Numerical method for calculating electromagnetic fields at geometrical singularities

The task of solving the boundary value problem for a cone with elliptical cross section is reduced to the solution of a two-parameter eigenvalue problem of two coupled Lame differential equations. The degree of singularity of the electromagnetic field is determined by the lowest-order eigenvalue pair. A numerical method for solving the eigenvalue problem is given. The method is based on an integration of the Lame differential equations, using a priori knowledge about parity, periodicity and number of zeros per interval of periodicity of Lame's functions. The numerical results include the calculation of the diffraction field of a 90-deg slot in a plane screen.