Inverse Scattering for Dirac Equations Arising in Waveguide Arrays

TL;DR

This paper develops and analyzes inverse scattering algorithms for Dirac equations modeling waveguide arrays, including convergence proofs and numerical validation.

Contribution

It introduces the inverse and reduced inverse Born series methods for Dirac equations in waveguide arrays, with rigorous analysis and numerical validation.

Findings

The inverse Born series converges under certain conditions.

Numerical experiments confirm the effectiveness of the proposed algorithms.

Error estimates are rigorously established for the inverse methods.

Abstract

We investigate inverse scattering problems for Dirac equations that arise as continuum models of waveguide arrays. We first establish the well-posedness of the forward models. For the associated inverse problems, we develop the inverse Born series and the reduced inverse Born series, providing analysis of convergence and rigorous error estimates. Numerical experiments are presented to validate the proposed algorithms and demonstrate their effectiveness.