| The interaction of few-cycle ultrashort laser pulses with mater is currently being a hot subject in the high intensity laser physics. Research on the extremely nonlinear optical phenomena induced by few-cycle laser pulses in media, such as atoms etc., will reveal unknown domain in nonlinear optics. It is sure that this work give great contributions to the advance of rising or cross disciplines such as optical physics, quantum information and attosecond physics etc.. Quantum coherent control is also a frontier area arisen in recent years. As an intersection frontier, coherent controls with few-cycle laser pulses have great academic significance and application potential.Based on the semi-classical theory, the Maxwell and Bloch equations are used to describe the laser fields and media. In this paper, the full Maxwell–Bloch equations without the rotating wave and slowly varying envelope approximations are solved by using a predictor-corrector finite-difference time-domain method. Under extreme nonlinear optics condition, the propagation properties and spectral effects of a few-cycle laser pulse in a V-type three-level atomic medium are investigated theoretically. And the populations are also analyzed and series new results are achieved. The main innovative results are as follows:1.We investigated the propagation of a few-cycle laser pulse and the population of each energy level in a dense Rb atomic medium. It is found that the Rabi frequency and the populations in a dense medium are quite different from those in a dilute medium. In a dilute medium, oscillations arise at the trailing edge of the pulse due to the time derivative of the electric field. While in the dense medium, oscillations appear at both the leading and trailing edges of the pulse due to strength increasing of macroscopic polarization, moreover, the larger the area of the input pulse is, the more obvious the oscillation amplitude is. In the dense medium, pulse group velocity is slower due to the increasing of medium refractive. And pulse splits easily due to the increasing carrier effects. At the input surface, the population transfer completely appears with the time evolution in a dilute medium. While in the distance of z≠0μm, the Rabi flopping of the populations only occur at the zero points of the optical field. The larger the area of the input pulse is, the more the times of the Rabi flopping are.In a dense medium, the propagation and populations in the two cases with and without LFC are much different. The pulse group velocity is larger with LFC than that without LFC. NDD interaction accelerates the pulse propagation and split. Moreover, this phenomenon is more obvious for a small pulse area. The appearing time of the Rabi flopping with LFC is earlier than that without LFC and NDD interaction accelerates the population transfer. The carrier-envelope phases between the cases with and without LFC are much different. The difference can go up toπ.2.Based on the work of chapter 4, we firstly investigate the influence of the ratio,γ, of the transition dipole moments on the propagation and the populations of the pulse. It is found that the ratio of the transition dipole moments has strong influence on the pulse propagation. When the initial area is some threshold value, the times of population Rabi flopping can be changed with differentγ. Whenγ≤1, the pulse group velocity is less with LFC and NDD interaction delays the pulse propagation and split. The phenomenon of time delay is more obvious with the decreasing of pulse area. Moreover, that phenomenon is more obvious with the decreasing value ofγdue to the decreasing effective pulse area. The ratio,γ, of the transition dipole moments also has strong influence on the appearing time and the Rabi flopping times of the population transfer. When the initial area is some threshold value, the times of populations Rabi flopping can be changed with differentγ. Whenγ≤1, NDD interaction delays the population transfer.3.The phase-dependent feature of few-cycle ultrashort pulse laser propagating is demonstrated. The carrier propagation and spectrum evolution of the pulse are sensitive to its initial phase and the phase sensitivity is more obvious for larger area pulse. For sub-pulses, the phase difference between two carrier envelope phasesφ=0πandφ=0.5πis bigger than that of main pulses at a same propagation distance. And the propagation distances of sub-pulses are much different. Comparing to the case ofφ=0π, the pulse propagation occurs delay phenomenon whenφ=0.5π. The phenomenon is more obvious with the increasing distance.Oscillatory features in spectra can be found, which are more obvious with the propagation distance increasing. For larger area pulse, the pulse spectra are broadened due to the influence of self-phase modulation. Significantly higher spectral components can occur and the oscillatory feature becomes more and more intense with the increasing of distance. Moreover, higher spectral components also exhibit a continuous feature. When the pulse area is a certain value and the pulse width is larger, the pulse is split easily and the oscillatory feature around the resonance frequency is more obvious. When the pulse width is smaller, the higher spectral components in the spectra are more obvious. Under the same condition, the pulse spectra are affected by the initial carrier-envelope phases due to the different coherence effect, which don't induce obvious changes of higher spectral components. Comparing to the case ofφ=0π, the consistent property of higher spectral components is better whenφ=0.5π. The higher spectral components are uniform and show better flat.4.By the numerical analyzing and simulation, we investigate the temporal evolution and spectral properties of the two-color ultrashort laser pulses propagating in a V-type three-level atomic medium and analyze the population of each energy level. It is found that the initial relative carrier envelope phase has strong influence on the time evolution and split of the pulse. With the relative phase increasing, the pulse amplitude is smaller and the pulse width becomes larger due to the strengthened coherent interaction. The number of sub-pulses can be reduced. When the relative phase is relatively smaller, dispersion plays a major role on the properties of pulse propagation. Moreover, the relative phase affects directly the population of each energy level. The Rabi flopping times of the population transfer can be decreased with the increasing of relative phase. At the input surface, the population transfer completely appears with the time evolution by adjusting the relative phase. Under different initial carrier envelope phase, the changes of higher spectral components in spectra are more obvious because the Rabi frequency and carrier Rabi flopping are influenced greatly by the different coherent effects. With a certain propagation distance, the spectra amplitude is induced and the higher spectral components are gradually weakened even disappeared with the increasing of the initial carrier envelope phase. The oscillatory feature around the resonance frequency depends crucially on both the initial relative phase and the delay time between the sub-pulses.5. We investigated the propagation and spectra of two-color ultrshort laser pulses in a dense Rb atomic medium. And the populations are also analyzed. It is found that in a dense medium, oscillations at the leading edges of the pulse are relatively strengthened with the relative phase increasing and it is gradually weakened at the trailing edges. Comparing with LFC, the pulse propagation appears delay phenomenon without LFC. And the phenomenon is more obvious with the increasing of initial relative phase. NDD interaction accelerates the pulse propagation and split. With medium density increasing, because of four-wave mixing and self-phase modulation, spectral properties get great influence that new features such as spectra splitting and components shift arise. The spectral component of central frequency gradually disappears and spectral blueshift (higher spectral components) and redshift (lower spectral components) of the corresponding spectra arise. The smaller the initial relative phase is, the more obvious the phenomenon of spectral blueshift and redshift is. Spectral amplitude depends mainly on the medium density. It is gradually decreased with the medium density increasing. The initial relative phase has a definite effect on spectral amplitude. With the increasing of initial relative phase, spectral amplitude is decreased and the higher spectral components are gradually weakened.This paper consists of night chapters, and in the first three chapters, we introduce simply the current research state, the main contents and the calculation method of this research subject. The first chapter gives a brief introduction of the development and applications of few-cycle ultrashort laser pulses, the interaction of few-cycle ultrashort laser pulses with matter and coherent control. In chapter 2, we introduce the basic theories on the propagation of the few-cycle laser pulses. The complex function form of the pulse eclectic field is presented first. Then we introduce simply the physical meaning of the pulse carrier phase, the main effects on the few- cycle pulse amplification and the traditional area theorem. In chapter 3, we derive Maxwell-Bloch equations beyond slowly varying envelope approximation (SVEA) and rotation-wave approximation (RWA), and detailed elucidate the predictor-corrector finite-difference time-domain method. From the fourth chapter to eighth chapter, my own study works are showed and the main results are alluded above. At last, the conclusions and prospect are given in the ninth chapter.
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