Turbulent Transitions in Optical Wave Propagation

Extreme transport of light in spheroids of tumor cells

Extreme waves are intense and unexpected wavepackets ubiquitous in complex systems. In optics, these rogue waves are promising as robust and noise-resistant beams for probing and manipulating the underlying material. Localizing large optical power is crucial especially in biomedical systems, where, however, extremely intense beams have not yet been observed. We here discover that tumor-cell spheroids manifest optical rogue waves when illuminated by randomly modulated laser beams. The intensity of light transmitted through bio-printed three-dimensional tumor models follows a signature Weibull statistical distribution, where extreme events correspond to spatially-localized optical modes propagating within the cell network. Experiments varying the input beam power and size indicate that the rogue waves have a nonlinear origin. We show that these nonlinear optical filaments form high-transmission channels with enhanced transmission. They deliver large optical power through the tumor spheroid, and can be exploited to achieve a local temperature increase controlled by the input wave shape. Our findings shed light on optical propagation in biological aggregates and demonstrate how nonlinear extreme event formation allows light concentration in deep tissues, paving the way to using rogue waves in biomedical applications, such as light-activated therapies.

Intense Wave Formation from Multiple Soliton Fusion and the Role of Extra Dimensions

We experimentally and numerically explore the role of dimensionality in multiple (three or more) soliton fusion supported by nonreciprocal energy exchange. Three-soliton fusion into an intense wave is found when an extra dimension, with no broken inversion symmetry, is involved. The phenomenon is observed for 2+1D spatial waves in photorefractive crystals, where solitons are supported by a spatially local saturated Kerr-like self-focusing and fusion is driven by the leading nonlocal correction, the spatial analog of the nonlinear Raman effect.

Classical Rayleigh-Jeans Condensation of Light Waves: Observation and Thermodynamic Characterization

Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the nonequilibrium formation of nonlinear coherent structures (solitons, vortices,…), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the first demonstration of a coherent phenomenon of self-organization that is exclusively driven by optical thermalization toward the Rayleigh-Jeans equilibrium.

Super rogue wave generation in the linear regime

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.

Single to multiple acoustic vortex excitations in the transition to defect-mediated dust acoustic wave turbulence

We experimentally investigate the cooperative excitations in the transition from a self-excited three-dimensional ordered plane wave to a defect-mediated turbulence (DMT) state with multiple unstable defect filaments in a dusty plasma system. It is found that, with increasing effective driving, a single acoustic vortex (AV) with positive or negative helicity winding around a long straight defect filament with small wiggling in the 2+1D (dimensional) space-time space starts to emerge along the center axis of the small dust cluster. The sequential ruptures of the crest surfaces from the cluster boundary followed by their reconnection with adjacent ruptured crest surfaces, or repelling one of the pairwise generated defects out of the boundary, are the key for the single AV generation. Further increasing driving makes the single defect filament exhibit helical excursion in the 2+1D space. The system eventually enters the state with a few short-lived AVs and the DMT state with multiple AVs. The gradual increasing defect filament fluctuations and defect number in the transition to the DMT more strongly distort the nearby waveforms, which leads to the transition from the emergence of distinct sideband peaks to the broadened peaks in the power spectra of temporal dust density fluctuation. For the system with a larger cluster size, the single AV states are skipped in the transition to the DMT state.

Anisotropic nonlinear refractive index measurement of a photorefractive crystal via spatial self-phase modulation

We show that the refractive index modification photoinduced in a biased nonlinear photorefractive crystal can be accurately measured and controlled by means of a background incoherent illumination and an external electric field. The proposed easy-to-implement method is based on the far-field measurement of the diffraction patterns of a laser beam propagating through a self-defocusing medium undergoing spatial self-phase modulation. For various experimental conditions, both saturation intensity and maximum refractive index modification have been measured. We also clearly evidence and characterise the anisotropic nonlinear response of the crystal in the stationary regime.

Multiscale Coherent Excitations in Microscopic Acoustic Wave Turbulence of Cold Dusty Plasma Liquids

We experimentally demonstrate the observation of thermally excited microscopic acoustic wave turbulence at the discrete level in quasi-two-dimensional cold dusty plasma liquids. Through multidimensional empirical mode decomposition of individual dust particle motions over a large area, the turbulence is decomposed into multiscale traveling wave modes, sharing self-similar dynamics. All modes exhibit intermittent excitation, propagation, scattering, and annihilation of coherent waves, in the form of clusters in the xyt space, with cluster sizes exhibiting self-similar power law distribution. The poor particle interlocking in the region with poor structural order is the key origin of the easier excitations of the large amplitude slow modes. The sudden phase synchronization of slow wave modes switches particle motion from cage rattling to cooperative hopping.

Coexistence of turbulence-like and glassy behaviours in a photonic system

Coexistence of physical phenomena can occur in quite unexpected ways. Here we demonstrate the first evidence in any physical system of the coexistence in the same set of measurements of two of the most challenging phenomena in complex systems: turbulence and spin glasses. We employ a quasi-one-dimensional random fibre laser, which displays all essential ingredients underlying both behaviours, namely disorder, frustration and nonlinearity, as well as turbulent energy cascades and intermittent energy flux between fluctuation scales. Our extensive experimental results are theoretically supported by a newly defined photonic Pearson correlation coefficient that unveils the role of the intermittency and describes remarkably well both the spin-glass Parisi overlap parameter and the distribution of turbulent-like intensity increments. Our findings open the way to unravel subtle connections with other complex phenomena, such as disordered nonlinear wave propagation, Lévy statistics of intensity fluctuations, and rogue waves.

Interacting Multiscale Acoustic Vortices as Coherent Excitations in Dust Acoustic Wave Turbulence

In this work, using three-dimensional intermittent dust acoustic wave turbulence in a dusty plasma as a platform and multidimensional empirical mode decomposition into different-scale modes in the 2+1D spatiotemporal space, we demonstrate the experimental observation of the interacting multiscale acoustic vortices, winding around wormlike amplitude hole filaments coinciding with defect filaments, as the basic coherent excitations for acoustic-type wave turbulence. For different decomposed modes, the self-similar rescaled stretched exponential lifetime histograms of amplitude hole filaments, and the self-similar power spectra of dust density fluctuations, indicate that similar dynamical rules are followed over a wide range of scales. In addition to the intermode acoustic vortex pair generation, propagation, or annihilation, the intra- and intermode interactions of acoustic vortices with the same or opposite helicity, their entanglement and synchronization, are found to be the key dynamical processes in acoustic wave turbulence, akin to the interacting multiscale vortices around wormlike cores observed in hydrodynamic turbulence.

Observation of replica symmetry breaking in disordered nonlinear wave propagation

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but it has never been observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity. When mode interaction dominates light dynamics in a disordered optical waveguide, different experimental realizations are found to have an anomalous overlap intensity distribution that signals a transition to an optical glassy phase. The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems.

Observation of polarization-maintaining light propagation in depoled compositionally disordered ferroelectrics

We investigate the evolution of the state of polarization of light propagating through bulk depoled composite ferroelectrics below the Curie temperature. In contrast to standard depoled ferroelectrics, where random birefringence causes depolarization and scattering, light is observed to suffer varying degrees of depolarization and remains fully polarized when linearly polarized along the crystal principal axes. The effect is found to be supported by the formation of polarized speckles organized into a spatial lattice and occurs as the ferroelectric settles into a spontaneous super-crystal, a three-dimensional coherent mosaic of ferroelectric clusters. The polarization lattices gradually disappear as the ferroelectric state reduces to a disordered distribution of polar nanoregions above the critical point.

Turbulence hierarchy in a random fibre laser

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.

Random fibre lasers constitute a class of lasers where the optical feedback is provided by multiple scattering in a disordered system. Here, González et al. theoretically and experimentally study the statistical turbulence behaviour in relation to the lasing transition in such lasers.