# Topology-optimized Dual-Polarization Dirac Cones

## TL;DR

This paper uses topology optimization to design photonic crystal structures with dual-polarization and dual-wavelength Dirac cones, enabling advanced control over light propagation in periodic media.

## Contribution

It introduces a large-scale computational approach for inverse design of photonic Dirac cones in various crystal geometries with different symmetries.

## Key findings

- Designs of photonic crystals with Dirac cones at different Brillouin zone points.
- Demonstration of dual-polarization and dual-wavelength Dirac cones.
- Potential applications in topological photonics and zero-index media.

## Abstract

We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization and dual-wavelength Dirac cones. We demonstrate the flexibility of this technique by designing photonic crystals of different symmetry types, such as ones with four-fold and six-fold rotational symmetry, which possess Dirac cones at different points within the Brillouin zone. The demonstrated and related optimization techniques could open new avenues to band-structure engineering and manipulating the propagation of light in periodic media, with possible applications in exotic optical phenomena such as effective zero-index media and topological photonics.