Space-time wave packets violate the universal relationship between angular dispersion and pulse-front tilt

Abstract

Introducing angular dispersion into a pulsed field tilts the pulse front with respect to the phase front. There exists between the angular dispersion and the pulse-front tilt a universal relationship that is device-independent, and also independent of the pulse shape and bandwidth. We show here that this relationship is violated by propagation-invariant space-time (ST) wave packets, which are pulsed beams endowed with precise spatio-temporal structure corresponding to a particular form of angular dispersion. We demonstrate theoretically and experimentally that underlying ST wave packets is -to the best of our knowledge -the first example in optics of non-differentiable angular dispersion, resulting in pulse-front tilt that depends on the pulse bandwidth even at fixed angular dispersion.

Engineering the optical vacuum: Arbitrary magnitude, sign, and order of dispersion in free space using space-time wave packets

“…We recently demonstrated that a broad family of pulsed beams that we denote 'space-time' (ST) wave packets [42][43][44][45], in which the spatial frequencies and wavelengths are tightly associated [46][47][48][49][50][51][52][53][54], is undergirded by a particular form of angular dispersion that is -surprisingly -non-differentiable at the carrier frequency [55]. As a result, some consequences associated with conventional differentiable angular dispersion can be sidestepped by ST wave packets.…”

“…As a result, some consequences associated with conventional differentiable angular dispersion can be sidestepped by ST wave packets. First, the 'universal' relationship that relates the pulse-front tilt to angular dispersion [21,22], which is device-independent and also independent of the pulse bandwidth and shape, is violated by ST wave packets whose pulse-front tilt is proportional to the square root of the bandwidth [55]. Second, despite the underlying angular dispersion, ST wave packets are propagation-invariant [44,[56][57][58][59][60], and can travel GVD-free at arbitrary group velocities [61][62][63][64][65].…”

Temporal Talbot effect in free space

“…Crucially, V-waves are endowed with differentiable angular dispersion, so they are amenable to the conventional perturbative theory [44] and they therefore can inculcate only anomalous GVD. In contrast, non-differentiable angular dispersion is introduced in the the dispersive ST fields examined here [43] and they can undergo either normal or anomalous GVD [16].…”

“…Rather than propagation-invariant ST wave packets, observing the temporal Talbot effect requires utilizing their counterparts exhibiting GVD in free space [16]. Because the angular dispersion underpinning ST wave packets is nondifferentiable [43], unlike conventional angular dispersion associated with tilted pulse fronts (TPFs) that is differentiable [23,24], ST wave packets can experience arbitrary GVD in free space [16], whereas TPFs can experience only anomalous GVD [23,24,44]. After introducing normal or anomalous GVD of large magnitude, periodically sampling the temporal spectrum of the ST wave packet produces the temporal Talbot effect with z T on the order of a few centimeters (≈ 2 cm here).…”

Isochronous space–time wave packets

“…The key distinguishing characteristic of ST wave packets is that each spatial frequency is associated with a single wavelength [9][10][11][12][13] so as to realize non-differentiable angular dispersion [14], which enables realizing wave packets endowed with propagation invariance [15][16][17] and tunable group velocities [18][19][20]. Specifically, the spatio-temporal spectrum of a ST wave packet in a nondispersive medium of index n lies at the intersection of the light cone k 2…”