Automated Discovery and Optimization of 3D Topological Photonic Crystals

Abstract

Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on the careful analysis of their bands and mode profiles, but recent theoretical advances have revealed new and powerful insights into the connection between band symmetry, connectivity, and topology. Here we propose a combined global and local optimization framework that integrates a flexible symmetry-constrained level-set parametrization with standard gradient-free optimization algorithms to optimize topological photonic crystals, a problem setting where the objective function may be highly nonconvex and noncontinuous. Our framework can be applied to any symmetry-identifiable band topology, and we demonstrate its applicability to several prominent kinds of three-dimensional band topologies, namely, Γ-enforced nodal lines, Weyl points, and Chern insulators. Requiring no prior examples of topological photonic crystals or prior knowledge on the connection between structure and band topology, our approach indicates a path toward the automated discovery of novel topological photonic crystal designs.