Spatio-temporal Evolution Of The Time-domain Hollow Ultrashort Pulse And The Interaction Between Pulse And Atoms

In recent years, with the development of pulsed laser technology, an ultrashort pulse with pulse duration in the range of attosecond has been generated in the laboratory. It opens a new field for the study in the ultrashort pulse area. In the existed theory for ultrashort pulse, the carrier-envelope approximation and rotating-wave approximation model are widely used.However, these models have intrinsic problems, and they can not be used when the duration of the ultrashort pulses reduce to single-cycle or sub-cycle region, as these approximations lead to non-physical results.Based on the theory of electromagnetic radiation of the oscillating electric dipole and the improved complex-source model, we obtained an analytical expression of the ultrashort laser pulses beyond the slowly varying envelope approximation. Our analytical expression is a rigorous solution of the Maxwell equations, which can be used to describe a variety of ultrashort laser pulses with different pulse durations. In the passed years,many efforts have been focused on the spatial hollow beams. In this thesis, we present a new time-domain dark hollow Gaussian(TDHG) pulse. The transmission characteristics of the pulses are analyzed. The TDHG pulses reduce to a Gaussian pulsed beam when n = 0, The envelope of the ultrashort Gaussian pulses will become flat and depression, and eventually turn into TDHG pulses as the order increases.The TDHG pulse can be regarded as two ultrashort pulses with fixed phase relation and adjacent to each other in time domain. Furthermore, the time interval of the two ultrashort pulses is related to the order and the duration time of the pulses. Numerical simulations show that the pulses can keep hollow characteristics as they propagating in free space at the single cycle or multi-cycle region. The hollow effect of the envelope of the TDHG pulses induced by the spatiotemporal coupling effect are found in the far-axis condition. Besides, the intrinsic chirp phenomenon of the single-cycle TDHG pulse is demonstrated. The envelope of intrinsic chirp of the single-cycle pulse shows time-domain hollow effects as the order of the pulse increases,which is similar to the electric field. And the intrinsic chirp of the multi-cycle pulses can be neglected.The interaction between ultrashort pulse and plasma has attracted many attentions in recent years. Using the continuity equation, mechanical equation and Maxwell equations in plasma medium, we derive the relative dielectric constant of the plasma, in which we introduce the collision coefficient and relativity factor. With the electrons in plasma accelerating in laser wake field, there appear obvious relativistic effects on the mass of the moving electrons, which lead to the longitudinal relativistic self-compression (RSC) effects of the ultrashort pulses. The full width at half maximum (FWHM) and the interval of the two peaks of the TDHG pulses get shorter because of the RSC effects, and the RSC effects are beneficial to the energy concentration of the pulses. However, the field amplitude decreases after long propagation time because of the diffraction effect and energy dissipation in plasma. The TDHG pulses show asymmetric envelope due to the anisotropy of the plasma medium at the initial stage, but the envelope of the pulses gets more symmetrical as they spread in relativistic plasma. The longitudinal RSC effects become more obvious as the plasma oscillation frequency increases or the order of the TDHG pulses decreases. The collision effect can strengthen the anisotropy of the plasma, and it leads to the more losses of the energy of the pulses. It is found that the collision effect have slightly influence on the compression of the width of the pulse. Besides, the evolution of the chirp of the pulses in plasma is calculated, which is induced by the nonlinear effect.The optical force on 87Rb atoms induced by the pulse is calculated by using the analytic expressions of the TDHG pulses. The neutral atoms can obtain an acceleration of 11 orders of magnitude bigger than the Earth's gravitational acceleration under the vector electric field of the TDHG pulse. The transverse light forces are related to the detuning of the pulses and the initial states of the atoms. The ultrashort laser pulses with large red-detuning can generate an ideal transverse focusing force on the neutral atoms. The light force becomes larger as the order of the TDHG pulses increases or tihe duration of the pulses decreases. It is found that the light force can change from a focusing force to a defocusing force as the pulses spread due to the spatial-temporal coupling effect. We note that the light force may allow us temporally control the movement of the neutral atom as the Rabi frequency of the pulse increases. The impact of initial phase on light force is also studied. The results obtained in this thesis may be helpful for some atomic optics experiments in future.