On the coupling coefficients in the "coupled-mode" theory

Abstract

The "coupled-mode" theory has proved itself to be an important tool in the analysis of energy exchange phenomena between traveling waves. In its original form [1] it is capable of yielding important qualitative results. To extend its range of usefulness into the quantitative domain, one needs to evaluate the coupling coefficients which govern the energy exchange. This is done in this paper where we treat the 'small coupling' case. We assume that in obtaining the coupling coefficients for the small coupling case we may use for the different physical observables their values in the absence of coupling. This procedure is analogous to that used in evaluating the Q of a cavity or the attenuation constant of a waveguide, for the small loss case, where the loss-free field solutions are used instead of the actual solutions in the presence of losses, and is a type of perturbation theory formulated on physical grounds.