ON SOLUTIONS FOR 2 WAVES WITH PERIODIC COUPLING

An exact solution for the coupling effects between two waves with a particular complex periodic coupling junction is presented; the particular coupling junction gives the same wave interactions as constant coupling but at a translated value of differential phase constant. A transformation is given which permits known theory for constant coupling to be applied to the periodic coupling case. Approximate solutions are given for periodically reversed coupling (sinusoidal or square wave) between two waves, and calculations are presented which indicate the solutions are valid for arbitrarily long coupling regions or arbitrarily large integrated coupling strengths. The region of validity for earlier perturbation theory is defined and proved to include the cases of interest for multimode circular electric waveguides. © 1968 The Bell System Technical Journal