The applicability of the Manley–Rowe relations is extended to the case of beams incident on a parallel-sided plate having rationally related frequencies but different angles of incidence. Distinct harmonic beams of the same frequency are distinguished by their different values of the transverse wave vector. The statement of the Manley–Rowe relations is changed only to the extent that terms corresponding to zero frequencies are omitted from the sums. This extension of the relations fills a gap which is inconvenient in discussions of the image-processing possibilities of nonlinear optical media.
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