A ray-by-ray integration (RBRI) method has been developed for the solution of light scattering by nonspherical dielectric particles. The principles of geometric optics are applied to solve the internal electric field within the scattering particles (near field) with the inclusion of complete phase and polarization configurations. The scattered field at the radiation zone (far field) and the extinction and absorption cross sections are obtained by integrating the near field along the propagation paths of geometric rays inside the scatterers by using a number of rigorous electromagnetic integral equations. In the computations of extinction cross section and single-scattering albedo, we demonstrate that the well-known anomalous diffraction approximation is a special case of the RBRI method when the scatterers are optically tenuous. The RBRI method is employed to compute the single-scattering properties of hexagonal ice crystals at visible and near-infrared wavelengths. Based on the reference results computed by the finite-difference time domain (FDTD) technique, we show that the RBRI method is more accurate than the conventional geometric ray-tracing technique and the anomalous diffraction approximation. The extinction efficiency and the single-scattering albedo computed by the RBRI method converge to the reference results when the size parameters along the ice crystal maximum dimension are larger than approximately 15. Substantial differences in terms of relative errors, in comparison with the FDTD solutions, are still noted in the phase function and polarization patterns computed by the RBRI method for size parameters of the order of 10.
© 1997 Optical Society of America
Original Manuscript: August 19, 1996
Revised Manuscript: January 21, 1997
Manuscript Accepted: January 21, 1997
Published: September 1, 1997
Ping Yang and K. N. Liou, "Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm," J. Opt. Soc. Am. A 14, 2278-2289 (1997)