Objective The motion and correlation of electrons are the most fundamental physical processes in all systems based on electromagnetic interaction, and their characteristic time is of the order of attoseconds (i.e., 10 -18 s). To investigate or control the ultrafast dynamics of electrons, it is necessary to use a tool with the same or even shorter time scale as a reference. The emergence of ultrashort laser pulses provides an ideal means for studying ultrafast phenomena. The changing light field is the fastest physical quantity which can be measured and controlled. Currently, femtosecond pulses shorter than 5 fs or even close to a single optical cycle (the oscillation cycle of an optical field with a wavelength of 800 nm is 2.67 fs) have been obtained, covering the spectrum from infrared to ultraviolet. To obtain attosecond pulses equivalent to the characteristic time of electron motion, the carrier wave spectrum must be shifted to the extreme ultraviolet (XUV) or even soft X-ray whose oscillation cycle is of the order of attoseconds. It requires the interaction of femtosecond laser pulses and gas atoms at a peak intensity that is close to 10 13 W/cm 2 or higher to generate high-order harmonics and attosecond pulses in the XUV band. Optical gating techniques based on high-order harmonic generation (HHG) in the XUV band have become crucial to obtain isolated attosecond pulses (IAP). An ultrashort IAP requires an ultrabroad continuous spectrum and its intrinsic chirp (atto-chirp) must be compensated.
Methods In the HHG process, after being ionized, the electrons obtain kinetic energy within half a cycle of the driving laser, and they then return and recombine with the ions to radiate XUV photons. The electrons ionized at different times gain different kinetic energies in the electric field, and they return and recombine at different times, causing the XUV photons radiated to have different energies and wavelengths. This process leads to a relative delay between photons with different energies. Thus, the XUV pulses produced via HHG are chirped, with inherent dispersion called atto-chirp. Based on the three-step model, we calculate the central photon energies and atto-chirps of attosecond pulses produced via the HHG process at specific driving laser intensities (Fig. 1). The atto-chirp of the calculated attosecond pulses are compensated by specific metal foils to obtain an IAP close to 50 as.
Results and Discussions The calculations showed that the material dispersions of zirconium (Zr), molybdenum (Mo), and tin (Sn) foil with specific thicknesses (Figs. 2 and 3) may compensate the atto-chirp of continuous XUV spectra centered at 98, 120, and 170 eV produced by laser-atom interaction, respectively. In the numerical simulation based on the strong-field approximation, we use polarization gating to generate a half-cycle linear polarized electric field by 750 nm, 5 fs laser pulses, and produce a continuous XUV spectrum centered near 120 eV in neon gas at an intensity of 9×10 14 W/cm 2. Simulation results showed that the chirp of the continuous XUV spectrum may be compensated by 150 nm of Mo foil to produce an attosecond pulse of 38 as (Fig. 4). Based on such a set of laser and material parameters, a beamline for attosecond pulse generation and measurement is designed (Fig. 5). Furthermore, polarization gating is selected to generate IAP, and the laser is focused through a combination of concave and convex mirrors to produce a high-order harmonic continuum. The attosecond pulse is focused on the gas target at the TOF entrance of attosecond streak camera using a toroidal mirror. The attosecond pulse width is measured through the noncollinear optical path, and the flat-field grating is imaged on the XUV spectrometer to measure the spectrum. In addition, the multiple iris and observation optical paths are set in the optical path to facilitate the adjustment of the optical path of the system.
Conclusions This study determines the parameters to produce IAP close to 50 as. Atto-chirp, the intrinsic dispersion of attosecond pulses produced via HHG processes, is usually compensated by various metal foil. Semiclassical calculation and numerical simulation are employed to determine the parameters to produce short attosecond pulses. Calculations show that the material dispersions of Zr, Mo, and Sn foil with specific thicknesses may compensate the atto-chirp of continuous XUV spectra centered at 98, 120, and 170 eV with acceptable transmittance, respectively. A previous study confirmed that a single pulse of 67 as was obtained around 98 eV. The numerical simulation shows that a supercontinuum with the central photon energy of 120 eV is produced and its atto-chirp is compensated by 150-nm Mo foil. This scheme can not only compensate well for the positive dispersion carried by the attosecond pulse as it is generated but also maintain a high transmission. Moreover, the Ti:sapphire laser pulse after spectral broadening and compression can generate high-order harmonics in this photon energy range with reasonable efficiency. Finally, for this scheme, we design the optical and vacuum systems of an XUV beamline, including a noncollinear attosecond streak camera and a flat-field XUV spectrometer, which can perform spectral measurement of high-order harmonics, generation, compression, and characterization of attosecond pulses.
