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

Michael Raju1,2,*, Baptiste Jayet1, and Stefan Andersson-Engels1,2

  • *Contact author: michaelraju@umail.ucc.ie
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Phys. Rev. Research 8, 033123 – Published 29 July, 2026

DOI: https://doi.org/10.1103/86th-pl8q

Abstract

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. The term generalized refers to the incorporation of evanescent wave field modes alongside propagating modes in the estimation of the S-matrix. To achieve this, we employed the scalar Kirchhoff-Helmholtz boundary integral formulation together with the Green’s function perturbation method, thereby extending the conventional Fisher-Lee relations to include evanescent modes. The estimated S-matrix, which satisfies the generalized unitarity and reciprocity relations, is modeled for a two-dimensional disordered waveguide. The generalized transmission matrix contained within the S-matrix is utilized to estimate the optimal phase-conjugate wavefront for focusing onto an evanescent mode. The phenomenon of a universal transmission value of 2/3 for such an optimal phase conjugate wavefront is demonstrated 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.

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Phys. Rev. Research 8, 033123– Published 29 July, 2026
  • Received 17 April 2024
  • Accepted 8 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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