Laser-assisted XUV double ionization of helium: Energy-sharing dependence of joint angular distributions

By numerically solving the time-dependent Schrödinger equation in full dimensionality, we discuss the dependance of joint photoelectron angular distributions on the energy sharing of the emitted electrons for the double ionization of helium atoms by ultrashort pulses of extreme ultraviolet (XUV) radiation in coplanar emission geometry with and without the presence of a comparatively weak infrared (IR) laser pulse. For IR-laser-assisted single-XUV-photon double ionization, our joint angular distributions show that the IR-laser field enhances back-to-back electron emission and induces a characteristic splitting in the angular distribution for electrons that are emitted symmetrically relative to the identical linear polarization directions of the XUV and IR pulse. These IR-pulse-induced changes in photoelectron angular distributions are (i) imposed by different symmetry constraints for XUV-pulse-only and laser-assisted XUV double ionization, (ii) robust over a large range of energy sharings between the emitted electrons, and (iii) consistent with the transfer of discrete IR-photon momenta to both photoelectrons from the assisting IR-laser field. While selection-rule forbidden at equal energy sharing, for increasingly unequal energy sharing we find back-to-back emission to become more likely and to compete with symmetric emission.

Figure 1

Schematics for (a) four different types of coplanar photoelectron emission patterns for the double ionization of helium: back-to-back emission, side-by-side emission, conic emission, and symmetric emission. (b) Corresponding main features in the joint angular distributions indicated by matching line styles and colors (See text).

Figure 2

Energetics for nonsequential double ionization of helium by two 45 or one 90 eV photons. $I_{p_1}$ and $I_{p_2}$ designate the first and second ionization threshold, respectively, leading a combined excess energy of the emitted electrons of $E_{\text{exc}}=E_1+E_2=11$ eV.

Figure 3

TDCSs in units of $be{V}^{-1}s{r}^{-2}$ for the double ionization of helium and fixed detection angles (a, b) ${\theta }_1=0^{\circ }$, (c) ${60}^{\circ }$, and (d) ${30}^{\circ }$, indicated by the back arrows. The central XUV-photon energy is 99 eV. The black dots with error bars are absolute experimental TDCSs from Ref. [6]. Our calculated results are shown as red dashed lines and normalized to the experimental data at (a) ${\theta }_2={110}^{\circ }$, (b) ${95}^{\circ }$, (c) ${295}^{\circ }$, and (d) ${275}^{\circ }$. (a, c) Equal energy sharing with $E_1=E_2=10\mathrm{eV}$ $\left(\varepsilon =0.5\right)$. (b, d) Unequal energy sharing with $E_1=3\text{eV}$ $\left(\varepsilon =0.15\right)$. The green dotted lines show theoretical results of (a) Huetz et al. [6, 10] and (b–d) Kheifets and Bray [6]. (c, d) The solid blue lines show TDCC results of Palacios et al. [15].

Figure 4

Calculated normalized joint angular distributions for the double ionization of helium by one $\hslash {\omega }_{\text{XUV}}=90$ eV XUV photon at (a) equal energy sharing $\left(\varepsilon =0.5\right)$, (b) unequal energy sharing $\left(\varepsilon =0.1\right)$, and (c) extremely unequal energy sharing $\left(\varepsilon =0.01\right)$. (d) Mutual angular distributions extracted from (a–c), displaying the angular distributions versus the angular difference ${\theta }_{12}$ of the emitted electrons, Eq. (16). The XUV pulse has a peak intensity of ${10}^{14}\text{W}/{\text{cm}}^2$ and pulse length of 1 fs.

Figure 5

Calculated normalized joint angular distributions for the double ionization of helium by two $\hslash {\omega }_{\text{XUV}}=45$ eV XUV photons at (a) equal energy sharing $\left(\varepsilon =0.5\right)$, (b) unequal energy sharing $\left(\varepsilon =0.1\right)$, and (c) extremely unequal energy sharing $\left(\varepsilon =0.01\right)$. (d) Mutual angular distributions extracted from (a–c). The XUV pulse has a peak intensity of ${10}^{14}\text{W}/{\text{cm}}^2$ and a pulse length of 1 fs. For two-photon DI, the angular distributions are insensitive to changes in the energy sharing.

Figure 6

Calculated normalized joint angular distributions for IR laser-assisted single-XUV-photon double ionization of helium by ${10}^{14}\text{W}/{\text{cm}}^2$ peak intensity $\hslash {\omega }_{\text{XUV}}=89$ eV XUV pulses assisted by coincident $3\times {10}^{12}\text{W}/{\text{cm}}^2$ IR-laser pulses. Contribution to the double-ionization yield from (a)–(c) odd and (d)–(f) even total effective numbers of XUV plus IR photons. Results for (a, d) equal energy sharing $\left(\varepsilon =0.5\right)$, (b, e) unequal energy sharing $\left(\varepsilon =0.1\right)$, and (c, f) extremely unequal energy sharing $\left(\varepsilon =0.01\right)$.

Figure 7

Mutual angular distributions for IR-laser-assisted single-XUV-photon double ionization of helium for different energy sharings $\varepsilon$. (a) Contributions to the double-ionization yield from (a) odd and (b) even total effective numbers of XUV plus IR photons. The XUV and IR pulse parameters are the same as described in the caption of Fig. 6. The insets zoom into the distributions near the mutual angles ${\theta }_{12}=0^{\circ }$.

Figure 8

Contributions to the mutual angular distributions for IR-laser-assisted single-XUV-photon double ionization of helium for (a) equal energy sharing and (b) extremely unequal energy sharing with $\varepsilon =0.01$. XUV- and IR-pulse parameters are the same as described in the caption of Fig. 6. The black solid curves correspond to XUV-pulse-only results, blue dotted lines to odd parity, and green dash-dotted lines display even parity. The red dashed curves show coherent additions of odd and even parity contributions.