On Solutions for Two Waves with Periodic Coupling

This paper describes some solutions for two waves with periodic coupling. Coupled waves have been important in a wide variety of communication devices: transmission lines, directional couplers, amplifiers, and in describing mode interchange phenomena generally.1 Multimode transmission lines have been advantageously described through coupled wave equations, and a particular situation of importance exists in the circular electric waveguide. As first shown by H. E. Rowe and W. D. Warters, 2 periodic straightness variations cause periodically reversed coupling from the circular electric wave to several other waves, and this interaction results in the most difficult tolerances on the fabrication and installation of the waveguide itself. Publications by H. E. Rowe and W. D. Warters have provided a comprehensive understanding of the fundamentals involved and have given explicit expressions based on perturbation theory for calculating the loss versus frequency varia1801 1812 T H E BELL SYSTEM TECHNICAL JOURNAL, OCTOBER