Fabry-P\'erot quasinormal modes for topological edge states

TL;DR

This paper introduces a Quasinormal Modal Expansion Method to analyze topological edge states in finite systems, revealing their complex spectra and analogy to Fabry-Pérot cavities, thus aiding the design of topological waveguides.

Contribution

It presents a novel framework for studying topological states in finite, open systems using quasinormal modes, bridging the gap between idealized infinite models and practical finite devices.

Findings

Complex discrete spectra describe topological states in finite systems.

Topological modes behave like leaky cavity modes with Fabry-Pérot analogy.

The method provides insights into topological waveguiding in realistic devices.

Abstract

Topological waveguides supporting quantum valley Hall interfacial states confine waves to interfaces and, due to topological protection, are resistant to backscattering even in the presence of defects. These topological insulators are typically studied by means of an infinite spectral problem. However, practical implementations are necessarily finite. In this work, we propose an alternative framework for analysing topologically non-trivial states in open, finite systems. Our approach is based on a Quasinormal Modal Expansion Method (QMEM), which directly characterizes the existence and excitation of these modes within the open system. The resulting spectrum is complex and discrete and fully describes the topologically non-trivial states, revealing an analogy of topological mode steering as a dispersive Fabry-P\'erot cavity, with a dispersion relation closely related to that of the corresponding infinite (Floquet-Bloch) ribbon problem. Our results illustrate how topologically protected waveguiding can be understood in terms of leaky cavity modes and offers a powerful framework for analysing finite topological devices.