Control of the helicity of high-order harmonics generated by bicircular laser fields

High-order harmonics generated by a bicircular laser field have helicities which alternate between $+1$ and $-1$. In order to generate circularly polarized high-harmonic pulses, which are important for applications, it is necessary to achieve asymmetry in emission of harmonics having opposite helicities. We theoretically investigated a wide range of bicircular field component intensities and found areas where both the harmonic intensity is high and the helicity asymmetry is large. We investigated the cases of $\omega –2\omega$ and $\omega –3\omega$ bicircular fields and atoms having the $s$ and $p$ ground states, exemplified by He and Ne atoms, respectively. We have shown that for He atoms, strong high harmonics having positive helicity can be generated using an $\omega –3\omega$ bicircular field with a much stronger second field component. For Ne atoms the helicity asymmetry can be large in a wider range of the driving-field component intensities and for higher harmonic orders. For the stronger second field component the harmonic intensity is higher and the helicity asymmetry parameter is larger for higher harmonic orders. The results for Ne atoms are illustrated with the parametric plots of an elliptically polarized attosecond high-harmonic field.

Figure 1

Focal-averaged results for the helicity asymmetry parameter [left panels (a) and (b)] and the logarithm of the harmonic intensity [right panels (c) and (d)] for HHG by He atoms and $\omega –2\omega$ [upper panels (a) and (c)] and $\omega –3\omega$ [lower panels (b) and (d)] bicircular field with fundamental wavelength 1300 nm. The results are presented in false colors as a function of the natural logarithm of the ratio of the component peak intensities, $\ln (I_r/I_1),r=2,3$, and of the harmonic order $n$. The sum of the component peak intensities is fixed to $I_1+I_r=1.0\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

Focal-averaged results for the helicity asymmetry parameter [upper panel (a)] and the logarithm of the harmonic intensity [lower panel (b)] for HHG by He atoms exposed to an $\omega –3\omega$ bicircular field, presented in false colors as a function of the natural logarithm of the ratio of the field component peak intensities and harmonic order $n$. Other parameters are as in Fig. 1.

Figure 3

Helicity asymmetry parameter presented in false colors as a function of the laser-field intensity $I=I_1=I_r,r=2,3$, and harmonic order $n$ for HHG by Ne atoms exposed to an $\omega –2\omega$ [upper panel (a)] and $\omega –3\omega$ [lower panel (b)] bicircular field with fundamental wavelength 1300 nm. Black solid curve connects the point in which the asymmetry parameter changes the sign.

Figure 4

Focal-averaged results for the helicity asymmetry parameter [left panels (a) and (b)] and the logarithm of the harmonic intensity [right panels (c) and (d)] for HHG by Ne atoms and $\omega –2\omega$ [upper panels (a) and (c)] and $\omega –3\omega$ [lower panels (b) and (d)] bicircular field with fundamental wavelength 1300 nm. The results are presented in false colors as a function of the natural logarithm of the ratio of the component peak intensities, $\ln (I_r/I_1),r=2,3$, and of the harmonic order $n$. The sum of the component peak intensities is fixed to $I_1+I_r=8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 5

Harmonic field of a group of harmonics from $n_1$ to $n_2$, with the values of $n_1$ and $n_2$ denoted in the upper-right corner of each subpanel. High harmonics are generated by Ne atoms exposed to an $\omega –2\omega$ or $\omega –3\omega$ bicircular field. The fundamental laser wavelength is 1300 nm, and the sum of the component peak intensities is fixed to $I_1+I_r=8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2,r=2,3$. Results are presented for different ratios of the intensities as denoted in the upper-left corner of each subpanel.