Numerical Approach To Interaction Of Intense Laser Fields With Atoms Using Linear-least-squares Fitting Method

In this thesis, an alternative theoretical approach for solving the time-dependent Schrodinger equation for atoms in an intense laser field is presented. In this method the time-dependent wave function is expanded in a basis set but the expansion coefficients are determined by linear-least-squares fitting of the wave function on discrete mesh points in configuration space, thus avoiding the need of evaluating a large number of matrix elements. In the present thesis, for a first time we use a linear combination of the B-splines functions and the finite Fourier series as a basis set. The major advantage of the basis set is that it can describe the atomic continuum states as well as the atomic bound states.We illustrated the method by computing wave functions, above-threshold ionization spectra, high harmonic generation spectra, and ionization probability of a model atom and compare the results with those obtained using the split-operator method. Meanwhile, we studied the process of the high harmonic generation for one-dimensional atom in intense laser field based on the basis function expansion and a linear-least-squares fitting method. We examine the influence of the bound states, continuum states and the interference between the bound and the continuum states of the model atom on the high harmonic generation. It is found that the main contributions to the low-energy harmonic generations come from the bound-bound interaction, while the high-energy harmonic generations are from the bound-continuum interaction. Beyond the cut-off, the interference of the bound-bound and bound-continuum interaction leads to the disappearance of the harmonic generation.