Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space

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Abstract
The finite-difference time domain (FDTD) method for the solution of light scattering by nonspherical particles has been developed for small ice crystals of hexagonal shapes including solid and hollow columns, plates, and bullet rosettes commonly occurring in cirrus clouds. To account for absorption, we have introduced the effective permittivity and conductivity to circumvent the required complex calculations in the direct discretization of the basic Maxwell equations. In the construction of the finite-difference scheme for the time-marching iteration for the near field the mean values of dielectric constants are defined and evaluated by the Maxwell–Garnett rule. In computing the scattered field in the radiation zone (far field) and the absorption cross section, we have applied a new algorithm involving the integration of the electric field over the volume inside the scatterer on the basis of electromagnetic principles. This algorithm removes the high-angular-resolution requirement in integrating the scattered energy for the computation of the scattering cross section. The applicability and the accuracy of the FDTD technique in three-dimensional space are validated by comparison with Mie scattering results for a number of size parameters and wavelengths. We demonstrate that neither the conventional geometric optics method nor the Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20.