Fraunhofer diffraction pattern due to spatial self-phase modulation of a Gaussian beam by a photorefractive crystal

The phase shift induced on a Gaussian beam interacting with a nonlinear medium determines the far field diffraction pattern characteristics. It is usual to consider that the induced phase shift by a nonlinear media is due only to the effects of the radius of curvature of the wavefront and the modulation of the refractive index triggered by the Gaussian intensity distribution of the incident beam. Accordingly, these equations have limited applicability when the nonlinear medium is a photorefractive crystal PRC. In this contribution, the equations are derived considering the influence of the photorefractive phenomenon on the induced phase shift. The Fresnel-Kirchhoff diffraction theory is used to obtain the intensity distribution of the far-field diffraction pattern of a Gaussian beam propagating through a photorefractive crystal. Simulations of this effect are presented and discussed.