Figure 1

Quasi-phase-matching with accelerating light pulses. The two shaded regions defined by the dashed lines represent two different pulses (or two temporal slices within a single pulse), copropagating with a constant group velocity $\sim c$. The periodic gray-white pattern represents counterpropagating light pulses establishing a spatiotemporal QPM scheme. In (a) and (b), the QPM pulses are counterpropagating with either a fixed velocity $\sim (-c)$ (a) or are accelerating (b), establishing the same (a), or different (b) QPM conditions for the two copropagating pulses.Reuse & Permissions

Figure 2

Identifying bursts of harmonic radiation. (a) The electric field of the driving laser (blue) and the generated high-harmonic field (red) (normalized) at the exit of the medium. The expanded inset shows three high-harmonic bursts in different temporal windows I, II, and III. (b) The accelerating spatiotemporal QPM modulation that quasi-phase-matches only those high harmonics emitted in temporal window II. The function $\mathrm{sgn}\left\{\cos \right[\phi (t,z]\}$ is plotted for part of the interaction region in space-time. The driving laser pulse propagates between the dashed lines. (arb. units = arbitrary units; a.u. = atomic units)Reuse & Permissions

Figure 3

Application of accelerating spatiotemporal QPM for selectively enhancing harmonics from different quarter cycles. Spectral and temporal high-harmonic emission at the end of the interaction region without (blue) and with (black) QPM. The roman numerals relate to the three temporal windows defined in Fig. 2, for which three different QPM patterns were applied to enhance the HHG emission in different quarter cycles for each simulation (i.e., the three cases are mutually exclusive). Left column: HHG spectral intensity at the corresponding temporal window. Right column: HHG electric field. (arb. units = arbitrary units; a.u. = atomic units).Reuse & Permissions

Figure 4

Dynamics of accelerating quasi-phase-matching. Normalized power evolution for each harmonic order as a function of the interaction distance. The roman numerals relate to the three different temporal windows defined in Fig. 2, for which three different QPM patterns were applied. The color scale corresponds to low for blue and high for red. Left column: without QPM. Right column: with accelerating QPM.Reuse & Permissions