In this thesis we study, analyze, extend and implement the nonperturbative nonlinear Maxwell-Schrodinger-Plasma (MASP) model, originally derived by Lorin et al. The model was developed to describe the high order optical nonlinearities and the low density free electron plasma generated due to laser field.
The MASP model has important advantages, it is based on the original, i.e. nonasymptotic, physical equations, and uses self-consistent description of the micro (quantum)- and macro (field)- variables. However, its major drawback is a high computational cost, which in practice means that only the shortest propagation lengths can be calculated. In order to reduce this cost, several extensions to this model were proposed and tested. One of these is discussed in the thesis: it is the MASP model enriched by a polarization evolution equation from its simplest version in a form of transport equation to more complex nonlinear variants. We show that homogeneous transport equation is a more universal tool to simulate the high harmonics spectra at shorter times and/or at a lower computational cost, while the nonlinear equation could be useful for modeling the pulse profiles when the ionization level is moderate. The gain associated with the considered modifications of the MASP model, being expressed in reduction of computational time and the number of processors involved, is 2-3 orders of magnitude.