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.
Similar content being viewed by others
References
H. C. van de Hulst, Scattering of Light by Small Particles [Russian translation], In. Lit., Moscow (1961).
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles [Russian translation], Mir, Moscow (1986).
M. I. Mishchenko, J. M. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles. San Diego, Academic Press (2000).
F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectr. Rad. Transf., 79–80, 775 (2003).
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.
N. V. Voshchinnikov and V. G. Farafonov, Astrophys. Sp. Sci., 204, 19 (1993).
Y. Han Y. and Z. Wu, “Scattering of a spheroidal particle illuminated by a Gaussian beam,” Appl. Opt., 40, 2501 (2001).
J. P. Barton, “Electromagnetic field calculations for an irregularly shaped, near-spheroidal particle with arbitrary illumination,” J. Opt. Soc. Amer. A., 19, 2429 (2002).
V. G. Farafonov, A. A. Vinokurov, and V. B. Il’in, Opt. Spektr, 102, 741 (2007).
V. G. Farafonov, Opt. Spektr, 30, 826 (2001).
F. M. Kahnert, “Surface-integral formulation for electromagnetic scattering in spheroidal coordinates,” J. Quant. Spectr. Rad. Transf., 77, 61 (2003).
V. B. Il’in, V. G. Farafonov, and E. V. Farafonov, Opt. Spektr, 102, 136 (2007).
V. G. Farafonov and V. B. Il’in, “Modification and investigation of the point-matching method,” Opt. Spektr, 100, 484 (2006).
D. Colton and R. Kress, Methods of Integral Equations in Scattering Theory [Russian translation], Mir, Moscow (1987).
J. A. Stratton, Theory of Electromagnetism [Russian translation], GITTL (1948).
P. M. Morse and H. Feshbach, Methods of Theoretical Physics [Russian translation], In. Lit. (1958).
V. I. Komarov, L. I. Ponomarev, and S. Yu. Slavyanov, Spheroidal and Coulomb Spheroidal Functions [in Russian], Nauka, Moscow (1976).
V. G. Farafonov, “Diffraction of a plane electromagnetic wave by a dielectric spheroid,” Diff. Uravn., 19, 1765 (1983).
V. G. Farafonov, Opt. Spektr, 92, 813 (2002).
V. F. Apeltsyn and A. G. Kyurkchan, Analytic Properties of Wave Fields [in Russian], MGU, Moscow (1990).
V. G. Farafonov, N. V. Voshchinnikov, and V. V. Somsikov, Appl. Opt., 35, 5412(1996).
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Vasilii Mikhailovich Babich with sincere gratitude
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 380, 2010, pp. 132–178.
Rights and permissions
About this article
Cite this article
Farafonov, V.G. A unified approach, using spheroidal functions, for solving the problem of light scattering by axisymmetric particles. J Math Sci 175, 698–723 (2011). https://doi.org/10.1007/s10958-011-0384-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-011-0384-9