Effects of nuclear motion on the ionization-induced terahertz radiation of ${\text{H}}_2{}^{+}$ in intense few-cycle laser pulses

We examine the residual current to investigate the conversion efficiency from the few-cycle laser pulse into the terahertz radiation of ${\text{H}}_2{}^{+}$ by solving the time-dependent Schrödinger equation in the non-Born-Oppenheimer approach. It is found that the nuclear motion and high vibrational states will improve the optical-to-terahertz conversion efficiency significantly, while with the increasing of the laser intensity, ionization saturation will suppress the effects of moving nuclei. Moreover, based on the dependence of the residual current on the delay time of the nuclear vibration, we conclude that the terahertz signal may serve as a tool to probe the nuclear dynamics.

Figure 1

Normalized RCD $j_{\text{norm}}$ as a function of the CEP $\varphi$ for ${\text{H}}_2{}^{+}, {\text{D}}_2{}^{+}, X_2{}^{+}$, and ${\text{H}}_2{}^{+}$ (BOA) at $I=1\times {10}^{15}\text{W}/{\mathrm{cm}}^2$.

Figure 2

(a) The propagation of EWP of ${\text{H}}_2{}^{+}$ (BOA) evolving over time at $I=1\times {10}^{15}\text{W}/{\mathrm{cm}}^2, {\varphi }_{\text{opt}}=0.8\pi$. Dotted pink lines indicate the absorbing borders used in the IIR calculation. (b) The average internuclear separations $〈R〉$ of ${\text{H}}_2{}^{+}, {\text{D}}_2{}^{+}$, and $X_2{}^{+}$ in the NBOA case at the same parameters. (c) The corresponding IIRs as function of time for ${\text{H}}_2{}^{+}$ (dashed black line), ${\text{D}}_2{}^{+}$ (dotted red line), $X_2{}^{+}$ (dash dotted blue line), and ${\text{H}}_2{}^{+}$ (BOA) (solid green line).

Figure 3

The maximum absolute value of normalized RCD $j_{\text{max}}$ as function of the laser intensity $I$ for NBOA and BOA cases. The relative differences are given near the data points.

Figure 4

(a) The propagation of EWP of ${\text{H}}_2{}^{+}$ (BOA) evolving over time at $I=1\times {10}^{16}\text{W}/{\mathrm{cm}}^2, {\varphi }_{\text{opt}}=\pi$. Dotted pink lines indicate the absorbing borders. (b) The average internuclear separations $〈R〉$ of ${\text{H}}_2{}^{+}, {\text{D}}_2{}^{+}$, and $X_2{}^{+}$ in the NBOA case. (c) The corresponding IIRs as function of time for ${\text{H}}_2{}^{+}$ (dashed black line), ${\text{D}}_2{}^{+}$ (dotted red line), $X_2{}^{+}$ (dash dotted blue line), and ${\text{H}}_2{}^{+}$ (BOA) (solid green line).

Figure 5

Normalized RCD of ${\text{H}}_2{}^{+}$ at different vibrational states as function of the CEP $\varphi$ at $I=1\times {10}^{15}\text{W}/{\mathrm{cm}}^2$.

Figure 6

The EWPs (a), (b) evolving over time for $v=0$, 5 and the corresponding IIRs (c), (d) at $I=1\times {10}^{15}\text{W}/{\mathrm{cm}}^2, \varphi =0.6\pi$. Dotted pink lines are the absorbing borders. The EWP shown in the dashed blue box indicates the earlier ionized electrons.

Figure 7

(a) The average internuclear separation $〈R〉$ and the average nuclear velocity $〈V〉$ as function of the time without interacting with the laser field. (b) The dependencies of the absolute normalized RCD on the time delay $t_{\text{del}}$ at $I=1,1.5,2\times {10}^{15}\text{W}/{\mathrm{cm}}^2$ at their optimal CEPs. The vertical dashed lines are located at $t_{\text{del}}=4.14$ and 12.43 fs, which indicate the times when nuclei reach their forward and reverse maximum velocities, respectively.

Figure 8

The IIRs (a) and the average internuclear separations $〈R〉$ (b) as a function of time with two cases of time delay 4.14 fs (solid red line) and 12.43 fs (dashed blue line) at $I=1\times {10}^{15}\text{W}/{\mathrm{cm}}^2$.