  Propagation-invariant or non-diffracting optical beams have received
considerable attention during the last two decades. However, the pulsed nature
of light waves and the structured property of optical media like waveguides are
often overlooked. We here present a four-dimensional spatiotemporal approach
that extends and unifies both concepts of conical waves and helicon beams,
mainly studied in bulk media. By taking advantage of tight correlations between
the spatial modes, the topological charges, and the frequencies embedded in an
optical field, we reveal propagation-invariant (dispersion- and
diffraction-free) space-time wavepackets carrying orbital angular momentum
(OAM) that evolve on spiraling trajectories in both time and space in bulk
media or multimode fibers. Besides their intrinsic linear nature, we show that
such wave structures can spontaneously emerge when a rather intense ultrashort
pulse propagates nonlinearly in OAM modes. With emerging technologies of
pulse/beam shaping, multimode fibers and modal multiplexing, our proposed
scheme to create OAM-carrying helicon wavepackets could find a plethora of
applications.
