  Multimode optical fibers has emerged as the platform that will bridge the gap
between nonlinear optics in bulk media and in single-mode fibers. However, the
understanding of the transition between these two research fields still remains
incomplete despite numerous investigations of intermodal nonlinear phenomena
and spatiotemporal coupling. Some of the striking phenomena observed in bulk
media with ultrashort and ultra-intense pulses (i.e., conical emission,
harmonic generation and light bullets) require a deeper insight to be possibly
unveiled in multimode fibers. Here we generalize the concept of conical waves
described in bulk media towards structured media, such as multimode optical
fibers, in which only a discrete and finite number of modes can propagate. The
modal distribution of optical fibers provides a quantization of conical
emission (e.g., quantized X-waves) through phase-matched resonant radiations
(i.e., dispersive waves) seeded by optical shocks or ultrashort wave structures
during spatiotemporal compression stages. Such quantized dispersion- and
diffraction-free waves are generated when a rather intense short pulse
propagates nonlinearly in a multimode waveguide, whatever the dispersion regime
and waveguide geometry. Future nonlinear experiments in commercially-available
multimode fibers could reveal different forms of conical emission and an easy
control of supercontinuum light bullets.
