Photoelectron momentum distributions of atomic and molecular systems in strong circularly or elliptically polarized laser fields

Photoelectron momentum distributions of a hydrogen atom in an elliptically polarized laser field and a hydrogen molecular ion in a circularly polarized laser field are studied by simulating the time-dependent Schrödinger equation. We demonstrate that, in both systems, the Coulomb interaction between a liberated electron and its parent ion is essential for the photoelectron momentum angular drift in a laser polarization plane. By decomposing the wave packet into the rescattered and directly ionized components in the case of a hydrogen molecular ion, we reveal that the rescattered component drifts by a larger angle. The drift angle of the photoelectron of the hydrogen atom decreases monotonically with longer wavelength, while a nonmonotonic dependence is shown for ${{\text{H}}_2}^{+}$. We attribute such nonmonotonicity to the fluctuation of the instant of ionization for ${{\text{H}}_2}^{+}$ as the laser wavelength is changed.

Figure 1

The PMDs for (a)–(f) H and (g)–(l) ${{\text{H}}_2}^{+}$ models with screened Coulomb potentials. The distributions are normalized so that the maximum value in each panel is equal to unity for better comparison. (a) and (g) The Coulomb potentials are completely neglected. (b)–(f) The cutoff radii were set as $r_0=2$, 6, 10, 15, and 100 a.u., respectively. (h)–(l) The cutoff radii were set as $r_0=3$, 4, 10, 15, and 100 a.u., respectively. The laser intensity was set at $1\times {10}^{14}\text{W}/{\text{cm}}^2$, and the wavelength was 800 nm for all the simulations in this figure. (a)–(f) The major axis of the polarization ellipse is along the $x$ axis. (g)–(l) The molecular axis is along the $x$ axis. The angle $\theta$ in (l) is used to quantify PMDs.

Figure 2

Sketch of possible paths for direct ionization (red solid arrow) and rescattering ionization (blue dashed arrow) components of the wave packet. Two boundaries $r_{\text{d}}=8$ a.u. and $r_{\text{s}}=5$ a.u. were used for the decomposition.

Figure 3

The PMDs of (a)–(c) direct ionization $|{\tilde{\mathrm{\Psi }}}_{\text{d}}{\left(\mathbf{p}\right)|}^2$, (d)–(f) rescattering ionization $|{\tilde{\mathrm{\Psi }}}_{\text{r}}{\left(\mathbf{p}\right)|}^2$, and (g)–(i) full ionization $|{\tilde{\mathrm{\Psi }}}_{\text{d}}\left(\mathbf{p}\right)+{\tilde{\mathrm{\Psi }}}_r{\left(\mathbf{p}\right)|}^2$ of (a), (d), and (g) H, (b), (e), and (h) $\mathrm{H}{{}_2}^{+}$ at internuclear distance 2 a.u., and (c), (f), and (i) $\mathrm{H}{{}_2}^{+}$ at internuclear distance 5 a.u. The laser pulse has the wavelength 800 nm and the intensities (a), (d), and (g) ${10}^{14}\text{W}/{\text{cm}}^2$, (b), (e), and (h) $1.42\times {10}^{14}\text{W}/{\text{cm}}^2$, and (c), (f), and (i) ${10}^{14}\text{W}/{\text{cm}}^2$. The PMDs are normalized so that the maximum values in (g)–(i) are equal to unity.

Figure 4

(a) Drift angle as a function of laser wavelengths and intensities. (b) The cut of (a) at a laser intensity $6\times {10}^{13}\text{W}/{\text{cm}}^2$ (black solid line). For reference, the drift angle of the PMD for H is shown by the red dashed curve when the same laser parameters are applied.

Figure 5

Time-dependent ionization rate for (a) H and (b) ${{\text{H}}_2}^{+}$. (c) Photoelectron emission timing $t_b$ of ${{\text{H}}_2}^{+}$ as a function of laser wavelengths. The laser intensity was $6\times {10}^{13}\text{W}/{\text{cm}}^2$. See the text for the calculation of $t_b$.

Figure 6

The PMD from ${{\text{H}}_2}^{+}$ aligned at the angles (a) 0, (b) $\pi /4$, and (c) $\pi /2$ from the major polarization axis. (d) Statistical average of the PMD assuming ${{\text{H}}_2}^{+}$ is randomly aligned in the laser polarization plane. The internuclear distance is fixed at $R=5$ a.u., the ellipticity of the laser field is $\epsilon =0.6$, and the laser intensity is $1\times {10}^{14}\text{W}/{\text{cm}}^2$.