Abstract
We have constructed a solution to the problem of scattering by a nonconfocal multilayer particle. The main difficulty was to join expansions constructed in two spheroidal systems on either side of each boundary. As a result of a detailed consideration of relations between scalar wave spheroidal and spherical functions, we have succeeded in finding a representation of the former in terms of the latter and vice versa. In the final form, the joining of solutions is described by only one matrix, which depends on coefficients of representations of angle spheroidal functions in terms of associated Legendre functions of the first kind. Since the problem has been solved using an approach that involves the method of extended boundary conditions, the dimension of the system for numerical determining unknown coefficients is equal to the number of terms that are taken into account in field expansions and does not depend on the number of particle layers. Previously performed numerical calculations for confocal particles have shown a very high efficiency of the algorithm not only for particles that are close to spheres in shape, but also for strongly prolate and strongly oblate spheroids. In addition, the algorithm makes it possible to calculate optical properties of particles that have dozens of layers.
Similar content being viewed by others
References
V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transfer 79–80, 599 (2003).
F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
A. Vinokurov, V. Farafonov, and V. Il’in, J. Quant. Spectrosc. Radiat. Transfer 110, 1356 (2009).
T. Onaka, Ann. Tokyo Astron. Observ. 18, 1 (1980).
V. Farafonov, N. Voshchinnikov, and V. Somsikov, Appl. Opt. 35, 5412 (1996).
I. Ciric and F. Corray, in Light Scattering by Non-Spherical Particles, Ed. by M. I. Mishchenko, J. W. Hovenier, and L. D. Travis (Academic, San Diego, 2000), pp. 89–130.
I. Gurwich, M. Kleiman, N. Shiloah, and B. Oaknin, J. Quant. Spectrosc. Radiat. Transfer 79–80, 649 (2003).
V. G. Farafonov, J. Math. Sci. 175, 698 (2011).
V. Farafonov and N. Voshchinnikov, Appl. Opt. 51, 1586 (2012).
V. G. Farafonov, Opt. Spektrosk. 90(5), 826 (2001).
Y. Han, H. Zhang, and X. Sun, Appl. Phys. 84, 485 (2006).
I. V. Komarov, L. N. Ponamorev, and S. Yu. Slavyanov, Spheroidal and Coulombian Spheroidal Functions (Nauka, Moscow, 1976).
V. Farafonov and V. Il’in, in Ligh Scattering Reviews, Ed. by A. A. Kokhanovsky (Springer-Praxis, Berlin, 2006), pp. 125–177.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.G. Farafonov, 2013, published in Optika i Spektroskopiya, 2013, Vol. 114, No. 3, pp. 462–473.
Rights and permissions
About this article
Cite this article
Farafonov, V.G. A new solution to the problem of scattering of a plane wave by a multilayer confocal spheroid. Opt. Spectrosc. 114, 421–431 (2013). https://doi.org/10.1134/S0030400X13030090
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0030400X13030090