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 nondifferentiable angular dispersion. This abstract mathematical feature allows us to tune the magnitude and sign of the different dispersion orders without introducing losses, 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 point toward their utility in nonlinear and quantum optics.

Space-time wave packets

“…It is now clear that the classical result in [269] makes two assumptions: on-axis propagation 𝜑 o = 0 and differentiable AD (i.e., 𝜑 (𝑛) o for all 𝑛 are finite and well-defined). Therefore, in the presence of non-differentiable AD, normal GVD can be produced in an on-axis ST wave packet [285,287], or by sculpting off-axis fields [128]. Both classes of ST wave packets exhibiting normal GVD in free space have been recently realized [286].…”

“…A host of nonlinear optical interactions are governed by phase-matching conditions, and TPFs have already been useful in various nonlinear effects (e.g., SHG [280,281] and THz generation [282]). The versatility afforded by ST wave packets in light of the non-differentiable AD underpinning them has yet to be exploited in nonlinear optics [286][287][288]. Moreover, the recent synthesis of 3D ST wave packets is expected to lead to breakthroughs in this area in the near future.…”

“…6. Arbitrary dispersion profiles can be readily realized involving any magnitude, sign, or order or superposition of several dispersion orders, each controlled independently [286,287].…”

Canceling and inverting normal and anomalous group-velocity dispersion using space-time wave packets

“…In our scheme, the angular dispersion profile ϕ(λ) can be controlled almost arbitrarily [Fig. 4]: each wavelength λ can be assigned a propagation angle ϕ(λ) independently of all other wavelengths, and we can thus tune v a and k 2a independently [60]. We demonstrate this capability in Fig.…”

“…Such angular dispersion can be produced by a recently developed pulsed-beam shaper that serves as a universal angular-dispersion synthesizer in one dimension [59]. We have recently shown that non-differentiable angular dispersion is the crucial ingredient for tuning the group velocity of a ST wave packet and introducing an arbitrary dispersion profile in free space [57,60]. This suggests the prospect for dispersion-cancellation in presence of either normal-or anomalous-GVD.…”