Wave propagation inside a two-dimensional perfectly conducting parallel-plate waveguide: hybrid ray-mode techniques and their visualizations

This work is intended as an educational aid, dealing with high-frequency (HF) electromagnetic wave propagation in guiding environments. It is aimed at advanced senior and first-year graduate students who are familiar with the usual engineering mathematics for wave equations, especially analytic functions, contour integrations in the complex plane, etc., and also with rudimentary saddle-point (HF) asymptotics. After an introductory overview of issues and physical interpretations pertaining to this broad subject area, detailed attention is given to the simplest canonical, thoroughly familiar, test environment: a (time harmonic) line-source-excited two-dimensional infinite waveguide with perfectly conducting (PEC) plane-parallel boundaries. After formulating the Green´s function problem within the framework of Maxwell´s equations, alternative field representations are presented and interpreted in physical terms, highlighting two complementary phenomenologies: progressing (ray-type) and oscillatory (mode-type) phenomena, culminating in the self-consistent hybrid ray-mode scheme, which usually is not included in conventional treatments at this level. This provides the analytical background for two educational MATLAB packages, which explore the dynamics of ray fields, mode fields, and the ray-mode interplay. The first package, RAY-GUI, serves as a tool to compute and display eigenray trajectories between specified source/observer locations, and to analyze their individual contributions to wave fields. The second package, HYBRID-GUI, may be used to comparatively display range and/or height variations of the wave fields, calculated via ray summation, mode-field summation, and hybrid ray-mode synthesis.