Reconstructing the scattering matrix using the quasi-bound states

Abstract

In this work we show how to construct the scattering matrix of an arbitrarily complex medium based on the quasi-bound states. In particular, we demonstrate how the complex energy eigenvalues of these states, together with their asymptotic scattering behaviour, provides sufficient information to build up the unitary scattering matrix of a system unambiguously and without any free parameters. We test this novel approach by comparing our results with independent numerical calculations for scattering through a disordered waveguide structure and find excellent agreement.