Fig. 1. (a) Schematic of proposed setup. A linearly -polarized spatiotemporal optical vortex (STOV, red torus) pulse with purely transverse orbital angular momentum (TOAM) is incident onto a solid plasma target. Harmonics can be generated in the reflected beam (blue torus). (b) Snapshots of electric field at . (c) Frequency spectrum of (b) generated by performing Fourier transform in the -direction. (d) Time-averaged energy density of the STOV beam. The overlaid white arrows represent the circulated momentum flux. (e) TOAM density with the subtracted propagation term. The red arrow in (b) shows the beam-propagating direction.

Fig. 2. (a) Two-dimensional high-harmonics spectra of reflected beam . The white line is a one-dimensional spectrum at . The inset in (a) shows the magnified third-harmonic spectrum region. (b)–(d) Field distributions of the (b) first, (c) third and (d) fifth harmonics. (e)–(g) TOAM densities and momentum fluxes of (b)–(d), respectively.

Fig. 3. (a) Spatial–temporal-coupled relativistic oscillating mirror (ST-ROM). Three typical oscillating patterns are shown: (a) , (b) and (c) . (d) Spectrum of the ST-ROM. The black dashed curve represents the local center angular frequency. The black line in (a)–(c) represents the density contour of at which the beam is reflected. The spatiotemporal singularity reaches the plasma surface at approximately , denoted by the triangle in (a).

Fig. 4. (a) TOAM values per photon of harmonics for STOV drivers with (square), 4 (circle), 6 (right-hand triangle) and 8 (left-hand triangle). The blue dashed line is a linear fit of the average TOAM for each order harmonic. (b) Energy conversion efficiencies with fitted lines of the power law of harmonics.

Fig. 5. Spectra of (a) and (b) components driven by a -polarized STOV beam with incident angle of . Field distributions of the (c) second and (d) third harmonics. (e), (f) TOAM densities of (c) and (d), respectively. The reflected beam propagates in the -direction.