Inverse Scattering for Dirac Equations Arising in Waveguide Arrays
This work provides theoretical and algorithmic foundations for inverse scattering in waveguide array design, but the results are incremental and domain-specific.
The authors develop inverse Born series methods for Dirac equations modeling waveguide arrays, providing convergence analysis and error estimates, with numerical validation of effectiveness.
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.