Characterization of optical nonlinearity in specially prepared photorefractive lithium niobate samples

A model for beam propagation through a nonlinear material that takes into account inhomogeneous induced refractive index changes due to the nonlinearity is first developed. The theory based on this model can be used to analyze the propagation of Gaussian beams through photorefractive lithium niobate. A focused Gaussian beam of circular cross-section incident on the sample emerges as an elliptic Gaussian after interaction in this material. We observe that the value of the nonlinearity coefficient derived from a z-scan of photorefractive lithium niobate compares favorably with that found by varying the power P of a Gaussian beam focused at a fixed longitudinal position within the sample and monitoring the far-field beam ellipticity. We use the value of the nonlinearity coefficient to determine the donor to acceptor ratio of dopants in photorefractive lithium niobate samples. We show how our theory can be extended to include two species of impurities in the photorefractive material.