COMPARISON OF THE PARAXIAL-RAY APPROXIMATION AND THE VARIATIONAL METHOD SOLUTIONS TO THE NUMERICAL RESULTS FOR A BEAM PROPAGATING IN A SELF-FOCUSING KERR MEDIUM

The analytic solutions for the amplitude and phase of a cw cylindrically symmetric beam propagating in a self-focusing Kerr medium obtained from the aberrationless paraxial approximation and the variational method are compared with the numerical results of the theory. For beam energies close to the critical focusing value, the variational method expression for the longitudinal phase is shown, except for an extremely small longitudinal distance of propagation, to give better qualitative and quantitative agreement with the numerical solutions. In particular, we confirm the variational method prediction that the regularized phase does not change sign.