# Photonic analogues of the Haldane and Kane-Mele models

## TL;DR

This paper presents exact photonic crystal analogues of the Haldane and Kane-Mele models, demonstrating topologically protected edge states in all-dielectric, anisotropic metamaterials through numerical simulations and theoretical analysis.

## Contribution

It introduces novel photonic implementations of the Haldane and Kane-Mele models using artificial graphene and anisotropic dielectrics, enabling observation of topological phenomena in photonics.

## Key findings

- Topologically protected gapless edge states are verified at interfaces.
- Photonic analogues replicate key features of condensed matter models.
- The approach enables all-dielectric realization of topological insulators.

## Abstract

The condensed matter Haldane and Kane-Mele models revolutionized the understanding of what is an "insulator", as they unveiled novel classes of media that behave as metals near the surface, but are insulating in the bulk. Here, we propose exact electromagnetic analogues of these two influential models relying on a photonic crystal implementation of "artificial graphene" subject to an effective magnetic field. For the Haldane model, the required effective magnetic field for photons can be emulated with a spatially variable pseudo-Tellegen response. For the Kane-Mele model, the spin-orbit coupling can be mimicked using matched anisotropic dielectrics with identical permittivity and permeability, without requiring any form of bianisotropic couplings. Using full wave numerical simulations and duality theory we verify that the nontrivial topology of the two proposed platforms results in the emergence of topologically protected gapless edge states at the interface with a trivial photonic insulator. Our theory paves the way for the emulation of the two condensed matter models in a photonic platform, and determines another paradigm to observe topologically protected edges-states in a fully reciprocal all-dielectric and non-uniform anisotropic metamaterial.