Abstract
This Note is devoted to a new variational formulation of the diffraction problem of plane monochromatic electromagnetic waves on an isolated anisotropic dielectric inclusion in a homogeneous isotropic dielectric medium. The proposed variational functional has a clear physical meaning: it is proportional to the forward amplitude of the scattering field and its imaginary part coincides with the scattering cross-section of the given inclusion. An approximate solution of the diffraction problem for spherical anisotropic inclusions is obtained with the help of this variational formulation. It is assumed that the wave field inside the inclusion is a plane wave with unknown amplitude and wave number. The latter are found from the stationarity of the variational functional of the problem. The comparison of the exact and approximate solutions in the case of an isotropic spherical inclusion is presented. The possible area of application of this approximation is self-consistent schemes of the solution of the many-particle problems for composite media.
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