Non-Linear Spatio-Temporal Dynamics of Optical Beams and Pulses in Kerr and Ionizable Media

The present thesis includes results of several investigations concerning the propagation of optical pulses in optical fibers and spatio-temporal beams in optical Kerr media and ionizable media. Both numerical and analytical methods play an important role in the investigations.<p /> Special emphasis has been given to new aspects of problems involving conversion of non-linear modes in optical pulses, fast adiabatic compression, wavebreaking-free pulses and passive mode-locking by dissipative four-wave mixing which have been described for the first time. The applicability of these phenomena for the problem of optical pulse generation and compression has been discussed.<p /> Several problems concerning the dynamics of spatial optical beams have been studied for one and two dimensions. The dynamics of TE polarized one-dimensional optical beams on planar slabs have been analyzed and a non-linear equaivalent to the Snell law has been found for the transmission-reflection of the beam thorugh the slab. Furthermore, the properties of the first azimuthal mode of a laser beam propagating in a cubic-quintic non-linear medium has been studied. It has been found that this mode is azimuthally stable provided the beam flux is over a certain a certain threshold which is calculated analytically. Finally the robust nature of the dynamics of a single azimuthal mode as well as of the mutual intercation between two modes are described.<p /> Full spatio-temporal dynamics of optical pulses in ionizable media have been studied for the cases of impact as well as field-induced ionizations. These calculations have beeen extended to include both forward and backward going light pulses and all the temporal scales by the development of a finite differences time domain code that solves the Maxwell equations in two dimensions together with the equations for the cold electron plasma. The compression of optical pulses by simultaneous scattering and blue shift has been demonstrated