Hybrid ray-mode formulation of parallel plane waveguide Green´s functions

A line-source excited parallel plane waveguide with perfectly conducting or surface impedance walls is investigated in the high frequency range where alternative field representations involve many rays or many modes. It is shown that a hybrid ray-mode field representation can be developed whereby the truncation remainder of a mode series can be expressed in terms of ray fields or, conversely, the truncation remainder of a ray series can be expressed in terms of guided modes. A great variety of appropriate ray-mode combinations, each determined from a physically well-founded criterion, is possible: with respect to propagation angles measured at the source, the retained modes are those whose characteristic plane wave propagation angles fill the void left by the truncated ray series and vice versa. The analysis thus clarifies and quantifies the intimate relation between a bundle of rays and a corresponding bundle of modes. The accuracy of various ray-mode mixtures, and computational simplifications gained thereby, are illustrated in several numerical examples covering different parameter ranges, with the conventional guided mode series serving as a reference solution.