A general formula for the size of the mode-coupling region

Abstract

Mode coupling takes place in a small, but non-zero, region around the coupling point. A general formula for the size of this coupling region is given. This formula is valid for anisotropic absorbing media with the inhomogenity in one direction and for a linear system of wave equations with an arbitrary number of fields and of arbitrary order; i.e. an arbitrary number of waves can couple and an arbitrary number of coupling points can coalesce. It is shown that the size is dependent on the number of modes that exist in the medium and the number of coupling points that coalesce. The formula is applied to some examples. A peculiar result that the formula shows is that as the temperature approaches infinity, the size of the mode-coupling region approaches a constant finite value, and in certain cases this size approaches zero; i.e. in these cases of extremely high temperature, mode coupling eventually vanishes.