We report on the excitation of large-amplitude waves, with a probability of around 1% of total peaks, on a photorefractive SBN crystal, by using a simple experimental setup at room temperature. We excite the system using a narrow gaussian beam and observe different dynamical regimes tailored by the value and time rate of an applied voltage. We identify two main dynamical regimes: a caustic one for energy spreading and a speckling one for peak emergence. Our observations are well described by a two-dimensional Schrödinger model with saturable local nonlinearity. https: //www.osapublishing.org/ol/abstract. cfm?uri=ol-44-11-2807

We study the selftrapping properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. It is shown that the spreading of the wavefunction in the presence of random nonlinearity, is always completely inhibited about fifty percent of all cases. The role of degeneracy associated with the flatbands is explained with the help of the n-simplex system, which can be solved in closed form.

In this work, we study the phenomena of Rogue waves (RW) on one-dimensional (1D) photonic lattices presenting diagonal and non-diagonal disorder. our results show the appearance of extreme events coming from the superposition of different, extended and localized, linear waves for weak disorder. We perform experiments on femtosecond laser written waveguide arrays having disorder in coupling constants, which is originated from a random waveguide distribution. Both, numerics and experiments, are in good agreement and show that RW are generically present in 1D lattices for weak disorder only, after a mandatory data filtering process. Rogue waves (RWs) are old phenomena, probably emerging at the very beginning of the universe. However, they were first described as large amplitude water waves on open ocean, suddenly appearing and disappearing without any cause and, sometimes, producing serious damages on ships 1,2. These waves are classified as extreme events (EE) in the sense of statistic due to their rare appearance but high amplitude, which is associated with long tails distributions. The origin of such extreme wave phenomena has been controversial, dividing the approaches between linear and nonlinear wave mixing processes 3. For example, wave tanks could naturally induce nonlinear phenomena due to their confining, which is completely absent in open sea, where waves suffer the interaction with other waves. Interestingly, due to the changes in global weather, an important increment in occurrence and severity of RWs have been reported 4 , making even more important their study due to the emergent damage on populated areas. Although initially RWs were applied to description of ocean phenomena, nowadays they are an important subject of complex systems research, going from oceanography, optics, and biology, to sociology, economy, etc. 5. Particularly in optics, nonlinear Schrödinger-like models 6-8 have associated the appearance of EEs with the excitation of coherent structures, including modulational instability and self focusing and defocusing processes 9-12. Recently, analogies between light and ocean phenomena have been reported 13 , including results supporting linear and nonlinear interpretations. Discrete systems 14,15 have been a bit outside of this discussion and only few numerical results have been reported to date 16-18 , which are focused mostly on nonlinear lattices presenting disorder. In particular, in Ref. 18 authors numerically found that weak disorder has an important effect on the appearance of Rogue Waves, results that could be associated with the concept of caustic effects coming from purely linear, large-amplitude events on an optical sea 19. In discrete linear lattices, dynamics is governed by ballistic propagation, having a characteristic Discrete Diffraction (DD) pattern when exciting a single bulk site 14. This implies that energy spreading across the lattice is mediated by the excitation of linear propagating waves, which explore the system with different velocities depending on their specific ...

No abstract

No abstract