Self-focusing of two orthogonally polarized light beams in a longitudinally inhomogeneous nonlinear medium with a quadratic permittivity profile

Nonlinear propagation of two Gaussian orthogonally polarized axial light beams in a longitudinally inhomogeneous medium with a quadratic permittivity profile is investigated in an aberration-free approximation. Analytic expressions for the transverse dimensions of Gaussian beams and radii of curvature of their wavefronts are obtained within this approximation. It is shown that the width and radius of curvature of wave beams in the final longitudinally homogeneous section of the nonliner medium can be controlled by varying the beam power and a gradient parameter. The results obtained can be used in the development of matching devices, bistable optical elements, optical transistors, and laser resonators.