Resonance-modulated wavelength scaling of high-order-harmonic generation from ${\mathrm{H}}_2{}^{+}$

Wavelength scaling of high-order harmonic generation (HHG) in a non-Born-Oppenheimer treatment of ${\mathrm{H}}_2{}^{+}$ is investigated by numerical simulations of the time-dependent Schrödinger equation. The results show that the decrease in the wavelength-dependent HHG yield is reduced compared to that in the fixed-nucleus approximation. This slower wavelength scaling is related to the charge-resonance-enhanced ionization effect, which considerably increases the ionization rate at longer driving laser wavelengths due to the relatively larger nuclear separation. In addition, we find an oscillation structure in the wavelength scaling of HHG from ${\mathrm{H}}_2^{+}$. Upon decreasing the laser intensity or increasing the nuclear mass, the oscillation structure will shift towards a longer wavelength of the laser pulse. These results permit the generation of an efficient harmonic spectrum in the midinfrared regime by manipulating the nuclear dynamics of molecules.

Figure 1

. Wavelength scaling of ${\mathrm{H}}_2{}^{+}$ by solving the TDSE in non-BO treatment (red circles with line) and in the fixed-nucleus approximation (blue squares).

Figure 2

(a) Mechanism of HHG enhancement in moving ${\mathrm{H}}_2{}^{+}$. For static ${\mathrm{H}}_2{}^{+}$, the ionization mainly occurs at the equilibrium distance, where the ionization threshold is high (Process 1). For moving ${\mathrm{H}}_2{}^{+}$, the nuclear wave packet is forced to a larger internuclear distance (Process 2) and then the ionization occurs with a lower ionization threshold (Process 3). (b) Harmonic spectra driven by a 1000-nm laser pulse with an intensity of $2.5\times {10}^{14}$ W/${\mathrm{cm}}^2$ for moving ${\mathrm{H}}_2{}^{+}$ (solid line) and static ${\mathrm{H}}_2{}^{+}$ (dashed line). (c) Time frequency analysis of the harmonic spectrum for static ${\mathrm{H}}_2{}^{+}$ in (b). (d) Time frequency analysis of the harmonic spectrum for moving ${\mathrm{H}}_2{}^{+}$ in (b), and time-dependent internuclear distance $\langle R\left(t\right)\rangle$ is also illustrated as the solid line.

Figure 3

(a) Ionization probability as a function of the laser wavelength. (b) Product of the wavelength-dependent ionization probability and the wavelength scaling $\sim {\lambda }^{-5.7}$ in static ${\mathrm{H}}_2{}^{+}$. For comparison, the wavelength-dependence HHG yield in moving ${\mathrm{H}}_2{}^{+}$ is also presented (circles).

Figure 4

Wavelength dependence of HHG yield for moving ${\mathrm{H}}_2{}^{+}$ with the driving laser intensity of $2.5\times I_0, 3\times I_0, 3.5\times I_0$, and $4\times I_0$, where $I_0=1\times {10}^{14}$ W/${\mathrm{cm}}^2$. HHG yields are shifted for clarity.

Figure 5

Wavelength dependence of HHG yield for moving ${\mathrm{H}}_2{}^{+}, {\mathrm{D}}_2^{+}$, and ${\mathrm{T}}_2^{+}$. Here the driving laser intensity is $4\times {10}^{14}$ W/${\mathrm{cm}}^2$ and HHG yields are shifted for clarity.