Topological classification of Chern-type insulators with the photonic Green function

TL;DR

This paper introduces a method to compute the topological Chern numbers of photonic systems directly from the Green function, bypassing the need for detailed band structure analysis, applicable to complex 3D photonic crystals.

Contribution

It presents a novel Green function-based approach to determine Chern numbers in photonics without relying on band structure or eigenwaves.

Findings

Chern numbers can be calculated from Green functions along complex frequency lines.

The method applies to arbitrary dispersive 3D photonic crystals.

It extends topological analysis to non-periodic electromagnetic continua.

Abstract

The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to calculate the gap Chern numbers of a photonic platform without having any detailed knowledge of its band structure, relying simply on the system photonic Green function. It is shown that the gap Chern number is given by an integral of the photonic Green function along a line of the complex frequency plane parallel to the imaginary axis. Our theory applies to arbitrary frequency dispersive fully three-dimensional photonic crystals, as well as to the case of electromagnetic continua with no intrinsic periodicity.