High-order Harmonic Emission And Isolated Attosecond Pulse Generation From Atoms Irradiated By Two-colour Laser Fields

With the rapid development of ultra-intense laser technology, the theoretical research on the interaction between intense lasers and matters, the explanation for the new experimental phenomena, the prediction for the behavior and the law of matters in the intense laser field, which is still out of labs'reach, have become active forefront research topic. Especially in recent years, the rapid development of ultra-short laser technology has greatly pushed the research on the interaction between lasers and matters. From a fundamental point of view, the key to investigate the laser-matter interaction is to study the impact of lasers on the electrons. Thus, ionization of the electrons is the main process during the interaction between intense laser fields and matters, where many novel phenomena have been caused by nonlinear interaction. As the laser intensity increases, there are several processes taking place one after the other: multiphoton ionization, above-threshold ionization, tunnelling ionization, over-the-barrier ionization, as well as laser-induced recombination of electrons, followed by high-order harmonic generation, etc.Media such as atoms, molecules or clusters can be irradiated by intense lasers to emit coherent radiation, whose frequencies are integral multiple of that of incident radiation, which is called high-order harmonic generation (HHG). A large number of experimental results show a characteristic feature of HHG: a sharp decline of the intensity for the first few harmonics, followed by a plateau consisting of many harmonics with the roughly same intensity and then an abrupt cutoff at a certain frequency. Due to the"plateau"structure of HHG spectra, HHG not only provides a valid approach to generate XUV and soft X-ray radiations, but also provides a preferred source for attosecond ( 10 ?1 8 s) pulse generation. In the past decades, the research on HHG has become a highly active field. Proceeding from recent practical application, people's essential pursuit of the HHG study is to extend the width of harmonic plateau, meanwhile, to enhance the emission efficiency. Since HHG is a highly nonlinear process, perturbative theory can't give a sound explanation yet. However, semi-classical three-step model brought forward by Corkum et.al has achieved success in explaining the cutoff position of HHG. This theory divided harmonic emission process into three steps: Firstly, electrons ionize with zero initial velocity in the laser field. The means of ionization depend sensitively on the intensity of the field, can be multiphoton ionization, tunnelling ionization or over-the-barrier ionization. Secondly, the ionized electrons can be accelerated by the laser field, and electronic trajectory depends on the phase of the field at the time of it birth;some of them will never come back and others will return to the vicinity of the nucleus. Finally, HHG occurs when some electrons recombine with the parent ion by emitting high energy photons. The cutoff frequency law is predicted by three-step model: E cutoff = Ip+3.17Up, where I p is ionization potential, U p= E 2 4ω2 is the pondermotive energy gained by electron in the laser pulse, E andωare the peak intensity and the frequency of the incident laser field, respectively. With regard to a single atom model, there are two direct methods to extend the harmonic plateau: (1) Increase the ionization potential I p, i.e., taking atoms or ions with larger ionization potential as targets. This is the reason why we select helium ion. (2) Increase the pondermotive energy U p. Owing to the parameter 3.17, it is more effective to extend harmonic plateau using this method. To realize the aim, it is necessary to raise the intensity of the laser pulse when laser wavelength is kept. But an atom will be depleted completely when the laser intensity rises up to a certain threshold amount, so that the corresponding harmonic emission process terminates. In order to overcome this difficulty, people resort to the intense ultrashort laser pulses. Nevertheless, the pulse duration of femtosecond lasers has reached the limitation. Therefore, these conventional methods come to an end. Results calculated in terms of three-step model indicate that the maximum kinetic energy electrons can gain in external laser field is 8U p, which implies that there are lots of electrons whose energy is larger than 3.17U p never return to the mother ions. In order to make full use of the lost energetic electrons, people must seek other methods.The essential goal of this letter is to extend the harmonic plateau as far as possible and to enhance the harmonic emission efficiency, especially the highest-order harmonics in the cutoff region, finally to attain"strong","short","isolated"attosecond pulses. As a starting point, we numerically solved the time-dependent Schr?dinger equation with the splitting-operator fast Fourier transform algorithm. The advantage of this method is that it can save much computational time. We firstly investigate the high-order harmonic generation from one-dimensional model of the helium ion initially prepared in the ground state in a two-color laser field, which is synthesized by adding a 10-fs, 394-nm high-frequency pulse to a 5-fs, 800-nm fundamental pulse. Our focus is to study how the intensity of high-frequency pulse influence the results. Numerical results reveal that the two-color scheme indeed can extend the harmonic plateau, specific here to I p + 4.5U′p. However, the harmonic spectra exhibit a two-plateau structure. In addition, there appears a broad supercontinuum spectrum in harmonic cutoff region. Then, we give reasonable explanations regarding the extension of harmonic plateau in terms of the three-step model theory and the wavelet transform. Harmonic order as a function of the ionization time and emission time can be given by semi-classical three-step model. If we define the path with earlier ionization time and later emission time as a"long"electronic trajectory, inversely define the path with later ionization time and earlier emission time as a"short"electronic trajectory, then, there exits a few electronic trajectories contributing to lower-order harmonics and two electronic trajectoried contributing to harmonics in the cutoff region. Generally speaking, two attosecond pulses can be generated by superposing the harmonics in the cutoff region. To gain single attosecond pulses, we have to select one from two electronic trajectories. When the high-frequency pulse has a relative weak intensity, both the long and short trajectories that differ in emission time contribute to the cutoff harmonics, of which the long one plays a greater role. Correspondingly, the supercontinuum spectrum in the second plateau can be synthesized to generate attosecond pulses with double peaks. If the intensity of the high-frequency pulse is comparable to that of the fundamental pulse, the long electronic trajectory is suppressed to a large extent, and the short trajectory plays a leading role. Meanwhile, the bandwidth of supercontinuum spectrum in the second plateau are extended largely, which leads to an isolated 63-as ultra-short pulse whose intensity are enhanced. These results lead to the following concludes: by changing the intensity of the two-color laser, peaple can control the electronic trajectories which participate in the HHG. When the long electronic trajectory is suppressed, there is only a short electronic trajectory ascribed to the HHG. As a result, isolated attosecond pulses are generated.Even if the two-color field scheme succeeds in extending the harmonic plateau, and the extended harmonics form a broader supercontinuum spectrum, however, the two-plateau structure limited the emission efficiency of the extended harmonics. How to enhance the emission efficiency of the highest-order harmonics and attain intense attosecond pulses is the next goal to achieve in this letter. We propose a novel scheme combined by the two-color field scheme with the coherent superposition state scheme in order to extend the harmonic plateau, meanwhile to enhance the harmonic emission efficiency. The two-color field we adopt is superposed by a 5 fs ,800 nm fundamental pulse and a 12 fs , 1600 nm low frequency pulse. Numerical results show that the harmonic spectrum exhibits a two-plateau structure when He+ ion initially prepared in the ground state is irradiated by the two-color field with a relative phase ? = 0. By preparing the initial state of the He+ ion as a coherent superposition of the ground state and the first excited state with equal population of 0.5, harmonic plateaus are enhanced by 3-4 orders of magnitude. For the case of ? = 0.25, the second plateau is further enhanced by three orders of magnitude. There appears only one harmonic plateau and one optimum xuv spectrum, which not only has an ultrabroad spectral band, but also has a smooth profile. To understand how a two-plateau structure forms and how the harmonic emission is enhanced more clearly, we analyze the emission time of each harmonic by virtue of the three-step model and calculate the ionization probability. In the case of ? = 0, there is only a main ionization time with fast ionization rate contributing to the first plateau, hence, harmonic spectrum exhibits a two-plateau structure. In the case of ? = 0.25π, there exits two ionization times with fast ionization rate which contribute to the first and second plateau, respectively. As a result, harmonic spectrum exhibits a single plateau structure. From the time-frequency analyse of harmonic spectrum we find that a single electronic trajectory can be picked out by adjusting the relative phase of the two-color field. Harmonics from 171st to 230th can be superposed to generate an intense 45-as isolated pulse.