Dichroism in two-color above-threshold ionization with twisted XUV beams and intense infrared laser fields

We theoretically investigate the two-color above-threshold ionization of atoms and ions by twisted XUV Bessel and Laguerre-Gaussian (LG) beams in the presence of a strong circularly polarized near-infrared (NIR) laser field. The presence of the NIR field modifies the continuum states accessible to the photoelectron. Based on the strong-field approximation, we explore the resulting energy and angular distributions of photoelectron as a function of the beam parameters. In particular, we analyze dichroism signals that arise due to the twisted nature of the XUV beam and the helicity of the NIR field. We focus on the comparison between LG beams and Bessel beams in the paraxial approximation. Here, we find that both beams yield similar results when the paraxial regime is valid. For localized targets, the dichroism signals strongly depend on the size and position of the atoms relative to the beam axis. Moreover, the dichroism signal tends to zero when the XUV LG beam is linear polarized. Detailed computations of the dichroism are performed and discussed for the $4s$ valence-shell photoionization of ${\mathrm{Ca}}^{+}$ ions.

Figure 1

Setup for the two-color ATI of an atom by a short twisted XUV beam (blue) and in the presence of a strong NIR field (orange). The vector $\mathit{b}$ denotes the impact parameter of the target with regard to the common beam axis. The photoelectron is emitted with asymptotic momentum $\mathit{p}$ under the polar emission angle ${\theta }_p$.

Figure 2

Intensity profiles of LG and Bessel beams: (a) the intensity profile of the LG beam on the $x\text{−}y$ plane at $z=0$ for the radial index $p_r=2$ and the OAM $m=4$. (b) and (c) show the comparison of the transverse intensity profile for the LG and Bessel beams with different radial indices, opening angles, and OAM.

Figure 3

Photoionization probabilities $P^{\left(l\right)}\left(\mathit{p}\right)$ for a macroscopic atomic target as a function of the sideband number $l$ and the emission angle ${\theta }_p$. The calculation was performed for (a) an XUV Bessel beam with opening angle ${\theta }_k=0.2\mathrm{rad}$ and frequency ${\omega }_X=3\mathrm{a}.\mathrm{u}.=81.6\mathrm{eV}$, (b) a circularly polarized XUV LG beam, and (c) a linearly polarized XUV LG beam with frequency ${\omega }_X=3\mathrm{a}.\mathrm{u}.$ and beam-waist ${\omega }_0=100\mathrm{nm}$. The chosen parameters for the NIR field are $A_L=0.1\mathrm{a}.\mathrm{u}.$ and ${\omega }_X=0.05\mathrm{a}.\mathrm{u}.=1.36\mathrm{eV}$.

Figure 4

Dichroism signals for the two-color photoionization of the $4s$ valence shell of ${\mathrm{Ca}}^{+}$ as a function of the emission angle ${\theta }_p$ and the sideband number $l$. Results are shown for Bessel beams with opening angles ${\theta }_k=0.2$ and ${\theta }_k=0.6\mathrm{rad}$, respectively, photon energy ${\omega }_X=3\mathrm{a}.\mathrm{u}.=81.6\mathrm{eV}$, and with the OAM $m=4$. The atomic target is placed on two different impact parameters $b_0$, namely, on the first maximum of transverse intensity on the $x\text{−}y$ plane and on the half of this impact parameter. The target size is ${\sigma }_b=10\mathrm{nm}$. The photoelectrons are observed at the azimuthal angle ${\phi }_p=\pi /2$. The black dotted curves indicate the sideband cutoffs.

Figure 5

The same as in Fig. 4 but for a Bessel beam with opening angle ${\theta }_k=0.2\mathrm{rad}$ and a LG beam with beam-waist ${\omega }_0=65\mathrm{nm}$, respectively. The photon energy of both beams is ${\omega }_X=3\mathrm{a}.\mathrm{u}.=81.6\mathrm{eV}$ and the OAM $m=4$. The atomic target is placed at impact parameter $b_0=65\mathrm{nm}$. As target sizes are chosen, ${\sigma }_b=1\mathrm{nm}$ (first and second columns) and ${\sigma }_b=100\mathrm{nm}$ (third and fourth columns). The photoelectrons are observed at the azimuthal angle ${\phi }_p=\pi /2$. The black dotted curves indicate the sideband cutoffs.