The travelling-wave amplification as a parametric process

The Manley-Rowe relations [1] were originally developed in an analysis of a circuit containing nonlinear reactive elements. Since the original discovery of this important formula, it has been found that there are a number of other physical systems that obey the Manley-Rowe relations. Penfield [2] and Sturrock [3] have shown that any physical system that can be described by energy-state functions obeys the Manley-Rowe relations. Jaynes [4], Weiss [5] and others pointed out the similarity between the Manley-Rowe relations and the well known quantum mechanical expression W = ħω, and noted that the Manley-Rowe formula is indeed equivalent to the conservation of quanta. On this basis, Jaynes [4] was able to establish the similarity between masers and parametric amplifiers.