Using a systematic approach based on a Bloch function expansionand the method of multiple scales, we present a rigorous derivationof the coupled- mode equations for light propagation through deepquadratically nonlinear gratings. The coupled-mode equations for deepgratings differ from those derived previously for shallow gratings inthat the coefficients have different values and additional nonlinearterms appear. In the shallow grating limit these equations reduce tothe standard coupled-mode equations. Our results show that deepgrating effects can be significant in GaAs-AlAs thin film stacks,while in glass optical fibers these effects are too small to play arole. Using a standard shooting technique, bright soliton solutionsto the new equations are obtained.
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