The Research Of Hyper-Raman Radiations In High-Order Harmonics Generation

The interaction of intense laser pulses with atoms, molecules, cluster, and solids can lead to high-order harmonics generation (HHG). In terms of the three-step model, the mechanism of HHG is often interpreted that the electron is ionized to the continuum state first by absorbing photons and then comes back again, recombines to the parent ion to emit a photon.Besides the odd order harmonic lines, it is predicted that there are also the hyper-Raman (HR) lines in the photon emission spectrum. These lines caused, differently from the HHG, by the atom first absorbs photos to a virtual energy from initial state and transits to another state and emits a photo. The HR lines are located at frequencies ofωhR = 2nω0±ωi, where n is an integer,ω0 is the frequency of laser pulse,ωi is the energy difference between the initial and final state. In my paper, the HR lines are caused mainly by the transition takes place from the first excited state to the ground state. So thatωi is the energy difference between the first excited state and the ground state.Although the physical process of the HR lines generation is well understood, they have never observed in the photon emission spectrum in an actual experiment. In this paper, we choose the proper laser pulse or prepare the initial states as the coherent superposition state between the ground and the first excited state. The HR lines can be seen in the photon emission spectrum with a long laser pulse that's the intensity relationally weak; moreover, we have demonstrated the advantage of using coherent superposition state to obtain the high conversion efficiency of the HR emission.Firstly, we discuss the influence of the peak field amplitude of the laser pulse on the HR emission. To illustrate this point, we choose different peak field amplitude F0 =0.08 and 0.14, respectively. When we take a field intensity of F0 =0.14., the emission spectrum presents a full comb of odd harmonic lines with the well plateau and cut-off position at the empirical formula I p + 3.17Up, and the HR lines are more likely to contribute only to the continuous background. When we take a field intensity of F0 =0.08a.u. , not only high harmonics but also the HR lines with other frequencies could be clearly observed in the emission spectrum; moreover, the positions of the HR lines are agreeable with the result from the empirical formula mentioned above:Under a condition with peak field amplitude is relatively high, the electrons are ionized mainly from the ground state and also recombine to the ground state. So the intensity of HHG is largely increased, while the HR lines are drowned by a noisy background. If the peak field amplitude is relatively low, the ionization of the ground state descends and leads to the conversion efficiency of the HHG decrease greatly. Because the HR lines are caused mainly by the atom first is excited from the ground state to the first excited state, then absorbs photos from the first excited state to a virtual energy, and transits to the ground state and emits a photo. In this process, the influence of the peak field amplitude of the laser pulse on the HR emission is weaker compare to the HHG. So the change in intensity of the HR lines is not as dramatic as the harmonics. The HR lines emerge from the noisy background. This makes we observe the HR lines more easily and clearly.Secondly, we find that if the initial state is prepared the initial state as the coherent superposition state between the ground and the first excited state, the conversion efficiency of the HR lines increases greatly. We present the emission spectrum whose initial state is entirely on the ground state, and the initial state as the coherent superposition state between the ground and the first excited state with different population distributions. It is show that the intensity of the HHG changes slightly. On the contras, the conversion efficiency of the HR lines is much more sensitive to the coherent superposition state (that can be enhanced five orders of magnitude).In my paper, the initial state is prepared the initial state as the coherent superposition state between the ground and the first excited state with different population distributions (the first excited state 1%or 10%, accordingly, the ground state 99%or 90%).because the HR lines are caused by the transitions between the ground and the first excited state, it is important that electron remains populated. Thus the choice of the coherent superposition state could make the conversion efficiency of the HR lines increases greatly. But for the HHG, 10% population of the first excited state is not enough to change the intensity of the HHG.In conclusion, we choose an optimal laser pulse to interact with a one-dimensional one-electron model molecular ion with two nuclei fixed, and investigated the conditions of the observation of the HR lines. It is indispensable to choose the suitable laser pulse and prepare the initial state as the coherent superposition state of ground state and the first excited state for the observation of HR lines in experiments.