We theoretically investigate the high-order harmonic generation (HHG) of helium atom driven by bichromatic counter-rotating circularly polarized laser fields. By changing the intensity ratio of the two driving laser fields, the spectral chirality of the HHG can be controlled. As the intensity ratio increases, the spectral chirality will change from positive- to negative-value around a large intensity ratio of the two driving fields when the total laser intensity keeps unchanged. However, the sign of the spectral chirality can be changed from positive to negative around a small intensity ratio of the two driving fields when the total laser intensity changes. At this time, we can effectively control the helicity of the harmonic spectrum and the polarization of the resulting attosecond pulses by adjusting the intensity ratio of the two driving laser fields. As the intensity ratio and the total intensity of the driving laser fields increase, the relative intensity of either the left-circularly or right-circularly polarized harmonic can be enhanced. The attosecond pulses can evolve from being elliptical to near linear correspondingly.

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The polarization property of high harmonics from N 2 molecule is investigated in a bichromatic counter-rotating circularly polarized laser field by solving the two-dimensional time-dependent Schrödinger equation. The left-and right-circularly polarized harmonics are investigated and the results show that the helicity of the harmonic is reversed at particular harmonic orders. We also show that the electron ionized at one lobe of laser field will recombine with two different N nuclei at the same and the following laser lobes, which results in different polarization properties. The spatial distribution of the harmonic degree of circular polarization are presented to illustrate the effect on polarization properties of the electron recombined with different nuclei. The semi-classical analysis and the time-dependent probability density of electron wave packet are also demonstrated which provide a clear picture of the electron recombination process.

We theoretically investigated the properties of the high-order harmonic generation from an argon atom by bichromatic counter-rotating circularly polarized (BCCP) laser field. The harmonic emission processes have been illustrated by numerically solving the two-dimensional time-dependent Schrödinger equation of an atom in intense laser fields. It is found that with the decrease of the right-circularly polarized laser wavelength, the harmonic spectra are gradually splitting and the harmonic orders move towards the higher frequency. Meanwhile, the integer and semi-integer harmonic emission will be generated when the frequency ratios of right- and left-circularly polarized lasers are semi-integer. The emission mechanism of the semi-integer-order harmonics has been investigated by using the rules of photon absorption and emission.

The recombination processes of the electrons in solid are illustrated by solving the time-dependent Schrödinger equation. The results show that the Bohmian trajectories and the time evolution of the electronic probability density agrees very well, which demonstrates that we can use the Bohmian trajectories to investigate the recombination processes of the electrons in solid. We select the region where the probability density of the electron reached the strongest and the weakest as the initial position of the calculated Bohmian trajectories, one can see that the Bohmian trajectories have similar structures. In addition, our results show that the emission time of the solid high-order harmonic generation (HHG) spectra from the time-frequency distribution agrees well with the time that the Bohmian trajectories change direction. By regulating the phase of the electric field, the electrons can move farther, which will result in the broad cutoff of the HHG. We have also demonstrated that the similar structure of the Bohmian trajectories of the solid with a defect for different initial positions disappears due to the broken periodic structure, which further illustrates that the motion processes of the electrons in solid depend on the structure of the solid.