Strong-field ionization, rescattering, and target structure imaging with vortex electrons

Manifestations of and possibilities related to vortex electrons in strong-field physics are discussed. We present a theory which extends the foundation of a powerful method of target structure and dynamics imaging to vortex electrons. The theory enables one to extract the differential cross section (DCS) for elastic scattering of a vortex electron on the parent ion—a collision property introduced here—from the observable photoelectron momentum distribution (PEMD). We illustrate this by considering strong-field ionization from $\pi$ orbitals in two atoms, Xe and ${\mathrm{He}}^{+}$, and a molecule, ${\mathrm{O}}_2$. The vortex DCS is shown to be sensitive to the target structure. The PEMDs formed by vortex electrons are predicted to be sensitive to the chirality of the target. Extracting vortex DCSs from experimental PEMDs may open a new avenue for rescattering photoelectron spectroscopy.

Figure 1

(a) Schematic of ionization and rescattering for $\sigma$ ($m=0$) and $\pi$ ($m=1$) orbitals of $\mathrm{Xe}\left(5pm\right)$ in a linearly polarized laser field, $\mathbf{F}\left(t\right)=F\left(t\right){\mathbf{e}}_z$. The surfaces on the left show phase fronts of wave packets returning for rescattering. Ionizing orbitals are illustrated on the right. (b) PEMDs $P(k_{\perp },k_z)$ for these orbitals generated by a pulse of amplitude $F_0=0.1$ and duration $T=240$ (frequency $\omega \approx 0.052$) obtained by solving the TDSE. Dashed white lines show the backward rescattering caustic $(k_{\perp }\left(\theta \right),k_z\left(\theta \right))$ parameterized by the scattering angle $\theta$ in the interval ${90}^{\circ }⩽\theta ⩽{180}^{\circ }$. The factorization formula, (4), holds in the vicinity of the caustic. (c) Solid black (TDSE) lines show cuts $P\left(\theta \right)$ of the PEMDs in (b) along the caustic. Dashed red (AA) lines show results obtained in the adiabatic approximation from Eq. (4). Short-dashed blue (right axis) lines show the DCSs along the caustic $|f_m{\left(\theta \right)|}^2$. DCSs are normalized to the AA results at $\theta ={180}^{\circ }$ for $m=0$ and at $\theta ={150}^{\circ }$ for $m=1$.

Figure 2

Top: PEMD $P(k_{\perp },k_z)$ for $\mathrm{He}\left(2p1\right)$ generated by a pulse with $F_0=0.055$ and $T=400$ ($\omega \approx 0.031$) obtained by solving the TDSE. The dashed line shows the caustic. Bottom: The solid black (TDSE) line shows a cut $P\left(\theta \right)$ of the PEMD along the caustic, the dashed red (AA) line shows adiabatic results obtained from Eq. (4), and the short-dashed blue (right axis) line shows the DCS along the caustic $|f_1{\left(\theta \right)|}^2$. The DCS is normalized to the AA results at $\theta ={120}^{\circ }$.

Figure 3

Similar to Fig. 2, but for the $1{\pi }_g$ orbital in ${\mathrm{O}}_2$ at the equilibrium internuclear distance $R=2.28$. The PEMD is generated by a pulse with $F_0=0.08$ and $T=260$ ($\omega \approx 0.048$). The DCS is normalized to the AA results at $\theta ={150}^{\circ }$. In addition, the dash-dotted magenta (right axis) line in the bottom panel shows the DCS for $R=3$.

Figure 4

DCSs $|f_m{(k,\theta )|}^2$ for ${\mathrm{O}}_2$ as functions of the incident momentum $k$ and scattering angle $\theta$ in a region relevant for applications of Eq. (4). Dashed lines show images of the caustic from Fig. 3. The values of $m$ and the internuclear distance $R$ are indicated.