Diffraction of Light Beams at Parametric Interaction in Nonlinear Photonic Crystals

We consider the parametric amplification of a light beam in nonlinear photonic crystals (NLPCs) under a high-frequency pump and periodic spatial modulation of the coefficient of nonlinear coupling of the waves. We study the behavior of the intensity of the amplified diffracting beam using the matrix approach. We compare our results with the parametric interaction of beams in homogeneous nonlinear optical crystals. We show that the analysis of diffraction effects at nonlinear optical interaction in NLPCs, taking into account only noncompensated quasi-phase mismatching, is incorrect.