LIGHT-SCATTERING BY HEXAGONAL ICE CRYSTALS - COMPARISON OF FINITE-DIFFERENCE TIME-DOMAIN AND GEOMETRIC OPTICS MODELS

We have developed a finite-difference time domain (FDTD) method and a novel geometric ray-tracing model for the calculation of light scatter ing by hexagonal ice crystals. In the FDTD method we use a staggered C artesian grid with the implementation of an efficient absorbing bounda ry condition for the truncation of the computation domain. We introduc e the Maxwell-Garnett rule to compute the mean values of the dielectri c constant at grid points to reduce the inaccuracy produced by the sta ircasing approximation. The phase matrix elements and the scattering e fficiencies for the scattering of visible light by two-dimensional lon g circular ice cylinders match closely those computed from the exact s olution for size parameters as large as 60, with maximum differences l ess than 5%. In the new ray-tracing model we invoke the principle of g eometric optics to evaluate the reflection and the refraction of local ized waves, from which the electric and magnetic fields at the particl e surface (near field) can be computed. Based on the equivalence theor em, the near field can subsequently be transformed to the far field, i n which the phase interferences are fully accounted for. The phase fun ctions and the scattering efficiencies for hexagonal ice crystals comp uted from the new geometric ray-tracing method compare reasonably well with the FDTD results for size parameters larger than approximately 2 0. When absorption is involved in geometric ray tracing, the adjusted real and imaginary refractive indices and Fresnel formulas are derived for practical applications based on the fundamental wave theory.