Solution of the Helmholtz equation for electromagnetic waves in an annular (segmented-annular) rectangular waveguide

Abstract

Formulation of the problem. When designing waveguides, spatial solutions are often in demand. However, from a methodological (including educational) point of view, mostly linear-extended structures with various sectional shapes are considered. The aim of this work is to consider a waveguide as a structure composed of segments bent in a plane with a certain radius. On the other hand, this solution is common for a plane-oriented waveguide path and, in the case of an infinitely large radius, converges to a solution for a straight waveguide. Practical significance. The presented solution of the Helmholtz equation for electromagnetic waves in an annular (segmentedannular) waveguide can be considered as a methodological basis for calculating a spatially oriented rectangular waveguide path. A step-by-step solution of the Helmholtz equation for a bent rectangular waveguide is presented; a methodology for determining the parameters of the electromagnetic field in a bent homogeneous waveguide is given. Expressions are derived for determining the parameters of the electromagnetic field components for waves of type E and H. General solutions are obtained that converge at an infinitely large bending radius to harmonic functions characteristic of solutions as applied to rectilinear waveguides. This technique can be applied both for analytical evaluation or numerical calculation and spatial modeling of waveguide parameters, and for designing the waveguide path as a whole. The presence of relatively simple analytical expressions greatly facilitates the task of analyzing and optimizing the waveguide path and building software and computing systems for their assessment, modeling and development.