We describe a class of minimal diffraction-free and dispersion-free superluminal wave packets ($X$ waves and focused $X$ 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 zeros as units of OAM, and therefore $\left|m\right|/2$ 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 packet experiences a blueshift proportional to $\left|m\right|$. As a result of the radial redshift and the OAM blueshift, the color 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.

• Received 10 October 2021
• Accepted 21 December 2021

DOI:https://doi.org/10.1103/PhysRevA.105.013509