Phase spectroscopy of topological invariants in photonic crystals

TL;DR

This paper introduces a phase spectroscopy method to measure topological invariants in photonic crystals, enabling the deduction of Chern numbers from reflection phase winding, with proofs and illustrations for 1D and 2D systems.

Contribution

It presents a novel phase spectroscopy technique to determine topological invariants in photonic crystals, linking reflection phase winding to Chern numbers.

Findings

Chern numbers can be deduced from reflection phase winding.

Edge states exist in systems with nonzero reflection phase winding.

Method demonstrated on 1D and 2D topological photonic crystals.

Abstract

We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of existence of edge states in system with nonzero reflection phase winding number is given. The method is illustrated for one- and two-dimensional photonic crystals of nontrivial topology.