Three-dimensional and boundary integral equations of the second kind in problems of diffraction by a bounded body in a layered anisotropic medium

This paper presents two variants of the Stratton-Chu integral relations for the intensity vectors of the electric and magnetic fields of harmonic excitation in a layered uniaxially anisotropic medium. These equations are then used to derive systems of two 3-D vector integrodifferential equations and two singular integral equations of the second kind for the description of the electromagnetic field in a layered anisotropic medium containing an arbitrary local heterogeneity. In the case of a local heterogeneity with a sufficiently smooth boundary and constant electromagnetic parameters, a system of two boundary (surface) vector singular integral equations of the second kind is obtained for the density vectors of surface electric and magnetic currents distributed over the surface of the heterogeneity.