Nonlinear Propagation of Optical Pulses and Beams

The propagation of optical beams and pulses under the influence of nonlinear effects is characterized by a rich variety of phenomena and many potentially important applications. We analyse two main topics in this context: nonlinear beam propagation, and nonlinear pulse propagation in optical fibers. The propagation of an optical beam is characterized by diffractive broadening. For Kerr-media, in which the refractive index increases with beam intensity, at a certain intensity, the beam may induce its own waveguide and propagate without broadening. For higher intensities, the nonlinearly induced refractive index causes self-focusing and in some cases even collapsing singularities. We demonstrate in this work that an analytical variational approach describes the dynamics of nonlinear beam propagation very well, in particular with respect to the phase modulation dynamics, which previous approaches are found to describe erroneously. The collapse can be removed by allowing the refractive index to saturate. Beam dynamics in saturable nonlinear media is therefore an important issue. Using the variational method, we manage to reproduce the essential features from numerical simulations, and to give a complete picture of optical beam dynamics in saturable nonlinear media. Another important effect in nolinear media is the modulational instability, which is well-known to break up broad beams into filaments. However, this instability can occur only in nonlinear focusing media. Considering a pulsed beam with a defocusing-in-time and focusing-in-space nonlinearity, we show that temporal breakup is possible due to the spatial instability, despite the fact that a purely temporal modulation is stable