Polarized light scattering by hexagonal ice crystals: theory

A scattering model involving complete polarization information for arbitrarily oriented hexagonal columns and plates is developed on the basis of the ray tracing principle which includes contributions from geometric reflection and refraction and Fraunhofer diffraction. We present a traceable and analytic procedure for computation of the scattered electric field and the associated path length for rays undergoing external reflection, two refractions, and internal reflections. We also derive an analytic expression for the scattering electric field in the limit of Fraunhofer diffraction due to an oblique hexagonal aperture. Moreover the theoretical foundation and procedures are further developed for computation of the scattering phase matrix containing 16 elements for randomly oriented hexagonal crystals. Results of the six independent scattering phase matrix elements for randomly oriented large columns and small plates, having length-to-radius ratios of 300/60 and 8/10 microm, respectively, reveal a number of interesting and pronounced features in various regions of the scattering angle when a visible wavelength is utilized in the ray tracing program. Comparisons of the computed scattering phase function, degree of linear polarization, and depolarization ratio for randomly oriented columns and plates with the experimental scattering data obtained by Sassen and Liou for small plates are carried out. We show that the present theoretical results within the context of the geometric optics are in general agreement with the laboratory data, especially for the depolarization ratio.