Dynamics Of Strong Laser Pulses And X-ray Spectroscopy In Molecular Media

In the past few decades, the availability of ultrashort and intense laser pulses as well as the development in high power synchrotron radiation sources and X-ray free electron lasers has promoted a rapid development in nonlinear optics and X-ray spectroscopy technologies, and extended their range of applications. Meanwhile, the appearance of varieties of novel nonlinear phenomena calls for much more accurate theoretical treatment in order to be explained.The main aim of this thesis is to develop further the nonlinear optical theories and methods and to explain and predict new phenomena occurred during the interaction of molecules with electromagnetic radiation ranging from infrared to X-ray region. This thesis consists of mainly four parts. The first part concerns the coherent control of quantum states by specifically designed laser pulses in resonant two-photon absorption (TPA) processes. The non-rotating wave approximation (NRWA) solution for the resonant TPA process in a multi-level system is derived, and the effects of the dynamical Stark shifts and the permanent dipole moments are included. In the second part, we investigate respectively the one-step and two-step TPA and optical limiting behavior of the ultrashort and microsecond long laser pulses. The third part is about the study and explanation of the supercontiuum generation, the formation of the attosecod laser pulses and the two-color superfluorescence related to the propagation of the ultrashort laser pulses. In the last part, a new scheme of X-ray pump-probe spectroscopy is proposed, i.e., strong infrared or optical laser pulse induced X-ray absorption and resonant inelastic X-ray Raman scattering. The main contents and results are summarized as follows.First, we study the quantum coherent control of two-photon absorption and two-photon absorption area theorem beyond the conventional RWA. In the past when people investigated theoretically the TPA processes, RWA was adopted. However, the RWA solution of TPA gives wrong expressions of the dynamical Stark shifts, and usually the dynamical Stark shifts of the energy levels induced by the external field were neglected (RWAZS) without any physical background. In this theis, we investigate in detail the near resonant TPA of multi-level systems, and obtain the NRWA solution for TPA in which the effects of the dynamical Stark shifts and the permanent dipole moments of the molecules are included. The RWA, RWAZS and NRWA analytical solutions are compared with the strict numerical solutions of the amplitude equations. It is found that even for the weak incident pulse where the Rabi frequency is much smaller than the carrier frequency of the field the RWA and RWAZS solutions break down completely. In contrast, our NRWA solution coincides very well with the strict numerical results. The NRWA solution also shows that the existence of the dynamical Stark shifts prevents the complete inversion of the population in resonant TPA processes. For fixed-in-space molecules, the compensation of the dynamical Stark effect can be achieved by proper phase tailoring or two-photon detunings. It is demonstrated that the orientational disorder diminishes significantly the efficiency of the two-photon induced population transfer and does not allow complete compensation of the dynamical Stark shifts. Based on the NRWA solution of the amplitude equations, the two-photon area theorem taking into account the dynamical Stark shifts and the permanent dipole moments are derived. Although the two-photon area theorem is strict only for single-color field, numerical simulations for ultrashort laser pulses show that the two-photon area theorem can explain qualitatively the dynamical properties of pulse propagation in a two-photon resonant medium, even if the propagation is accompanied by the generation of fields with new frequencies.Second, we investigate respectively the TPA induced optical limiting effects of the femtosecond ultrashort and miscrosecond long pulses. By solving numerically the full-wave Maxwell-Bloch equation with the predictor-corrector FDTD method, we investigate the propagation of the ultrashort laser pulses in the organic 4, 4'-bis(dimethylamino) stilbene molecules under the condition of TPA. It is found that for ultrshort laser pulses mainly one-step coherent TPA occurs, and the two-photon area therorem can describe qualitatively the optical limiting behavior of the ultrashort pulses. From the relation between the transmittance of the pulse intensity and the incident intensity the dynamical TPA cross section of the 4, 4'-bis(dimethylamino) stilbene molecule is calculated. It shows that the dynamical TPA cross section of the molecule increases with the increase of pulse duration due to the enhancement of two-step TPA.A dynamical theory of the sequential two-photon absorption involving strong triplet-triplet transitions and of the propagation of laser pulses with durations in the microsecond time domain is presented. Making use of the decay time hierarchy of the energy levels, the system can be devided into fast and slow subsystems. The subsystem with fast decay rates will follow adiabatically the slow dynamics of the population of the ground and the lowest triplet states. Combining the adiabatic approximation of the fast subsystem with the particle conservation law, the rate equations can be reduced to a single dymamical equation for the ground state population. Taking into account the transverse inhomogeneity of the laser pulse, the Cranck-Nicholson method is used to solve numerically the paraxial wave equation of the field intensity. The general theory is applied to fullerene C60 because of its good optical limiting properties. It is shown that the main mechanism of optical limiting for long pulses in C60 is the sequential (singlet-singlet)×(triplet-triplet) two-photon absorption. The effective rate of population transfer from the ground state to the lowest triplet state increases with the increase of the field intensity. Due to this circumstance, the front part of the pulse propagates with mainly linear absorption, while the main body of the pulse is significantly attenuated due to the strong nonlinear sequential two-photon absorption. An incident pulse with a gaussian transverse distribution is strongly absorbed near the axis due to the higher intensity there. Different optical limiting behavior can be obtained by tuning the excitation wavelength because of the wavelength sensitivity of the singlet-singlet and triplet-triplet photoabsorption cross sections. Simulations show that the propagation effect which depends on the field intensity, the length of the absorber and the molecular concentration plays an important role in the sequential TPA induced optical power limiting performance.In the third part, the propagation of ultrashort laser pulses in both nondipolar and dipolar media is studied and special attention has been paid to supercontinuum generation, formation of attosecond laser pulses and superfluorescence. When an ultrashort pulse propagates in a two-level nondipolar or dipolar medium, supercontinuum of the spectrum is generated mainly due to the self-phase modulation of the foregoing subpulse which is strongly compressed during propagation. The supercontinuum generation of the spectrum and the formation of attosecond pulse can be constructed or destructed by the permanent dipole moment, depending on its value relative to the transition dipole moment. They are also very sensitive to the carrier-envelope phase of the incident few-cycle pulse. Multiphoton ionization of the medium weakens the oscillating feature and the intensity of the basic spectral component. Strong ionization also weakens the intensity of the high spectral components and of the forgoing attosecond subpulse. When an ultrashort laser pulse propagates in a cascade three-level nondipolar molecular medium, it is found that the intensity of the two-color superfluorescence is enhanced for large number density of the molecule, while the fast dephasing of the dipole coherence reduces the intensity of the cooperative radiation and delays the emission times or even inhibits the formation of the emission. The delay time of the superfluorescence radiation deceases with the increase of the intensity of the excitation pulse, of the molecular number density and of the propagation distance. A well-shaped up-conversion laser pulse is generated when the concentration of the molecule is large and when the dephasing rate of the dipole coherence is small.In the last part of this thesis, a new scheme of X-ray pump-probe experiment, namely X-ray absorption (XA) and resonant inelastic X-ray scattering (RIXS) accompanied by core-hole hopping induced by a strong laser field, is presented. The relevant theory is developed and is exemplified in detail with the nitrogen molecule. It is shown that a strong-laser-field induced promotion of core holes opens the scattering channels that are forbidden by the dipole selection rules and gives rise to new features in the X-ray absorption and scattering spectra. The strength of the symmetry forbidden channels strongly depends on the competition of the time of Rabi flopping between the core holes and the effective duration of the scattering process or the duration of the X-ray pulse. The XA and RIXS spectra depend on the orientation of the molecule and the relative polarization directions of the X-ray and IR-laser fields. Expressions of the XA and RIXS cross sections for both fixed-in-space and randomly oriented molecules are derived. The Rabi splitting of the core-excited states induced by the strong IR pulses results in broadening of the XA profile and decreases the XA and RIXS probabilities. Moreover, the resonant frequencies are shifted due to the Rabi splitting and the interplay of the Raman and non-Raman components of the scattering process. The RIXS profile is sensitive to the absolute carrier-envelope phase of the few-cycle strong IR field and is independent of the phase of the high-frequency X-ray pulse.