Nondispersive Space–Time Wave Packets Propagating in Dispersive Media

Abstract

Space-time wave packets can propagate invariantly in free space with arbitrary group velocity thanks to the spatio-temporal correlation. Here it is proved that the space-time wave packets are stable in dispersive media as well and free from the spread in time caused by material dispersion. Furthermore, the law of anomalous refraction for space-time wave packets is generalized to the weakly dispersive situation. These results reveal new potential of space-time wave packets for the applications in real dispersive media.

Transverse spin angular momentum of space-time surface plasmon polariton wave packet

“…The concept of designing the dispersion relation on the propagation axis by strictly adjusting k x and k y has already been experimentally demonstrated for light pulses in free space and is known as a Space-Time (ST) wave packet [67][68][69]. ST wave packets with a variety of novel propagation characteristics have been reported, including diffraction-free property [67], arbitrary group velocity [77], acceleration and deceleration in unprecedented ranges [78,79], the introduction of dispersion properties into a light pulse in free space [80,81], and non-dispersive propagation in a dispersive media [82].…”

Canceling and Inverting Normal and Anomalous Group‐Velocity Dispersion Using Space‐Time Wave Packets

“…which can be recognized as the law of refraction for a ST wave packet in a dispersive medium derived in refs. [50,51] that governs the change in group velocity from ṽa = c ña in free space to ṽ = c ñ in the medium. Indeed, the quantity n m (ñ m − ñ) is a refractive invariant for ST wave packets at normal incidence on planar interfaces between dispersive media, which we have called the "spectral curvature" because it is related to the curvature of the parabolic (k x , 𝜔 c )-projection in the vicinity of k x = 0.…”

“…By equating the first ‐order $$\Omega$$ terms in Equation (), we obtain $$$$\begin{equation} 1-\widetilde{n}_{\mathrm{a}}=n_{\mathrm{m}}(\widetilde{n}_{\mathrm{m}}-\widetilde{n}) \end{equation}$$$$which can be recognized as the law of refraction for a ST wave packet in a dispersive medium derived in refs. [50, 51] that governs the change in group velocity from $$\widetilde{v}_{\mathrm{a}}\!=\!\tfrac{c}{\widetilde{n}_{\mathrm{a}}}$$ in free space to $$\widetilde{v}\!=\!\tfrac{c}{\widetilde{n}}$$ in the medium. Indeed, the quantity $$n_{\mathrm{m}}(\widetilde{n}_{\mathrm{m}}-\widetilde{n})$$ is a refractive invariant for ST wave packets at normal incidence on planar interfaces between dispersive media, which we have called the “spectral curvature” because it is related to the curvature of the parabolic $$(k_{x},\tfrac{\omega }{c})$$‐projection in the vicinity of $$k_{x}\!=\!0$$.…”