# Designing Photonic Topological Insulators with Quantum-Spin-Hall Edge States using Topology Optimization

## TL;DR

This paper introduces a novel inverse design method using topology optimization to create photonic topological insulators with enhanced performance, larger band gaps, and low-loss sharp bends, surpassing traditional intuition-based designs.

## Contribution

The authors develop a topology optimization framework for designing photonic topological insulators, achieving larger band gaps and improved edge mode transmission compared to prior methods.

## Key findings

- Band gaps at least 50% larger than previous designs
- Directional beta factor exceeds 99%
- Low-loss sharp bends demonstrated

## Abstract

Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of photonic topological insulators as an inverse design problem and use topology optimization to maximize the transmission through an edge mode with a sharp bend. Two design domains composed of two different, but initially identical, C$_\text{6v}$-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a photonic topological insulator reminiscent of the shrink-and-grow approach to quantum-spin-Hall photonic topological insulators but with notable differences in the topology of the crystal as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50 \% larger than previous designs. Furthermore, we find a directional beta factor exceeding 99 \%, and very low losses for sharp bends. Our approach allows for the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto unexplored symmetry constraints.