Fig. 1. (a) Few-cycle pulse laser (red solid line) interacting with gas atoms (blue solid line) will radiate extreme ultraviolet HHs (violet solid line). When a perturbing field carrying spatiotemporal coupling effects (pink dashed line) is introduced to perturb the HHG process, it will affect the trajectories of free electrons (blue dashed line), thus influencing the performance of the HHs. (b) A two-slit interference model can be used to explain the perturbation mechanism. (c) The normalized frequency shift of the 33rd-order harmonic in the near field with delay and space. The horizontal axis represents delay (T0 is the optical cycle of the driving field), the vertical axis represents spatial coordinates xf in the near field, and the color map represents the amount of frequency shift of the 33rd-order harmonic.

Fig. 2. (a) Variation of the center of mass of the 33rd-order harmonic spectrum in the near field with delay and space after introducing the perturbing field with spatial chirp effect from the simulation (T0 is around 2.6 fs, which is an optical cycle of the center wavelength of 780 nm). Two spatial positions are selected to compare the reconstruction results; the selected positions are indicated by the red and black dashed lines, respectively. (b) A comparison of the reconstructed and original spectrum for the position indicated by the red dashed line. Panel (c) is the same as panel (b) but for the position indicated by the black dashed line. Panels (d) and (e) are the reconstructed and original two-dimensional electric fields with spatial chirp effect, respectively. Panels (f) and (g) show the comparison of the reconstructed and original electric fields at locations indicated by the red and black dashed lines in panel (a), respectively.

Fig. 3. (a) Experimental layout of the all-optical spatiotemporal oscilloscope. The few-cycle NIR pulse centered at 780 nm is split by a beam splitter. The transmission beam serves as a driving field, and the reflection beam serves as a perturbing field. Two beams are recombined by another beam splitter and focused into a gas jet for HHG. The driving field and the perturbing field have the same focus. A 200-nm-thick aluminum film is situated behind the gas cell to filter the NIR field. Finally, the spectrum of the HHs is detected by an extreme ultraviolet spectrometer. BS, beam splitter; QP1, 330-μm quartz plate; QP2, 470-μm quartz plate; CM, concave mirror with a focal length of 500 mm; TS, movable reflecting mirror; Al, aluminum film; IR spectrometer, infrared spectrometer consisting of a 10× objective lens, a slit, a motorized stage, and a spectrometer (FLAME-T-VIS-NIR, Ocean Optics). (b) Measured spatial spectrum of the perturbing field in the region where the HHG is generated. The vertical axis represents the spatial axis along the x direction.

Fig. 4. (a) Variation of the center of mass of the 25th-order harmonic spectrum in the far field with delay and space. Six points are chosen evenly in space for reconstruction. (b) A comparison of the reconstructed and original spectra for six selected points in space [the blue (red) line is the original (reconstructed) spectrum, and the orange line is the reconstructed phase]. (c) The original and reconstructed spatial spectra of the perturbing field. The dashed lines indicate the spatial chirp effect. (d) The waveform reconstruction results of the perturbing field in the near field.