Origins of complex interference structures in harmonic emission from stretched molecular ion with large internuclear distances
Authors: Li Wei-Yan  , Liu Na  , Wang Shang  ,   1 School of Mathematics and Science, Hebei Key Laboratory of Optoelectronic Information and Goe-detection Technology, Hebei GEO University, Shijiazhuang 050031, China;,   2 College of Physics, Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang 050024, China
Published: March 2023

We study high-order harmonic generation (HHG) from stretched molecular ions with large internuclear distances numerically and analytically. We focus on the fine structure of the HHG spectrum related to the contributions of short electron trajectory. In our simulations through numerical solution of time-dependent Schrodinger equation (TDSE), we use a trajectory-dependent filtering procedure to separate the short-trajectory contributions from other contributions of long trajectory and multiple returns. Our TDSE results show that the short-trajectory HHG spectra of molecular ion with larger internuclear distances show some complex interference structures characterized by some remarkable dips and the positions of the dips are sensitive to the laser parameters. With a developed model arising from strong-field approximation (SFA), we are able to identify the physical origins of the complex interference structures. This model considers the charge-resonance effect which induces the strong coupling between the ground state and the first excited state of the molecular ion at large internuclear distance. In this model, the well-known effect of two-center interference occurs in terms of the canonical momentum instead of the momentum related to the instantaneous velocity of the electron in the general SFA. We show that some dips in TDSE results arise from two-center interference of the electronic wave between these two atomic cores of the molecule in the ionization process, while others come from that in the recombination process. These ionization and recombination dips alternately appear in the HHG spectra, with forming the complex interference structures. The main differences between the interference effects in the ionization and the recombination processes are twofold. Firstly, in the ionization process, the destructive two-center interference strongly suppresses the forming of the continuum wavepacket, while in the recombination process, the recombination of the rescattering electron to other bound eigenstates with small weights can also contribute to HHG bedsides the recombination to the ground state and the first excited state with large weights. As a result, in TDSE results, the ionization dips are deeper and more remarkable than the recombination ones. Secondly, in the recombination process, the Coulomb acceleration remarkably changes the de Broglie wavelength of the rescattering electron and therefore changes the position of the interference-induced dip, while in the ionization process, the Coulomb potential plays a small role in the interference effect. As a result, the interference dips in the ionization and the recombination processes differ from each other.