Fig. 1: Spatiotemporally resolved ultrahigh-order wave mixing spectra.

a Schematic representation: The \({\omega }_{1}\) beam is positioned in the horizontal plane, while \({\omega }_{2}\) the beam points downwards at an angle of θ ~ 18 mrad, forming a plane parallel to the entrance slit of the XUV spectrometer. b, c Ultra-high-order wave-mixing spectra generated from the superposition of an intense pump fundamental \({\omega }_{1}\) (800 nm) at zero time delay and the second harmonic weaker probe field (400 nm) in the α-quartz sample, with both pulses linearly polarized to the Γ-M (b) and Γ-K (c) directions of the Brillouin zone, respectively. The number inside the bracket \((m,n)\) represents the number of absorbed photons from the pump and probe pulses, respectively, i.e., \(\Omega (m,n)\propto (m{\omega }_{1}+n{\omega }_{2})\). d, e represent the noncollinear simulations considering inversion symmetry parallel to the two electric fields, either in the Γ-M (b) or Γ-K (c) directions of the Brillouin zone. The color bars are normalized to their maximum harmonic yields and presented on a logarithmic scale. The symbol × indicates the second-order diffraction signal.