Generalized Mode-Matching Technique in the Theory of Guided Wave Diffraction. Part 1: Fresnel Formulas for Scattering Operators

Abstract

A generalization of the conventional mode‐matching technique corresponding to a new formulation of the problem of wave diffraction by waveguide discontinuities is рresented. The matrix‐operator formalism used in the study for the modal analysis is briefly described. Fresnel formulas are derived for the sought‐for operators of mode reflection and transmission in the canonical problem of step discontinuity in the guide. The correctness of the found matrixoperator model is proved analytically. It is shown that the obtained results are valid for a wide class of scalar problems of wave diffraction by step‐like discontinuities in the waveguide. The developed generalization of the mode‐matching technique is intended for efficient and rigorous analysis of waveguide units and microwave devices