Self-focusing dynamics of nonlinear waves in media with parabolic-type inhomogeneities

The possibility of accelerating the self-focusing dynamics of light beams in nonlinear and dispersive media with either a constant or a weakly oscillating parabolic density profile is investigated. It is shown that the self-compression of wave packets, that freely self-focus in homogeneous media, can be enhanced by the action of appropriate parabolic inhomogeneities, whose lensing influence shortens the focal time of the wave. A similar property also occurs when the scalar envelope of a nonlinear waveform interacts with a uniform external magnetic field. The motion of light beamlets, originating from the filamentation instability of an incident beam, is analytically described for inhomogeneous media with focusing and defocusing density profiles. (C) 1997 American Institute of Physics.