LINEAR FORMULATION OF NONLINEAR PROPAGATION OF OPTICAL BEAMS AND PULSES

A new method of scaled complex rays is introduced to treat the nonlinear propagation in Kerr media. The analytical solution is made possible by assuming an appropriate parabolic variation of the refractive index and a Gaussian shape of a beam cross-section. Then, a proper scaling of the propagation distance, phase-front curvature and the beam amplitude reduces the soliton-like propagation to the well-known problem of Gaussian linear propagation. The Scaled Complex Ray Method is able to treat the propagation of higher order solitons in terms of higher order Hermite-Gaussian beams.