A physics-inspired approach to overcome oscillatory loss landscapes in the inverse design of optical components

Abstract

Machine Learning offers the potential to revolutionize the inverse design of complex nanophotonic components. In addition to the celebrated numerical techniques, such as Finite-Element and Finite-Difference methods, Machine Learning can predict the scattering properties of complex optical components using artificial neural networks. A benefit of this neural network based approach is that it is especially suited for inverse design. The goal of inverse design is to obtain an optimal optical component that closely matches a desired optical response. The process consists of two steps. The first step trains a neural network to predict the response of an optical system based on its input parameters, such as material and geometric parameters. In the second step, the neural network is used to optimize these input parameters to obtain a desired optical response. An interesting problem can arise in this second step. In resonant systems, the optimization of the input parameters leads to gradient descent in a highly oscillatory loss landscape. The loss landscape contains a lot of local minima in which the gradient descent can get stuck, leading to a sub-optimal optical design. To address this problem, we propose a physics-inspired algorithm which adds the Fourier transform of the desired spectrum to the optimization procedure. The additional Fourier transform provides a way to differentiate between different minima such that the global minimum can be found. We investigate our approach on the transmission and reflection spectra of Fabry-Perot resonators and Bragg reflectors. We show that our method successfully finds optimal optical designs.