Fig. 7: Measured complex-field amplitude and phase profiles for 3D ST wave packets with and without OAM.

a Measured amplitude ∣ψ(x, y)∣ (first row) and phase ϕ(x, y) (second row) at a fixed axial plane z = 30 mm (see Figs. 5 and 6) at delays τ = −5 ps, τ = 0 corresponding to the wave-packet center, and τ = 5 ps for a superluminal 3D ST wave packet with ℓ = 0 and a ℓ = 1. c Iso-amplitude contour \(I=0.6{I}_{\max }\) for the 3D ST wave packet from (a) and ST-OAM from (b). d Same as c but for the iso-amplitude contour \(I=0.15{I}_{\max }\).