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.

Miniaturized photogenerated electro-optic axicon lens Gaussian-to-Bessel beam conversion.

We experimentally demonstrate an electro-optic Gaussian-to-Bessel beam-converter miniaturized down to a 30×30 µm pixel in a potassium-lithium-tantalate-niobate (KLTN) paraelectric crystal. The converter is based on the electro-optic activation of a photoinduced and reconfigurable volume axicon lens achieved using a prewritten photorefractive funnel space-charge distribution. The transmitted light beam has a tunable depth of field that can be more than twice that of a conventional beam with the added feature of being self-healing.

Diffraction-free light droplets for axially-resolved volume imaging.

An ideal direct imaging system entails a method to illuminate on command a single diffraction-limited region in a generally thick and turbid volume. The best approximation to this is the use of large-aperture lenses that focus light into a spot. This strategy fails for regions that are embedded deep into the sample, where diffraction and scattering prevail. Airy beams and Bessel beams are solutions of the Helmholtz Equation that are both non-diffracting and self-healing, features that make them naturally able to outdo the effects of distance into the volume but intrinsically do not allow resolution along the propagation axis. Here, we demonstrate diffraction-free self-healing three-dimensional monochromatic light spots able to penetrate deep into the volume of a sample, resist against deflection in turbid environments, and offer axial resolution comparable to that of Gaussian beams. The fields, formed from coherent mixtures of Bessel beams, manifest a more than ten-fold increase in their undistorted penetration, even in turbid milk solutions, compared to diffraction-limited beams. In a fluorescence imaging scheme, we find a ten-fold increase in image contrast compared to diffraction-limited illuminations, and a constant axial resolution even after four Rayleigh lengths. Results pave the way to new opportunities in three-dimensional microscopy.

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.

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.

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.

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.

Intrinsic irreversibility of Markovian chains.

We show that for a large class of stationary Markov processes the total variation distance between the final equilibrium distribution and that at a given time is a strongly monotonic vanishing function. We illustrate this for basic paradigmatic processes and discuss how, for systems susceptible to a canonical description, this can be interpreted as a statistical arrow of time that exists besides the standard decrease of free energy.

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.

Observation of electro-activated localized structures in broad area VCSELs.

We demonstrate experimentally the electro-activation of a localized optical structure in a coherently driven broad-area vertical-cavity surface-emitting laser (VCSEL) operated below threshold. Control is achieved by electro-optically steering a writing beam through a pre-programmable switch based on a photorefractive funnel waveguide.

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).

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.

Shock wave far-field in ordered and disordered nonlocal media.

We investigate the far field of a spatial dispersive shock wave generated from a Gaussian beam propagating in nonlinear nonlocal colloidal disordered media. The interplay between nonlinearity and structural randomness is quantified in terms of the threshold power for the occurrence of the shock wave.

Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time.

We demonstrate rejuvenation in scale-free optical propagation. The phenomenon is caused by the non-ergodic relaxation of the dipolar glass that mediates the photorefractive nonlinearity in compositionally-disordered lithium-enriched potassium-tantalate-niobate (KTN:Li). We implement rejuvenation to halt aging in the dipolar glass and extend the duration of beam diffraction cancellation.

Measurement of scaling laws for shock waves in thermal nonlocal media.

We are able to detect the details of spatial optical collisionless wave breaking through the high aperture imaging of a beam suffering shock in a fluorescent nonlinear nonlocal thermal medium. This allows us to directly measure how nonlocality and nonlinearity affect the point of shock formation and compare results with numerical simulations.

Beam instabilities in the scale-free regime.

The instabilities arising in a one-dimensional beam sustained by the diffusive photorefractive nonlinearity in out-of-equilibrium ferroelectrics are theoretically and numerically investigated. In the "scale-free model," in striking contrast with the well-known spatial modulational instability, two different beam instabilities dominate: a defocusing and a fragmenting process. Both are independent of the beam power and are not associated with any specific periodic pattern.

Shock waves in disordered media.

We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of disorder and scales with wave amplitude. Evidence for the existence of a phase diagram in terms of nonlinearity and amount of randomness is reported. The results are in quantitative agreement with a theoretical approach based on the hydrodynamic approximation.

Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses.

We report the simultaneous diffraction cancellation for beams of different wavelengths in out-of-equilibrium dipolar glass. The effect is supported by the photorefractive diffusive nonlinearity and scale-free optics, and can find application in imaging and microscopy.