Generalized Coupled Mode Theory

Abstract

The pairwise coupling of modes in distributed systems such as the traveling-wave parametric electron-beam amplifier and many other types is shown to permit only two types of interaction. One type, called β coupling, results in the periodic interchange of the signal between the modes, as typified in the Kompfner-null coupler. The other, γ coupling, results in the exponential growth of the mode, as in the TWT and in the pump section of a parametric amplifier. The nature of the resultant interaction is a direct consequence of the underlying relations contained in the conservation law that applies throughout the system, i.e., in the separate parts of the system and that is independent of the various coupling coefficients. The ``rank'' and ``signature'' of the metric that expresses this conservation law is sufficient to determine the type of behavior. The direction of flow of energy in the coupled modes imposes a duality on these relations. Where modes of opposite directionality are coupled, β coupling causes system amplification, while γ coupling causes system interchange. These relations are generalizations of effects that have been studied in detail for many specific systems. They are not, however, consequences of the details of the system but are, rather, the only alternatives possible under assumptions that are broad in scope and generally applicable to devices of interest.