Differentiable Scattering Matrix for Optimization of Photonic Structures

TL;DR

This paper introduces a robust, differentiable algorithm for computing the derivatives of the scattering matrix in photonic structures, enabling efficient optimization of metasurfaces and other optical components.

Contribution

A novel algorithm that accurately computes scattering matrix derivatives without eigen-decomposition differentiation, improving photonic structure optimization.

Findings

Successfully applied to optimize metasurface structures.

Achieves accurate and robust derivative computations.

Enhances the design process for photonic devices.

Abstract

The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the structure's optical performance changes with respect to design parameters, that is, the scattering matrix's derivatives (or gradient). Here we address this need. We present a new algorithm for computing scattering matrix derivatives accurately and robustly. In particular, we focus on the computation in semi-analytical methods (such as rigorous coupled-wave analysis). To compute the scattering matrix of a structure, these methods must solve an eigen-decomposition problem. However, when it comes to computing scattering matrix derivatives, differentiating the eigen-decomposition poses significant numerical difficulties. We show that the differentiation of the eigen-decomposition problem can be completely sidestepped, and thereby propose a robust algorithm. To demonstrate its efficacy, we use our algorithm to optimize metasurface structures and reach various optical design goals.