Numerical method for studying the spectrum of surface waves of an open inhomogeneous rectangular dielectric waveguide

The problem of surface waves in a regular open waveguide of rectangular cross section is considered, which is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. To determine the solution, a variational formulation of the problem is used. A technique based on the combination of a version of the projection (Galerkin's) method and parameter shooting is proposed and applied for practical calculations.