Abstract
The applicability of an analog of the extended boundary condition method, which is popular in light-scattering theory, is studied in combination with the standard spherical basis for the solution of an electrostatic problem appearing for spheroidal layered scatterers the sizes of which are small as compared to the incident radiation wavelength. In the case of two or more layers, polarizability and other optical characteristics of particles in the far zone are shown to be undeterminable if the condition under which the appearing systems of linear equations for expansion coefficients of unknown fields are Fredholm systems solvable by the reduction method is broken. For two-layer spheroids with confocal boundaries, this condition is transformed into a simple restriction on the ratio of particle semiaxes a/b< \(\sqrt 2 \) + 1. In the case of homogeneous particles, the solvability condition is that the radius of convergence of the internal-field expansion must exceed that of the expansion of an analog of the scattering field. Since homogeneous spheroids (ellipsoids) are unique particles inside which the electrostatic field is homogeneous, it is shown that the solution can be always found in this case. The obtained results make it possible to match in principle the results of theoretical and numerical determinations of the domain of applicability for the extended boundary condition method with a spherical basis for spheroidal scatterers.
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References
P. Barber and C. Yeh, Appl. Opt. 14, 2864 (1975).
F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
V. G. Farafonov and V. B. Il’in, Single Light Scattering: Computational Methods. Light Scattering Reviews, Ed. by A. A. Kokhanovsky (Springer-Praxis, Berlin, 2006).
R. F. Millar, Rad. Sci. 8, 785 (1973).
A. G. Kyurkchan and A. I. Kleev, Radiotekh. Elektron. (Moscow) 40, 897 (1995).
A. G. Dallas, Techn. Rept. Univ. Delaware 7, 1 (2000).
V. G. Farafonov, Opt. Spektrosk. 92(6), 813 (2002).
V. G. Farafonov, V. B. Il’in, and M. S. Prokopjeva, J. Quant. Spectrosc. Radiat. Transfer 79–90, 599 (2003).
A. A. Vinokurov, V. G. Farafonov, and V. B. Il’in, J. Quant. Spectrosc. Radiat. Transfer 110, 1356 (2009).
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983; Mir, Moscow, 1986).
V. G. Farafonov and M. V. Sokolovskaya, J. Math. Sci. 194, 104 (2013).
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, New York, 1984; Mir, Moscow, 1987).
P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953; Inostrannaya Literatura, Moscow, 1958, 1959).
V. F. Apel’tsin and A. G. Kyurkchan, Analytical Properties of Wave Fields (Mosk. Gos. Univ., Moscow, 1990) [in Russian].
V. B. Il’in, A. A. Loskutov, and V. G. Farafonov, Comp. Math. Math. Phys. 44, 329 (2004).
V. B. Il’in and V. G. Farafonov, Opt. Lett. 36, 4080 (2011).
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Original Russian Text © V.G. Farafonov, V.B. Il’in, 2013, published in Optika i Spektroskopiya, 2013, Vol. 115, No. 5, pp. 836–843.
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Farafonov, V.G., Il’in, V.B. On the applicability of a spherical basis for spheroidal layered scatterers. Opt. Spectrosc. 115, 745–752 (2013). https://doi.org/10.1134/S0030400X13110052
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DOI: https://doi.org/10.1134/S0030400X13110052