Abstract

The nonlinear Kukhtarev equations can be decoupled in the steady state to yield a nonlinear differential equation for the space charge field. Under suitable approximations, we can express the induced refractive index profile explicitly in terms of the intensity profile, its spatial derivative, and the dark conductivity of the material. We can thus also derive a nonlinear extension of the paraxial wave equation for the optical field propagating through a photorefractive material. Using a thin sample approximation, we first study beam fanning in BaTiO₃ and compare our results with existing ones derived from the linearized Kukhtarev equations. Analytically, the far-field profile may be expressed in terms of an Airy pattern and the Fourier transform of the input beam profile. Numerical results based on thick sample calculations are also provided.

© 1992 Optical Society of America