Spontaneous photonic lattices and nonlinear waves in nanodisordered ferroelectrics

In this Thesis we deal with nanodisordered ferroelectric perovskite crystals. These material have been demonstrated to be a good test-bed to study nonlinear optical phenomena due to their strong optical properties. In fact, their embedded disorder enhances their response at the phase transition and makes these materials suitable to sustain solitons and rogue waves also with low optical power. We first use self-focusing at the paraelectric phase to study nonlinear wave propagation. Our experiments are conceived to investigate the evolution of structured waves in time and in space. We make three beams to interfere to optically observe the Fermi-Pasta-Ulam-Tsingou recurrence. We experimentally verify its analytic solution provided by Grinevich-Santini that allows us to predict the exact position of each recurrence. Moreover, we demonstrate that the periodic behavior is lost if the system ceases to be integrable. We study the appropriate interference pattern in the form of nondiffractive Bessel beams to investigate what happens to such waves in a self-focusing medium. We identify two regimes: a Bessel beam selftrapping and a breathing soliton. Furthermore, we demonstrate the feasibility of Bessel beam writing to build a scalable and rewritable network of waveguides inside the bulk ferroelectric medium. We also studied the unique properties of the ferroelectric phase. The most evident outcome is the so-called super-crystal that is a spontaneous photonic 3D lattice that emerges from the interplay between material order and disorder. We study the super-crystal in different ways and we recover the periodic behavior for linear and nonlinear propagation. In detail we report a periodic pattern for birefringence and second harmonic generation. The main result is that we have observed the highest value of the refractive index reported in literature for visible light and we have connected the effect to the super-crystal. This material allows, in theory, to transmit light without any information loss, that is without diffraction and chromatic dispersion. The physics of diffraction is also investigated with the introduction of an innovative method to achieve super-resolution. We exploit a confocal microscope and a remote knifeedge technique. This allows us to directly study the role of evanescent waves in superresolution imaging forming, i.e. they are filtered out as the super-resolved image approaches to the diffraction-limited one. Experiments here are performed with a terahertz frequency, λ ∼ 1.00 mm, to easily accede the near field and capture the information carried by the evanescent waves