Mechanism of laser intensity-dependent below-threshold harmonic generation

Abstract

<sec> High-order-harmonic generation (HHG) is a fundamental atomic and molecular process in strong laser fields and plays a crucial role in the development of ultrafast science and technology. The essential features in HHG, such as the above-threshold harmonic plateau and cutoffs, can be well understood by the semiclassical three-step model. The HHG cutoff occurs approximately at the energy <inline-formula><tex-math id="M1">\begin{document}$3.17{U_{\rm p}} + {I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M1.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}${I_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M2.png"/></alternatives></inline-formula> is the atomic ionization potential, and <inline-formula><tex-math id="M3">\begin{document}${U_{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20191883_M3.png"/></alternatives></inline-formula> is the ponderomotive potential.</sec><sec> In the past, most studies focused on the HHG above the ionization threshold, and the general pattern of the HHG spectrum can be qualitatively explained by means of the strong field approximation (SFA) and the quantum treatment of three-dimensional time-dependent Schr?dinger equation (TDSE). However, the SFA results in inadequate description for the process in the harmonic generation below the ionization threshold since it neglects the Coulomb potential and the detailed electronic structure of atoms. Recently, as a promising method to produce vacuum-ultraviolet frequency comb, the HHG in the near- and below-ionization threshold has been increased considerably. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored.</sec><sec> Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of hydrogen atom by means of the time-dependent generalized pseudospectral method. We study the intensity dependence of the harmonic spectra below the ionization threshold of hydrogen atom in the intense laser field. The high-order harmonic spectra are calculated by the Fourier transform of the atom induced dipole moment in the laser field. The below-threshold harmonic spectra yield is scaled as a function of the laser peak intensity. We find that the spectra yield in below-threshold harmonic generation (BTHG) dependents on the light intensity in the multiphoton ionization regime. And the laser intensity plays an important role in the channel selection process for BTHG. There are mainly two kinds of quantum channels to be responsible for the BTHG. Namely, the generalized short trajectories and the long trajectories, in which the long trajectories are more sensitive to the laser field intensity. Combining with wavelet time-frequency transform, semiclassical trajectories simulation, and quantum channel analysis associated with the laser intensity, the dynamical origin of the BTHG is uncovered.</sec>