Determination of the green tensor functions in electrodynamic problems for a layered anisotropic medium

The Green tensor functions optimizing the solutions of electrodynamic problems for layered anisotropic media are considered. Differential equations representing off-diagonal elements of the Green tensor through its diagonal elements are derived. This reduces the problem of calculating the tensor functions to the determination of their diagonal components. The latter problem is in turn reduced to the calculation of two functions, each being a solution to the corresponding Helmholtz-type equation with boundary conditions. These two functions are the fundamental solution to the electrodynamic problem for a layered anisotropic medium. The results of this work simplify the calculation of electromagnetic fields produced by arbitrarily oriented dipole sources of both types. The representations obtained for the electromagnetic field confirm validity of the reciprocal relations for the components of the electrical and magnetic filed vectors in layered, vertically inhomogeneous and transversely anisotropic media.