Nonperturbative Study of Attosecond Transient Absorption Spectra and Low-energy Structure of Above-threshold-ionization Spectra

我們提出非微擾的計算方法來研究阿秒瞬態吸收光譜。我們使用廣義擬譜方法以及Floquet 理論，並運用第四階的 Runge-Kutta 方法計算時變展開係數，同時我們使用兩種時頻分析技術以探討發射光譜的次週期震盪現象，最後我們將阿秒瞬態吸收光譜學的技術應用至研究超閥值電離譜的低能量結構。Conventionally the absorption features of atoms or molecules are probed by using the femtosecond laser pulse. Nuclear motion in molecules and the formation of chemical bonds have been detected by the femtosecond (10-15 s) pump-probe spectroscopy. However, the resolution offered by femtosecond pulse is insufficient to track the dynamics of electronic motion (10-18 s) in atoms and molecules. Recently, experiments have been combining the attosecond and the femtosecond pulses to detect the absorption features. The advancement of using the attosecond sampling interval includes discovering of Aulter-Townes effect, light-induced states, absorption on a sub-cycle time scale on the near-infrared field and enables the laser control of Fano lines. The delay time between the near-infrared(NIR) pulse and the extreme ultraviolet(XUV) pulse will alter the absorption spectra. When the NIR pulse comes first, we can probe the electron movement in the valence shell of the ions. If the XUV pulse comes first, we can use the attosecond transient absorption spectroscopy(ATAS) spectra to determine the lifetime of excited states. The most prominent features occurred when the NIR pulse and the XUV pulse are overlapped, the absorption lines are dominated by sub-cycle oscillations. When the intensity of the XUV pulse is weak, the time-dependent perturbation theory can be applied to compute the absorption cross section. Nevertheless, as the intensity of the NIR and the isolated attosecond pulses(IAP) increased, the perturbation theory is no longer applicable. Moreover, the concept of absorption cross-section will also disappear in strong field. In this thesis, we propose a non-perturbation approach, which is applicable under the strong laser field to explain the experiment results. We use a generalized pseudospectral(GPS) method and Floquet theorem for the numerical solutions. We use the fourth-order Runge-Kutta method to solve the time-dependent expanding coefficients. The emission spectra show the excitation from the ground state (1s) to the excited (np) states. We also observed the laser-induced virtual states in the two photons (one XUV and one NIR) absorptions and three photons (one XUV and two NIR) absorptions. The simulation results showed half-cycle oscillation in the period of NIR frequency. In addition, we applied the synchrosqueezing(SST)-Morlet method, which is a time-frequency analysis approach, to investigate the time profile with different time delays. We also use the technique of ATAS to investigate the low-energy structures(LES) of above threshold ionization(ATI) region.1. Introduction 1 1.1. Attosecond Transient Absorption Spectroscopy 4 1.1.1. Introduction 4 1.1.2. Simulation Results Based on The Time-dependent Perturbation Theory………………. 10 1.1.3. Absorption Spectra from Experiments 13 1.2. Low-energy Structure 17 2. Numerical Methods 29 2.1. Generalized Pseudospectral Time-dependent Method 29 2.1.1. Generalized Pseudospectral Method for TDSE 29 2.1.2. Split-Operator Method 35 2.1.3. HHG Calculations 38 2.2. Floquet Theory 39 2.2.1. Floquet Formalism in a Periodic Field 40 2.2.2. The Properties of Time-independent Floquet Hamiltonian 43 3. Theory for Non-perturbation Treatment of ATAS Spectra and Low-energy Structure 45 3.1. Theory of ATAS Spectra 45 3.1.1. Formulation 46 3.1.2. The Fourth Order Runge-Kutta Method 52 3.1.3. Dipole Moment and Power Spectra 53 3.1.4. Perturbation Theory of Sub-cycle Oscillation 55 3.2. Theory of Electron Spectra of LES in ATI 57 3.2.1. Formalism 58 3.2.2. Krammers-Henneberger Frame 60 3.2.3. Expression of the Coulomb Interaction with the Core atom 62 4. Theory of Time-frequency analysis 67 4.1. Morlet Wavelet Transform 68 4.2. Synchrosqueezing Transform Method 68 5. Results and Discussion 73 5.1. Emmision Spectra of ATAS problem in hydrogen atom 73 5.1.1. Emission Spectra with Specific Time delay 74 5.1.2. Intensity-dependent Emission Spectra of ATAS problem 76 5.1.3. Sub-cycle Oscillation Features about Emission Lines 79 5.2. Time-frequency Analysis 89 5.2.1. Morlet Wavelet transform 91 5.2.2. SST-Morlet 93 5.3. Low-energy Structure in ATAS 95 6. Conclusion 105 Appendix A 107 Proof of Floquet Theorem 107 References 11