Abstract
The group velocity of 'space-time' wave packets - propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations - can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum - and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced 'pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.
Highlights
Ever since Brittingham proposed in 1983 a pulsed optical beam that is transported rigidly in free space at a group velocity equal to the speed of light c [1], there has been significant interest in the study of propagationinvariant wave packets [2,3,4,5,6,7,8,9,10]
We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatiotemporal spectrum – and not by the beam size, bandwidth, or pulse width
We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced ‘pilot envelope’ that travels at a group velocity equal to the speed of light in vacuum
Summary
Ever since Brittingham proposed in 1983 a pulsed optical beam that is transported rigidly in free space at a group velocity equal to the speed of light c [1], there has been significant interest in the study of propagationinvariant wave packets [2,3,4,5,6,7,8,9,10]. A variety of examples have been identified [11,12,13] whose group velocity in free space – intriguingly – take on arbitrary values Such pulsed optical fields are endowed with tight spatio-temporal spectral correlations [14,15,16], whereby each spatial frequency underlying the beam spatial structure is associated with a single wavelength, and we refer to them as ‘spacetime’ (ST) wave packets [17, 18]. We observe a DGD on the order of ±150 ps for pulses of width ∼ 4 ps, representing a delay-bandwidth product of ∼ 35 This record-high observed DGD value is at least three orders-of-magnitude larger than the best previously reported results [20, 22] (4 orders-of-magnitude larger than in [33]), which is enabled by reducing the spectral uncertainty to ∼ 20 pm. We will show below in detail how relativistic causality is upheld when considering realistic finite-energy ST wave packets
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