Ice-crystal absorption: a comparison between theory and implications for remote sensing

Light extinction and absorption by arbitrarily oriented finite circular cylinders by use of geometrical path statistics of rays

From the geometrical path statistics of rays in an anomalous-diffraction theory (ADT) [Opt. Lett. 28, 179 (2003)] closed-form expressions for the geometrical path distribution of rays and analytical formulas for the optical efficiencies of finite circular cylinders oriented in an arbitrary direction with respect to the incident light are derived. The characteristics of the shapes of the cylinders produce unique features in the geometrical path distributions of the cylinders compared with spheroids. Gaussian ray approximations, which depend only on the mean and the mean-squared geometrical paths of rays, of the optical efficiencies of finite circular cylinders and spheroids are compared with the exact optical efficiencies in ADT. The influence of the difference in shape between cylinders and spheroids on the optical efficiencies in ADT is illustrated by their respective geometrical path distributions of rays.

Light scattering on hexagonal ice columns

Light scattering on finite dielectric cylinders having noncircular cross sections has become of growing importance in remote-sensing applications. For analyzing their scattering characteristics at moderate size parameters, i.e., at a region where ray-tracing techniques fail, a few methods have been developed, among which an approximation based on the generalized separation-of-variables method has become very successful. This approach reveals two interesting features, which we discuss, that reduce the numerical effort drastically if applied to hexagonal (in general, 2n-periodic) boundary surfaces. Finally, some results for the phase function of hexagonal ice columns are given.

Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results

A general method is developed to formulate extinction and absorption efficiency for nonspherical particles at arbitrary and random orientations by use of anomalous diffraction theory (ADT). An ADT for finite circular cylinders is evaluated as an example. Existing ADT's for infinite cylinders at arbitrary orientations and for finite cylinders at the normal incidence are shown to be special cases of the new formulation. ADT solutions for finite cylinders are shown to approach the rigorous T-matrix results when the refractive indices approach unity. The importance of some physical processes that are neglected in the ADT approximation are evaluated by comparisons between ADT and rigorous calculations for different particle geometries. For spheres, van de Hulst's ADT and Mie theory are used, whereas the ADT that we present and T-matrix calculations are used for cylinders of different diameter-to-length ratios. The results show that the differences in extinction between ADT and exact solutions generally decrease with nonsphericity. A similar decrease occurs for absorption at wavelengths of relatively strong absorption. The influence of complex refractive index is evaluated. Our results suggest that ADT may provide a useful approximation in parameterization and remote sensing of cirrus clouds in the Christiansen bands where the real part of the refractive index approaches unity and/or where relative absorption is strong.