High-order Harmonic Generation From O₂ Molecules

As a very important phenomena of strong-field physics, high order harmonic generation(HHG) has been one of the hottest topics in this field. The long plateau characteristic of high order harmonic spectra makes it a potential source of attosecond pulse. It is also an important tool for molecular structure investigation, such as tomography of electron wave function. In this dissertation, HHG of O2 molecules are investigated as follows:(1) Frequency domain method based on formal scattering theory is adopted. First, the dependence of O2 high order harmonic on angle θ between the molecular axis and laser polarization direction is calculated in the case that the molecular axis lies in the plane perpendicular to the laser propagation. The results show that the intensities of all order harmonics reach maximum when θ equals to about 45 degrees. Then HHG of O2 is investigated in the case that the molecular axis lies in the plane made by laser polarizing direction and laser propagation direction. It is found that the θ dependency of O2 high order harmonics are same for these two cases. The reason for this is due to O2 molecule is rotational symmetric around nuclear axis.(2) Time domain theory is used to study HHG of O2. First Leiwenstein theory which is successfully used in calculating HHG of atoms is extended to calculate the HHG of molecules. by using the Gaussian expression of wave function and Saddle point method, the analytical expression of HHG is given. In the expression, there lies infinite sum of product of four Bessel function. How to change this infinite summation to finite summation without accuracy lose is solved. The result shows that HHG of O2 not only contains odd harmonics but also weak even harmonics. The intensity difference between odd and even harmonics decreases with increasing harmonic order. The intensity dependence of HHG on θ is same with that obtained by frequency domain, that is, the all order harmonics reach maximum when 0 equals to about 45 degree.The time domain theory is a good method for high order harmonic investigation. Besides further analysis of calculated results, the effects of ionization, amplitude and pulse width of laser will be studied in the future.