| Recently the subject of strong laser-atom interaction system has been a hot topic in atomic physics. With the intensity of laser increased a series of new phenomena appears, for example, Multiple Photon lonization (MPI), Above Threshold lonization(ATI), Tunnel lonization(Tl), Stable lonization(SI) and so on. At the same time the ionized electron under the strong laser field may return to the vicinity of the nucleus and recombine to the groud state. Subsequently a photon of high energy may be emitted. This is high-order harmonic generation (HHG). HHG is very important in atom physics. Two aspects manifest the importance of studying HHG. On the one hand it can accelerate the development of non-perturbation theory; on the other hand, the emission of HHG may supply a kind of coherent-light of short wavelengh and even be applied to the field of biology.During the past decades the HHG has been extensively studied. The HHG is characterized by a rapid drop at low orders, followed by a broad plateau where all the harmonics have the same strength, and a sharp cut-off at energy given by I p + 3.2Up ,where I p is the binding energy of the initial state, and U p is the ponderomotive energyof the electron in the laser field.However, The above-mentioned character of HHG is general. In fact, there are many elements which influence the special character, such as the intensity and frequency of the laser, the binding energy of atom, an additional field and so on. We studied the effects of pulse-shape, an additional static electric field and different initial states on ionization probability and HHG. We did so by representing the results of a series of numerical experiments on a one-dimensional model hydrogen atom. The laser pulse used is a realistic process including three sections :turn-on,plateau region and turn-off.This thesis is divided into six chapters. The first chapter is our introdiction, which briefly discussed the progress on the laser-atom interaction studies in literatures. We stressed on the ionization, HHG and the applications in strong laser field. The chapter two presents microscopic theory and numerical model about HHG. The semiclassical interpretation describes three processes of HHG very visually, but it doesn't give the details. Lewenstein theory explains the position of Cut-off by using a quantized method. In chapter three the pulse-shape effects of laser-atom interaction system are discussed. The series of results showed that there is a close relationship between the ionization probability and the pulse-shape, which in turn affects the HHG. When the pulse is turned on very slowly or rapidly the character of HHG won't be obvious. Only if the turn-on is proper the spectrum of HHG will be ideal. In addition, the time- width of pulse also influences HHG. To some extent the spectrum of HHG will become better when the time is prolonged. In chapter four the effects of a static electric field and different initial states on HHG are studied. Under an additional electric field the spectrum exhibits a double-plateau structure. Furthermore, the ionization probability and HHG also behave differently when the hydrogen atom is in different initial states. So far we discuss the ionization and HHG of hydrogen atom by using numerical method in which the laser field is treated as a classical extent field.Chapter five is another part of our work. We studied the electronic wave packet in a quantized laser field where the electron and the field was treated as a close system. Generally, the electron and photons become entangled as the electronic wave packet evolves. If initial photon state is a coherent state and we neglected the transferred photons then the quantized-field calculation is equivalent to the semiclassical calculation. If the initial photon state is a Fock state, the probability density of the electron exhibits bifurcation and confluence and the corresponding photon distribution is a time-periodic function which result from the energy exchange between the electron and field. Our results also...
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