Extending Rytov Approximation to Vector Waves for Tomography of Anisotropic Materials

Liquid crystal phases exhibit distinctive properties due to their unique molecular ordering, making them central to materials science and soft matter physics. Their orientational ordering induces birefringence, which can be detected by optical microscopy. However, the analysis of 3D orientation, material distribution, and anisotropy from scattered light poses significant challenges due to the vector nature of the light-matter interaction. In this study, we formulate a scattering theory based on the Rytov approximation, commonly employed in scalar wave tomography, tailored to accommodate vector waves by modifying the scattering matrix. Using this formulation, we reveal the intricate 3D structure of liquid crystals with multiple topological defects. Specifically, we visualize the 3D structures of topological defects that were indistinguishable using conventional 2D imaging methods.