Fig. 1. Sketch of the discrete spatial electric dipole approximation. A STOV pumping pulse irradiates a blob of hydrogen atoms, and atoms at different X positions experience different phase and intensity of the driving field, then generating STOV high harmonics. (X,Y,Z) denotes the space coordinate system. (x,y,z) is the local atomic coordinate system, whose origin is located at (X,Y=0,Z=0).

Fig. 2. (1st column) Spatial-resolved HHG spectra driven by STOV pulses and retrieved spatiotemporal (2nd column) intensity and (3rd column) phase distributions of the 35th harmonic. (a) Only FW field with λFW=1600  nm; two-color STOV pulses with the phase difference (b) ϕ=0 and (c) ϕ=1.1π between FW and TH fields, respectively. The FW intensity is fixed as IFW=1×1014  W/cm2, and the TH intensity is ITH=9×1012  W/cm2. The black dashed line represents the ionization potential of H atom. o.c. is the FW period throughout.

Fig. 3. Diagrams of the time-frequency analyses of the HHG emission (X=0) generated by (a) single STOV pulse and (b), (c) two-color STOV pulses. (a)–(c) correspond to Figs. 2(a1)–2(c1), respectively.

Fig. 4. Classical electron trajectories driven by laser fields at X=0. (a)–(c) correspond to Figs. 2(a1)–2(c1), respectively. The blue, green, yellow, and red curves represent an electron trajectory with one, two, three, and four or more returns, respectively. The line thickness represents the relative magnitude of the ionization rate after logarithmic treatment. Note that only trajectories where electrons are able to return and the ionization rate is greater than 10% of the maximum ionization rate are shown, and about half of the laser field is shown by the black dashed line.

Fig. 5. Retrieved spatiotemporal intensity distributions of APT in (a), (b), and (c) correspond to Figs. 2(a1), 2(b1), and 2(c1), respectively. (d) Temporal intensity profiles of a single attosecond pulse sampled from the black rectangle in (c). The red dotted curve represents a Gaussian fitting with an FWHM of 613 as.

Fig. 6. Spatially-resolved 35th harmonic spectra, ITH=9×1012  W/cm2 for (a1) and ITH=4.9×1013  W/cm2 for (a2). (b) Time-dependent ionization probability for (a) calculated via TDSE. (c1) and (c2) are reconstructed HHG spectra by the quantum-orbit model. The intensity ratios ITH/IFW are taken to be 0.09 and 0.49, respectively. IFW=1×1014  W/cm2 is fixed in all panels. The X=0 position is considered in (b) and (c).

Fig. 7. Distribution of cos(2ωt−2φf) in the X–t plane, where φf is the azimuthal angle in the space-time plane.