Nonlinear X-waves: light bullets in normally dispersive media?

Colored conical emission by means of second-harmonic generation

“…u m (r, t, z) = q m (r, t) exp(imβz) [14]. In the normal GVD regime, q m (r, t) exist for β < 0 in the form of a polichromatic superposition of J 0 beams [12], so-called nonlinear X-waves [14], which exist also in the linear limit [15]. In SHG when the J 0 perturbations are amplified at the expense of an out-of-phase pump beam, they develop the right sign of nonlinear phase-shift (β < 0) for the formation of a nonlinear X-wave.…”

Nonlinear X‐Waves

“…During these experiments, it was found that AD-free input beams lead to unexpected spatio-temporal localization. Numerical simulations showed the emergence of an X-type structure, and the results were explained by the existence of a stationary nonlinear X-wave acting as an attractor for the nonlinear dynamics [5,6,12]. The reported observation were then confirmed by more accurate experiments, that ultimately lead to the "spatio-temporal tomography" of the generated nonlinear X-wave [9,8].…”

“…In this respect the experimental observation of optical 3D propagation-invariant pulses, so-called "light bullets", in a nonlinear medium with normal dispersion (k > 0), i.e. in a regime where both LW and SW were not expected to exist, did really appear as an astonishing result [5,6]. The spatio-temporal far-field spectrum of the observed light bullets clearly appeared as an "X" [7], and an accurate and sophisticated experimental reconstruction ("tomography") of the spatio-temporal profile unveiled the double conical structure of the wave-packet [8,9] in agreement with theoretical and numerical analysis [10,11,12,13,14,15,16].…”

Quadratic solitons: recent developments

“…Novel engineered tandem material structures [69] and pumping techniques are currently investigated today with such goal in mind. The so-called X-pulse techniques, pioneered in this context by Di Trapani, Trillo, and coworkers constitutes an important spin-off of this program [33], [34], which might find wide applications in several areas of nonlinear optics.…”

“…Thus, in their present form they cannot be employed to form fully 3-D light bullets. Therefore, new concepts, such as the so-called X-pulses, are currently under investigation to generate spatio-temporal trapping of light [33], [34].…”