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Isolated attosecond pulses make it possible to study and control the ultrafast electron processes in atoms and molecules. High order harmonic generation (HHG) is the most promising way to generate such pulses, which is benefited from the broad plateau structure of the typical HHG spectrum. In previous HHG studies on the polarization gating pulse with longer pulse duration, one needs to dramatically increase the separation in time between the two counter-rotating circularly-polarized pulses to generate the nearly-linear half-cycle " polarization gate”. This leads to a low harmonic conversion efficiency because the field outside the polarization gate is much stronger than inside the polarization gate. In this paper, by using Lewenstein model, we theoretically simulate the high-order harmonic generation from helium atom subjected to the polarization gating pulse with 10 fs pulse duration. It is found that high-order harmonic spectra each with a higher efficiency and regular structure can still be obtained by reasonably adjusting the delay time ratio and the amplitude ratio of electric fields between the two counter-rotating pulses. Further, a single 175 as pulse in the time domain is obtained by Fourier transforming the 80th order harmonics into the 172nd order harmonic without compensating for the harmonic chirp. This scheme has two main advantages. First, the adjustment of the polarization gate width from half optical cycle into nearly one cycle ensures higher intensity of the synthesized electric field inside the polarization gate. Second, the suitable adjustment of the amplitude ratio between two electric fields ensures the low ionization probability before the polarization gate, and thus further fulfills the harmonic phase matching condition in the process of the propagation.

Isolated attosecond pulses make it possible to study and control the ultrafast electron processes in atoms and molecules. High order harmonic generation (HHG) is the most promising way to generate such pulses, benefiting from the broad plateau structure of the typical HHG spectrum. In previous HHG studies on the polarization gating scheme, atomic ionization caused by the laser cycles before the polarization gate not only places a limit on the pulse width and intensity of the driving laser, but also affects the phase matching of harmonics generated in a polarization gate. According to these, in this paper we propose a new double optical gating scheme, in which the polarization of the laser pulse changes from linear to elliptical and back to linear again. Thus, only the linearly polarized field in the leading of the pulse contributes to high harmonic generation. By using a strong field approximation theory, we first simulate high order harmonic and attosecond pulse generation from helium atom irradiated by a double optical gating pulse based on the orthogonal polarization field. Here the orthogonal polarization field consists of two linearly polarized pulses with a certain time delay, orthogonal polarization directions and equal amplitudes. And for the double optical gating pulse, the second harmonic of the driving field is added to an orthogonal polarization field with an appropriate phase and energy. It is found that the high harmonic spectrum with higher efficiency and supercontinuum plateau is obtained by reasonably adjusting the parameters of the combined pulse. After inverse Fourier transform, an isolated 143-as pulse with higher intensity can be realized by superposing supercontinuum harmonics from the 50th to the 150th order. Compared with the double optical gating scheme proposed by Chang et al. (Zhao K, Zhang Q, Chini M, Wu Y, Wang X, Chang Z 2012 Opt. Lett. 37 3891), our scheme not only overcomes the limit on the pulse duration and intensity of the incident pulse laser, but also avoids the harmonic phase mismatching in the process of the propagation due to unwanted ionization of the gas target caused by the laser cycles before the polarization gate.

We theoretically study high-order harmonics generation (HHG) and isolated attosecond pulse (IAP) generation in a spatially inhomogeneous chirped two-color (5 fs/800 nm and 12 fs/1600 nm) laser field by solving numerically the time-dependent Schrdinger equation(TDSE) for a one-dimensional (1D) model of He+ ion by the splitting-operator fast-Fourier transform technique. Results show that the inhomogeneity of the laser field plays an important role in the HHG process. The harmonic spectra exhibit a two-plateau structure, and the cutoff of high-order harmonics is extremely extended to 851th order and the smooth supercontinuum harmonic spectrum is obtained in a chirped two-color inhomogeneous laser field. To further understand the physical mechanism of HHG, we give a reasonable explanation for the extension of harmonic plateau by using the semi-classical three-step model, the time-frequency profile of the time-dependent dipole, and the classical electron trajectories. Explicitly, the harmonic order as a function of the ionization time and emission time can be given by the semi-classical three-step model. If we define the path with earlier ionization time and later emission time as a ongelectronic trajectory, and the path with later ionization time and earlier emission time as a short electronic trajectory, then, there exist a few electronic trajectories that contribute to the harmonics in cutoff region. Numerical results show that the short quantum path is enhanced, and the long quantum path is suppressed in spatially inhomogeneous fields, and this is advantageous to generate an IAP. We find that the quantum path can be controlled by increasing inhomogeneity parameter of the laser field. Effects of the time delay on HHG is also discussed. We find that the smooth supercontinuum harmonic spectrum is obtained by adjusting the time delay. When the time delay is t0=1.6up/1, the cutoff of the harmonics can be extended remarkably. By synthesizing the 600th to 680th (80th) order harmonics in the continuum region, an isolated 32 attosecond pulse can be generated by a spatially inhomogeneous chirped two-color laser field with parameters =0.25, =0.00105, t0=1.6/1.

We have investigated the characteristics of high harmonic and attosecond pulse generated by helium atom exposed to the combined field of two laser pulses with the same color and a midinfrared laser pulse in nano-structure plasmon by solving the one-dimensional time-dependent Schrödinger equation. It is shown that the cut-off position of the harmonics is obviously extended in the combined field, however, the plasmon structure determined effect of absorbing the electron in the continuum states has an important influence on the cut-off position of the harmonics. It is found that the contribution from some single trajectory of electron is enhanced and other trajectories are suppressed by changing the plasmon position, so a single isolated attosecond pulse is obtained. Comparison with the scenario of atoms driven in homogeneous field, the width of the pulse decreases greatly, and an isolated pulse is achieved to be as short as 28 attoseconds.

We theoretically study the high-order harmonic generation (HHG) of a model He atom exposed to a combined field of 1600 nm and 800 nm laser pulses. The changing of rising rate and falling rate with time for the combined filed during main HHG, can present the different characteristics of high-order harmonic generation from the short electron trajectories and the long electron trajectories. By superimposing several harmonics generated from He atom driven by the combined field, we could obtain shorter attosecond pulses. Finally, by adjusting the time delay between two laser pulses, we can effectively suppress the contribution of the short electron trajectories to HHG, and obtain an isolated attosecond pulse with duration 33.7 as.

We theoretically investigate the high-order harmonic and attosecond pulse generation by numerically solving the one-dimensional time-dependent Schrödinger equation from a hydrogen atom in a two-color laser field, which is synthesized by adding a suitable multicycle infrared pulse to a multicycle 800 nm fundamental pulse. Our results clearly show that when there are 12 Ti: sapphire optical cycles in the pulse envelope, by adding a suitable second optical field, the electric field of the synthesized pulse presents three-segments, and only amplitude of the electric field in middle segment makes a major contribution to the plateau and cutoff region of the harmonic spectrum. By analyzing the compression mechanism of two-color electric field, we further enlarge the duration of the synthesized pulse to 60 fs, and obtain a single 160 as short pulse. This has been the longest pulse duration used for obtaining single attosecond pulse so far. Here the effect of synthesized pulses is similar to the effect of single 5 fs ultrashort pulse. This scheme greatly reduces the requirements for the pump laser system used traditionally for generating an isolated attosecond pulse, and it allows us to use a well-established conventional high-power pumping laser.

We theoretically investigate the effects of additional pulse wavelength at different frequencies on attosecond pulse generation from the hydrogen atom exposed to multicycle two-color laser field, by numerically solving the one-dimensional time-dependent Schrödinger equation. The results show that when the wavelength of the additional pulse is set to be 1600 nm, the cutoff position of the harmonic spectra is extended dramatically compared with the scenario in the case of 533 nm pulse in visible waveband, accordingly the bandwidth of supercontinuum is widened, finally 78 attosecond pulse is obtained by wavelet transform. In this paper, we explain the effects of additional pulse wavelength in different wavebands on high order harmonic generation for the first time according to the optical oscillation frequency of the synthesized field. Also, such a result is conducible to choosing the appropriate additional pulse frequency in order to obtain the isolated attosecond pulse.

The propagation of high-order harmonics with attosecond ionization gate is simulated with three-dimensional propagation equation. After 0.5 mm propagation distance， the short trajectories in the harmonics， which are generated by two 5 fs laser pulses centered at 800 and 400 nm， are selected and a highly efficient smooth supercontinuum with the bandwidth of about 80 eV is obtained in the plateau， because of the phase matching. Simulation results of different propagation distances show the broadband supercontinuum can last steadily. A highly efficient pure isolated attosecond pulse with the duration of about 135 as can be generated by directly filtering out of the harmonics from 60—90 eV in the supercontinuum， and a single 50 as pulse can be generated， which facilitates the experimental implementation for the isolated attosecond pulse generation.

By numerically solving time-dependent Schrdinger equation, we obtain high-order harmonic generation （HHG） spectra from the one-dimensional H atom model submitted to linear polarization bichromatic field. It is found that, appropriate bichromatic field could be a source of attosecond pulse generation since it produces a ligher line-density in harmonic generation spectra （HGS）. Based on it, we analyze the mechanism of generating denser HHG spectral lines in detail, and give density-selection numerical experiential formulas for different pulses duration, to achieve further control of the line density of HGS.