Stability of narrow beams in bulk Kerr-type nonlinear media - art. no. 023814

We consider (2 + 1)-dimensional beams, whose transverse size may be compara ble to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schrodinger equation derived from Maxwell's equati ons. As this equation is very cumbersome, we also study, in parallel, its s implified version, which keeps the most essential term, namely the term tha t accounts for the nonlinear diffraction. The full equation additionally in cludes terms generated by a deviation from the paraxial approximation and b y a longitudinal electric-field component in the beam. Solitary-wave statio nary solutions to both the full and simplified equations are found, treatin g the terms that modify the nonlinear Schrodinger equation as perturbations . Within the framework of the perturbative approach, a conserved power of t he beam is obtained in an explicit form. It is found that the nonlinear dif fraction affects stationary beams Much stronger than nonparaxiality and lon gitudinal field. Stability of the beams is directly tested by simulating th e simplified equation, with initial configurations taken as predicted by th e perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.