Phd in MATHEMATICAL MODELS FOR ENGINEERING, ELECTROMAGNETICS AND
NANOSCIENCES

Thesis title: Photonics in the ferroelectric super-crystal phase

Nanodisordered ferroelectric perovskites belong to the family of relaxor ferroelectrics, and have long been attracting considerable attention in view of their unique physical properties. The introduction of compositional disorder on the nanoscale leads to the appearance of a broad temperature and frequency dependent peak in the dielectric susceptibility that manifests thermal, electric field, and strain hysteresis and is associated with anomalous relaxation. The presence of different compounds introduces, for specific composition concentrations, competing structural phases leading to unique polarization properties, such as the anomalous large capacitance and the giant piezoelectric effect. Recently, a new ferroelectric phase of matter, the spontaneous super-crystal phase (SC), has been discovered in bulk solid-solution of nanodisordered ferroelectric perovskite, several degrees below the Curie point. In this phase, domains, instead of locking into a disorganized pattern of clusters, form a 3D regular lattice of spontaneous polarization with micrometer lattice constant across macroscopic samples. This phase mimics standard solid-state structures but on scales that are thousands of times larger. The work presented in this thesis is an experimental investigation, through several photonics techniques, of the SC phase. In order to investigate the properties of the underlying ferroelectric domains, we first analyze the light-polarization dynamics which emerge from the interplay of mesoscopic domain ordering and anisotropy. Results indicate that polarized light propagating through the SC spatially separates in its polarization components, of mutually orthogonal linear polarization states. Furthermore, performing diffraction and refraction experiments, we discover that the SC phase is also accompanied by a broadband giant refraction (GR). Here the effective index of refraction is greater than 26 across the entire visible spectrum, even though no optical resonance is in place. The result is a material with no chromatic aberration and no diffraction. The discovery of GR opens up a wholly new realm of study, allowing us to expand our investigation to the field of nonlinear optics. Enhanced response causes wavelength conversion to occur in the form of bulk Cherenkov radiation with an arbitrarily wide spectral acceptance, more than 100 nm in the near infrared spectrum, an ultra-wide angular acceptance, up to ±40°, with no polarization selectivity. From a more fundamental point of view, trying to understand the behavior and physics of complexity-driven GR, in particular the role played by ferroelectric clusters, using a 3D orthographic cross-polarizer projection technique, we provide for the first time, direct imaging of fractal cluster percolation. We also study the effect that the SC, of micrometer-scale, has on the average atomic structure, using several results, obtained through different experimental techniques, from X-ray diffraction, to calorimetry. What we have found, is that the emergence of the SC is accompanied by a large scale and coherent anomalous lattice deformation. Alongside the investigation of the SC phase, we have exploited the strong nonlinear optical response of disordered ferroelectric crystals at the phase transition, which makes these materials suitable to study the physics of nonlinear waves. In our study, we focus principally on the exploration of applications in electro-optic integrated circuits, based on linear and nonlinear waves, and on the analysis of the physical origin of so-called soliton rogue waves.