A hybrid projective method for analysis of longitudinally non-uniform dielectric transition in circular waveguide

The problem of electromagnetic wave scattering at a junction of two circular waveguides, where one of them contains an axially symmetrical layered longitudinally non-uniform dielectric transition of finite length is considered. A numerical algorithm is developed for solution of the problem on the basis of the hybrid projective method including projective matching of the fields on the transition boundaries, projection of the Maxwell equations on the transverse wave vector functions of the waveguide containing the transition, and application of the one-dimensional finite element method in a projective formulation.