SELF-FOCUSING AND SELF-TRAPPING OF SPHERCIAL BEAMS IN A NONLINEAR MEDIUM

Abstract

Self-focusing and self-trapping of optical beams are studied by obtaining the asymptotic solution of the nonlinear reduced wave equation

\[ \nabla^2 u +k^2n^2(|u|^2)u=0\]

in three dimensional space where the incident waves are assumed to be spherical waves . In order to discuss diffraction effects and self-focusing effects of the beam, the concepts of diffraction length and focal length are introduced. It is shown that diffraction effects and self-focusing effects occur in different regions. This means that diffraction cannot, in general, influence self-focusing. In the special case where diffraction effects and self-focusing effects are balanced, a self-trapped beam is shown to exist.