Enhancement of nonlinear Raman-Nath diffraction in two-dimensional optical superlattice.

We study second harmonic generation via nonlinear Raman-Nath diffraction in an optical superlattice that maintains a periodic modulation of the second-order nonlinear coefficient χ((2)) in transverse direction but undergoes random modulation in longitudinal direction. We show that the random χ((2)) modulation offers a continuous set of reciprocal lattice vectors to compensate for the phase mismatch of nonlinear Raman-Nath diffraction in the longitudinal direction, leading to more efficient harmonic generation for a wide range of wavelengths. We also characterize the intensity dependence of nonlinear Raman-Nath diffraction on the degree of randomness of the optical supperlattice.