Measurement of a topological edge invariant in a microwave network

TL;DR

This paper demonstrates the measurement of topological invariants in a microwave network, revealing edge states and the effects of loss, providing a direct observation method for topological properties in electromagnetic systems.

Contribution

It introduces a novel experimental approach to measure topological invariants directly in microwave networks, advancing understanding of topological insulators in electromagnetic systems.

Findings

Winding numbers of scattering matrix eigenvalues were measured.

Topological edge states were observed in the microwave network.

Loss effects on topological invariants and edge states were analyzed.

Abstract

We report on the measurement of topological invariants in an electromagnetic topological insulator analog formed by a microwave network, consisting of the winding numbers of scattering matrix eigenvalues. The experiment can be regarded as a variant of a topological pump, with non-zero winding implying the existence of topological edge states. In microwave networks, unlike most other systems exhibiting topological insulator physics, the winding can be directly observed. The effects of loss on the experimental results, and on the topological edge states, is discussed.