Attosecond pulses are currently the shortest radiation pulses that can be obtained, and their ultra-fine temporal and spatial resolution has become an important tool to study ultra-fast electron dynamics in atoms and molecules. At present, the high-order harmonic generation from the interaction of femtosecond pulses with atoms or molecules is the only effective means to produce desktop attosecond pulse radiation sources. Thus, researchers have proposed many advanced techniques for generating isolated attosecond pulses in experiments and theories, such as few-cycle laser pulses, dual-color or multi-color fields, and polarization gating schemes. The orthogonally polarized dual-color fields, composed of two linearly polarized pulses with different wavelengths and perpendicular polarization directions, have become an effective way to control electron motion with the characteristics of polarization modulation and two-color field. By numerically simulating the interaction between helium atoms and orthogonally polarized dual-color fields composed of 4 fs/800 nm driving pulses and 8 fs/400 nm gating pulses, we obtain a 54 as high-intensity isolated attosecond pulse. The advantage of this scheme is that a single quantum trajectory (short trajectory) can be selected during a single atomic response. Additionally, the isolated attosecond pulse is less affected by the relative phase between the two pulses and by the change in the electric field intensity of the gating pulse.

The high-order harmonic generation from the interaction of the orthogonally polarized two-color field with helium atom is studied numerically by the strong field approximation theory. Attosecond pulses are synthesized by superimposing the super-continuum harmonic spectra. The ionization rate of helium atoms is calculated through the ADK tunneling ionization theory model, and the classical trajectory of electrons is calculated using the semi-classical three-step model theory proposed by Corkum.

An orthogonally polarized bichromatic field consisting of a 4 fs/800 nm driving pulse and an 8 fs/400 nm gating pulse interacting with helium atoms is employed to obtain a super-continuous harmonic spectrum with high intensity and small oscillation amplitude. The supercontinuum harmonic range extends from 120th to 180 th order (Fig. 1), which is fully consistent with the calculation results of the semi-classical three-step model theory [Figs. 2(a) and (b)]. The electron trajectory shows that the platform harmonics mainly come from the contribution of short-orbit electrons. Due to its short motion time, less wave packet diffusion, and no interference with the harmonics generated by long-orbit electrons, the high-order harmonic spectrum in the direction of the driving pulsed electric field presents the characteristics of a super-continuous platform region with higher intensity and smaller modulation amplitude [Fig. 2(c) and (d)]. To further verify the rationality of the classic analysis, we adopt the wavelet transform method to calculate the time-frequency analysis diagram of the high-order harmonic emission when the orthogonally polarized two-color field irradiates the helium atom. The obtained results are consistent with the above supercontinuum harmonic spectrum range (Fig. 3). By superimposing the entire supercontinuum band in the spectrum, an isolated attosecond pulse with a duration of 54 as and an intensity of 3.2×10^-6 is generated [Fig. 4(b)]. The results are three orders of magnitude stronger and shorter than the isolated attosecond pulse with a duration of 126 as and an intensity of 1.9×10^-9 generated in a single 800 nm titanium sapphire laser pulse [Fig. 4(a)]. In addition, we find that under the current selected pulse laser parameters, the selection requirements of the relative phase among the combined pulses are not strict, and isolated attosecond pulses with shorter pulse widths can be obtained in the range of 0.3π. Additionally, controlling the change of pulse electric field intensity exerts little effect on the above numerical simulation results (Fig. 5). Furthermore, in terms of the cutoff position of the harmonic emission spectrum and harmonic conversion efficiency, the proposed orthogonally polarized bichromatic field scheme has obvious advantages over the parallel polarized bichromatic field scheme with the same parameters.

We obtain the broadband super-continuous harmonic spectrum with small oscillation amplitude through the orthogonally polarized bichromatic field synthesized by a titanium gemstone pulse and its second harmonic pulse interacting with helium atoms. The origin of the super-continuous harmonic spectrum is explained based on analyzing the electronic motion orbit, and it is attributed to a single contribution of short-track electrons with a short motion time and less wave packet dispersion. By performing Fourier transformation on the supercontinuum harmonic, a high-intensity isolated attosecond pulse with a duration of 54 as is obtained. The isolated attosecond pulse is less affected by the relative phase between the two pulses and by the change in the electric field intensity of the gating pulse.