Αριθμητική μοντελοποίηση μη - γραμμικής διάδοσης υπερβροχέων παλμών λέϊζερ σε διαφανή υλικά

This thesis is focused on the study and control of femtosecond light filaments in transparent materials. Since filamentation is a complex phenomenon in which multiple physical effects take place, the understanding and modeling of the whole process is of great importance. The thesis starts with a brief introduction of the linear and nonlinear effects that take place in the filamentation process. It is followed by the description of the numerical model used in the simulations and the main limitations and approximations are stated. Throughout this work numerical simulation will be used in conjuncture with laboratory experiments to study and ultimately control the nonlinear propagation of filaments. The control of the attributes of light filaments, or else filamentation tailoring, is investigated in mainly two different ways; by the use of optical periodic lattices and second by use of various non-diffracting waves.It is shown that photonic periodic lattices can be used to spatially tailor a light filament in respect to its peak intensity and beam waist. In addition it is shown that the stabilizing effect of the lattice can result in the generation of intense dynamic light bullets. The tailoring properties of multiple lattice geometries are explored in materials as water, fused silica glass and BK7 glass both through simulations and experiments.The use of nondiffracting beams as driving pulses for filaments reveals never seen before light structures in the nonlinear regime. The use of Bessel beams is demonstrated to increase the length and homogeneity of filaments in air. In addition Bessel filaments are shown to generate linear X-waves through means of cross-phase modulation in fused silica glass. The propagation dynamics of 2D high power nonlinear Airy beams is investigated in great detail in both air and water. In one spatial dimension the existence of a stationary nonlinear Airy solution in the presence of high nonlinear losses is presented. Finally the use of a new type of abruptly autofocusing wavepacket is studied in the nonlinear regime, revealing that it can overcome intensity clamping issues which are observed in all Gaussian filaments. In addition it is shown that the nonlinear focus shift of autofocusing waves cannot be described by Marburgers formula as in the case of Gaussians, and a new semi-empirical formula is given. Finally the creation of a nonlinear quazi-light bullet structure is reported for abruptly autofocusing waves carrying multiple critical powers