Dichroism in short-pulse two-color XUV plus IR multiphoton ionization of atoms

Circular and linear dichroism in the angular distributions of photoelectrons in multiphoton ionization of unpolarized atoms by a combination of two short pulses in the extreme ultraviolet (XUV) and infrared (IR) range is theoretically considered. A noticeable circular dichroism is predicted in the case when both XUV and IR pulses are circularly polarized. Here the dichroism may be observed not only in angle-resolved but also in angle-integrated experiments. When the XUV photons are linearly polarized while the IR pulses are circularly polarized, the circular dichroism can be observed only in angle-resolved experiments. In this case the dichroism averaged over a spectral line is small. When both pulses are linearly polarized, the photoelectron yield strongly depends on the angle between the polarizations, which leads to the considerable linear dichroism.

Figure 1

Color-scale plots of DDCS and CD${}^{\left(\mathrm{circ}\right)}$ as functions of photoelectron energy and polar emission angle $\vartheta$. Left panel: DDCS calculated for photoionization of He by right-hand circularly polarized XUV photons at the energy of 120 eV in the field of right-hand circularly polarized IR laser (800 nm, $3.5\times {10}^{12}$ W/cm${}^2$). See other parameters in text. Right panel: Circular dichroism [Eq. (15)] calculated for the same parameters.

Figure 2

Theoretical spectrum (in arbitrary units) for laser-assisted photoionization by right circularly polarized XUV and IR light (red dashed line) and CD${}^{\left(\mathrm{circ}\right)}$ in absolute units (black solid line) at emission angle $\vartheta =\pi /2$. The results are averaged over the time delay between IR and XUV pulses within one optical period. The parameters are the same as in Fig. 1. Dot-dashed line shows the dichroism calculated for a long IR pulse using Eqs. (16, 17, 18).

Figure 3

Calculated angular distributions of photoelectrons (in arbitrary units) generated by left (blue long-dashed line) and right (red short-dashed line) circularly polarized IR light and angular distribution of CD${}^{\left(\mathrm{circ}\right)}$ in absolute units (black solid line): (a) for the central line at the energy of 95.4 eV and (b) for the first sideband at the energy of 97.0 eV. The results are averaged over the time delay between IR and XUV pulses within one optical period. All parameters are the same as in Fig. 1.

Figure 4

Angle-integrated cross section (red dashed curve) in arbitrary units and CD${}^{\left(\mathrm{circ}\right)}$ in absolute units (black solid curve), calculated for the same parameters as in Fig. 1. The results are averaged over the time delay between IR and XUV pulses within one optical period.

Figure 5

Color-scale plots of DDCS and CD${}^{\left(\mathrm{lin}\right)}$ as functions of photoelectron energy and azimuthal emission angle $\varphi$ in the plane perpendicular to the photon beams ($\theta =\pi /2$). Left panel: DDCS calculated for photoionization of He by linearly polarized XUV photons at the energy of 120 eV in the field of right-hand circularly polarized IR laser (800 nm, $2\times {10}^{12}$ W/cm${}^2$). See other parameters in text. Right panel: Circular dichroism [Eq. (15)] calculated for the same parameters.

Figure 6

Theoretical spectrum (in arbitrary units) for laser-assisted photoionization by linearly polarized XUV light in the field of right circularly polarized IR laser (red dashed line) and CD${}^{\left(\mathrm{lin}\right)}$ in absolute units (black solid line) at emission angle $\varphi ={45}^{\circ }$, in the plane perpendicular to the photon beams ($\theta =\pi /2$). The calculations have been done for the same parameters described in the legend of Fig. 5.

Figure 7

Calculated angular distributions of photoelectrons (in arbitrary units) generated by linearly polarized XUV light in the field of right (red long-dashed line) and left (blue short-dashed line) circularly polarized IR light; the angular distribution of CD${}^{\left(\mathrm{lin}\right)}$ in absolute units is shown by black solid line: (a) for the central line at the energy of 95.4 eV and (b) for the first sideband at the energy of 97.0 eV. The observation plane is perpendicular to the photon beams ($\theta =\pi /2$). All parameters are the same as described in the legend of Fig. 5. The dot-dashed lines show the averaged CD (see text).

Figure 8

Color-scale plots of DDCSs and LD as functions of photoelectron energy and azimuthal angle $\varphi$ in the plane perpendicular to the beams ($\theta =\pi /2$). Left panel: DDCS calculated for photoionization of He by linearly polarized XUV photons at the energy of 120 eV in the field of linearly polarized IR laser for parallel polarizations of the beams. Central panel: the same for perpendicular polarizations of the beams. Right panel: LD [Eq. (21)]. All parameters are the same as described in the legend of Fig. 5

Figure 9

Theoretical spectrum (in arbitrary units) for laser-assisted photoionization by linearly polarized XUV pulse in the field of linearly polarized IR laser for parallel (blue short-dashed line) and perpendicular (red long-dashed line) polarizations, and LD in absolute units (black solid line) at the emission angle $\varphi ={40}^{\circ }$ in the plane perpendicular to the beams ($\theta =\pi /2$). The parameters of the beams are the same as described in the legend of Fig. 5.

Figure 10

Calculated angular distributions of photoelectrons (in arbitrary units) generated by linearly polarized XUV and IR pulses with parallel (blue short-dashed line) and perpendicular (red long-dashed line) polarizations and angular distribution of LD in absolute units (black solid line): (a) for the first sideband at the energy of 97.0 eV and (b) for the second sideband at the energy of 98.5 eV. All other parameters are the same as described in the legend of Fig. 5.

Figure 11

Angle-integrated yield of photoelectrons (in arbitrary units) generated by linearly polarized XUV and IR lights with parallel (blue short-dashed line) and perpendicular (red long-dashed line) polarizations and the LD in absolute units (black solid line): (a) for the IR field of $2\times {10}^{12}$ W/cm${}^2$ and (b) for the IR field of $8\times {10}^{10}$ W/cm${}^2$. All other parameters are the same as described in the legend of Fig. 5.