimization spaces for photonic and quantum photonic devices. In this review, recent results using conventional optimization methods, such as the adjoint method and particle swarm, are examined along with ML optimization using convolutional neural networks, Bayesian optimizations with deep learning, and reinforcement learning in the context of new applications to photonics and quantum photonics.
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