| The study of interactions between lasers and materials has reached a highly nonlinear field and has a found scientific importance and wide applications. Among the interactions, multi-photon ionization of an atom is a basic problem and becomes the focal point of the academia. And photoelectron angular distributions are one of main theoretical bases developing multi-photon ionization. Early experimental and theoretical study of photoelectron population in polarization plane with respect to azimuth angle was reported; the main result was focus on showing angular distribution different, when changing polarized direction of laser fields. In view of quantum interference, the main points of this article are to discuss the ionization coherence influence in the ionization process on photoelectron angular distributions. The energy and spatial distribution of the photoelectrons and particles population relation to energy levels are described simultaneously via the interference pattern .Researching interference pattern will have practical meaning on structure of atoms or molecules.Part one:It mostly describes transition process and some basic theories relevant to what discussed in our study. Hamiltonian operator in different representations and their transformation relations are given firstly. And then particles population relation to levels with respect to time is analyzed by means of density matrix equation in the process of excitation and ionization. Finally the general expressions of ionization rate and probability with multi-passage are given. And based on the principle of angular momentum, the explicit expressions of ionization probabilities are clearly calculated separately. It is shown that the transition probability expressions are different as selection rules are varied in different excitation scheme.Part two:Taking Na atom for example, on the basic of the principle of photoelectron imaging spectrometry, and by using two-photon resonant and three-photo ionization and the new method, which is used to expand continuous wave into partial waves, we study photoelectron angular distributions with a greater emphasis on interference from D degenerated excitation levels. By changing excitation laser, we study the influence of interference with dual-channel on the angular distributions.Part three:As K atom for example, particles population relation to energy states are obtained by using single-photon and three-photon ionization. Based on the theory of photoelectron imaging and ionization probabilities, we mainly analyze influence of interference of two ionization channels on photoelectron image. In this passage two conditions are considered :â‘ when collision of a large number of particles on energy levels are neglected. Ionization probabilities from K atom 4p degenerate state formed in the Gaussian distribution on detect. And the conclusion is demonstrated through analysis of photoelectron angular distributions.â‘¡when collision of a large number of particles on energy levels are considered .Ionization rates are established in greater complex law, namely Voight law. Photoelectron probabilities of wide-angle scattering become stronger as the existence of collision leading to a number of electrons ionizing speed faster. So as to out circle distributions of photoelectrons on detect become denseness; relatively center distributions of photoelectrons get less than the former. And obtaining center patterns of photoelectrons from planar interference into line interference. The interference of photoelectron is mainly studied. The figure clearly presents the energy and space distributions of photoelectron. This result has an important meaning for analyzing photoelectron imaging pattern. |