Theoretical Study Of High Harmonics And Attosecond Pulse Generation On Atoms And Molecules In Intense Laser Fields

Attosecond science can describe and trace ultrafast electron dynamics in anatom or a molecule. It can also be used as a source of soft X-ray. A HHG spectrumhas a general characteristic: It decreases rapidly for first few harmonics, thenexhibits a broad plateau, and finally ends up with a sharp cutoff. A harmonicgeneration process can be well described by the semi-classical three-step model,which says that an electron first tunnels out of a Coulomb potential barriersuppressed by the laser field and moves away from the parent ion; then thefreed-electron is pulled back and accelerated when the laser field direction isreversed; finally it recombines with the parent ion and emits a harmonic photon. Alarge number of schemes have been proposed to produce an isolated attosecondpulse, such as a polarization gating technique, two-color field control, spatiallyinhomogeneous fields, and so on. In this paper, we theoretically investigate thehigh-order harmonic generation (HHG) and attosecond pulse generation on atomsand molecules in intense laser fields, which can be explicitly described as follows:First, by solving a two-dimensional time-dependent Schr¨odinger equation weinvestigate high harmonic generation (HHG) and isolated attosecond pulsegeneration for the H2+molecular ion in a circularly polarized laser pulse combinedwith a Terahertz (THz) field. When an atom or molecule is irradiated by a circularly polarized laser pulse, the ionized electron can hardly return to the vicinity of theparent ion and emit energetic photons. Attosecond pulses generated by this way arevery weak due to low efficiency of HHG. When we add a THz field, the harmonicintensity can be greatly enhanced by about4-6orders of magnitude in contrast withthe purely circularly polarized laser pulse. A continuum spectrum with a spectralwidth of about225eV can be achieved. The time-frequency shows that the emissionof photon exhibits an evident periodic property and the intensity of HHG is very lowwhen in the case of the circularly polarized laser pulse. When a THz field is added,only the short trajectory has contribution to HHG and the quantum pathscontributing to the harmonics can be controlled. A supercontinuous harmonicplateau can be formed. We also use the classical three-step model, where theelectron has non-zero initial transverse velocity, to further explain the mechanism ofHHG irradiated by the circularly polarized laser pulse. The three-step model showsthat the periodicity of electron’s recombination in the circularly polarized laser pulsefield is destroyed by adding the THz field. The temporal evolution of the probabilitydensity of electron wave packet presents a clear picture of the electron’s two-timerecombination, which is consistent with the result of the three-step model. We alsopresent the electron trajectories for the case of the circularly polarized laser pulseand the circularly polarized laser pulse combined with the THz field, respectively.For the case of the circularly polarized laser pulse, the electron can return to theparent ion with proper transverse velocity. Since the distance traveled by theelectron is very short, it cannot be accelerated and it will gain less energy. On thecontrary, if the electron moves longer distance, the electron can be effectivelyaccelerated and it will gain more energy. The distance of the electron motion in thecircularly polarized laser pulse combined with the THz field is much farther than inthe circularly polarized laser pulse. The harmonic cutoff can be extended.Second, we theoretically propose a three-color laser scheme to enhance thehigh-order harmonic intensity and generate an isolated attosecond pulse. By addinga3fs,1600nm laser pulse to a synthesized two-color laser field (5fs,800nm and10fs,1200nm), the harmonic intensity is effectively enhanced and an isolated attosecond pulse with duration41as is generated. In this scheme, the short trajectoryis suppressed; the selection of the long quantum path can be achieved. We alsoinvestigate emission time of harmonics in terms of the time-frequency analysis andthe semi-classical three-step model to illustrate the physical mechanism ofhigh-order harmonic generation. It is very interesting to investigate the high-orderharmonic generation by few-cycle laser pulse. Then we theoretically study theselection of the quantum path in high-order harmonics (HHG) and isolatedattosecond pulse generation from a one-dimensional (1D) model of H2+molecule infew-cycle inhomogeneous laser fields. The result shows that the inhomogeneity ofthe laser fields plays an important role in the HHG process. The cutoff of theharmonics can be extended remarkably and the harmonic spectrum becomes smoothand has fewer modulations. Time-frequency profile of the time-dependent dipole isalso investigated, the result shows that, the short quantum path is enhanced, and thelong quantum path disappears in spatially inhomogeneous fields. The semi-classicalthree-step model is also applied to illustrate the physical mechanism of HHG. Theinfluence of driving field carrier-envelop phase (CEP) on HHG is also discussed. Bysuperposing a series of properly selected harmonics, an isolated attosecond pulse(IAP) with duration53as can be obtained by a15fs,1600nm laser pulse with theparameter0.0013.Third, we theoretically investigate the high-order harmonic generation (HHG)and isolated-attosecond-pulse generation from a full one-dimensional (1D) model ofH2+molecule in3fs,800nm laser pulses by using numerical solutions of thenon-Born-Oppenheimer time-dependent Schr dinger equation. The numericalresults with moving nuclei and the static nuclei are compared together. Theharmonic spectrum from the22nd to the cutoff becomes smooth and fewermodulations and an isolated-attosecond pulse with duration129as is generated thenuclear motion is considered. The emission time of harmonics in terms of thetime-frequency analysis shows that, with moving nuclei, the long trajectory issuppressed, and the short trajectories is enhanced. We apply the nuclear andelectronic probability density and the simulation of classical electron trajectory to illustrate the physical mechanism of HHG.