Two-dimensional soliton-induced refractive index change in photorefractive crystals

An analysis of light-induced space-charge field, valid for the propagation of two-dimensional solitons in photorefractive (PR) crystals, is carried out. Under conditions appropriate to the formation of self-trapped beams, the equation for the electrostatic potential is simplified and solved, to obtain an analytical expression for the space-charge field, and thus the refractive index change. The expression exhibits an excellent agreement with the numerical calculation for a variety of localized two-dimensional light beams, in particular for the bright fundamental and higher-order vortex spatial screening solitary waves. Based on analytical results, a class of models for the local isotropic two-dimensional space-charge field is proposed. They are compared to the general nonlocal anisotropic model, using the propagation and breakup of vortex beams as an example.