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 optical beam in nonlinear anisotropic media with centrosymmetry. As an application of the equation, we obtain the nonlinear refractive index (NRI) in three uniaxial crystals belonging to the symmetry classes 6/mmm of the hexagonal system, 4/mmm of the tetragonal system, and m of the trigonal system, respectively, and consider the self-trapping and self-focusing of the beam propagating in any direction in these crystals. We conclude that NRI, critical power and self-focusing length are all anisotropic (dependent upon the propagation direction) for an extraordinary light but isotropic for an ordinary light, and that there exists an elliptical self-trapping beam for the extraordinary light.