Topological interface modes in systems with damping

TL;DR

This paper extends the theory of topological interface modes to damped systems, demonstrating that localized eigenfrequencies persist with damping and characterizing their decay rates using transfer matrix methods.

Contribution

It introduces a framework for analyzing topological interface modes in damped systems, applying Rouché's theorem and transfer matrix techniques.

Findings

Localized eigenfrequencies persist with damping

Decay rates of interface modes are explicitly characterized

The spectral problem is formulated as a root-finding problem

Abstract

We extend the theory of topological localised interface modes to systems with damping. The spectral problem is formulated as a root-finding problem for the interface impedance function and Rouch\'e's theorem is used to track the zeros when damping is introduced. We show that the localised eigenfrequencies, corresponding to interface modes, remain for non-zero dampings. Using the transfer matrix method, we explicitly characterise the decay rate of the interface mode.