Journal of Mathematical Sciences

, Volume 175, Issue 6, pp 698–723 | Cite as

A unified approach, using spheroidal functions, for solving the problem of light scattering by axisymmetric particles


A theory that joins three well-known methods is suggested. These methods are the separation of variables, extended boundary conditions and point matching, where the fields are represented by their expansions in (spheroidal) wave functions. Applying similar field expansions, the methods essentially differ in formulation of the problem, and thus they were always discussed in the literature independently. An original approach is employed, in which the fields are divided in two parts with certain properties, and special scalar potentials are selected for each of the parts. The theory allows one to see the similarity and differences of the methods under consideration. Analysis performed earlier shows that the methods significantly supplement each other and the original approach used with a spheroidal basis gives reliable results for particles of high eccentricity for which other techniques do not work. Thus, the suggested theory provides a ground for development of a universal efficient algorithm for calculating optical characteristics of nonspherical scatterers in a very wide region of their parameter values. Bibliography: 21 titles.


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  1. 1.
    H. C. van de Hulst, Scattering of Light by Small Particles [Russian translation], In. Lit., Moscow (1961).Google Scholar
  2. 2.
    C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles [Russian translation], Mir, Moscow (1986).Google Scholar
  3. 3.
    M. I. Mishchenko, J. M. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles. San Diego, Academic Press (2000).Google Scholar
  4. 4.
    F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectr. Rad. Transf., 79–80, 775 (2003).CrossRefGoogle Scholar
  5. 5.
    V. G. Farafonov and V. B. Il’in,“Single light scattering: computational methods,” in: A. A. Kokhanovsky (ed.) Light Scattering Reviews, Berlin, Springer-Praxis (2006), p. 125.CrossRefGoogle Scholar
  6. 6.
    N. V. Voshchinnikov and V. G. Farafonov, Astrophys. Sp. Sci., 204, 19 (1993).CrossRefGoogle Scholar
  7. 7.
    Y. Han Y. and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt., 40, 2501 (2001).CrossRefGoogle Scholar
  8. 8.
    J. P. Barton, “Electromagnetic field calculations for an irregularly shaped, near-spheroidal particle with arbitrary illumination,” J. Opt. Soc. Amer. A., 19, 2429 (2002).MathSciNetCrossRefGoogle Scholar
  9. 9.
    V. G. Farafonov, A. A. Vinokurov, and V. B. Il’in, Opt. Spektr, 102, 741 (2007).Google Scholar
  10. 10.
    V. G. Farafonov, Opt. Spektr, 30, 826 (2001).Google Scholar
  11. 11.
    F. M. Kahnert, “Surface-integral formulation for electromagnetic scattering in spheroidal coordinates,” J. Quant. Spectr. Rad. Transf., 77, 61 (2003).CrossRefGoogle Scholar
  12. 12.
    V. B. Il’in, V. G. Farafonov, and E. V. Farafonov, Opt. Spektr, 102, 136 (2007).Google Scholar
  13. 13.
    V. G. Farafonov and V. B. Il’in, “Modification and investigation of the point-matching method,” Opt. Spektr, 100, 484 (2006).Google Scholar
  14. 14.
    D. Colton and R. Kress, Methods of Integral Equations in Scattering Theory [Russian translation], Mir, Moscow (1987).Google Scholar
  15. 15.
    J. A. Stratton, Theory of Electromagnetism [Russian translation], GITTL (1948).Google Scholar
  16. 16.
    P. M. Morse and H. Feshbach, Methods of Theoretical Physics [Russian translation], In. Lit. (1958).Google Scholar
  17. 17.
    V. I. Komarov, L. I. Ponomarev, and S. Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions [in Russian], Nauka, Moscow (1976).Google Scholar
  18. 18.
    V. G. Farafonov, “Diffraction of a plane electromagnetic wave by a dielectric spheroid,” Diff. Uravn., 19, 1765 (1983).MathSciNetGoogle Scholar
  19. 19.
    V. G. Farafonov, Opt. Spektr, 92, 813 (2002).Google Scholar
  20. 20.
    V. F. Apeltsyn and A. G. Kyurkchan, Analytic Properties of Wave Fields [in Russian], MGU, Moscow (1990).Google Scholar
  21. 21.
    V. G. Farafonov, N. V. Voshchinnikov, and V. V. Somsikov, Appl. Opt., 35, 5412(1996).CrossRefGoogle Scholar

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© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.State University of Aerocosmic InstrumentationSt.PetersburgRussia

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