Inverse scattering for waveguides in topological insulators
For researchers in topological insulators and inverse scattering, this provides a theoretical and numerical framework for reconstructing perturbations, though the linearized and smallness constraints limit immediate practical impact.
The paper solves the inverse scattering problem for waveguides in topological insulators, showing that a short-range perturbation can be fully reconstructed from scattering data in linearized and finite-dimensional settings, with numerical validation.
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.