Probing the ionization wave packet and recollision dynamics with an elliptically polarized strong laser field in the nondipole regime

We explore ionization and rescattering in strong mid-infrared laser fields in the nondipole regime over the full range of polarization ellipticity. In three-dimensional photoelectron momentum distributions (3D PMDs) measured with velocity map imaging spectroscopy, we observe the appearance of a sharp ridge structure along the major polarization axis. Within a certain range of ellipticity, the electrons in this ridge are clearly separated from the two lobes that commonly appear in the PMD with elliptically polarized laser fields. In contrast to the well-known lobes of direct electrons, the sharp ridge is created by Coulomb focusing of the softly recolliding electrons. These ridge electrons are directly related to a counterintuitive shift of the PMD peak opposite to the laser beam propagation direction when the dipole approximation breaks down. The ellipticity-dependent 3D PMDs give access to different ionization and recollision dynamics with appropriate filters in the momentum space. For example, we can extract information about the spread of the initial wave packet and the Coulomb momentum transfer of the rescattering electrons.

Figure 1

Reconstructed isosurface of a 3D PMD with a partial cut in the polarization plane $(p_x,p_y)$. The 3D PMD is produced by a mid-IR laser pulse with a center wavelength of $3.4\mu \mathrm{m}$, a pulse length of 50 fs, a peak intensity of $6\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$, and an ellipticity of $\epsilon =0.11$. The ridge structure (which is due to rescattering of ionized electrons with the parent ion) around $p_y=0$ is clearly separated from the common main lobes (which are due to direct electrons).

Figure 2

PMDs in the polarization plane measured at a peak intensity of $6\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$ for the ellipticities 0, 0.03, 0.07, 0.11, 0.15, 0.19, in (a) to (f), respectively. The central spot stemming from Rydberg states was covered by a black dot for illustration purposes [51, 52]. The PMDs shown are projections from the range $|p_z|<0.06$ a.u. onto the polarization plane. These PMDs reveal a sharp line structure for ellipticities of $\epsilon =0.07$ and $\epsilon =0.11$ (indicated by black arrow) that disappears for larger ellipticity. Corresponding classical trajectory Monte-Carlo (CTMC) calculations with $\epsilon =0.07$ are shown in (g) and (h). In (h), the Coulomb potential is neglected for the CTMC calculation, and no ridge structure is visible.

Figure 3

(a) $p_z$ position of the peak of the complete projection of the measured PMDs onto the beam propagation axis ($p_z$) as a function of ellipticity for constant intensity. We observe a transition from negative to positive values of $p_z$ with a zero crossing at $\epsilon \approx 0.12$. (b) Projection of a complete reconstructed 3D PMD recorded at a peak intensity of $6\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$ and an ellipticity of $\epsilon =0.11$ together with the corresponding result from CTMC simulations. The sharp line structure is clearly visible around $p_y=0$. (c) Projections of the PMD onto the beam propagation axis ($p_z$) for direct electrons (blue marker, with filter $|p_y|>0.05$ a.u. applied) and CF electrons (red marker, with filter $|p_y|<0.05$ a.u. applied) together with the corresponding result from CTMC simulations (solid). The peak of the CF electrons is shifted opposite to the beam propagation direction, whereas the direct electrons are shifted in beam propagation direction.

Figure 4

CTMC calculations for electrons that originate within the central half cycle of the pulse. The central figures (d) show the ridge region for two ellipticities $\epsilon =0$ (left) and for $\epsilon =0.07$ (right). We show the PMDs projected over the range $|p_z|<0.06$ a.u. Characteristic points Bn indicate trajectories with $n$ recollisions with the parent ion. The sharp ridge is visible as a line through the points Bn. Panels (a)–(c) and (e)–(g) show the initial conditions for the trajectories having final momenta near points B2 (a) and (e), B3 (b) and (f), and B4 (c) and (g). The final momentum is within a ${\left(0.01\right)}^3$ a.u. bin around the points Bn: $p_x\left(B2\right)=0.61$, $p_x\left(B3\right)=0.44$, $p_x\left(B4\right)=0.29$. Note that there is a positive offset in $p_{yi}$ of the structures in the right column, which arises due to the ellipticity. The additional offset in the $p_{zi}$ direction is caused by the combined influence of the magnetic field and the Coulomb potential. (h) Schematic of the different contributions to the shift of the ring of the initial momenta with respect to the linear case in dipole approximation. The ellipticity induces a shift of $\delta p_{yi}$ in $p_y$ direction whereas the nondipole effects induce a shift in the $p_z$ direction of $\delta p_{zi}$. $|{\mathbf{p}}^C|$ denotes the Coulomb momentum transfer upon recollision.

Figure 5

Offsets of the peak of the projection of the PMDs from CTMC simulations onto the beam propagation axis ($p_z$) as a function of ellipticity. In (a) we show the offsets for various atomic species. The peak intensity was kept at a constant value of $6\times {10}^{13}{\text{W/cm}}^2$. We observe a transition from negative to positive values that is only weakly dependent on the species. In (b) we show the offsets for various momentum spreads of the initial wave packet with respect to the one expected from xenon. The results show a clear dependence of the zero transition on the momentum spread of the initial wave packet.