Controlling Photon Transverse Orbital Angular Momentum in High Harmonic Generation

High harmonic generation (HHG) with longitudinal optical orbital angular momentum has attracted much attention over the past decade. Here, we present the first study on the HHG with transverse orbital angular momentum driven by the spatiotemporal optical vortex (STOV) pulses. We show that the produced spatial-resolved harmonic spectra reveal unique structures, such as the spatially spectral tilt and the fine interference patterns. We show these spatiospectral structures originate from both the macroscopic and microscopic effect of spatiotemporal optical singularity in HHG. Employing two-color counterspin and countervorticity STOV pulses, we further discuss a robust method to control the spatiotemporal topological charge and spectral structure of high-order harmonics. The conservation rule of photon transverse orbital angular momentum in HHG process is also discussed when mixing with photon spin angular momenta.

Figure 1

(a) Spatiotemporal distribution of the electric field of the fundamental STOV. (b) The spatial chirp of the fundamental STOV. In (b), the pseudocolor map indicates the spatiospectral weight of $|F(x,\omega )|$, the white line indicates the 400-nm angular frequency (i.e., ${\omega }_0=0.114\mathrm{a}.\mathrm{u}.$), and the black dashed curve represents the local center angular frequency. (c), Spatial-resolved HHG spectrum driven by the fundamental STOV with hydrogen atoms.

Figure 2

(a) Illustration for the temporal character of HHG bursts. The harmonic bursts are separated into cluster $A$ and cluster $B$ in time domain by the phase singularity. (b) and (c) are HHG spectra from cluster $A$, cluster $B$, and their superposition, respectively. The $x$ positions for (b) and (c) are taken to be $x=0$ and $x={\lambda }_{400}$, respectively. (d) Spatial-resolved HHG spectrum from Eq. (5). In (d), the black dashed curves are the results from Eq. (4).

Figure 3

The intensity (a) and phase (b) spatiotemporal profiles of the 17th harmonic.

Figure 4

(a) Spatial-resolved HHG spectrum driven by two-color countervorticity STOVs ($400\mathrm{nm}+800\mathrm{nm}$). (b) Spatial-resolved HHG spectrum driven by two-color counterspin and countervorticity STOVs. Here, ${\omega }_0^{\prime }=0.057\mathrm{a}.\mathrm{u}.$ denotes the angular frequency of the 800-nm field. The peak electric field strength of 400-nm and 800-nm light fields in (a) and (b) are both taken to be 0.12 a.u. (c) and (d) are the intensity and phase spatiotemporal profiles of the 17th harmonic, respectively.

Figure 5

Spatial-resolved HHG spectrum driven by two-color counterspin and countervorticity STOVs at different intensity ratios ($I_{400}/I_{800}$). The intensity ratio is (a) 0.25 and (b) 4, respectively.