Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns

The applicability of various approximations for computing the absorption ef ficiency and single-scattering albedo of a randomly oriented hexagonal colu mn is tested versus electromagnetic theory. To calculate the absorption eff iciency and single-scattering albedo of the hexagonal column from electroma gnetic theory we used a generalization to the separation-of-variables metho d, which enables continuous calculation of optical properties up to size pa rameters of 86. We found that the asymptotic absorption efficiency is indep endent of particle shape, and that, as the size parameter increases, the he xagonal column tends to its asymptotic absorption value more quickly than M ie theory. The asymptotic absorption limit of the hexagonal column is calcu lated accurately (to within 1%) and rapidly by use of the complex-angular-m omentum approximation, indicating that this approximation could be used to calculate the absorption limit of nonspherical particles. The equal-volume sphere best approximates the hexagonal column single-scattering albedo at a strongly absorbing wavelength (e.g., 11.9 mu m for an ice particle). Howev er, in the resonance region (e.g., 80 mu m for an ice particle) Mie theory fails to approximate the single-scattering albedo of the hexagonal column, but as the size parameter exceeds 10 the error in the sphere approximation reduces to within 2%. At 80-mu m wavelength there is a characteristic rippl e structure superimposed on the hexagonal column absorption efficiency solu tions between size parameters from approximately I to 4. The ripple structu re is indicative of surface-wave interference and is similar to the sphere but less pronounced on the hexagonal column. We investigated the applicabil ity of ray tracing for calculating the single-scattering albedo at absorbin g wavelengths relevant to remote sensing of ice particles in the atmosphere and found it to be within 4% for size parameters between 3 and 42 at 3.7-m u m wavelength. At mid-infrared wavelengths (e.g., 8.5 and 11.9 mu m) ray t racing is within 5% of electromagnetic theory for size parameters exceeding 10. We also tested the Bryant and Latimer absorption approximation to anom alous diffraction theory by using the separation-of-variables method. (C) 2 000 Optical Society of America OCIS codes: 080.2720, 010.2940, 260.2110, 28 0.0280, 290.4020.