Edge Modes of Scattering Chains with Aperiodic Order

TL;DR

This paper explores the existence and properties of topological edge modes in aperiodic scattering chains of electric dipoles, revealing new insights into their localization and potential for designing advanced optical materials.

Contribution

It introduces the study of topological edge states in aperiodic electromagnetic scattering systems using the vectorial Green's matrix method, extending topological concepts beyond tight-binding models.

Findings

Edge-localized scattering states exist within fractal energy gaps.

Topological edge modes with power-law envelopes are found in open aperiodic systems.

Coexistence of topological and traditional localized modes observed.

Abstract

We study the scattering resonances of one-dimensional deterministic aperiodic chains of electric dipoles using the vectorial Green's matrix method, which accounts for both short- and long-range electromagnetic interactions in open scattering systems. We discover the existence of edge-localized scattering states within fractal energy gaps with characteristic topological band structures. Notably, we report and characterize edge-localized modes in the classical wave analogues of the Su-Schrieffer-Heeger (SHH) dimer model, quasiperiodic Harper and Fibonacci crystals, as well as in more complex Thue-Morse aperiodic systems. Our study demonstrates that topological edge-modes with characteristic power-law envelope appear in open aperiodic systems and coexist with traditional exponentially localized ones. Our results extend the concept of topological states to the scattering resonances of complex open systems with aperiodic order, thus providing an important step towards the predictive design of topological optical metamaterials and devices beyond tightbinding models.