Steady state analysis of self-organization of light into a scattering ringdue to induced reflection gratings in photorefractive materials

We present a steady state theory and derive the eigenmodes for the nonlinea r self-organization of light into a scattering ring in photorefractive mate rials such as potassium niobate, due to the formation of reflection grating s. The configuration we consider comprises solely of a mismatched sample of potassium niobate in air, with no external feedback mirror. This is the fi rst part of the two-step process involved in the self-organization of light into a hexagonal pattern observed in this and other materials. Complete st eady state solutions are derived and amplitude and phase variations of the counterpropagating main beam and its spatial sidebands (responsible for rin g formation) with propagation are shown. Our computations show the bifurcat ion diagrams of the amplitudes and phases as a function of the photorefract ive gain parameter. Dependence of the results on the amount of linear scatt ering is also demonstrated. Connections with available experimental results are made, and improvements on the model used are proposed. (C) 2000 Publis hed by Elsevier Science B.V. All rights reserved.