Modeling scattering matrix containing evanescent modes for wavefront shaping applications in disordered media

We developed an open-source scalar wave transport model to estimate the generalized scattering matrix (S matrix) of a disordered medium in the diffusion regime. Here, the term generalization refers to the incorporation of evanescent wave field modes in addition to propagating modes while estimating the S matrix. For that we used the scalar Kirchhoff-Helmholtz boundary integral formulation together with the Green's function perturbation method to generalize the conventional Fisher-Lee relations to include evanescent modes as well. The estimated S matrix, which satisfies generalized unitarity and reciprocity conditions, is modeled for a 2D disordered waveguide. The generalized transmission matrix contained in the S matrix is used to estimate the optimal phase-conjugate wavefront for focusing onto an evanescent mode. The phenomena of universal transmission value of 2/3 for such an optimal phase conjugate wavefront is also shown in the context of evanescent wave mode focusing through a diffusive disorder. The presented code framework may be of interest to wavefront shaping researchers for visualizing and estimating wave transport properties in general.