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

Abstract

Spatial structuring of an optical pulse can lead in some cases upon free propagation to changes in its temporal profile. For example, introducing conventional angular dispersion into the field results in the pulse encountering group-velocity dispersion in free space. However, only limited control is accessible via this strategy. Here we show that precise and versatile control can be exercised in free space over the dispersion profile of so-called 'space-time' wave packets: a class of pulsed beams undergirded by non-differentiable angular dispersion. This abstract mathematical feature allows us to tune the magnitude and sign of the different dispersion orders without introducing lossess, thereby realizing arbitrary dispersion profiles, and achieving dispersion values unattainable in optical materials away from resonance. Unlike optical materials and photonic structures in which the values of the different dispersion orders are not independent of each other, these orders are addressable separately using our strategy. These results demonstrate the versatility of space-time wave packets as a platform for structured light and points towards their utility in nonlinear and quantum optics.

Refraction of space-time wave packets: I. Theoretical principles

“…Rather, it is reduced to one dimension (1D) by enforcing an association between the spatial and temporal frequencies such that ψ(k x , Ω) → ψ(k x )δ(Ω − Ω(k x ; θ)), where Ω(k x ; θ) is a deterministic mapping that dictates the functional dependence between k x and Ω, and θ is a real continuous parameter identifying this association [1][2][3]6]. In other words, angular dispersion is introduced into the field [8,54,65,66]. To achieve propagation invariance, Ω(k x ; θ) must impose the constraint k z = b + Ω/ v, where b ≤ nk o is a constant and v is the group velocity.…”

“…We recently introduced a phase-only spatio-temporal spectral synthesis methodology [6,40] that affords precise preparation of ST wave packets. This strategy has facilitated observing substantial and unambiguous departures from conventional behaviors, including propagation invariance [6,[41][42][43][44]; arbitrary group velocities in free space [44][45][46], dielectrics [47,48], planar waveguides [49], and as surface plasmon polaritons at metal-dielectric interfaces [50]; self-healing [51]; time diffraction [24,29,41,52]; axial acceleration and deceleration [53]; and arbitrary dispersion in free space [54].…”

Isochronous space–time wave packets

“…Finally, our work here is based on the refraction of propagation-invariant ST wave packet in non-dispersive media. It will be interesting to extend this work to dispersive materials [24,25], and to study the refraction of recently developed ST wave packets that undergo controllable axial evolution, such as accelerating or decelerating wave packets [26], and those endowed with axial spectral encoding [27] or group-velocity dispersion in free space [28]. Disclosures.…”

Temporal Talbot effect in free space

“…1(b)]. This surprising effect is made possible by exploiting dispersive 'space-time' (ST) wave packets [16]. In general, ST wave packets [17][18][19] are pulsed beams endowed with a precise spatio-temporal structure [20][21][22] inculcating angular dispersion [23,24], by virtue of which they display a variety of unique behaviors, including propagation invariance [25][26][27][28][29][30]; tunable group velocities in absence of dispersion [31][32][33]; selfhealing [34]; free-space acceleration/deceleration [35][36][37][38]; among many other possibilities [39][40][41][42].…”

“…In general, ST wave packets [17][18][19] are pulsed beams endowed with a precise spatio-temporal structure [20][21][22] inculcating angular dispersion [23,24], by virtue of which they display a variety of unique behaviors, including propagation invariance [25][26][27][28][29][30]; tunable group velocities in absence of dispersion [31][32][33]; selfhealing [34]; free-space acceleration/deceleration [35][36][37][38]; among many other possibilities [39][40][41][42]. 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].…”