High-order harmonic generation (HHG) is one of the hottest topics in strong field atomic and molecular physics. In this paper, frequency domain theory which is based on formal scattering theory is extended to study the HHG of O2 molecules under a linearly polarized single mode laser field. The dependence of HHG on the angle θ0 between the laser polarization direction and nuclear axis is investigated. In our calculation, we only consider the contribution of highest occupied molecular orbital (HOMO) and use the single electron approximation. The HOMO is obtained from quantum chemical software Molpro. The intensity of the laser is 5.18 × 1014 W/cm2 and the wavelength is 800 nm. On the one hand, in the case that the nuclear axis lies in the plane perpendicular to the laser propagation direction, we find that the yields of all order harmonics increase with θ0 increasing until the yields reach the maximum values whenθ0 is equal to about 45◦. Then the yields decrease withθ0 increasing and have the minimum values whenθ0 is equal to about 90◦. The analysis shows that the yield of HHG is dominated by the density of electrons in HOMO along the laser polarizing direction in momentum space. On the other hand, in the case that the nuclear axis lies in the plane parallel to laser propagation direction, the dependence of HHG on θ0 is the same as that when the nuclear axis is in the plane perpendicular to laser propagation direction. The reasons for the same results for the two cases lie in the following fact. The HOMO of O2 molecule has πg symmetry which is not rotationally symmetric around nuclear axis. So HHG yield relies on the πg extension orientation. Since the πg extension orientation cannot be fixed, the HHG of O2 should be averaged over the contributions to HHG at all possibleπg extension orientations. This average is equivalent to that the electron density is rotationally symmetric around the nuclear axis and hence leads to the fact that the HHG yield of O2 depends onθ0 rather than the plane that the nuclear axis lies in.
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