Steady-state spatial screening solitons in photorefractive materials with external applied field

Ring-shaped quantum droplets with hidden vorticity in a radially periodic potential

We study the stability and characteristics of two-dimensional circular quantum droplets (QDs) with embedded hidden vorticity (HV), i.e., opposite angular momenta in two components, formed by binary Bose-Einstein condensates (BECs) trapped in a radially periodic potential. The system is modeled by the Gross-Pitaevskii equations with the Lee-Huang-Yang terms, which represent the higher-order self-repulsion induced by quantum fluctuations around the mean-field state, and a potential which is a periodic function of the radial coordinate. Ring-shaped QDs with high winding numbers (WNs) of the HV type, which are trapped in particular circular troughs of the radial potential, are produced by means of the imaginary-time-integration method. Effects of the depth and period of the potential on these QD states are studied. The trapping capacity of individual circular troughs is identified. Stable compound states in the form of nested multiring patterns are constructed too, including ones with WNs of opposite signs. The stably coexisting ring-shaped QDs with different WNs can be used for the design of BEC-based data-storage schemes.

Ultra-broadband interconnection between two SPP nanostrips by a photorefractive soliton waveguide

We propose a very efficient approach to interconnect together two metallic nanostrips supporting the propagation of surface plasmon polariton (SPP) waves by fabricating a photorefractive soliton guide. By designing a multilayer geometry for plasmon systems, it is possible to control the diffraction of light at the end of the metallic nanostrip, reducing its angular dispersion and directing it towards the second nanostrip. Between the two, a photorefractive crystal allows the self-confinement of light, creating a waveguide that can be used both by the light that wrote it and by other wavelengths sent as signals. These signals can be recoupled in the form of SPP waves in the second nanostrip with an efficiency of about 40% for a broad band of wavelengths.

Supervised learning of soliton X-junctions in lithium niobate films on insulator

In this Letter, the first implementation, to our knowledge, of X-junctions between photorefractive soliton waveguides in lithium niobate-on-insulator (LNOI) films is reported. The experiments were performed on 8 µm thick films of congruent undoped LiNbO₃. Compared with bulk crystals, the use of films reduces the soliton formation time, allows more control over the interaction between the injected soliton beams, and opens a route to integration with silicon optoelectronics functions. The created X-junction structures show effective supervised learning, directing the signals propagated inside the soliton waveguides into the output channels highlighted by the control assigned by the external supervisor. Thus, the obtained X-junctions have behaviors analogous to biological neurons.

Supervised and unsupervised learning using a fully-plastic all-optical unit of artificial intelligence based on solitonic waveguides

The software implementations of neuronal systems have shown great effectiveness, even if the natural hardware separation between the processing and memory areas in computers slows down the analysis capacity. To overcome these limitations, new hardware configurations are moving towards neuromorphic models, capable of unifying the processing/memory dichotomy. Recently, integrated photonic X-junctions formed by waveguides written by spatial solitons have shown the ability to perform supervised learning. The solitonic technology, compared to the traditional one, offers the advantage of realizing plastic circuitry, a typical characteristic of biological neural networks. This work extensively studies both supervised and unsupervised learning of photonic soliton X-junctions. By exploiting the plasticity of the nonlinear refractive index at the base of the soliton formation, X-junctions can readdress their behaviours forwarding data to different outputs. In this article, we will extend the state-of-the-art: starting from supervised learning, for which all possible cases are now investigated, a material sensitive to the transported signals will be introduced to allow the junction to carry out unsupervised learning. In this way, the junction autonomously recognises the transported signals without the external intervention of the operator. Learning and memory now physically coincide in fact, learning means that the junction slowly switches based on the information sent; any further unknown information sent will find the junction in the modified state which corresponds to the learned information and will be recognised as well (reasoning based on comparison with stored information).

Nondegenerate Bright Solitons in Coupled Nonlinear Schrödinger Systems: Recent Developments on Optical Vector Solitons

Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons display rich nonlinear phenomena. Due to their fascinating and intriguing novel properties, the theory of optical vector solitons has been developed considerably both from theoretical and experimental points of view leading to soliton-based promising potential applications. Mathematically, the dynamics of vector solitons can be understood from the framework of the coupled nonlinear Schrödinger (CNLS) family of equations. In the recent past, many types of vector solitons have been identified both in the integrable and non-integrable CNLS framework. In this article, we review some of the recent progress in understanding the dynamics of the so called nondegenerate vector bright solitons in nonlinear optics, where the fundamental soliton can have more than one propagation constant. We address this theme by considering the integrable two coupled nonlinear Schrödinger family of equations, namely the Manakov system, mixed 2-CNLS system (or focusing-defocusing CNLS system), coherently coupled nonlinear Schrödinger (CCNLS) system, generalized coupled nonlinear Schrödinger (GCNLS) system and two-component long-wave short-wave resonance interaction (LSRI) system. In these models, we discuss the existence of nondegenerate vector solitons and their associated novel multi-hump geometrical profile nature by deriving their analytical forms through the Hirota bilinear method. Then we reveal the novel collision properties of the nondegenerate solitons in the Manakov system as an example. The asymptotic analysis shows that the nondegenerate solitons, in general, undergo three types of elastic collisions without any energy redistribution among the modes. Furthermore, we show that the energy sharing collision exhibiting vector solitons arises as a special case of the newly reported nondegenerate vector solitons. Finally, we point out the possible further developments in this subject and potential applications.

Solitonic waveguide reflection at an electric interface

A refractive index interface is dynamically induced in a bulk photorefractive material by biasing two adjacent regions with different electric fields, thus building up an electric wall. Effects of this interface on reflection, refraction and breathing of bright photorefractive solitons and their associated waveguides are numerically and experimentally studied as a function of the induced purely electric field gradient. Reflection and refraction efficiency depends on the amplitude and sign of the applied voltages that affect both the self-confining beam and the signals propagating inside the waveguide. Experimental tests are performed in nominally undoped lithium niobate samples.

Self-Induced Diffusion in Disordered Nonlinear Photonic Media

We find that waves propagating in a 1D medium that is homogeneous in its linear properties but spatially disordered in its nonlinear coefficients undergo diffusive transport, instead of being Anderson localized as always occurs for linear disordered media. Specifically, electromagnetic waves in a multilayer structure with random nonlinear coefficients exhibit diffusion with features fundamentally different from the traditional diffusion in linear noninteracting systems. This unique transport, which stems from the nonlinear interaction between the waves and the disordered medium, displays anomalous statistical behavior where the fields in multiple different realizations converge to the same intensity value as they penetrate deeper into the medium.

All-Optical Reinforcement Learning In Solitonic X-Junctions

Ethology has shown that animal groups or colonies can perform complex calculation distributing simple decision-making processes to the group members. For example ant colonies can optimize the trajectories towards the food by performing both a reinforcement (or a cancellation) of the pheromone traces and a switch from one path to another with stronger pheromone. Such ant’s processes can be implemented in a photonic hardware to reproduce stigmergic signal processing. We present innovative, completely integrated X-junctions realized using solitonic waveguides which can provide both ant’s decision-making processes. The proposed X-junctions can switch from symmetric (50/50) to asymmetric behaviors (80/20) using optical feedbacks, vanishing unused output channels or reinforcing the used ones.

Optical amplification of Airy beams by photorefractive two-wave mixing

We propose and demonstrate nonlinear amplifications of self-accelerating Airy beams by two-wave mixing in photorefractive crystals both numerically and experimentally. By employing a broad Gaussian beam as the pump beam, we show that weak signal Airy beams can be significantly amplified under both diffusion and drift mechanisms. It is revealed that not only higher optical gains but also faster response time can be achieved in the presence of an external electric field, where the drift mechanism dominates. We verify that the self-accelerating and self-healing characteristics of the Airy beams are well preserved during the nonlinear amplification.

Interactions between self-accelerating beams in photorefractive media

We investigate interactions between in-phase or out-of-phase Airy beams and nonlinear accelerating beams in photorefractive crystals by means of direct numerical simulations. Since self-accelerating beams possess infinite energy, we evaluated the propagation of two shifted counter beams by truncating the oscillating tails. The numerical results show that the external bias electric field has a profound effect on the propagation dynamics and the solitons shed from the Airy beam. We also found that during interactions between two nonlinear accelerating beams, single solitons, soliton pairs, and bound breathing solitons were produced. When the nonlinear accelerating beam collides with a soliton beam, the main lobe continues accelerating while the soliton intensity fluctuates with the lobes.

Model of anisotropic nonlinearity in self-defocusing photorefractive media

We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

Numerical method for an analysis of nonlinear light propagation in photorefractive media--time nonlocal approach

Nonlinear light propagation in photorefractive media can be analyzed by numerical methods. The presented numerical approach has regard to the effects of time nonlocality. Two algorithms are presented, and compared in terms of physical results and computing times. The possibility to address the issue of time nonlocality in two ways is attributed to the fact that, it is possible to completely separate carrier dynamics evaluation and wave equation calculation. This in turn, allows to choose a short integration time for carrier dynamics and a longer one to solve the wave equation. The tests of the methods were carried out for a one-carrier model that describes most of photorefractive media, and for a model with bipolar transport and hot electron effect, used in descriptions of semiconductor materials.

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.

Interactions between self-channeled optical beams in soft-matter systems with artificial nonlinearities

We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.

Observation of photorefractive surface waves in self-defocusing LiNbO3:Fe crystal

Photorefractive (PR) surface waves (SWs) in self-defocusing LiNbO(3):Fe are studied theoretically and experimentally. We demonstrate that SWs can also be formed in a self-defocusing nonlinear medium and that the nonlocal nonlinearity (such as the diffusion component of PR nonlinearity in this Letter) is the essential cause. The forming process of PR SWs with a self-deflection course of light beams has been observed. The results indicate the possibility of concentrating light energy in self-defocusing media, taking advantage of SWs.

Localized surface waves at the interface between linear dielectric and biased centrosymmetric photorefractive crystals

We study localized surface waves at the interface between linear dielectric and biased centrosymmetric photorefractive (CP) crystals. If the propagation constant b is fixed, the energy of localized surface waves increases with the order of localized surface waves. For low b values, the considerable part of the energy of localized surface waves is concentrated in the linear dielectric and decreases with an increase in b. For high b values, the part of the energy of localized surface waves concentrated in the nonlinear CP crystals is always higher than that in the linear dielectric and increases with b. The stability properties of these localized surface waves are also discussed in detail.

Dark surface waves in self-focusing media with diffusion and photovoltaic nonlinearities

Dark surface waves with photorefractive diffusion and photovoltaic nonlinearities are predicted for the first time. We find it is extraordinary that this type of dark surface waves should be in self-focusing media, which is very different from the surface dark solitons or other nonlinear dark surface waves. An oscillator model is proposed by which the above extraordinary phenomenon is demonstrated. In this model an equivalent force function is established, whose form determines the varieties of surface waves (bright surface waves, dark surface waves or others).

Observation of surface dark photovoltaic solitons

Surface dark solitons in photovoltaic nonlinear media are reported. Taking advantage of diffusion and photovoltaic nonlinearities we demonstrated the surface dark solitons and their behaviors near surface theoretically and experimentally in LiNbO₃ crystal. It is very interesting that surface dark soliton is just half of dark soliton in bulk. Another interesting thing is that transverse modulation instability can be perfectly suppressed by surface dark soliton in virtue of surface. In addition, surface waveguides were written successfully utilizing surface dark soliton.

Optical spatial solitons: historical overview and recent advances

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Writing and probing light-induced waveguides thanks to an endlessly single-mode photonic crystal fiber

We demonstrate writing and probing of light-induced waveguides in photorefractive bulk LiNbO3 crystal using an endlessly single-mode photonic crystal fiber. The optical waveguides are written at visible wavelengths by slightly raising the ferroelectric crystal temperature to benefit from the pyroelectric-driven photorefractive effect and the guiding properties are investigated at telecom wavelengths using the same photonic crystal fiber. End butt coupling with this photonic crystal fiber enables writing and probing of optical waveguides due to the self-alignment properties of spatial solitons.

Multistable dissipative structures pinned to dual hot spots

We analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow "hot spots" (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while the linear loss acts in the host medium. This system can be realized as a spatial-domain one in optics and also in Bose-Einstein condensates of quasiparticles in solid-state settings. Recently, exact solutions were found for localized modes pinned to the single HS represented by the δ function. The present paper reports analytical and numerical solutions for coexisting two- and multipeak modes, which may be symmetric or antisymmetric with respect to the underlying HS pair. Stability of the modes is explored through simulations of their perturbed evolution. The sign of the cubic nonlinearity plays a crucial role: in the case of the self-focusing, only the fundamental symmetric and antisymmetric modes, with two local peaks tacked to the HSs, and no additional peaks between them, may be stable. In this case, all the higher-order multipeak modes, being unstable, evolve into the fundamental ones. Stability regions for the fundamental modes are reported. A more interesting situation is found in the case of the self-defocusing cubic nonlinearity, with the HS pair giving rise to a multistability, with up to eight coexisting stable multipeak patterns, symmetric and antisymmetric ones. The system without the self-interaction, the nonlinearity being represented only by the local cubic loss, is investigated too. This case is similar to those with the self-focusing or defocusing nonlinearity, if the linear potential of the HS is, respectively, attractive or repulsive. An additional feature of the former setting is the coexistence of the stable fundamental modes with robust breathers.

Self-accelerating optical beams in highly nonlocal nonlinear media

We find self-accelerating beams in highly nonlocal nonlinear optical media, and show that their propagation dynamics is strongly affected by boundary conditions. Specifically for the thermal optical nonlinearity, the boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the initial trajectory. Under strong self-focusing, the accelerating beam decomposes into a localized self-trapped beam propagating on an oscillatory trajectory and a second beam which accelerates in a different direction. We augment this study by investigating the effects caused by a finite aperture and by a nonlinear range of a finite extent.

Surface dark screening solitons

We report on the existence of surface dark screening solitons at the interface between a dielectric medium (air) and a self-defocusing nonlinear material, taking advantage of photorefractive diffusion and drift nonlinearities. It is very interesting that a surface dark soliton is just like half of a dark soliton in bulk, but not a whole dark soliton propagating along surface. The excitation, propagation, and stability of this type of soliton are studied by using the beam-propagation method. Another interesting thing is that this type of dark soliton can be excited by a planar light beam without a necessary dark notch.

Self-accelerating self-trapped optical beams

We present self-accelerating self-trapped beams in nonlinear optical media, exhibiting self-focusing and self-defocusing Kerr and saturable nonlinearities, as well as a quadratic response. In Kerr and saturable media such beams are stable under self-defocusing and weak self-focusing, whereas for strong self-focusing the beams off-shoot solitons while their main lobe continues to accelerate. Self-accelerating self-trapped wave packets are universal, and can also be found in matter waves, plasma, etc.

Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses

Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.

Autoresonant propagation of incoherent light-waves

We study, theoretically and experimentally, the evolution of optical waves with randomly-fluctuating phases in a spatially chirped nonlinear directional coupler. As the system crosses its linear resonance, we observe collective self-phase-locking (autoresonance) of all mutually-incoherent waves, each with its own pump, and simultaneous amplification until the pumps are exhausted. We show that the autoresonant transition in this system exhibits a sharp threshold, common to all mutually-incoherent waves comprising the light beam.

Diffusion-trapped Airy beams in photorefractive media

We report the first experimental observation of self-trapped Airy beams in a nonlinear medium. As opposed to screening or photovoltaic spatial solitons, this new class of self-localized beams owes its existence to carrier diffusion effects. The asymmetric action of two-wave mixing supports the asymmetric intensity profile of the Airy states, with a balance that is independent of the beam intensity (unlike solitons). Further, the self-trapped wave packets self-bend during propagation at an acceleration rate that is independent of the thermal energy associated with the diffusive nonlinearity.

Observation of photorefractive simultons in lithium niobate

Spatial and temporal locking of fundamental and second harmonic pulses was realized by means of photorefractive nonlinearity and highly mismatched harmonic generation. Due to the presence of both phase-locked and unlocked second harmonic pulses, a twin simultonic state was observed. Simultonic filamentation occurring at high pumping rates allowed us to determine a relation between the simulton's waist and its intensity.

Slow optical soliton pairs via electron spin coherence in a quantum well waveguide

In this paper, we theoretically investigate the propagation properties of probe and mixing fields in a quantum well waveguide. This waveguide is driven by two strong control (pumping and coupling) fields and a weak probe field. Under appropriate parameters condition, the electron spin coherence can suppress the absorption and enhance the nonlinear susceptibilities of the probe (or mixing) field. This study reveals that probe (or mixing) field can form soliton pairs and propagate in the quantum well waveguide with slow group velocity. We also study the soliton collision and dynamics evolution. The results show that the propagation of soliton can be strongly modified by the electron spin coherence.

Pyroliton: pyroelectric spatial soliton

The concept of optical beam self-trapping in pyroelectric photorefractive medium is presented. We show that the temperature controlled spontaneous polarisation of ferroelectric crystals produces an optical nonlinearity that can lead to formation of 2-D spatial soliton named pyroliton. Experimental demonstrations performed in lithium niobate crystals illustrate that efficient self-trapping occurs either for ordinary or extraordinary polarisation under moderate temperature increase. For instance, a 15 microm diameter pyroliton can be formed with a 10 degree temperature raise.

Chaotic spatial soliton rays in smooth two-dimensional optical lattices

The light ray of a spatial soliton in an optical film whose refractive index is smoothly modulated (wavelength much larger than the typical soliton width) in both spatial directions is shown to possess chaotic regimes for which the propagation is erratic. This is interpreted as a parametric driven pendulum, obtained by what we believe to be a new perturbative approach of the Maxwell's equation. These findings are then demonstrated to compare well to the eikonal law of light ray propagation (nonlinearity compensates diffraction).

Autoresonant dynamics of optical guided waves

We study, theoretically and experimentally, autoresonant dynamics of optical waves in a spatially chirped nonlinear directional coupler. We show that adiabatic passage through a linear resonance in a weakly coupled light-wave system yields a sharp threshold transition to nonlinear phase locking and amplification to predetermined amplitudes. This constitutes the first observation of autoresonance phenomena in optics.

Slow vector optical solitons in a cold five-level hyper V-type atomic system

A new scheme of five-level hyper V-type atomic system is proposed with the aim of generating slow temporal vector optical solitons. Two transitions in the five-level atomic medium independently interact with the two orthogonally polarized components of a low intensity linear-polarized pulsed probe field, while two other transitions are driven by control laser fields. We demonstrate that various distortion-free slow temporal vector optical solitons, such as bright-bright, bright-dark, dark-bright and dark-dark vector solitons, can be evolved from the probe field. Besides, we also show that the modified Hubbard model that includes the Manakov system may be realized by adjusting the corresponding self- (cross-) phase modulation and dispersion effects of this system.

Spatiotemporal pulse-train solitons

We propose spatiotemporal solitons that consist of trains of short pulses. The pulses are collectively trapped in the transverse directions by a slow nonlinearity and each pulse is self-trapped in the longitudinal direction by a fast nonlinearity. We demonstrate numerically spatiotemporal bright pulse-train solitons (trains of light bullets) and temporally-dark spatiotemporal pulse-train solitons in an experimentally feasible scheme.

Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit

This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

Symmetry breaking in honeycomb photonic lattices

We study the phenomena associated with symmetry breaking in honeycomb photonic lattices. As the honeycomb structure is gradually deformed, conical diffraction around its diabolic points becomes elliptic and eventually no longer occurs. As the deformation is further increased, a gap opens between the first two bands, and the lattice can support a gap soliton. The existence of the gap soliton serves as a means to detect the symmetry breaking and provide an estimate of the size of the gap.

Impact of tensorial nature of the electro-optic effect on vortex beam propagation in photorefractive media

Influence of the anisotropic tensorial electro-optic effect of LiNbO(3):Fe photorefractive defocusing medium on propagation of a vortex beam is numerically and experimentally investigated. Characteristic behaviors are depicted by varying light polarization, sign of vortex angular momentum and propagation directions.

Observation of soliton tunneling phenomena and soliton ejection

We study, theoretically and experimentally, the nonlinear dynamics of a wave packet launched inside a trap potential. Increasing the power of the wave packet transforms its dynamics from linear tunneling through a potential barrier, to soliton tunneling, and eventually, above a well-defined threshold, to the ejection of a soliton from the potential trap.

Observation of all-optical bump-on-tail instability

We demonstrate an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially coherent spatial beams. For weak wave coupling, we observe momentum transfer with no variation in intensity. For strong wave coupling, modulations appear in intensity and evidence appears for wave (Langmuir) collapse at large scales. Borrowing plasma language, these limits represent regimes of weak and strong spatial optical turbulence. In both limits, the internal spectral energy redistribution is observed by recording and reconstructing a hologram of the evolving dynamics. The results are universal and can appear in any wave-kinetic system with short-wave-long-wave coupling.

Dispersive shock waves in nonlinear arrays

We experimentally study dispersive shock waves in nonlinear waveguide arrays. In contrast with gap solitons, the nonlinearity here pushes the propagation constant further into the transmission bands, facilitating Bloch mode coupling and energy transport. We directly observe this coupling, both within and between bands, by recording intensity in position space and power spectra in momentum space.

Phason dynamics in nonlinear photonic quasicrystals

We study the dynamics of phasons in a nonlinear photonic quasicrystal. The photonic quasicrystal is formed by optical induction, and its dynamics is initiated by allowing the light waves inducing the quasicrystal to nonlinearly interact with one another. We show quantitatively that, when phason strain is introduced in a controlled manner, it relaxes through the nonlinear interactions within the photonic quasicrystal. We establish experimentally that the relaxation rate of phason strain in the quasicrystal is substantially lower than the relaxation rate of phonon strain, as predicted for atomic quasicrystals. Finally, we monitor and identify individual 'atomic-scale' phason flips occurring in the photonic quasicrystal as its phason strain relaxes, as well as noise-induced phason fluctuations.

Self-bending of dark and gray photorefractive solitons

We investigate the effects of diffusion on the evolution of steady-state dark and gray spatial solitons in biased photorefractive media. Numerical integration of the nonlinear propagation equation shows that the soliton beams experience a modification of their initial trajectory, as well as a variation of their minimum intensity. This process is further studied using perturbation analysis, which predicts that the center of the optical beam moves along a parabolic trajectory and, moreover, that its minimum intensity varies linearly with the propagation distance, either increasing or decreasing depending on the sign of the initial transverse velocity. Relevant examples are provided.

Nonlocal surface-wave solitons

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the interface between a dielectric medium (air) and a nonlinear material with a very long-range nonlocal response. These surface solitons are always attracted toward the surface, and unlike their Kerr-like counterparts, they do not exhibit a power threshold.

Information throughput of photorefractive spatial solitons in the telecommunication range

Photorefractive spatial solitons are attractive elements because they can be used as controllable optical interconnectors for all-optical devices. To our knowledge, until now their properties were investigated in terms of energy transportation. We suggest considering photorefractive spatial solitons as optically induced information channels. The experimental technique to measure the information throughput of photorefractive spatial solitons in accordance with Shannon's definition was developed and demonstrated by us. We experimentally demonstrated that in the wavelength range of 1520-1630 nm it can be estimated as large as approximately 90 Tbits/s. We also experimentally demonstrate a measurement of the group-velocity dispersion and show the limitation of the pulse transfer rate of the induced waveguides to approximately 6.2 THz.