Polarization effects in the total rate of biharmonic $\omega +3\omega$ ionization of atoms

The total ionization rate of biharmonic ($\omega +3\omega$) ionization is studied within the independent particle approximation and the third-order perturbation theory. Particular attention is paid to how the polarization of the biharmonic light field affects the total rate. The ratios of the biharmonic ionization rates for linearly and circularly polarized beams as well as for corotating and counter-rotating elliptically polarized beams are analyzed, and how they depend on the beam parameters, such as photon frequency or phase between $\omega$ and $3\omega$ light beams. We show that the interference of the biharmonic ionization amplitudes determines the dominance of a particular beam polarization over another and that it can be controlled by an appropriate choice of beam parameters. Furthermore, we demonstrate our findings for the ionization of neon $L$ shell electrons.

Figure 1

Schematic representation of the electric dipole ionization pathways in biharmonic $\omega +3\omega$ ionization of atoms. Both the one- and three-photon ionization always lead to at least one partial wave of the free electron that coincides with and gives rise to the interference effects in the total biharmonic rates.

Figure 2

Schematic representation of the electric dipole ionization pathways in biharmonic $\omega +3\omega$ ionization of atoms for a specific case of the $s$ electron. Both the one- and three-photon ionization pathways lead to the $s\to p$ ionization pathway which proceeds through different paths. In this example, the one-photon ionization pathway interferes with two three-photon ionization pathways.

Figure 3

Total biharmonic $\omega +3\omega$ ionization rate as a function of incident photon energy. The rates are shown for ionizing the neon $2s_{1/2}$ (left) and $2p_{3/2}$ electrons (right) by linearly (top) and circularly (bottom) polarized biharmonic light. An intensity of the fundamental light beam $I^{\left(\omega \right)}=1.0\times {10}^{14}\text{W}/{\text{cm}}^2$ was used, while the intensity of the third-harmonic beam was chosen to be $I^{\left(3\omega \right)}=1.1\times {10}^{11}\text{W}/{\text{cm}}^2$ for ionization of the $2s_{1/2}$ electrons and $I^{\left(3\omega \right)}=8\times {10}^{11}\text{W}/{\text{cm}}^2$ for $2p_{3/2}$ electrons. The phase difference between the fundamental and third-harmonic light beam was set to zero in the above plots.

Figure 4

The ratio of the ionization rates for linear polarization vs circular polarization is plotted against the photon energy. The above plot describes the ionization of $2s_{1/2}$ (top) and $2p_{3/2}$ (bottom) electrons for three different phase differences between the first- and third-harmonic light beams. In the above plots, an intensity of the fundamental light beam $I^{\left(\omega \right)}=1.0\times {10}^{14}\text{W}/{\text{cm}}^2$ was applied, while the intensity of the third-harmonic beam was fixed to be $I^{\left(3\omega \right)}=1.1\times {10}^{11}\text{W}/{\text{cm}}^2$ for the ionization of the $2s_{1/2}$ electrons and to $I^{\left(3\omega \right)}=8\times {10}^{11}\text{W}/{\text{cm}}^2$ for $2p_{3/2}$ electrons.

Figure 5

Ionization of neon $2s_{1/2}$ electrons by corotating (solid blue) and counter-rotating (dash-dotted orange) biharmonic $\omega +3\omega$ beams. The photon energy was chosen near to the threshold at $\omega =26.7\mathrm{eV}$, the polarization of the third harmonic is chosen to be right-circular ${\gamma }^{\left(3\omega \right)}=1$, while the ellipticity of the fundamental frequency ${\gamma }^{\left(\omega \right)}$ is varied. The intensity of the fundamental beam $I\left(\omega \right)={10}^{14}{\mathrm{W}/\mathrm{cm}}^2$ and of the third harmonic $I\left(3\omega \right)=1.1\times {10}^{11}{\mathrm{W}/\mathrm{cm}}^2$ which gives rise to the same one- and three-photon ionization rates. Rates for ionization by biharmonic beams with $\varphi =0,\pi /2,\text{and}\pi$ phase difference (top three plots, respectively) are shown as functions of the ellipticity of the fundamental beam ${\gamma }^{\left(\omega \right)}$. The dichroism parameter corresponding to these three considerations is shown at the bottom.