We have developed a theory for the computation of the polarization of infrared radiation in optically anisotropic media, with specific application to horizontally oriented ice crystals that frequently occur in cirrus clouds. Both emission and scattering contributions are accounted for in the basic formulation concerning the transfer of thermal radiation in anisotropic media. The symmetry relations of the phase matrix elements for horizontally oriented ice crystals, which are required in the infrared polarization formulations, are presented for the first time to our knowledge. Phase matrix elements for horizontally oriented hexagonal ice crystals are computed by a geometric ray-tracing technique. Radiance and linear-polarization patterns at a 10-μm wavelength that are emergent from cirrus clouds that contain plates and columns oriented in two-dimensional space are presented and discussed in physical terms. Downward polarization emergent from the cloud base is negative, while upward polarization emergent from the cloud top has a positive maximum value near the limb directions. These polarization configurations differ distinctly from the configurations of polarization emergent from ice clouds that contain randomly oriented ice crystals in three-dimensional space. Given these results, it appears feasible to infer the orientation characteristics of ice crystals in cirrus clouds with the use of infrared polarization measurements either above or below the cloud.
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