Modified Manley-Rowe relations for parametric interaction with small linear losses

For parametrically coupled oscillators with small linear losses, modified Manley-Rowe relations, where the effects of losses are accounted for, are shown to hold. Under restrictive assumptions about the losses, the output powers are shown to be Manley-Rowe-related to suitable functions of the input powers. When the losses do not satisfy those assumptions, such a calculation yields quantities bigger than the actual output powers but approximating to them better than those given by the lossless Manley-Rowe relations. Some of these considerations also apply to coupled travelling waves.