Minimum principles in electromagnetic scattering by small aspherical particles: Extension to differential cross-sections

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Department of Physics


In this work we extend earlier findings that optically small and randomly oriented ovaloids extinguish more radiation than equal volume spheres [1], to differential cross-sections. Rather than working with the normalized phase function as is typically done in radiative transfer and in remote sensing, we compute absolute un-normalized differential scattering cross-sections Cscatt(θ) and show that for optically small to moderate size parameters, not only does the integrated extinction by randomly oriented spheroids Cext(θ) exceed that of equal volume spheres but it does so at each scattering angle (θ). Furthermore, at each θ, the effect is monotonic with the aspect ratio (AR) and its magnitude is appreciable for realistic refraction indices of terrestrial aerosols. Spherical shape optimality holds for absorption cross-sections as well. Absorption is not only volume-dependent but increases substantially with asphericity, rising by two orders of magnitude near resonant lines. We also compare the asymmetry parameter (g) and single scattering albedo (ω0) of randomly oriented spheroids to that of equal volume spheres and find that while the dependence of the ratios on the axis ratio is monotonic, change of either sign is possible, depending on the index of refraction. Ice in the microwave and quartz in the thermal IR are used to illustrate applications in atmospheric remote sensing.

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Journal of Quantitative Spectroscopy and Radiative Transfer