Spherical particlesThe classic solution for homogeneous sphere was suggested in 1899 by A.E.N. Love [330], in 1908 by G. Mie [342] and in 1909 by P. Debye [199]. In 1910 Lord Rayleigh [422] obviously knowing nothing about the works of Mie and Debye removed a mistake in the paper of Love. Traditionally the theory of light scattering by a sphere is called the Mie theory. The solution for a focused Gaussian beam (called the generalized Mie solution) was first derived in the work [230] (see [236]) and developed further in [236,333]. The same problem was recently considered in [61] and its detailed analysis see in [329]. With the appearance of powerful PCs the computation using the Mie theory practically became a routine. Nevertheless, even in 1994 we find a paper [19] published on the Mie theory where a closed integral representation of the extinction cross-section was obtained (in other words the Mie series was transformed into an integral). To some extent unusual results for magnetic spheres were presented in [279].The generalization of the Mie theory for core-mantle spheres was made in 1951-2 by A.L. Aden and M. Kerker [133] and K.S. Shifrin [125] and for the case of an arbitrary number of layers in [343,490]. Detailed results for layered spheres can be found in [274,276,277]. A core-mantle sphere as the model of biological particles was first considered in [168,169,198], a detailed study of this and three-layered model of cells was done in [46,49,50]. For an inhomogeneous sphere with an arbitrary radial distribution of the refractive index, the general formal solution was obtained in [504,505] (see also [325,435]), and in [501] all refractive index profiles for which the radial solutions are expressed via the known functions were given. A thorough investigation of the problem of light scattering by inhomogeneous spheres was done by the group of A.P. Prishivalko [71,72] (nearly all literature on this question is cited in the monograph [72]) and in the recent paper of A.Ya. Perelman [67]. The exact solutions of the Mie problem for an optically active sphere (i.e. a sphere of optically active material [7]) and for a sphere with an optically active mantle were first obtained in 1974-5 by S. Bohren [158,159]. As it was mentioned, for a sphere of anisotropic material, the solution of the general type like the Mie theory does not exist. Nevertheless for spheres with the axial anisothropy of material a successful attempt to separate variables was undertaken in 1989 by J.S. Monzon [371] who not only got the expansions of the fields, but also obtained numerical results. The approximate methods of treatment of anisotrophic particles are considered below. V.I. Rosenberg [76] generalized the Mie solution for the case of an arbitrary number of spherical particles by using the theorems of summation of the spherical harmonics [196]. Last years the problem of light scattering by clusters of spherical particles is very extensively studied (see the papers [21,99,107,110,111,114,195,219,220,221,222,280,286,317,354,355,362] and references therein), but the work [76] remains apparently unknown to western scientists. |
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