Energy shedding during nonlinear self-focusing of optical beams

Self-focusing of intense laser beams and pulses of light in real nonlinear media is in general accompanied by material losses that require corrections to the conservative Nonlinear Schrödinger equations describing their propagation. Here we examine loss mechanisms that exist even in lossless media and are caused by shedding of energy away from the self-trapping beam making it to relax to an exact solution of lower energy. Using the conservative NLS equations with absorbing boundary conditions we show that energy shedding not only occurs during the initial reshaping process but also during oscillatory propagation induced by saturation of the nonlinear effect. For pulsed input we also show that, depending on the sign and magnitude of dispersion, pulse splitting, energy shedding, collapse or stable self-focusing may result.