Geodesic
Construction of the Rayleigh approximation for axisymmetric multilayered particles using the eigenfunctions of the Laplace operator
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 187-211 
V. G. Farafonov; M. V. Sokolovskaja. Construction of the Rayleigh approximation for axisymmetric multilayered particles using the eigenfunctions of the Laplace operator. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 42, Tome 409 (2012), pp. 187-211. http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a11/
@article{ZNSL_2012_409_a11,
     author = {V. G. Farafonov and M. V. Sokolovskaja},
     title = {Construction of the {Rayleigh} approximation for axisymmetric multilayered particles using the eigenfunctions of the {Laplace} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--211},
     year = {2012},
     volume = {409},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a11/}
}
TY  - JOUR
AU  - V. G. Farafonov
AU  - M. V. Sokolovskaja
TI  - Construction of the Rayleigh approximation for axisymmetric multilayered particles using the eigenfunctions of the Laplace operator
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 187
EP  - 211
VL  - 409
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a11/
LA  - ru
ID  - ZNSL_2012_409_a11
ER  - 
%0 Journal Article
%A V. G. Farafonov
%A M. V. Sokolovskaja
%T Construction of the Rayleigh approximation for axisymmetric multilayered particles using the eigenfunctions of the Laplace operator
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 187-211
%V 409
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_409_a11/
%G ru
%F ZNSL_2012_409_a11

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The Rayleigh approximation is constructed from solution of the electrostatic problem for axisymmetric multilayered particles. The approach used is based on consideration of the surface integral equations analogous to those used in the extended boundary condition method (EBCM) applied to solve the electromagnetic problems. The electric fields are related with the scalar potentials that are represented by their expansions in terms of the eigenfunctions of the Laplace operator written in spheroidal and spherical coordinates. The unknown expansion coefficients are derived from infinite linear algebraic equations. The explicit solution found in spheroidal coordinates for multilayered spheroids coincides with the known solutions for the homogeneous and core-mantle particles.

[1] Kh. K. Van de Khyulst, Rasseyanie sveta malymi chastitsami, IL, M., 1961

[2] K. Boren, D. Khaffmen, Pogloschenie i rasseyanie sveta malymi chastitsami, Mir, M., 1986

[3] F. M. Morc, G. Feshbakh, Metody teoreticheskoi fiziki, IL, M., 1958

[4] L. D. Landau, E. M. Livshits, Elektrodinamika sploshnykh sred, Nauka, M., 1982

[5] V. V. Klimov, Nanoplazmonika, Fizmatlit, M., 2009

[6] M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles, Academic Press, San Diego, 2000

[7] M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles, Cambridge Univ. Press, Cambridge, 2002

[8] V. G. Farafonov, “Difraktsiya ploskoi elektromagnitnoi volny na dielektricheskom sferoide”, Differents. uravn., 19 (1983), 1765–1777 | MR

[9] N. V. Voshchinnikov, V. G. Farafonov, “Optical properties of spheroidal particles”, Astrophys. Space Sci., 204 (1993), 19–86 | DOI

[10] V. G. Farafonov, N. V. Voshchinnikov, V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle”, Appl. Opt., 35 (1996), 5412–5426 | DOI

[11] V. G. Farafonov, N. V. Voshchinnikov, “Light scattering by a multilayered spheroidal particle”, Appl. Opt., 51 (2012), 1586–1597 | DOI

[12] V. G. Farafonov, “Novoe reshenie zadachi rasseyaniya ploskoi volny mnogosloinym nekonfokalnym sferoidom”, Opt. spektr., 114:3 (2013) (to appear)

[13] H. Kang, G. W. Milton, “Solutions to the Polya–Szego Conjecture and the Weak Eshelby Conjecture”, Arch. Ration. Mech. Anal., 188 (2008), 93–116 | DOI | MR | Zbl

[14] V. G. Farafonov, A. A. Vinokurov, S. V. Barkanov, “Elektrostaticheskoe reshenie i priblizhenie Releya dlya malykh nesfericheskikh chastits v sferoidalnom bazise”, Opt. spektr., 111:6 (2011), 1026–1038 | MR

[15] D. Kolton, R. Kress, Metody integralnykh uravnenii v teorii rasseyaniya, Mir, M., 1987 | MR

[16] V. G. Farafonov, V. B. Il'in, “Single light scattering: computational methods”, Light Scattering Reviews, ed. A. A. Kokhanovsky, Springer-Praxis, Berlin, 2006, 125–177 | DOI

[17] V. I. Komarov, L. I. Ponomarev, S. Yu. Slavyanov, Sferoidalnye i kulonovskie sferoidalnye funktsii, Nauka, M., 1976 | MR