FINITE-DIFFERENCE TIME-DOMAIN METHOD FOR LIGHT-SCATTERING BY SMALL ICE CRYSTALS IN 3-DIMENSIONAL SPACE

The finite-difference time domain (FDTD) method for the solution of li ght scattering by nonspherical particles has been developed for small ice crystals of hexagonal shapes including solid and hollow columns, p lates, and bullet rosettes commonly occurring in cirrus clouds. To acc ount for absorption, we have introduced the effective permittivity and conductivity to circumvent the required complex calculations in the d irect discretization of the basic Maxwell equations. In the constructi on of the finite-difference scheme for the: time-marching iteration fo r the near field the mean values of dielectric constants are defined a nd evaluated by the Maxwell-Garnett rule. In computing the scattered f ield in the radiation zone (far field) and the absorption cross sectio n, me have applied a new algorithm involving the integration of the el ectric field over the volume inside the scatterer on the basis of elec tromagnetic principles. This algorithm removes the high-angular-resolu tion requirement in integrating the scattered energy for the computati on of the scattering cross section. The applicability and the accuracy of the FDTD technique in three-dimensional space are validated by com parison with. Mie scattering results for a number of size parameters a nd wavelengths. me demonstrate that neither the conventional geometric optics method nor the Mie theory can be used to approximate the scatt ering, absorption, and polarization features ibr hexagonal ice crystal s with size parameters from approximately 5 to 20. (C) 1996 Optical So ciety of America.