Gapless surface states in a lattice of coupled cavities: a photonic analog of topological crystalline insulators

TL;DR

This paper demonstrates that a lattice of coupled cavities can serve as a photonic analog of topological crystalline insulators, exhibiting gapless surface states within an omnidirectional band gap, characterized by a $Z_{2}$ topological invariant.

Contribution

It introduces a new photonic system that mimics topological crystalline insulators, showing how to realize and characterize such states in a lattice of dielectric cavities.

Findings

Presence of omnidirectional band gap with gapless surface states

Photonic crystal characterized by a $Z_{2}$ topological invariant

Feasible realization in microwave regime with dielectric particles

Abstract

We show that a tetragonal lattice of weakly interacting cavities with uniaxial electromagnetic response is the photonic counterpart of topological crystalline insulators, a new topological phase of atomic band insulators. Namely, the frequency band structure stemming from the interaction of resonant modes of the individual cavities exhibits an omnidirectional band gap within which gapless surface states emerge for finite slabs of the lattice. Due to the equivalence of a topological crystalline insulator with its photonic-crystal analog, the frequency band structure of the latter can be characterized by a $Z_{2}$ topological invariant. Such a topological photonic crystal can be realized in the microwave regime as a three-dimensional lattice of dielectric particles embedded within a continuous network of thin metallic wires.