Extended scattering channels for random matrix simulations of polarized light transport

Abstract

Modeling the propagation of light through disordered media is central to understanding and controlling wave transport in diverse optical and mesoscopic applications. Here, we present a random matrix simulation framework for modeling the transport of polarized light through random media composed of arbitrary particulate scatterers. Our approach employs extended scattering channels applied to angular spectral decompositions of the underlying fields, enabling flexible representations of arbitrary illumination and detection profiles. In contrast to previous work, this framework provides a rigorous treatment of scattering matrix correlations and offers novel geometric insights into the optical memory effect. We provide a detailed exposition of the underlying theory and illustrate several key features through numerical simulations. Our work is supported by a free accompanying codebase.

Figures (7)

• Figure 1: Example scattering channel partitions of $K$: (a) square lattice, (b) hexagonal lattice, (c) polar grid, and (d) randomly generated Voronoi diagram. In (a), several regions are indexed according to the indexing scheme described in the text.
• Figure 2: 3-dimensional analogue of the intersection $(K_i \times K_j \times K_u \times K_v)\cap \Pi_x \cap \Pi_y$. Going from (a) to (d), the line segment associated with the cube's vertical axis is translated vertically downwards, causing the cube to shift downwards relative to the planes and the intersection to decrease in length.
• Figure 3: Left $y$-axis: 6-dimensional intersection volume $\sigma$ as a function of the dual-lattice radius $|\mathbf{q}_{ijuv,0}|$. Right $y$-axis: relative frequency of region quadruples at a given dual-lattice radius. Insets: examples of dual-lattice radii for (a) square and (b) hexagonal grids.
• Figure 4: Incident and reflected fields for Hermite--Gaussian illumination. The top row, (a) and (b), shows the incident field, while the bottom row, (c) and (d), shows the reflected field. The first column, (a) and (c), shows the magnitude of the $y$-component of the Fourier-space representation of the field, while the second column, (b) and (d), shows the magnitude of the $y$-component of the field at the front face of the scattering medium. Each plot uses an independent color map in arbitrary units.
• Figure 5: (a)--(c): Fourier-space intensity of the field reflected by a thin scattering medium under illumination by three $x$-polarized plane waves with distinct incident wavevectors. Prominent features that shift in accordance with the memory effect are highlighted by dashed white boxes. (d): Argument of the ratio of the reflected field due to a tilted and untitled incident plane wave.