Extended Data Fig. 4: Simulated and measured orbital period of a wave packet synthesized from a square root correlation function.
From: Broadband control of topological–spectral correlations in space–time beams
a, Correlations obtained from equation (1) using p = 0.5 (red) and, for comparison, p = 1 (yellow). The other parameters of the equation are Δℓ = 30, ℓ1 = 40, Δω/2π = 137 THz, ω2/2π = 566 THz. b, Experimental square root correlation function. c Azimuthal position of the maximum of the rotating pulse as a function of time obtained from the simulations using p = 0.5 (red) or p = 1 (yellow). By fitting the slopes corresponding to the angular velocity Ω we obtain the orbital periods Torb = 2π/Ω reported in the plots, indicating that the complex correlation function produces a shorter Torb and a larger Ω. The inset shows how the azimuthal position is extracted at a given time from the maximum of the rotating space-time beam intensity. The simulation assumes a frequency chirp in the input beam equivalent to a group delay dispersion of 79 fs2, as the one measured experimentally using hyperspectral holography. d Azimuthal position as a function of time obtained from the experimental space-time beam synthesized using the square root correlation function, giving a value close to the simulated one for p = 0.5.
