Molecular Symmetry-Mixed Dichroism in Double Photoionization of ${\mathrm{H}}_2$

Dichroism in double photoionization of ${\mathrm{H}}_2$ molecules by elliptically polarized extreme ultraviolet pulses is formulated analytically as a sum of atomiclike dichroism (AD) and molecular symmetry-mixed dichroism (MSMD) terms. The MSMD originates from an interplay of ${{}^1\mathrm{\Sigma }}_u^{+}$ and ${{}^1\mathrm{\Pi }}_u^{+}$ continuum molecular ionization amplitudes. For detection geometries in which the AD vanishes, numerical results for the sixfold differential probabilities for opposite pulse helicities show that the MSMD is significant in the electron momentum and angular distributions and is controllable by the ellipticity.

Figure 1

Two geometries for detecting the outgoing electron momenta, ${\mathbf{p}}_1$ and ${\mathbf{p}}_2$, that allow direct access, measurement, and control of the MSMD in DPI of fixed-in-space ${\mathrm{H}}_2$ by an elliptically polarized light pulse whose propagation direction, $\widehat{\mathbf{k}}\parallel \widehat{\mathbf{z}}$, is perpendicular to the molecular vector, $\mathbf{R}\parallel \widehat{\mathbf{x}}$. (a) Perpendicular electron ejection with ${\mathbf{p}}_1\parallel \widehat{\mathbf{k}}$ and ${\mathbf{p}}_2$ in the laser polarization plane $(\widehat{\mathit{\epsilon }},\widehat{\mathit{\zeta }})$ with spherical angles, ${\theta }_2=\pi /2$, ${\phi }_2$. (b) Back-to-back electron ejection in the polarization plane with ${\theta }_1={\theta }_2=\pi /2$ and ${\phi }_2={\phi }_1-\pi$. In all panels, $0\le {\phi }_2\le 2\pi$ and we fix $\widehat{\mathbf{k}}\parallel \widehat{\mathbf{z}}$, $\widehat{\mathit{\epsilon }}\parallel \widehat{\mathbf{x}}$, and $\widehat{\mathit{\zeta }}\parallel \widehat{\mathbf{y}}$. The origin of coordinates is at the center of mass of the nuclei.

Figure 2

TDSE results (12) (in units of ${10}^{-8}\mathrm{a}.\mathrm{u}.$) for the ${\mathbf{p}}_2$ distributions in the polarization $xy$ plane for DPI of ${\mathrm{H}}_2$ by a right- (column 1) or left-handed (column 2) elliptically polarized (REP or LEP) attosecond pulse, with $\widehat{\mathbf{k}}\perp \mathbf{R}$ (indicated by the dumbbell shape), for the geometry in Fig. 1. The circular polarization degree is $\xi =\pm 1$ (rows 1,2), $\xi =\pm 0.8$ (row 3), and $\xi =\pm 0.38$ (row 4). The two electrons share the excess energy $0.1\le E\le 41.6\mathrm{eV}$ in the ratio $ϵ\equiv E_1/E$: row 1 (UES), $ϵ=25\%$; rows 2,3,4 (EES), $ϵ=50\%$.

Figure 3

(a) Energy-integrated angular distributions for RCP (solid line) and LCP (dashed line) obtained from the SDPs shown in Figs. 2 and 2 for UES; (b) Corresponding results for EES from Figs. 2 and 2; (c) Energy-sharing sensitivity of the energy-integrated MSMD [obtained as the RCP-LCP difference of the results in each of (a) and (b)]; (d) Dependence of the energy-integrated MSMD for EES on the degree of circular polarization $\xi$.