Large-Scale Photonic Ising Machine by Spatial Light Modulation.

Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving the way to new ultrafast hardware for machine learning. However, the proposed systems are either tricky to scale or involve a limited number of spins. We design and experimentally demonstrate a large-scale optical Ising machine based on a simple setup with a spatial light modulator. By encoding the spin variables in a binary phase modulation of the field, we show that light propagation can be tailored to minimize an Ising Hamiltonian with spin couplings set by input amplitude modulation and a feedback scheme. We realize configurations with thousands of spins that settle in the ground state in a low-temperature ferromagneticlike phase with all-to-all and tunable pairwise interactions. Our results open the route to classical and quantum photonic Ising machines that exploit light spatial degrees of freedom for parallel processing of a vast number of spins with programmable couplings.

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.

Turbulent Transitions in Optical Wave Propagation.

We report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.

Intrinsic Negative Mass from Nonlinearity.

We propose and provide experimental evidence of a mechanism able to support negative intrinsic effective mass. The idea is to use a shape-sensitive nonlinearity to change the sign of the mass in the leading linear propagation equation. Intrinsic negative-mass dynamics is reported for light beams in a ferroelectric crystal substrate, where the diffusive photorefractive nonlinearity leads to a negative-mass Schrödinger equation. The signature of inverted dynamics is the observation of beams repelled from strongly guiding integrated waveguides irrespective of wavelength and intensity and suggests shape-sensitive nonlinearity as a basic mechanism leading to intrinsic negative mass.

Volume integrated phase modulator based on funnel waveguides for reconfigurable miniaturized optical circuits.

We demonstrate the integration of a miniaturized 30(x) µm×30(y) µm×2.7(z) mm electro-optic phase modulator operating in the near-IR (λ=980 nm) based on the electro-activation of a funnel waveguide inside a paraelectric sample of photorefractive potassium lithium tantalate niobate. The modulator forms a basic tassel in the realization of miniaturized reconfigurable optical circuits embedded in a single solid-state three-dimensional chip.

Spatial Rogue Waves in Photorefractive Ferroelectrics.

Rogue waves are observed as light propagates in the extreme nonlinear regime that occurs when a photorefractive ferroelectric crystal is undergoing a structural phase transition. The transmitted spatial light distribution contains bright localized spots of anomalously large intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The isolated wave events form as out-of-equilibrium response and disorder enhance the Kerr-saturated nonlinearity at the critical point. Self-similarity associable to the individual observed filaments and numerical simulations of the generalized nonlinear Schrödinger equation suggests that dynamics of soliton fusions and scale invariance can microscopically play an important role in the observed rogue intensities and statistics.

Continuous Solitons in a Lattice Nonlinearity.

We study theoretically and experimentally the propagation of optical solitons in a lattice nonlinearity, a periodic pattern that both affects and is strongly affected by the wave. Observations are carried out using spatial photorefractive solitons in a volume microstructured crystal with a built-in oscillating low-frequency dielectric constant. The pattern causes an oscillating electro-optic response that induces a periodic optical nonlinearity. On-axis results in potassium-lithium-tantalate-niobate indicate the appearance of effective continuous saturated-Kerr solitons, where all spatial traces of the lattice vanish, independently of the ratio between beam width and lattice constant. Decoupling the lattice nonlinearity allows the detection of discrete delocalized and localized light distributions, demonstrating that the continuous solitons form out of the combined compensation of diffraction and of the underlying periodic volume pattern.

Anti-diffracting beams through the diffusive optical nonlinearity.

Anti-diffraction is a theoretically predicted nonlinear optical phenomenon that occurs when a light beam spontaneously focalizes independently of its intensity. We observe anti-diffracting beams supported by the peak-intensity-independent diffusive nonlinearity that are able to shrink below their diffraction-limited size in photorefractive lithium-enriched potassium-tantalate-niobate (KTN:Li).

Photorefractive light needles in glassy nanodisordered KNTN.

We study the formation of 2D self-trapped beams in nanodisordered potassium-sodium-tantalate-niobate (KNTN) cooled below the dynamic glass transition. Supercooling is shown to accelerate the photorefractive response and enhance steady-state anisotropy. Effects in the excited state are attributed to the anomalous slim-loop polarization curve typical of relaxors dominated by non-interacting polar-nano-regions.

Aging solitons in photorefractive dipolar glasses.

We study experimentally the aging of optical spatial solitons in a dipolar glass hosted by a nanodisordered sample of photorefractive potassium-sodium-tantalate-niobate (KNTN). As the system ages, the waves erratically explore varying strengths of the nonlinear response, causing them to break up and scatter. We show that this process can still lead to solitons, but in a generalized form for which the changing response is compensated by changing the normalized wave size and intensity so as to maintain fixed the optical waveform.

Super-crystals in composite ferroelectrics.

As atoms and molecules condense to form solids, a crystalline state can emerge with its highly ordered geometry and subnanometric lattice constant. In some physical systems, such as ferroelectric perovskites, a perfect crystalline structure forms even when the condensing substances are non-stoichiometric. The resulting solids have compositional disorder and complex macroscopic properties, such as giant susceptibilities and non-ergodicity. Here, we observe the spontaneous formation of a cubic structure in composite ferroelectric potassium-lithium-tantalate-niobate with micrometric lattice constant, 10(4) times larger than that of the underlying perovskite lattice. The 3D effect is observed in specifically designed samples in which the substitutional mixture varies periodically along one specific crystal axis. Laser propagation indicates a coherent polarization super-crystal that produces an optical X-ray diffractometry, an ordered mesoscopic state of matter with important implications for critical phenomena and applications in miniaturized 3D optical technologies.