Rogue waves are giant perturbations that form out of noise, reach enormous amplitudes that would be impossibly rare for Gaussian distributed statistical events, and rapidly decay back into noise. Although rogue events appear in many diverse field of science, from water waves to optical propagation, their origin is still not understood, a situation that has led to an ever-growing interest in the scientific community. Scientists now argue about links between rogue waves and other complex phenomena as wave turbulence and glassy behavior. A major hurdle in this research effort is the difficulty in investigating abnormal waves in controlled laboratory conditions.
The goal of this proposal is providing experimental evidence of the link between rogue waves and the so-called replica symmetry breaking transition, as well as their relation with strong turbulence. An extensive theoretical background based on the theory of integrability and disordered nonlinear waves will be developed and tested using beam propagation in photorefractive media.
The proposers carried out pioneering studies in nonlinear optics, discovering new regimes such as scale-free optics (Nat.Photon.2011) and anti-diffraction (Nat.Photon.2015). In recent developments, they reported the observation of rogue waves in photorefractive media (PRL2015) and three-dimensional rogue waves (APL2015) and developed a novel theoretical framework based on statistical mechanical models and paradigms taken from the science of complex systems (OPTICA2015, Opt.Exp.2017).The authors also reported the first experimental evidence of replica symmetry breaking in photonics (Nat.Comm.2015).
We pool together three groups at the Physics Department: P1) the experimental group of Eugenio Del Re with a leading international role in nonlinear optics; P2) the theoretical group of Paolo Maria Santini with a world-renowned expertise in solitons; P3) the group of Claudio Conti who pioneered the science of complexity in nonlinear waves.
Motivation for the Objectives
Rogue waves represent a rapidly expanding field in nonlinear physics that is, in many respects, largely in its infancy. In analogy to what happened for solitons and shock-waves, the finding of rogue events in optical fibers (Nature2007) is heralded as the turning point in rogue wave investigation, the implication being that rogue wave experiments in optics, combined with large scale water tank experiments in hydrodynamics, may pave the way to their understanding, prediction, and even to their use in applications. This said, over the past decade, although interest has grown enormously in the photonics community, there has been a limited expansion of experimental platforms in optics able to investigate the foundations of rogue phenomena. At the same time, the initial proposals aimed to unveil the origin and universality of rogue waves have come to a stall point and new ideas are in this moment particularly crucial.
The project aims at establishing a new direction for the understanding of optical rogue waves putting together paradigmatic concepts of complex systems and nonlinear wave theory into the unique experimental capability of light beam propagation in disordered photorefractive ferroelectrics. Specifically, focusing our attention on the role of disorder, we propose to address the rogue wave puzzle from a glassy physics point of view (Objective III). This is motivated by the breakthrough experimental observation that replica symmetry breaking can occur in highly-nonlinear disordered propagation, concomitantly with the appearance of extreme events (Objective I). Assessing for the first time a link supported by experimental evidence between glassy physics and rogue waves would open unprecedent scenarios in theoretical and experimental nonlinear wave theory, with specific applications in nonlinear optics. Moreover, a predictive theory in the integrable framework that includes the full evolution of the nonlinear field in the wake of rogue waves (Objective II) goes beyond the existing basic model; photorefractive propagation offers a testbed to its validation and to understand the relevance of integrable solutions in natural environments (Objective I). This may provide an unprecedented relation between wave turbulence and analytic solutions of integrable systems.
Innovations of the Proposal
To address the goal, the project introduces a number of innovative idea and approaches.
Innovation 1). The use of light beam propagation in photorefractive media as an extremely versatile arena for rogue waves.
At present, rogue waves in optics have been observed in fiber propagation and in optical cavities, where, however, the dynamics is strongly affected by artificial mechanism, such as the strictly one-dimensional geometry of fibers and dissipation in cavities. Our recent discovery of rogue waves in the spatial domain in photorefractive crystals (PRL2015) gives us the opportunity of harnessing a wealth of techniques and schemes developed for soliton studies to investigate fundamental unresolved point in the physics of rogue waves. For example, by means of a proper tuning of the optical intensities, wave dynamics can pass from being integrable to far from integrability in a single photonics laboratory experiments. Therefore, we are able to possibly crack the integrability riddle in rogue waves.
Innovation 2). The use of spin-glass theory in seeking for a universal rogue waves understanding.
In recent years, the concept of replica symmetry breaking originally proposed by Giorgio Parisi has been applied to understand the behavior of complex optical systems, such as random lasers. The proposing group has pioneered this approach (PRL2006) and extended it to nonlinear waves in disordered media (PRB2011).
Recently the authors has reported the first experimental evidence of replica symmetry breaking (Nat.Commun.2015) in random lasers. The analogous observation in beam propagation (Objective I) would represent a complete innovation, open the possibility of a new interpretation of rogue waves that directly associate the extreme event to a minimum of the underlying energy potential.
Innovation 3). An analytic description using the finite gap method and matched asymptotic expansions.
Particular analytic solutions of the nonlinear Schrodinger, the so-called breathers, has been extensively referred as prototypes of rogue waves and their recent observation in optics have received remarkable attention (Nat.Phys.2010, PRX2013, Nat.Comm.2016). However, an analytical description of the full evolution of the unstable field has remained elusive. Here, we develop this theory using the finite gap method and matched asymptotic expansions. The results allow to completely predict the rogue wave properties from the input condition, a breakthrough opening to the experimental control of extreme events generation.