SPECTRAL PROBLEM FOR THE JONES MATRIX IN REMOTE SCATTERING

The paper addresses the study of anisotropy in remote scattering basing on the spectral problem. The spectral problem is formulated as the determination of eigenpolarizations and eigenvalues for the Jones matrix, which describe the optical anisotropy of the medium. Jones matrices of media with complex anisotropy (media characterized by several types of anisotropy) are considered in terms of a homogeneous (differential) approach. The essence of this approach is that the anisotropy of the class of media under consideration does not depend on the thickness of this medium. An analysis of the Jones matrices for arbitrary homogeneous media (media characterized by all four main types of optical anisotropy: linear, circular, phase and amplitude anisotropy) and media characterized by two types of anisotropy as a special case has been peformed. The main tool for such an analysis was the inhomogeneity parameter of the medium, which allows characterizing the latter as a medium with orthogonal or non-orthogonal eigenpolarizations. The study reveals the peculiarities of complex anisotropy types (elliptical birefringence and Hermitian dichroism, improper dichroism, non-Hermitian dichroism, and degenerate anisotropy) based on the inhomogeneity parameter. A geometric interpretation of eigenpolarizations using the inhomogeneity parameter is demonstrated. The conditions for the anisotropy parameters under which the above-mentioned complex types of anisotropy are realized in the studied classes of medium were calculated. The research was motivated by the fundamental results of van de Hulst and Hovenier formed the basis of the analysis of the Jones and Mueller matrices inner structure. The results obtained contribute to a deeper understanding of polarization phenomena in electromagnetic scattering and provide a basis for future research in polarization diagnostics and remote sensing.