Vibrational-state and isotope dependence of high-order harmonic generation in water molecules

We report calculations on high-order harmonic generation in water molecules. Spectra are determined for various initial vibrational states of ${\mathrm{H}}_2\mathrm{O}$ and its isotope ${\mathrm{D}}_2\mathrm{O}$. It is demonstrated that the ratio of the spectra for ${\mathrm{D}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{O}$ is close to unity when the initial state is the vibronic ground state, indicating that nuclear dynamics is of minor importance. For vibrationally excited initial states, the high-harmonic intensities show a clear dependence on both the initial-state quantum number and the isotopic species.

Figure 1

Harmonic spectra of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$ calculated for a laser wavelength of 800 nm and an intensity of ${10}^{15}$ W/${\mathrm{cm}}^2$. The lower panel shows a spectrum for the case of frozen nuclear motion.

Figure 2

Harmonic spectra of ${\mathrm{H}}_2\mathrm{O}$ (upper panel) and ${\mathrm{D}}_2\mathrm{O}$ (lower panel) calculated for a laser wavelength of 800 nm and an intensity of $0.5\times {10}^{15}$ W/${\mathrm{cm}}^2$.

Figure 3

Modulus squared of the autocorrelation functions for ${\mathrm{H}}_2\mathrm{O}$. Shown is the time dependence for different vibrational states with quantum numbers $j$, as indicated.

Figure 4

Dependence of the intensity of the harmonic peak at harmonic order $n$ on the quantum number of the initial vibrational state in the neutral molecule. Shown are the ratios $R_j({\omega }_n)=S_j({\omega }_n)/S_0({\omega }_n)$ of the signals for two values of $n$ and for the isotopes ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}$, as indicated. Also shown is the ratio $|c_j({\tau }_n)/c_0({\tau }_n)|{}^2$ of autocorrelation functions for ${\mathrm{H}}_2\mathrm{O}$ at the classical excursion time ${\tau }_n$ at which the corresponding harmonic frequency is produced.

Figure 5

Ratio of harmonic signals from ${\mathrm{D}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{O}$ as a function of the quantum number of the initial vibrational state in the neutral molecule. Shown are the ratios of integrated harmonic peaks for two different harmonic orders $n$ (solid blue and dashed red curves) as well as the corresponding ratios expected from the autocorrelation function (dotted blue and dot-dashed red curves).