A Homotopy Method for Calculating Cylindrical Waveguide Guided Waves with an Impedance Boundary

Abstract

A mathematical model for a rectangular waveguide with an impedance boundary condition has been formulated and substantiated. The model is based on the application of the Galerkin boundary method. It is assumed that the surface impedance is not a constant, but is a function of the coordinates on the surface. The solution is represented as a linear combination of coordinate functions, each of which exactly satisfies Maxwell’s equations inside a cylindrical domain. The set of coordinate functions at the border forms a complete system. The coefficients are determined from the orthogonality condition for the surface residual to the system of projection functions. Because of the use of the Galerkin method, the projection functions coincide with the system of coordinate functions. To calculate the guided waves of a rectangular waveguide with an impedance boundary, a homotopy method has been proposed and justified. The decomposition of the solution into a power series in a small parameter has also been constructed.