Perturbation methodThe perturbation method is based on the small-parameter expansion of an unknown solution of the light scattering problem in a vicinity of the exact solution. In application to non-spherical particles it means that one searches for a solution in the form of small deviations from the Mie solution caused by small deviations of the particles shape from a sphere. The first solution of this kind was obtained in 1960 by T. Oguchi [383] (the often cited paper [507] appeared 4 years later). The general approach to solution of the problem by the perturbation method was developed in 1969 by V.A. Erma [213] (see also the papers [212,289,372,373] on concrete applications of the method and recent paper [12]).With the development of more efficient algorithms for non-spherical particles the perturbation methods lost its meaning. The only probably exclusion is the case of anisotropic particles for which the rigid solution is either impossible or too complicated. For such problems the perturbation method can give information of the first approximation, which is important for understanding of the basic principles of influences of the material anisotropy. A good illustration here is a large number of investigations made by the Minsk group of A.P. Prishivalko for weakly anisotropic spheres [32,33,35,36,37,38,39,40,72]. As the basic solution of this problem, one takes the Mie solution for an average refractive index, and the anisotropy is represented by small deviations from it. More details can be found in the book [72]. |
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