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

Applied Optics, Vol. 39, Issue 30, pp. 5560-5568 (2000)

http://dx.doi.org/10.1364/AO.39.005560

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### Abstract

The applicability of various approximations for computing the absorption efficiency and single-scattering albedo of a randomly oriented hexagonal column is tested versus electromagnetic theory. To calculate the absorption efficiency and single-scattering albedo of the hexagonal column from electromagnetic theory we used a generalization to the separation-of-variables method, which enables continuous calculation of optical properties up to size parameters of 86. We found that the asymptotic absorption efficiency is independent of particle shape, and that, as the size parameter increases, the hexagonal column tends to its asymptotic absorption value more quickly than Mie theory. The asymptotic absorption limit of the hexagonal column is calculated accurately (to within 1%) and rapidly by use of the complex-angular-momentum 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 µm for an ice particle). However, in the resonance region (e.g., 80 µm 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-µm wavelength there is a characteristic ripple structure superimposed on the hexagonal column absorption efficiency solutions between size parameters from approximately 1 to 4. The ripple structure is indicative of surface-wave interference and is similar to the sphere but less pronounced on the hexagonal column. We investigated the applicability of ray tracing for calculating the single-scattering albedo at absorbing 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-µm wavelength. At mid-infrared wavelengths (e.g., 8.5 and 11.9 µm) ray tracing is within 5% of electromagnetic theory for size parameters exceeding 10. We also tested the Bryant and Latimer absorption approximation to anomalous diffraction theory by using the separation-of-variables method.

© 2000 Optical Society of America

**OCIS Codes**

(010.2940) Atmospheric and oceanic optics : Ice crystal phenomena

(080.2720) Geometric optics : Mathematical methods (general)

(260.2110) Physical optics : Electromagnetic optics

(280.0280) Remote sensing and sensors : Remote sensing and sensors

(290.4020) Scattering : Mie theory

**History**

Original Manuscript: November 18, 1999

Revised Manuscript: July 10, 2000

Published: October 20, 2000

**Citation**

Anthony J. Baran and Stephan Havemann, "Comparison of electromagnetic theory and various approximations for computing the absorption efficiency and single-scattering albedo of hexagonal columns," Appl. Opt. **39**, 5560-5568 (2000)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-30-5560

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