Theoretical investigation of atomic low-order harmonics under irradiation of two high frequency laser pulses

With the development of laser technology, the extreme ultraviolet and X-ray light sources can be obtained by utilizing the high-order harmonic radiation and the free electron laser. When an atom is irradiated by an intense highfrequency laser, many nonlinear phenomena can be observed, such as high-order harmonic emission, threshold ionization and ionization stability of atom, etc. The emission spectra with some new features appear when the atom is irradiated by a high-frequency laser pulse.The harmonic spectra with a clear cut-off plateau do not appear, and the three-step model is no longer valid for explaining the results. In addition to the odd-order harmonic radiation observed in the emission spectra, many super-Raman lines can be seen clearly. These radiations are generated from the transition between the dressed eigenstates of the atom. When the incident high-frequency laser pulse is strong enough, the peak of the harmonic splits into many sub-peaks. The generation of the sub-peaks of harmonic is due to the contributions from the rising and falling parts in the pulse. With the development of free electron laser technology, one can obtain a combined pulse with different frequencies. Many new two-color schemes are proposed for the experiment, such as the realization of two-photon spectrometer, pump-probe spectrometer. In this work, we investigate the optical radiation of the atom irradiated by a combined laser pulse, whose energies are higher than the ionization energy of the atom. It is found that the odd harmonics of the two high frequencies are shown in the emission spectra, and many satellite peaks appear in the vicinity of these odd harmonics. Furthermore, the intensities of the satellite peaks are enhanced exponentially with the increase of the incident laser intensity, and the frequency difference between the two adjacent peaks is the frequency difference between the two incident laser pulses. We study the time-frequency profile of the harmonic emission by analyzing the wavelets. With the two-color scheme one can achieve coherent soft X-ray and produce short coherent pulse. We also calculate the high-order harmonic spectrum of hydrogen in the two-color laser pulse, the multi-peak structure in the emission spectra can also be found, and the positions and intensity distribution of the emission peaks are consistent well with those from the one-dimensional calculation. In our two-color scheme, by changing the peak intensity and frequency of one of the combined laser pulses, the multi-plateau structure can be shown in the harmonic spectra. Taking advantage of the harmonic plateau, the soft X-ray radiation and ultra-short attosecond pulse chain can be generated.