Nonlinear light beam propagation in uniaxial crystals: nonlinear refractive index, self-trapping and self-focusing

We derive the nonlinear paraxial wave equation for the propagation of an op tical beam in nonlinear anisotropic media with centrosymmetry. As an applic ation of the equation, we obtain the nonlinear refractive index (NRI) in th ree uniaxial crystals belonging to the symmetry classes 6/mmm of the hexago nal system, 4/mmm of the tetragonal system, and (3) over bar m of the trigo nal system, respectively, and consider the self-trapping and self-focusing of the beam propagating in any direction in these crystals. We conclude tha t NRI, critical power and self-focusing length are all anisotropic (depende nt upon the propagation direction) for an extraordinary light but isotropic for an ordinary light, and that there exists an elliptical self-trapping b eam for the extraordinary light.