This thesis describes an experimental, numerical and theoretical investigation of nonlinear optical phenomena in disordered photorefractive ferroelectrics in proximity of their phase-transition temperature. The work addresses different physical issues that find in nonlinear optics a common fertile research arena and are closely related to each other in the considered systems. Nonlinear wave dynamics in the spatial domain, where self-interaction of propagating waves generally results into non-spreading localized wavepackets such as spatial solitons, is extended in photorefractive ferroelectrics to non-equilibrium regimes characterized by stochastic instabilities and large material fluctuations. We discover the emergence of rogue waves, localized perturbations of abnormal intensity, whose understanding is challenging in various physical contexts and resides in the general problem of long-tail statistical distributions in complex systems. We identify their origin in spatiotemporal soliton dynamics in a saturable nonlinearity which can support scale-invariant waveforms. Properties and predictability of the observed extreme events are investigated, and, in particular, we demonstrate their active control through the spatial incoherence scale of the optical field. Moreover, we report how their emergence is sustained by turbulent transitions to an incoherent and disordered optical state triggered by modulational instability. The onset of strong turbulence for propagating optical waves has remained unobserved up to now and our results demonstrate a new experimental setting for its study. When the functional form of the nonlinearity is turned into a nonlocal one due to diffusive fields, this setting also exploits photonics to address fundamental physical problems and access to otherwise hidden phenomena. The natural spreading of waves during propagation, representing the wavelength-defined ultimate limit to spatial resolution, can be eliminated and reversed leading to diffraction cancellation and anti-diffraction of light. Since these behaviors on modifying the nature of underlying Schrödinger equation, we are the first to demonstrate how nonlinearity can make the spatial light distribution behave as the wavefunction of a quantum particle with negative mass. All these findings have roots in the nonlinear optical response of critical disordered ferroelectric crystals, which are also extremely interesting from the condensed matter point of view. In fact, competition of different microscopic structural phases and the associated polar-domain dynamics at the nanoscale results into non-ergodic dipolar-glass behaviors giving giant responses such as giant polarization, piezoelectricity and electro-optic effect. Disordered ferroelectrics crystals are investigated electro-optically across their ferroelectric phase-transition, where we report the observation of an anomalous electro-optic effect compatible with ultracold dipolar reorientation. In compounds presenting spatial inhomogeneity in their chemical composition, we discover a new ferroelectric phase of matter in which polar domains spontaneously coordinate into a mesoscopic coherent polarization super-crystals. This phase mimics standard solid-state structures but on scales that are thousands of times larger and represent the first spontaneous three-dimensional photonic crystal.
Nonlinear optical waves in disordered ferroelectrics / Pierangeli, Davide. - (2017 Feb 17).