Inverse scattering for waveguides in topological insulators

TL;DR

This paper investigates the inverse scattering problem in topological insulator waveguides, demonstrating full reconstruction of perturbations, stability, and numerical solutions within a Dirac system model.

Contribution

It introduces a method for reconstructing waveguide perturbations from scattering data in a topological insulator context, including stability analysis and numerical implementation.

Findings

Perturbations can be fully reconstructed from scattering data.

A stability result is established in suitable topologies.

Numerical simulations validate the theoretical approach.

Abstract

This paper concerns the inverse scattering problem of a topologically non-trivial waveguide separating two-dimensional topological insulators. We consider the specific model of a Dirac system. We show that a short-range perturbation can be fully reconstructed from scattering data in a linearized setting and in a finite-dimensional setting under a smallness constraint. We also provide a stability result in appropriate topologies. We then solve the problem numerically by means of a standard adjoint method and illustrate our theoretical findings with several numerical simulations.