Pulse-duration dependence of the double-to-single ionization ratio of Ne by intense 780-nm and 800-nm laser fields: Comparison of simulations with experiments

Accurate ab initio calculations of the ratio of double-to-single ionization of Ne atoms in strong laser fields are difficult due to the many-electron nature of the target. Here, with accurate total cross sections carefully evaluated by using the state-of-the-art many-electron $R$-matrix theory for both electron-impact ionization and electron-impact excitation of ${\mathrm{Ne}}^{+}$, we simulate the total double-ionization yields of ${\mathrm{Ne}}^{2+}$ in strong laser fields at 780 and 800 nm for pulse durations in the range from 7.5 to 200 fs based on the improved quantitative rescattering model. The corresponding single-ionization yields of ${\mathrm{Ne}}^{+}$ are calculated within the nonadiabatic tunneling model of Perelomov, Popov, and Terent'ev. The ratio of double-to-single ionization of Ne is then obtained from the calculated double- and single-ionization yields. By normalizing the ratio to the one calculated from solving the time-dependent Schrödinger equation for a short few-cycle pulse, we make quantitative comparisons of our results with experimental data to show that our model predicts the experimental findings very well. Finally, we analyze the pulse-duration dependence of the double-to-single ionization ratio.

Figure 1

Total cross sections for electron-impact ionization and excitation of ${\mathrm{Ne}}^{+}$ from the ground state. Excitation of the configurations (a) $2s2p^6, 2s^{2}2p^{4}3s, 2s^{2}2p^{4}3p$, and $2s^{2}2p^{4}3d$; (b) $2s^{2}2p^{4}4s, 2s^{2}2p^{4}4p, 2s^{2}2p^{4}4d$, and $2s^{2}2p^{4}4f$; (c) $2s^{2}2p^{4}5s, 2s^{2}2p^{4}5p, 2s^{2}2p^{4}5d$, and $2s^{2}2p^{4}5f$. Panel (d) shows the summed total cross sections for ionization and excitation of all configurations in panels (a)–(c).

Figure 2

Returning electron wave packets $W_R\left(E_r\right)$ for Ne in linearly polarized 800-nm laser fields with pulse durations of (a) 7.5 fs, (b) 12 fs, (c) 50 fs, and (d) 200 fs at single peak intensities of 3, 6, and $10\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, respectively. The sharp rapid oscillations in the returning electron wave packets were smoothed out to improve the visibility.

Figure 3

Double- and single-ionization yields for Ne exposed to linearly polarized laser pulses at 800 nm with pulse durations of (a) 200 fs and (b) 50 fs. The experimental data shown in panels (a) and (b) are taken from Larochelle et al. [41] and Bhardwaj et al. [16], respectively. The simulated results from the QRS model for double ionization and the PPT model for single ionization are normalized for good visual agreement with experiment. The calculations include the integration over the focal volume of the laser. The inset shows the measured knee structure in the double-ionization yield for 200 and 50 fs pulses, respectively.

Figure 4

Comparison of the returning electron wave packets from TDSE and SFA2 for Ne in a linearly polarized 800-nm laser field with parameters of (a) 5 fs and $1.8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, (b) 10 fs and $1.8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, and (c) 5 fs and $3.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. Panel (d) shows the ratio of the single-ionization yield from TDSE ($Y_{\text{TDSE}}^{+}$) over the single-ionization yield of PPT ($Y_{\text{PPT}}^{+}$) for Ne in a linearly polarized 800-nm laser field as a function of intensity for pulse durations of 5 and 10 fs, respectively. In panels (a)–(c), the returning electron wave packets of SFA2 are renormalized according to the corresponding TDSE results.

Figure 5

Ratio between double and single ionization as a function of intensity for Ne exposed to linearly polarized laser pulses with (a) pulse duration of 200 fs at a wavelength of 800 nm and pulse duration of 120 fs at a wavelength of 780 nm, and (b) pulse durations of 7.5, 12, 50, and 200 fs at a wavelength of 800 nm. In panel (a), the present simulations are compared with the experimental data of Larochelle et al. [41] and Sheehy et al. [12], as well as with the $S$-matrix calculations of Becker and Faisal [10]. In panel (b), the present results are compared with the experimental data of Bhardwaj et al. [16]. See text for details.

Figure 6

Pulse-duration dependence of the ratio between the total yield of returning electrons $Y^{\text{R}}$ and the total yield of single ionization $Y^{+}$ for Ne in an 800-nm pulse at a peak intensity of $6.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The ratio $Y^{\text{R}}/Y^{+}$ is normalized to unity at 50 fs. See text for details.