| The interaction of the intense laser pulses with atoms, molecules, clusters, and solids can lead to high-order harmonic generation (HHG) whose frequencies are the integral multiple of that of the incident laser frequency, as a consequence of highly nonlinear dynamics. The unremitting pursuit in HHG studies is to widen and heighten the HHG plateau simultaneously on a large scale. The cutoff frequency is predicted byωc utoff = I p + EK(where I p is the atomic ionization potential and Ek is the electronic kinetic energy obtained in the field when the electron comes back to the parent ion). Considering the cutoff law, we notice that for a single atom response, there were two direct methods to extend the harmonic plateau width: one is to take the ions as target gases in order to obtain larger ionization potential. The other direct way is to increase the kinetic energy. To realize this aim, it is necessary to raise the intensity of the laser pulse when the laser wavelength is kept constant. However, an atom will be depleted completely when the laser intensity rises up to a certain threshold value, so that the corresponding harmonic emission process also terminates. To avoid the depletion, one has to recourse to strong and short laser pulses.As is well kown, with regard to enhancing the harmonic emission efficiency, there are two factors: (1) The intrinsic attribution of atoms is very important for the harmonic conversion efficiency. It's main reflection is the intensity of coupling between the ground state and the continuum state. (2) The harmonic emission per se is a complex process of stimulated and the harmonic emission efficiency is closely related to the populations of the electrons in the ground state and continuum state at the recombination moments. Especially for the higher-order harmonics, under the condition that the ground state has substantial population, the greater the populations of energetic electrons in high continuum state is , the higher the emission efficiency of the higher-order harmonics is. Only if these two factors are met with, we can expect the higher-order harmonic emission with great efficiency.The importance of the HHG researches consist in the fact that it is not only a promising way of generating coherent light in the extreme ultraviolet and x-ray region but also a means to produce attosecond x-ray pulses. At the present time, there are three methods raised for attosecond pulses generation: the Fourier Synthesized method, the Stimulated Raman Scattering (SRS) and the high-order harmonic emission method. The energy conversion efficiency of the HHG is relatively lower than other two methods, however, its merit consist in that a single-attosecond pulse can be abstracted from the pulse sequences. Hence, it has become the preferred route to generate attosecond pulses.At present, the dominant scheme in utilizing HHG for a single attosecond pulse is called the two-colour laser field scheme, whose theory is that, by superposing two laser pulses, it is possible to extend the harmonic plateau, and a super-continuum spectrum with long enough bandwidth is available. Finally, a single sub-100 as pulse can be attained by synthesized the harmonics within super-continuum spectrum. However, the drawback of this scheme consisted in that the intensity of the pulse attained is too low to find application. The essential goal of this letter is to enhance the intensity of the attosecond pulses, and to reduce the duration of the pulse down to sub-50-as using the two-colour laser field scheme.We theoretically investigate the HHG and attosecond pulses generation from one-dimension He+ ion irradiated by a two-colour laser field. As is well know, for a given atomic system, the desire to gain harmonics with great efficiency requires a desired situation that both the ground state and the continuum state have considerable populations. To achieve this aim, we can choose mild laser intensity so that the first-excited state can be wholly ionized leaving the ground state unperturbed, which is the reason why we prepare the initial state as the superposition of the ground state and the first-excited state. With respect to extending the harmonic plateau, we employ the He+ ion as the target gas owing to its higher ionization energy; in addition, if the pondermotive energy is enhanced, the harmonic plateau can also be extended. Our calculated results show that the two-color laser field scheme is helpful to extend the harmonic plateau. Based on these thoughts above, we investigate the harmonic generation from the He+ ion initially prepared in the superposition state irradiated by a two-colour laser field and the harmonic spectrum exhibits a double-plateau structure, where the height and width of the harmonic plateau are enlarged. These results are included in the third chapter and explained in terms of the three-step model.We adopt the high-order harmonic emission method in the generation of attosecond pulses. Double-peak attosecond pulses have been observed through superposing harmonics from 355th order to 405th order. Due to the fact that the time interval between two peaks is too small, as well as the emission efficiency of the second plateau is too low, the pulses synthesiced have little meaning to practical application duo to theirs poor energy. But how to attain a single attosecond pulse? For each harmonic emission, there are long electronic trajectory and short electronic trajectory contributing. Thereinto, the path with earlier ionization time and later emission time is called the long electronic trajectory, the path with later ionization time and earlier emission time is called the short electronic trajectory. The reasons engender a chain of attosecond pulses is the interference between the long trajectory and the short trajectory. If we are able to shut down the channel of harmonic emission from the long electronic trajectory, the interference can be eliminated. By adjusting the relative phase of the two-colour laser field, we attain a single 45-as pulse by superposing harmonics from 171st order to 230th order in the supercontinuum spectrum. It is because the long electronic trajectory channel is shut down and only the short trajectory makes contribution to harmonics. Meanwhile, the intensity of the attosecond pulse is greatly enhanced. To sum up, we succeed in attaining isolated sub-50-as pulse using the two-colour laser field scheme.
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