The proposers have recently demonstrated the existence of a new mesoscopic phase in nanodisordered ferroelectrics known as a super-crystal. The super-crystal is characterized by unique and unexpected properties, such as binary birefringence and giant broadband refraction. These are accompanied by a strongly enhanced optical nonlinearity that has allowed the proposers to study numerous new scenarios in nonlinear wave physics, these including the observation of replica-symmetry-breaking in waves, Fermi-Pasta-Ulam-Tsingou recurrences, along with more speculative rogue waves. The FRACFER proposal aims at experimentally exploring ferroelectric cluster percolation during a structural transition. Using giant broadband optical refraction, we will use 3D orthographic projection imaging in ferroelectric KTN:Li to provide, for the first time, direct imaging evidence of self-similar fractal percolation.
The basic goals of the project are
G.I) demonstrate direct cluster imaging in the volume using crossed-polarizer experiments in a super-crystal;
G.II) collect dynamical data on ferroelectric cluster dynamics under the influence of external control parameters, these including temperature and bias static electric fields;
G.III) determine the percolation thresholds, critical parameters and fractal dimension of the percolative chain.
In FRACFER, focus is on the experimental study of the alteration in the structure of a ferroelectric super-crystal leading to its ultimate breakdown. Experiments will be carried out in solid-solutions of KTN:Li (potassium-lithium-tantalate-niobate).
Key expected outcomes of FRACFER are:
O.I) the determination of the fractal dimension of cluster percolation during the breakdown of a ferroelectric super-crystal through direct-imaging;
O.II) the elaboration of a physical model that connects fractal percolation to the susceptibility of the topologically dominated structure of a ferroelectric super-crystal.
Key expected outcomes of FRACFER are:
O.I) the determination of the fractal dimension of cluster percolation during the breakdown of a ferroelectric super-crystal through direct-imaging.
To date, no direct volume imaging technique is available to investigate transition dynamics in transparent bulk ferroelectrics. The reason is that ferroelectric clusters occur in a millimetric volume but can have spatial scales that range from several tens of nanometers to tens of microns. No standard imaging technique can allow a wide-area imaging of such a system embedded in a volume. The use of giant broadband refraction will thus be a key advancement in the study of ferroelectric transitions. Furthermore, it will represent a first important application of giant refraction and shed light on the still little-understood physics of super-crystals. Finally, the study of super-crystal susceptibility is key to electrically controlling giant refraction, and achievement that will open up vast applicative scenarios, such as the ability to modulate giant refraction on command.
O.II) the elaboration of a physical model that connects fractal percolation to the susceptibility of the topologically dominated structure of a ferroelectric super-crystal.
At the heart of the difficulties in understanding the physics of ferroelectric super-crystals and hence of harnessing their potential in cutting edge imaging applications, such as achromatic integrated optics, is the underlying polar structure composed of polarization vortices. The study of percolation threshold, dimensionality, and directionality will allow a better understanding of the underlying polarization field topology, shedding light onto the origin of giant refraction and, in general, of the peculiar and remarkable response of relaxor ferroelectrics.