Geometrical-optics solution for self-focusing in nonlinear optics

Envelope equations are derived that describe two-dimensional electromagnetic waves in a nonlinear medium in geometrical-optics approximation. Paraxial approximation is specifically avoided. A simple solution with focusing rays is obtained by writing the equations in ray coordinates and separating the variables. Comparison is made with a paraxial solution developed by S. A. Akhmanov et al. [ Sov. Phys. JETP23, 1025– 1033 ( 1966)].