Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions

The three dimensional problem of diffraction of a skew incident plane wave by a wedge with anisotropic impedance boundary conditions is explicitly solved by the probabilistic random walk method. The problem is formulated in terms of two certain components of the electric and magnetic fields which satisfy independent Helmholtz equations but are coupled through the first-order boundary conditions. The solution is represented as a superposition of the geometric waves that are completely determined by elementary methods and of the waves diffracted by the apex of the wedge. The diffracted field is explicitly represented as the mathematical expectation computed over the trajectories of a two-state random motion which runs in a complex space and switches states under the control of stochastic equations determined by the problem's geometry and by the boundary conditions.