Fig. 1. Perfect spatiotemporal optical vortex (STOV) wavepackets. (a)–(d) 3D iso-intensity profiles of a perfect STOV of l=+5 and corresponding sliced phase patterns (at y=0) at different locations L=75, 150, 225, and 300 mm after the spatiotemporal pulse shaper. (e) Comparison of spatiotemporal Laguerre–Gaussian wavepackets (STLG), spatiotemporal Bessel–Gaussian wavepackets (STBG), and perfect STOV with topological charge l=+1,+5, +10.

Fig. 2. Experimental setup for synthesizing and characterizing perfect STOV wavepackets. The setup includes three sections: a holographic pulse shaper, a time delay line system for fully measuring the 3D profile of the generated perfect STOV wavepacket, and a pulse compressor system. The computer-generated hologram (CGH) embedded on the SLM comprises two parts of the phase: (1) the phase distribution of a spatial–spectral Bessel–Gaussian mode; (2) a phase-only diffraction grating for controlling the spatial–spectral amplitude modulation. M, mirror; BS, beam splitter; CL, cylindrical lens.

Fig. 3. Theoretical and experimental results for the generated perfect STOV wavepacket and its comparison with the spatiotemporal Laguerre–Gaussian wavepacket. (a) and (b) Reconstructed intensity iso-surface and sliced phases (y=0 plane) of generated perfect STOVs and spatiotemporal Laguerre–Gaussian wavepackets with topological charge l=+1,+5,+10, respectively. (c) and (d) Dependence of the spatial (temporal) diameter on the topological charge of the generated perfect STOVs and spatiotemporal Laguerre–Gaussian wavepackets.

Fig. 4. Spatiotemporal collision of perfect STOVs with time-varying transverse OAM. (a1)–(c1) Measured iso-intensity profile of the collision of two perfect STOVs with the same spatial and temporal diameters and different topological charges of l1=+4,l2=−2. (a2)–(c2) Retrieved phase distribution in the meridional plane corresponding to (a1)–(c1). (d1)–(f1) Measured iso-intensity profile of the collision of two perfect STOVs with different spatial and temporal diameters and different topological charges of l3=+4,l4=−2. (d2)–(f2) Retrieved phase distribution in the meridional plane corresponding to (d1)–(f1). Linear phases along the spectral direction with opposite signs are applied on the left/right side of the input light field to advance/delay input wavepackets in the corresponding time domain. The phase is expressed as φ(ω)=kt(ω−ω0). From (a) to (c) [(d) to (f)], the linear phase coefficient kt changes from −1.5  ps to 1.5 ps. The arrow direction indicates the direction in which the perfect STOV is shifted in the time domain.

Fig. 5. Numerical simulation for the spatiotemporal evolution dynamics of the generated perfect STOV wavepacket of l=+5 in an anomalous dispersive medium of β2=−164  fs2/mm. z0=πw02/λ≈60  mm in this case.

Fig. 6. Reconstructed intensities and phases of generated perfect STOVs with different l.

Fig. 7. Reconstructed intensities and phases of generated spatiotemporal Laguerre–Gaussian wavepackets with p=0 and different l.