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Applied Optics

Applied Optics


  • Vol. 31, Iss. 3 — Jan. 20, 1992
  • pp: 373–386

Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel–Kramers–Brillouin method

James D. Klett and Robert A. Sutherland  »View Author Affiliations

Applied Optics, Vol. 31, Issue 3, pp. 373-386 (1992)

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Several approximate methods for modeling the electromagnetic (em) scattering properties of nonspherical particles are examined and evaluated. Although some of the approaches are applicable to arbitrary shapes we confine our attention here mainly to spheres and cylinders, for which exact solutions are available for comparisons. Evaluations include comparisons of the computed angular phase function, total extinction efficiency, and backscatter efficiency. Approximate methods investigated include the Rayleigh–Gans (RG) approximation, the Wentzel–Kramers–Brillouin or WKB approximation [and the closely related eikonal approximation (EA)], diffraction theory, and the second-order Shifrin iterative technique. Examples using spheres indicate that for weakly absorbing particles of moderate- to large-size parameters with a real refractive index near unity (i.e., the optically soft case), all models work well in representing the phase function over all scattering angles, with the Shifrin approximation showing the best agreement with the exact solutions. For larger refractive indices, however, the Shifrin approximation breaks down, whereas the WKB method continues to perform relatively well for all scattering angles over a wide range of particle sizes, including those appropriate in both the RG (small particle) and the diffraction (large particle) limits. The relationship between the WKB, eikonal, and anomalous diffraction descriptions of particle extinction is discussed briefly. Backscatter is also discussed in the context of the WKB model, and two modifications to improve the description are included: one to add an internal-reflected internal wave and the other to add a multiplicative scaling factor to preserve the correct backscatter result for strong absorption in the geometric optics limit. A major conclusion of the paper is that the WKB method offers a viable alternative to the more widely used RG and diffraction approximations and is a method that offers significant improvement in accuracy with only a slight increase in mathematical complexity.

© 1992 Optical Society of America

Original Manuscript: February 7, 1990
Published: January 20, 1992

James D. Klett and Robert A. Sutherland, "Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel–Kramers–Brillouin method," Appl. Opt. 31, 373-386 (1992)

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  1. B. R. Johnson, “Invariant imbedding T matrix approach to electromagnetic scattering,” Appl. Opt. 27, 4861–4873 (1988). [CrossRef] [PubMed]
  2. G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988). [CrossRef] [PubMed]
  3. M. F. Iskander, A. Lakhtakia, C. H. Durney, “A new procedure for improving the solution stability and extending the frequency range of the EBCM,” IEEE Trans. Antennas Propag. AP-31, 317–324 (1983). [CrossRef]
  4. K. S. Shifrin, Scattering of Light in a Turbid Medium (Moscow, 1951); NASA Tech. Transl. TT F-477 (National Technical Information Service, Springfield, VA, 1968).
  5. C. Acquista, “Light scattering by tenuous particles: a generalization of the Rayleigh-Gans-Rocard approach,” Appl. Opt. 15, 2932–2936 (1976). [CrossRef] [PubMed]
  6. D. S. Saxon, “Lectures on the scattering of light,” UCLA Department of Meterological Science Rep. 9 (University of California at Los Angeles, Los Angeles, Calif., 1955).
  7. D. S. Saxon, in UCLA Conference on Radiation and Remote Probing of the Atmosphere, J. G. Kuriyan, ed. (University of California at Los Angeles, Los Angeles, Calif., 1974), pp. 227–308.
  8. Y. Ikeda, “Extension of the Rayleigh-Gans theory,” in Electromagnetic Scattering, M. Kerker, ed. (Pergamon, Oxford, 1963).
  9. L. D. Cohen, R. D. Haracz, A. Cohen, C. Acquista, “Scattering of light from arbitrarily oriented finite cylinders,” Appl. Opt. 22, 742–748 (1983). [CrossRef] [PubMed]
  10. R. D. Haracz, L. D. Cohen, A. Cohen, “Perturbation theory for scattering from dielectric spheroids and short cylinders,” Appl. Opt. 23, 436–441 (1984). [CrossRef] [PubMed]
  11. R. D. Haracz, L. D. Cohen, A. Cohen, “Scattering of linearly polarized light from randomly oriented cylinders and spheroids,” J. Appl. Phys. 58, 3322–3327 (1985). [CrossRef]
  12. R. D. Haracz, L. D. Cohen, A. Cohen, R. T. Wang, “Scattering of linearly polarized microwave radiation from a dielectric helix,” Appl. Opt. 26, 4632–4638 (1987). [CrossRef] [PubMed]
  13. J. W. S. Rayleigh, “On the propagation of waves through a stratified medium, with special reference to the question of reflection,” Proc. R. Soc. London Ser. A 86, 207–223 (1912). [CrossRef]
  14. H. Jeffreys, “On certain approximate solutions of linear differential equations of the second order,” Proc. London Math. Soc., 23, 428–436 (1923). [CrossRef]
  15. H. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  16. D. Deirmendjian, “Theory of the solar aureole, part II: applications to atmospheric models,” Ann. Geophys. 15, 218–249. (1959).
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  18. T. W. Chen, “High energy light scattering in the generalized eikonal approximation,” Appl. Opt. 28, 4096–4102 (1989). [CrossRef] [PubMed]
  19. S. K. Sharma, D. J. Somerford, “The eikonal approximation revisited,” Nuovo Cimento 12, 719–748 (1990). [CrossRef]
  20. L. P. Bayvel, A. R. Jones, Electromagnetic Scattering and its Applications (Applied Science, London, 1981). [CrossRef]
  21. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).
  22. G. L. Stephens, “Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders,” Appl. Opt. 23, 954–959 (1984). [CrossRef] [PubMed]

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