Reexamining the high-order harmonic generation of HD molecule in non-Born-Oppenheimer approximation

All-optical reconstruction of k-dependent transition dipole moment by solid harmonic spectra from ultrashort laser pulses

Band structure and transition dipole moment play important roles in high-order harmonic generation from solid materials. In this work we provide a new all-optical technique to reconstruct the momentum-dependent transition dipole moment using the harmonic spectrum from MgO crystal driven by an ultrashort mid-infrared laser pulse. Under the influence of the ultrashort laser pulse, the emitted photon energy and the crystal momentum form a one-to-one match, in the same way between the intensity of the harmonic above the minimum bandgap and the square of the amplitude of the transition dipole moment, resulting in a realization of directly probing the transition dipole moment. Our all-optical method paves a way to image the two-dimensional transition dipole moment of crystals with the inversion symmetry.

A redshift mechanism of high-order harmonics: Change of ionization energy

We theoretically study the high-order harmonic generation of H₂⁺ and its isotopes beyond the Born-Oppenheimer dynamics. It is surprising that the spectral redshift can still be observed in high harmonic spectra of H₂⁺ driven by a sinusoidal laser pulse in which the trailing (leading) edge of the laser pulse is nonexistent. The results confirm that this spectral redshift originates from the reduction in ionization energy between recombination time and ionization time, which is obviously different from the nonadiabatic spectral redshift induced by the falling edge of the laser pulse. Additionally, the improved instantaneous frequency of harmonics by considering the changeable ionization energy can deeply verify our results. Therefore, this new mechanism must be taken into account when one uses the nonadiabatic spectral redshift to retrieve the nuclear motion.

Even harmonic generation in isotropic media of dissociating homonuclear molecules

Isotropic gases irradiated by long pulses of intense IR light can generate very high harmonics of the incident field. It is generally accepted that, due to the symmetry of the generating medium, be it an atomic or an isotropic molecular gas, only odd harmonics of the driving field can be produced. Here we show how the interplay of electronic and nuclear dynamics can lead to a marked breakdown of this standard picture: a substantial part of the harmonic spectrum can consist of even rather than odd harmonics. We demonstrate the effect using ab-initio solutions of the time-dependent Schrödinger equation for and its isotopes in full dimensionality. By means of a simple analytical model, we identify its physical origin, which is the appearance of a permanent dipole moment in dissociating homonuclear molecules, caused by light-induced localization of the electric charge during dissociation. The effect arises for sufficiently long laser pulses and the region of the spectrum where even harmonics are produced is controlled by pulse duration. Our results (i) show how the interplay of femtosecond nuclear and attosecond electronic dynamics, which affects the charge flow inside the dissociating molecule, is reflected in the nonlinear response, and (ii) force one to augment standard selection rules found in nonlinear optics textbooks by considering light-induced modifications of the medium during the generation process.