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 X(2) in transverse direction but undergoes random modulation in longitudinal direction. We show that the random X(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.