Nonlinear Raman-Nath diffraction of femtosecond laser pulses in a 2D nonlinear photonic crystal

We study second-harmonic generation (SHG) of femtosecond laser pulses in a rectangular two-dimensional nonlinear photonic crystal (NLPC). Multiple SH beams were observed in the vicinity of the propagation direction of the fundamental beam. It has been verified that the angular positions of these beams obey the conditions of nonlinear Raman-Nath diffraction (NRND). The measured SH spectra of specific NRND orders consist of narrow peaks that experience a high-frequency spectral shift as the order grows. We derive an analytical expression for the process studied and find the theoretical results to be in good agreement with the experimental data. We estimate the enhancement factor of nonlinear Raman-Nath diffraction in 2D NLPC to be 70.