Limit on Differential Group Delay Achievable by Space-Time Wave Packets

Abstract

We investigate the effects of the spectral uncertainty on the maximum differential group delay (DGD) for a finite-energy space-time wave-packet, showing the maximum DGD that can be obtained with respect to a reference pulse at c.

Space-time wave packets localized in all dimensions

“…It is crucial that this task be achieved with high spectral resolution. Previous studies have shown that the critical parameter determining the propagation distance of ST wave packets is the 'spectral uncertainty' δλ, which is the finite spectral uncertainty in the association between spatial and temporal frequencies [41]. Our measurements indicate that the optimal spectral uncertainty after the CBG arrangement is δλ∼35 pm, which is achieved for a 2-mm input beam width [Supplementary Material Fig.…”

“…A subtle distinction emerges between the subluminal and superluminal wave packets regarding the axial evolution of their spatio-temporal profile. It can be shown that in presence of finite spectral uncertainty δλ, the realized ST wave packet can be separated into the product of an ideal ST wave packet traveling indefinitely at v and a long 'pilot envelope' traveling at c. The finite propagation distance L max is then a consequence of temporal walk-off between the ST wave packet and the pilot envelope [41]. For subluminal ST wave packets, this results initially in a 'clipping' of the leading edge of the wave packet in [Fig.…”

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

“…At first sight, this is a completely reasonable assumption that needs no reconsideration, especially for narrow bandwidths. However, our recent strategy for preparing ST wave packets is capable of incorporating arbitrarily prescribed angular dispersion into the field [22,23,[27][28][29][30], which necessitates a reassessment of this assumption.…”

“…1(e). The resulting ST wave packet propagates rigidly in free space at a group velocity v = c tan θ, or an effective group index n = cot θ [27,28,32]. In the paraxial regime…”

“…To the best of our knowledge, this is the first prediction of its kind based on the non-differentiability of the angular dispersion. Another consequence of the non-differentiable angular dispersion is the GVD-free propagation-invariance of the ST wave packet [27,28], in contrast to the anomalous GVD induced by differentiable angular dispersion [1,5,6].…”