Fig. 1. General scheme of the proposed technique for a 2D measurement introducing the walk-off in the (a) +x and (b) +y directions.

Fig. 2. Scheme of the experimental set-up. (a) Configuration to generate a single optical vortex with an OAM of ℓ=+2. (b) Set-up to generate two delayed optical vortices with different OAM, ℓ=+2 and ℓ=0. (c) Scheme of our spatiotemporal technique used to characterize experiments.

Fig. 3. Amplitude swing measurement for the optical vortex of the proof of concept at position (x,y)=(0,−0.5)  mm. (a) Experimental amplitude swing trace, (b) retrieved trace, and (c) retrieved pulse intensity and phase. Temporal width FWHM of 77.8 fs and RMSE (root mean square error) of 0.024 are obtained. Note that Φ is the azimuthal angle of the optical axis of the amplitude swing rotating retarder plate.

Fig. 4. (a) Retrieved spatiospectral intensity and (b) phase at 798 nm of the same optical vortex using the algorithm 2D4Quad and measuring the spatial spectrum of the ordinary beam with two walk-off crystals: (a1), (b1) BBO and (a2), (b2) calcite. Note that the retrievals are shown spatially interpolated with a spatial step of 10 μm.

Fig. 5. Azimuthal phase comparison for a 600-μm-radius ring for each walk-off crystal (BBO and calcite) and the theoretical azimuthal phase (Theo.).

Fig. 6. Amplitude swing measurement for the two delayed optical vortices at position (x,y)=(0,−0.5)  mm. (a) Experimental amplitude swing trace, (b) retrieved trace, and (c) retrieved pulse intensity and phase. Temporal width FWHM of 78.4 fs and RMSE of 0.027 are obtained. Note that Φ is the azimuthal angle of the optical axis of the amplitude swing rotating retarder plate.

Fig. 7. (a) Retrieved spatiotemporal intensity and (b) phase of the average pulse for three different times using the 2D2Quad approach: (a1), (b1) t1=−45  fs, (a2), (b2) t2=0  fs, and (a3), (b3) t3=+45  fs. Note that the retrievals are shown spatially interpolated with a spatial step of 10 μm.

Fig. 8. (a) Simulated spatiotemporal intensity and (b) phase of the combination of two ultrashort optical vortices with different OAMs (ℓ=+2 and ℓ=0) with a delay of 63 fs: (a1), (b1) t1=−45  fs, (a2), (b2) t2=0  fs, (a3), (b3) t3=+45  fs.