The shift of harmonics with different initial vibrational states in the H${}_{2}^{+}$ molecular ion

Abstract

Molecular high-order harmonic generation of H + 2 and its isotopes is investigated by numerical simulations of the non-Born-Oppenheimer time-dependent Schrödinger equations. The general characteristic of the typical high-order harmonic generation (HHG) spectra for the H + 2 molecule indicates that only the odd harmonics can be generated. Here we show that how the initial vibrational states and nuclear dynamics break down this standard characteristic, i.e. a redshift or blueshift of the harmonics appears. We investigate the effect of the initial vibrational states on the redshift or blueshift of the HHG spectrum under trapezoidal laser pulses. The ionization probability and time-frequency analysis are used to illustrate the physical mechanism of the shift of the harmonics. We also show the HHG spectra from the different isotopes of H + 2 molecule with different initial vibrational states.

Spectral redshift of high-order harmonics by adding a weak pulse in the falling part of the trapezoidal laser pulse

“…[16] Morales et al [17] investigated the electron localization on the HHG, and found that the even-order harmonic generation can be observed. The shift of HHG spectrum with variational initial vibrational states was reported, [18] the redshift and blueshift of HHG can be controlled by changing the initial vibrational state, and the shift of the HHG spectrum can be observed by increasing the nuclear distance R.…”

Spectral shift of solid high-order harmonics from different channels in a combined laser field

“…Through the time-frequency analysis, it is indicated that the spectral redshift can be observed when a weak VUV pulse is added in the falling part of the fundamental pulse. The relationship between the harmonic instantaneous frequency and the laser field intensity is given by ω q (t) = qω + α q [∂ I(t)/∂t], [23,24] where ω 0 is the frequency of the laser field, q is the harmonic order. In the rising part of the laser field, the amplitude of continuous laser cycles is larger than that of the previous laser cycle, ∂ I(t)/∂t > 0.…”

High-order harmonic generation from molecular ions in the coherent electronic states

“…Moreover, by increasing the intensity of the second pump pulse, the population of the 3dσ g state is greatly enhanced and the related dependence of harmonic spectra on the delay time between the second pump pulse and the probe pulse exhibits an obvious redshift. As a frequency modulation of HHG spectra, the redshift has attracted more attention due to its stableness of probing the nuclear motion [25][26][27][28][29]. Both for the parallel orientated resonant system based on the BOA [12] and for the arbitrary aligned nonresonant system based on the NBOA [26], the redshift can be observed.…”

“…Both for the parallel orientated resonant system based on the BOA [12] and for the arbitrary aligned nonresonant system based on the NBOA [26], the redshift can be observed. Moreover, Liu et al revealed the variation of the harmonics from redshift to blueshift with the enhancement of the initial vibrational state for H + 2 [27]. For the molecular system in the single electronic state, the redshift was generally viewed as the frequency modulation of intercycle HHG dynamics on the falling edge of the intense laser field [25][26][27][28][29].…”

“…Moreover, Liu et al revealed the variation of the harmonics from redshift to blueshift with the enhancement of the initial vibrational state for H + 2 [27]. For the molecular system in the single electronic state, the redshift was generally viewed as the frequency modulation of intercycle HHG dynamics on the falling edge of the intense laser field [25][26][27][28][29]. Furthermore, for the molecular system in the coherent state, Bandrauk et al tentatively attributed the redshift in a few-cycle short probe laser field to the single-electron return within one-half laser cycle [30].…”