Abstract

We theoretically study second-harmonic generation in two-dimensional nonlinear photonic crystals and obtain a unified expression that combines nonlinear Raman–Nath diffraction, Čerenkov-type second-harmonic generation, and nonlinear Bragg diffraction. The analytical solution is deduced, and the theoretical result coincides well with the nonlinear Raman–Nath, nonlinear Čerenkov, and nonlinear Bragg diffraction phase-matching conditions. This method has potential applications in second-harmonic generation of more complicated two-dimensional and even three-dimensional nonlinear photonic crystals.

© 2017 Optical Society of America

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