Broadband X-waves with orbital angular momentum

Abstract

We describe the minimal diffraction-free and dispersion-free, superluminal wave packets (X-waves and generic superluminal localized waves) that can carry a given amount of units m of orbital angular momentum (OAM) per photon. Even if their frequency spectrum is wide enough to synthesize a unipolar pulse, OAM imposes a temporal pulse shape with as many zeroes as units of OAM, and therefore |m|/2 temporal oscillations. All the frequencies in the broadband spectrum are displayed, like in a rainbow, from the bluer ones in the vicinity of the vortex to the redder ones in the wave periphery. At the same time, the whole wave paclet experiences a blue shift proportional to |m|. As a result of the radial red shift and the OAM blue shift, the colour of the brilliant ring around the central vortex is independent of OAM, and solely determined by the broadband source spectrum. Given the very peculiar properties of X-waves with OAM, their generation and use, instead of standard Laguerre-Gauss modes, could improve the performance of OAM-based communication and quantum cryptographic systems, as well as the efficiency of the generation of high harmonics and attosecond pulses with OAM.

Space-time wave packets

“…Finally, a recent theoretical development indicates an intriguing relationship between pulse width (a temporal DoF) and the maximum OAM-order of the beam (a spatial DoF). It appears that the pulse width sets an upper limit on the maximum OAM-order that can be sustained by the wave packet [65,66,[383][384][385][386]. This limit has been examined so far in the context of X-waves and awaits to be studied for baseband ST wave packets.…”