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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.

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We investigate the ellipticity of the high-order harmonic generation from the oriented $\textrm{H}_{2}^{+}$ exposed to a linearly polarized laser field by numerically solving the two dimensional time-dependent Schr$\ddot{\textrm{o}}$dinger equation (2D TDSE). Numerical simulations show that the harmonic ellipticity is remarkably sensitive to the alignment angle. The harmonic spectrum is highly elliptically polarized at a specific alignment angle $\theta = 30^\circ $, which is insensitive to the variation of the laser parameters. The position of the harmonic intensity minima indicates the high ellipticity, which can be attributed to the two-center interference effect. The high ellipticity can be explained by the phase difference of the harmonics. The results that we obtain facilitates the synthesis of a highly elliptical isolated attosecond pulses with duration down to 65 as, which can be served as a powerful tool to explore the ultrafast dynamics of molecules and study chiral light-matter interaction.

We investigate the high-order harmonic generation (HHG) of the helium atom at the various intensity ratios of the counter-rotating two-color circularly polarized laser fields. The results show that the cutoff energy of the harmonic spectra can be affected by changing the intensity ratios. By comparing the results from different intensity ratios, we find that the distances the electrons travel are short when the intensity ratio is increased. The dependence of the cutoff position in the HHG on the intensity ratios usually results from the classical trajectories of the electrons. As the intensity ratio increases, the electrons cannot be accelerated and it will gain less energy. As a result, the harmonic spectra are cut off at the lower energy. We compare the quantum and classical trajectories results to illustrate the reasons of the cut off dependence.