Observation of Nonlinear Self-Trapping of Broad Beams in Defocusing Waveguide Arrays

Abstract

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.

Polariton condensation in solitonic gap states in a one-dimensional periodic potential

“…In nonlinear photonic crystal fibres, such solitary waves have already demonstrated propagation without any distortion14. Besides, truncated Bloch waves have been more recently described and observed10111213. They arise in deep lattices and the localisation mechanism is self-trapping15, which prevents the tunnelling of particles from a strongly occupied to an empty lattice site.…”

“…In the absence of interactions, a defect state appears when the periodicity of the lattice is locally perturbed, for instance, by adding a local potential2, or by slightly changing the periodicity3 or the material refractive index4. In the case of strong interactions or strong nonlinearities, other types of localized states, like gap solitons (GSs)56789 and truncated Bloch waves10111213 can be generated, even without any perturbation of the periodic potential. GSs, typical for shallow lattice potentials, result from the interplay between the negative effective mass at the edge of the Brillouin zone and the particle repulsion.…”

Optical Gap solitons and Truncated Nonlinear Bloch Waves in Temporal Lattices

“…TBW like the one shown in Fig. 2(d) do not bifurcate from the first band like fundamental gap solitons, but when increasing the power the defocusing nonlinearity shifts them out of the first band before they localize in the first band gap [16][17][18]. A TBW which features an internal defect, as is displayed in Fig.…”

Asymmetric solitons and domain walls supported by inhomogeneous defocusing nonlinearity

“…Thus far, only symmetric solitons were predicted in settings of this type, while neither strongly asymmetric modes nor their limit form representing domain walls (DWs), which separate filled and empty domains, have been discovered. Such DWs have been studied only in materials with linear-refractiveindex landscapes [22][23][24][25].In this Letter we show that asymmetric defocusing nonlinearities characterized by different rates of the nonlinearity growth in the positive and negative transverse directions, can give rise to asymmetric bright solitons that may be stable. They turn into stable DWs if the nonlinearity becomes uniform in one direction.…”

“…Thus far, only symmetric solitons were predicted in settings of this type, while neither strongly asymmetric modes nor their limit form representing domain walls (DWs), which separate filled and empty domains, have been discovered. Such DWs have been studied only in materials with linear-refractiveindex landscapes [22][23][24][25].…”