Full Quantum Theory Of High Harmonic Generation And Its Cutoff Law

High harmonic is an important nonlinear optical effect in the process when strong laser fields interacting with matters including atoms, molecules, clusters and plasmas. Based on the formal scattering theory of Guo, Aberg, and Crasemann (GAC), which has no artificial assumptions, High harmonic generation (HHG) is studied from the first principle at the first time. Using the properties of ordinary Bessel functions and the Einstein photoelectric law in the strong-field case, we reveal a new cutoff law of HHG. Since the GAC theory was created from the study of above-threshold ionization and later was verified experimentally by the Kapitza-Dirac (KD) effect in the strong fields, the KD diffraction effect is also theoretically investigated in this thesis. The results are as follows.1) Based on the formal scattering theory of GAC, which has no artificial assumptions, HHG is studied from the first principle at the first time. The HHG spectra of different atoms are also calculated. The depressing of even-order harmonics is an automatic feature of this theory. The new cutoff law of HHG is discussed in details.2) Using the properties of ordinary Bessel functions and the Einstein photoelectric law in the strong-field case, we reveal a new cutoff law qchω= 3.34Up+1.83Ip of HHG with mathematical deduction method and graphical method, which coincides well with the T. Popmintchev’s experimental result published on Science in 2012. This cutoff law also agrees well with the calculation using our new HHG transition rate formula. Thus, we obtain four independent evidences for the same cutoff law of HHG.3) We theoretically reproduce the KD diffraction pattern in Batelaan’s experiment: for a strictly parallel standing light wave, a perpendicularly incident electron beam cannot diffract due to energy-momentum conservation; while a nonperpendicularly incident electron beam can diffract when a focused standing light wave with a thin waist We get theoretically a critical minumum laser intensity in the KD diffraction effect, and predict that the electron diffraction pattern will have sidebands.