Ray optics for absorbing particles with application to ice crystals at near-infrared wavelengths

Highlights: • We derived a ray-optics solution that takes into account the inhomogeneous waves for absorbing particles large compared to the wavelength of light. • We evaluated the solution through comparisons against an exact method, the discrete exterior calculus. • We computed scattering for ice crystals through the NIR spectrum, and found a systematic increase in the single-scattering albedo when inhomogeneous waves were considered. Light scattering by particles large compared to the wavelength of incident light is traditionally solved using ray optics which considers absorption inside the particle approximately, along the ray paths. To study the effects rising from this simplification, we have updated the ray-optics code SIRIS to take into account the propagation of light as inhomogeneous plane waves inside an absorbing particle. We investigate the impact of this correction on traditional ray-optics computations in the example case of light scattering by ice crystals through the extended near-infrared (NIR) wavelength regime. In this spectral range, ice changes from nearly transparent to opaque, and therefore provides an interesting test case with direct connection and applicability to atmospheric remote-sensing measurements at NIR wavelengths. We find that the correction for inhomogeneous waves systematically increases the single-scattering albedo throughout the NIR spectrum for both randomly-oriented, column-like hexagonal crystals and ice crystals shaped like Gaussian random spheres. The largest increase in the single-scattering albedo is 0.042 for hexagonal crystals and 0.044 for Gaussian random spheres, both at $\lambda =2.725$ µm. Although the effects on the 4 × 4 scattering-matrix elements are generally small, the largest differences are seen at 2.0 µm and 3.969 µm wavelengths where the correction for inhomogeneous waves affects mostly the backscattering hemisphere of the depolarization-connected P₂₂/P₁₁, P₃₃/P₁₁, and P₄₄/P₁₁. We evaluated the correction for inhomogeneous waves through comparisons against the discrete exterior calculus (DEC) method. We computed scattering by hexagonal ice crystals using the DEC, a traditional ray-optics code (SIRIS3), and a ray-optics code with inhomogeneous waves (SIRIS4). Comparisons of the scattering-matrix elements from SIRIS3 and SIRIS4 against those from the DEC suggest that consideration of the inhomogeneous waves brings the ray-optics solution generally closer to the exact result and, therefore, should be taken into account in scattering by absorbing particles large compared to the wavelength of incident light.