In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wave function of the molecular orbital from which the electron is removed. The orbital wave functions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory. We show that the asymptotic wave function can be improved with an iteration method and after one iteration accurate asymptotic wave functions and structure parameters are determined. With the new parameters we examine the alignment-dependent tunneling ionization probabilities for several molecules and compare with other calculations and with recent measurements, including ionization from inner molecular orbitals.

We report theoretical calculations of high-order harmonic generation (HHG) by intense infrared lasers in atomic and molecular targets taking into account the macroscopic propagation of both fundamental and harmonic fields. On the examples of Ar and N2, we demonstrate that these ab initio calculations are capable of accurately reproducing available experimental results with isotropic and aligned target media. We further present detailed analysis of HHG intensity and phase under various experimental conditions, in particular, as the wavelength of the driving laser changes. Most importantly, our results strongly support the factorization of HHG at the macroscopic level into a product of a returning electron wave packet and the photorecombination transition dipole under typical experimental conditions. This implies that the single-atom or single-molecule structure information can be retrieved from experimentally measured HHG spectra.

We investigate high-order harmonic generation (HHG) in a thin macroscopic medium by solving Maxwell’s equation using microscopic single-atom induced dipole moment calculated from the recently developed quantitative rescattering (QRS) theory. We show that macroscopic HHG yields calculated from QRS compared well with those obtained from solving the single-atom time-dependent Schrödinger equation but with great saving of computer time. We also show that macroscopic HHG can be expressed as a product of a “macroscopic wave packet” and the photorecombination cross section of the target gas. The latter enables us to extract target structure from the experimentally measured HHG spectra, thus paves the way to use few-cycle infrared lasers for time-resolved chemical imaging of transient molecules with few-femtosecond temporal resolution.

In recent years intense mid-infrared lasers with wavelength of a few microns have become the standard tools for research in strong field physics laboratories worldwide. These lasers offer the opportunities to extend the traditional study of high-order harmonics generation and attosecond sciences from the extreme ultraviolet to soft x-rays. In this tutorial we revisit the familiar strong field approximation and its simplification—the quantum orbits theory. We draw special emphasis on the factorization of laser induced dipole moment as the product of a returning electron wave packet with the photo-recombination dipole transition matrix element. The former depends on the laser properties only (up to a normalization constant) while the latter is related to laser-free photoionization transition dipole. The factorization leads to the suggested modification beyond the strong field approximation—the quantitative rescattering theory. In applying these theories to mid-infrared lasers, we analyze the behavior of the returning electron wave packet and its scaling properties vs the wavelength of the laser. A few examples are given to demonstrate how the quantitative rescattering theory is capable of reproducing experimental harmonic spectra under various conditions. Future opportunities in employing harmonics generated by optimized mid-infrared lasers for probing molecular structure and for serving as useful table-top coherent light sources up to the x-ray region are also discussed.

High-order harmonic generation (HHG) from hexagonal boron nitride is simulated by solving extended multiband semiconductor Bloch equations under strong laser fields. By changing the angle of the laser polarization with respect to the crystal orientation, we find that harmonic spectra present a double-plateau structure and HHG is dominantly emitted along Γ-M direction in the first plateau, but special anisotropic distribution is observed in the secondary plateau. In-depth analyses reveal that two plateaus originate from different pair of conduction band and valence band, and the shapes of band dispersion and transition dipole moment determine anisotropic harmonic emission in $h$-BN crystal. Furthermore, we show that band energies of high-lying unoccupied bands and low-lying occupied ones can be directly extracted from laser polarization dependent high harmonic spectra. This paves a way to image the two-dimensional band information of solid materials by using laser-induced HHG.