DiscreteX-Wave Formation in Nonlinear Waveguide Arrays

Abstract

We present experimental evidence for the spontaneous formation of discrete X waves in AlGaAs waveguide arrays. This new family of optical waves has been excited, for the first time, by using the interplay between discrete diffraction and normal temporal dispersion, in the presence of Kerr nonlinearity. Our experimental results are in good agreement with theoretical predictions.

Optical-fluid dark line and X solitary waves in Kerr media

“…The results that we derive below have relevance also for di erent contexts where the same hyperbolic NLSE applies, such as the propagation in suitably engineered lattices giving rise to e ective negative di raction [30,31] (in this case t represents in Eq. (1) an additional spatial variable).…”

“…This nding opens a novel path for the excitation and manipulation of line and X waves in nonlinear optics and in other areas where the NLSE applies, from Bose-Einstein condensation to acoustics. In fact, the nonlinear dark line and X solitary wave solutions of the NLSE are potentially observable in the regimes investigated experimentally in [15,16,31] and also in [10,13,38,39]. Of course any nite energy realization of the present type of solutions should consider a spatiotemporal envelope modulation of the X solitary wave that decays to zero su ciently slowly in (t, y) when compared with the extension of the solitary central notch, similarly to the case of dark solitons in ( + )D [40] and ( + )D [41].…”

Cylindrically polarized nondiffracting optical pulses

“…Polychromatic superpositions of Bessel beams, commonly called X-waves, in fact, have been studied quite extensively in the past years [31], and very recently, OAM-carrying X-waves have been proposed [30]. Firstly introduced in acoustics [32,33], X-waves have provided many interesting results in many different areas physics, like nonlinear optics [34,35], condensed matter [36], quantum optics [37], integrated optics [38,39] and optical communications [40]. We believe that the interplay between the nondiffracting character typical of X-waves and the properties of cylindrically polarized beams can open new possibilities for fundamental and applied research.…”

Some special solutions to the Hyperbolic NLS equation

“…For example, it arises in plasma physics [53] and in normally dispersive optical waveguide arrays modeling [14,39]. In the context of water waves the HypNLS equation is the leading order model of the wave envelope evolution.…”