Coupled mode theory of intrinsic modes in a wedge

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Abstract
Recent theoretical studies of acoustic wave propagation in a model waveguide consisting of a homogeneous wedge with one reflecting and one penetrable boundary have established the utility of the concept of an intrinsic mode, which generalizes for nonseparable problems the normal mode of separable configurations. In this paper, it is shown by explicit calculations on the same model problem that direct orthogonal expansion (in local normal modes) of the intrinsic mode produces the same expansion coefficients as those obtained by a perturbation analysis of the coupled mode equations. The perturbation method used is that of renormalization, in which the mode coupling operator is iteratively diagonalized up to a certain order in the nonseparability parameter, which, in this case, is the wedge angle α.

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