Automated Discovery and Optimization of 3D Topological Photonic Crystals

TL;DR

This paper introduces a novel optimization framework that automates the design of 3D topological photonic crystals by integrating symmetry constraints with gradient-free algorithms, enabling discovery of complex topological structures without prior examples.

Contribution

It presents a flexible, symmetry-aware optimization method for designing topological photonic crystals, applicable to various 3D topologies, advancing automated design capabilities.

Findings

Successfully optimized topological photonic structures with complex band topology.

Demonstrated applicability to Weyl points, nodal lines, and Chern insulators.

No prior examples or knowledge required for design process.

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 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 parameterization with standard gradient-free optimization algorithms to optimize topological photonic crystals, a problem setting where the objective function may be highly non-convex and non-continuous. Our framework can be applied to any symmetry-identifiable band topology, and we demonstrate its applicability to several prominent kinds of three-dimensional band topology, namely $\Gamma$-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 towards the automated discovery of novel topological photonic crystal designs.