Ray theory and perturbation analysis are combined to analyze the cumulative growth of nonlinear effects resulting from excitation of a single nonplanar mode in a two‐dimensional waveguide whose walls are rigid. The first‐order (linear) signal is decomposed into a pair of obliquely propagating planar waves. The signal associated with each ray is required to satisfy the inhomogeneous second‐order wave equation. A single ray emanating from its source is followed to its first incidence at one wall, and the reflection of such a ray is determined by requiring that incident and reflected rays combine to satisfy the hard‐wall boundary condition. The method of images then leads to a generalization of the result to the case of a ray that undergoes multiple reflections. Nonuniform validity of the ray signal determined in this manner is corrected by the method of renormalization, which leads to the conclusion that a ray behaves like a simple nonlinear planar wave, except that the propagation distance is measured by tracing the ray back to its source. The overall signal at a specified field point is determined by superposing the signals associated with the two rays that intersect at that location. The result is shown to be in complete agreement with earlier modal analyses of the same problem, provided that the frequency is sufficiently low to inhibit resonant energy transfer between nearly parallel rays. Although the analysis is less direct than that used previously, it yields physical insight into the distortion process not previously available.

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