26 June 2017 Simulating propagation of coherent light in random media using the Fredholm type integral equation
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Studying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g. Radiative Transfer Theory and Monte Carlo methods) but they do not treat coherence properties of light directly. Some variations of these methods allows to predict behavior of coherent light but only for an averaged realization of the scattering medium. This limits their application in studying many physical phenomena connected to a specific distribution of scattering particles (e.g. laser speckle). In general, numerical simulation of coherent light propagation in a specific realization of random medium is a time- and memory-consuming problem. The goal of the presented research was to develop new efficient method for solving this problem. The method, presented in our earlier works, is based on solving the Fredholm type integral equation, which describes multiple light scattering process. This equation can be discretized and solved numerically using various algorithms e.g. by direct solving the corresponding linear equations system, as well as by using iterative or Monte Carlo solvers. Here we present recent development of this method including its comparison with well-known analytical results and a finite-difference type simulations. We also present extension of the method for problems of multiple scattering of a polarized light on large spherical particles that joins presented mathematical formalism with Mie theory.
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Maciej Kraszewski, Maciej Kraszewski, Jerzy Pluciński, Jerzy Pluciński, } "Simulating propagation of coherent light in random media using the Fredholm type integral equation", Proc. SPIE 10330, Modeling Aspects in Optical Metrology VI, 1033002 (26 June 2017); doi: 10.1117/12.2270313; https://doi.org/10.1117/12.2270313

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