High-order harmonic generation of 1-nonene under linearly polarized laser pulses

High-order harmonic generation of the long-chain molecule 1-nonene (${\mathrm{C}}_9{\mathrm{H}}_{18}$) under a few-cycle linearly polarized laser field was studied using time-dependent density-functional theory. The efficiency and the cutoff frequency of the ${\mathrm{C}}_9{\mathrm{H}}_{18}$ harmonic spectrum are significantly higher than those of the BF molecule irradiated by the same laser pulse. By analyzing the time-frequency behavior of the harmonic and the classical simulation of electron, it is found that the ${\mathrm{C}}_9{\mathrm{H}}_{18}$ harmonics near the cutoff energy are caused by the recombination of electrons from one atom to others of the parent molecule. In addition, the high-order harmonic generation of the long-chain molecule 1,3-Butadiene (${\mathrm{C}}_4{\mathrm{H}}_6$) is also investigated. The harmonics generated by this mechanism can be applied to produce high-intensity isolated attosecond pulses.

Figure 1

The HHG spectra of ${\mathrm{C}}_9{\mathrm{H}}_{18}$ (black solid line), ${\mathrm{C}}_4{\mathrm{H}}_6$ (red dashed line), and BF (blue dotted line). The electric field is polarized along the molecular axis $I=2.84\times {10}^{14}\text{W}/{\mathrm{cm}}^2, \lambda =800\text{nm},\phi =0$.

Figure 2

The dependence of the harmonic cutoff frequency with the peak intensity of the laser pulse for ${\mathrm{C}}_9{\mathrm{H}}_{18}$ (black circle), ${\mathrm{C}}_4{\mathrm{H}}_6$ (red square), and BF (blue triangle) molecules.

Figure 3

Time-frequency behavior (color image) and classical analysis (curves) for the harmonic spectra from (a) ${\mathrm{C}}_9{\mathrm{H}}_{18}$, (b) ${\mathrm{C}}_4{\mathrm{H}}_{16}$, and (c) BF. Classical trajectory analysis is divided into three categories. The black curve represents the calculation result for ignoring the spatial scale of the molecule, which corresponds to the RC mechanism. When considering the spatial scale of the molecule, the red and white curves correspond to the HRC and HDC mechanisms, respectively. The parameters of the driving laser pulse are the same as Fig. 1.

Figure 4

Schematic diagram of the HHG mechanism of ${\mathrm{C}}_9{\mathrm{H}}_{18}$. The black dotted dashed line represents the laser electric field polarized along the molecular axis and the arrowed curve represents the movement of ionized electrons in the laser electric field. The harmonic emission time $t_2$ of the RC mechanism (black dashed line with arrow) originates from the ionization time $t_1$. Two ionization moments $t_1$ and $t_2$ lead to the same harmonic emission time $t_3$, which correspond to HRC (red solid line with arrow) and HDC mechanisms (blue dotted line with arrow), respectively.

Figure 5

Time-dependent evolution of the ionized electronic probability of ${\mathrm{C}}_9{\mathrm{H}}_{18}$. (a)–(j) corresponds to different instants $t$ = 0.6 o.c. to $t$ = 1.5 o.c., and the time interval $\mathrm{\Delta }t=0.1$ o.c. The lasers' parameters are the same as Fig. 1.

Figure 6

(a) Harmonic spectra of ${\mathrm{C}}_9{\mathrm{H}}_{18}$ at different CEPs, $\phi =0\sim 2\pi$ (interval $\pi /18)$; (b) attosecond pulses synthesized by supercontinuum harmonics from different CEPs, $\phi =0\sim 2\pi$ (interval $\pi /6)$. The other parameters of the laser pulse are the same as Fig. 1.

Figure 7

(a) The HHG spectra of the ${\mathrm{C}}_9{\mathrm{H}}_{18}$ molecule, the orientation angle $\theta$ = $0\sim 2\pi$ (interval $\pi /18$). (b) The HHG spectra (black solid line) of the ${\mathrm{C}}_9{\mathrm{H}}_{18}$ molecule when $\theta$ = 0, the isotropic HHG spectrum (red dashed line) and the HHG spectrum (blue dotted line) of the BF molecule when $\theta$ = 0.