We present an extension of the rigorous coupled-wave analysis technique to analyze second-harmonic generation (SHG) in periodic optical nanostructures in the undepleted-pump approximation. We apply this method to analyze SHG in two example nanostructures for which we predict enhanced nonlinearity due to transverse near-field localization of the fundamental optical field in the nonlinear material. First, we examine a periodic nanostructure that yields up to twice the transmitted SHG intensity output compared with the bulk nonlinear material but only for small nanostructure depths because of mismatch of the fundamental and second-harmonic mode phase velocities. Second, we develop and analyze a modified nanostructure and find that this nanostructure concurrently achieves transverse localization and phase matching for SHG. In principle, this permits an arbitrary coherent interaction length, and for several specific nanostructure depths we predict a transmitted SHG intensity output more than two orders of magnitude greater than that of the bulk material.
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