Spatial optical periodic structures in quadratically nonlinear media

We offer a model of induced gratings describing a stationary transverse periodical distribution of FF and SH amplitudes by trigonometrical functions risen to the definite power. Dependences of a lattice contrast, and peak amplitude on the spatial period of the structure as well as the phase mismatch are found. The least period of the gratings corresponds with a critical value of period, at which the periodic structure degenerates into a plane wave. We obtain also that such lattices except the high contrast structures are unstable at long distances of about tens of the diffraction lengths. The modulation instability of the lattices under the effect of the low frequency amplitude noise was investigated. Moreover, all-optical switching effects for such structures in the quadratically nonlinear media were obtained.