Influence of second-order diffraction on linear and nonlinear optical effects near a surface with a periodic relief

An analytic theory of the diffraction of light by a surface with a sinusoidal relief is developed allowing for the zeroth, first, and second diffraction orders. The surface relief may be set in advance or it may be generated by laser radiation. Inclusion of the second diffraction order alters the dispersion law of diffracted waves, which makes it possible to explain quantitatively the experimentally observed shift of dips in the angular dependence of the reflectivity of the surface and also the reduction in the period of surface gratings generated by laser radiation as their amplitude increases.