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Fast scattering-matrix solver using augmented partial factorization

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MWSW02 - Theory of wave scattering in complex and random media

The scattering matrix fully characterizes the response of a complex medium, but its computation requires solving the inhomogeneous wave equation for numerous inputs, which is slow and currently can only be done for relatively small systems. We introduce the “augmented partial factorization” (APF) method, which directly computes the full scattering matrix without solving for unnecessary field profiles and without a loop over the inputs [1]. APF is a full-wave method applicable to any complex structure, with no approximation beyond discretization. Using APF , the full scattering matrix of a 500-wavelength-by-100-wavelength dense disordered system can be computed within 3 minutes using one CPU , which is 1,000 to 30,000,000 times faster than existing methods. We have made this code open-source [2]. Using APF , we demonstrate two-photon coherent backscattering from disorder [3], open channel for 3D vectorial waves [4], non-invasive imaging deep inside disorder through scattering matrix tomography [5], and the inverse design of nonlocal metasurfaces [6]. [1] H.-C. Lin, Z. Wang, and C. W. Hsu, Nature Computational Science 2, 815–822 (2022)[2] M. Safadi, O. Lib, H.-C. Lin, C. W. Hsu, A. Goetschy, and Y. Bromberg. Nature Physics (2023)[4] H.-C. Lin and C. W. Hsu, in preparation.[5] Z. Wang, Y. Zhang, and C. W. Hsu, in preparation.[6] S. Li, H.-C. Lin, and C. W. Hsu, in preparation.

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