Observation of discrete quadratic solitons

Topological Pumping of Multifrequency Solitons

We report on the topological pumping of quadratic optical solitons, observed through their quantized transport in a dynamic optical potential. A distinctive feature of this system is that the two fields with different frequencies, which together form the quadratic soliton, evolve in separate yet topologically equivalent dynamic optical potentials. Pumping in this system exhibits several notable differences from pumping in cubic media. While Chern indices characterizing quantized transport for uncoupled fundamental and second harmonic waves are nonzero, small-amplitude solitons with narrow spectra do not move, thus revealing a nontopological phase. As the nonlinearity increases, the system undergoes a sharp transition, depending on the velocity of one of the sublattices forming dynamical potential, into the phase where the quantized transport of quadratic solitons governed by nonzero Chern numbers is observed. The power level at which this transition occurs increases with increase of pumping velocity, and the transition is observed even in the regime when the adiabatic approximation no longer applies. Unlike in cubic media, in a quadratic medium neither breakup of topological pumping nor fractional pumping at high power levels are observed.

Observation of temporal optical solitons in a topological waveguide

Photonic topological systems may be exploited in topological quantum light generation, the development of topological lasers, the implementation of photonic routing systems and optical parametric amplification. Here, we leverage the strong light confinement of an ultra-silicon-rich nitride (USRN) topological waveguide adopting the 1D Su-Schrieffer-Heeger (SSH) system with a topological domain wall. We present the formation and propagation of temporal optical solitons in the topological waveguide, exhibiting two-fold temporal compression. We further observe a saturation in the output power at sufficiently high input powers. It is further observed that pulse propagation through a trivial, non-topological waveguide does not lead to similar temporal soliton dynamics. The demonstrated topological system allows for the temporal compression to be manipulated through power tuning via topological control of delocalization of the topological mode. This design degree of freedom allows temporal solitons to be generated in a topological waveguide while providing straightforward control of temporal pulses in practical applications.

Universality of light thermalization in multimoded nonlinear optical systems

Recent experimental studies in heavily multimoded nonlinear optical systems have demonstrated that the optical power evolves towards a Rayleigh-Jeans (RJ) equilibrium state. To interpret these results, the notion of wave turbulence founded on four-wave mixing models has been invoked. Quite recently, a different paradigm for dealing with this class of problems has emerged based on thermodynamic principles. In this formalism, the RJ distribution arises solely because of ergodicity. This suggests that the RJ distribution has a more general origin than was earlier thought. Here, we verify this universality hypothesis by investigating various nonlinear light-matter coupling effects in physically accessible multimode platforms. In all cases, we find that the system evolves towards a RJ equilibrium-even when the wave-mixing paradigm completely fails. These observations, not only support a thermodynamic/probabilistic interpretation of these results, but also provide the foundations to expand this thermodynamic formalism along other major disciplines in physics.

Multifrequency Solitons in Commensurate-Incommensurate Photonic Moiré Lattices

We predict that photonic moiré patterns created by two mutually twisted periodic sublattices in quadratic nonlinear media allow the formation of parametric solitons under conditions that are strongly impacted by the geometry of the pattern. The question addressed here is how the geometry affects the joint trapping of multiple parametrically coupled waves into a single soliton state. We show that above the localization-delocalization transition the threshold power for soliton excitation is drastically reduced relative to uniform media. Also, the geometry of the moiré pattern shifts the condition for phase matching between the waves to the value that matches the edges of the eigenmode bands, thereby shifting the properties of all soliton families. Moreover, the phase-mismatch bandwidth for soliton generation is dramatically broadened in the moiré patterns relative to latticeless structures.

Discrete light bullets in coupled optical resonators

We consider arrays of coupled nonlinear optical cavities subject to coherent optical injection. These devices are described by the discrete generalized Lugiato-Lefever equation. We predict that stable three-dimensional localized structures, often called discrete light bullets, and clusters of them may form in the output of the coupled optical resonators. We consider both anomalous and normal dispersion and show that it results in the generation of, respectively, bright and dark discrete light bullets.

Discrete light bullets in passively mode-locked semiconductor lasers

In this paper, we analyze the formation and dynamical properties of discrete light bullets in an array of passively mode-locked lasers coupled via evanescent fields in a ring geometry. Using a generic model based upon a system of nearest-neighbor coupled Haus master equations, we show numerically the existence of discrete light bullets for different coupling strengths. In order to reduce the complexity of the analysis, we approximate the full problem by a reduced set of discrete equations governing the dynamics of the transverse profile of the discrete light bullets. This effective theory allows us to perform a detailed bifurcation analysis via path-continuation methods. In particular, we show the existence of multistable branches of discrete localized states, corresponding to different number of active elements in the array. These branches are either independent of each other or are organized into a snaking bifurcation diagram where the width of the discrete localized states grows via a process of successive increase and decrease of the gain. Mechanisms are revealed by which the snaking branches can be created and destroyed as a second parameter, e.g., the linewidth enhancement factor or the coupling strength is varied. For increasing couplings, the existence of moving bright and dark discrete localized states is also demonstrated.

Dynamics of Gaussian beam modeled by fractional Schrödinger equation with a variable coefficient

In the paper, we investigate the propagation dynamics of the Gaussian beam modeled by the fractional Schrödinger equation (FSE) with a variable coefficient. In the absence of the beam's chirp, for smaller Lévy index, the Gaussian beam firstly splits into two beams, however under the action of the longitudinal periodic modulation, they exhibit a periodically oscillating behaviour. And with the increasing of the Lévy index, the splitting behaviour gradually diminishes. Until the Lévy index equals to 2, the splitting behaviour is completely replaced by a periodic diffraction behaviour. In the presence of the beam's chirp, one of the splitting beams is gradually suppressed with the increasing of the chirp, while another beam on the opposite direction becomes stronger and exhibits a periodically oscillating behaviour. Also, the oscillating amplitude and period are investigated and the results show that the former is dependent on the modulation frequency, the Lévy index and the beam's chirp, the latter depends only on the modulation frequency. Thus, the evolution of the Gaussian beam can be well manipulated to achieve the beam management in the framework of the FSE by controlling the system parameters and the chirp parameter.

Manipulating discrete solitons and routing the light-transmitting paths in the silicon waveguide array by a d.c. electric-field

Discrete solitons (DS), which could propagate without diffraction in the waveguide array (WA), have attracted great attention. However, its applications are limited to incident light with high power. Here, based on the d.c. Kerr effect in the silicon, we propose and demonstrate theoretically an electrically reconfigurable ridge waveguide array. By applying sech-function bias voltages on the WA, a Kerr-type DS could be mimicked by a low-power incident light. The transmitting paths of DS and low-power light in the WA can be rerouted with great flexibility by changing the local bias voltages applied on the waveguide. Our proposed silicon WA provides new opportunities for electric-controlled optical devices, which may open a gateway towards rerouting light on-chip and designing integrated optics devices.

Dynamical phase diagram of Gaussian wave packets in optical lattices

We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.

Controlled switching of discrete solitons in periodically poled lithium niobate waveguide arrays

We suggest an effective method for controlling nonlinear switching in one-dimensional waveguide arrays formed by the periodically poled lithium niobate. We demonstrate that the ability of switching for discrete solitons is relative to the coupling coefficient that is determined by the applied external electrical field on periodically poled lithium niobate waveguide arrays. Besides the external electrical field, the switching of the discrete solitons is also determined by the excited beams tilted angle. It provides us an easy way to control the light beam propagation in such waveguide arrays based on electro-optical effects when an external electric field is applied.

Seeding of picosecond and femtosecond optical parametric amplifiers by weak single mode continuous lasers

Optical parametric amplifiers are typically seeded with either parametric superfluorescence or broadband continuum pulses. We show both with picosecond and femtosecond pump pulses, that single longitudinal mode cw lasers with mW power can be well used to generate nearly Fourier-transform-limited output pulses. The 532 nm pumped picosecond system is seeded in the near infrared and fully tunable from 1260 to 1630 nm. The femtosecond system operates stable with just hundreds of seed photons. The output spectral width matches closely to the width of individual spectral features found in single shot spectra of parametric superfluorescence. Both systems provide interesting radiation sources for nonlinear optics experiments that need highly controlled and clean excitation.

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.

Spectral pulse transformations and phase transitions in quadratic nonlinear waveguide arrays

We study experimentally and numerically the dynamics of a recently found topological phase transition for discrete quadratic solitons with linearly coupled SH waves. We find that, although no stationary states are excited in the experimental situation, the generic feature of the phase transition of the SH is preserved. By utilizing simulations of the coupled mode equations we identify the complex processes leading to the phase transition involving spatial focusing and the generation of new frequency components. These distinct signatures of the dynamic phase transition are also demonstrated experimentally.

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.

Quantum entanglement in coupled lossy waveguides

We investigate the viability of coupled waveguides as basic units of quantum circuits. We study entanglement when the waveguides are fed in by light produced by a down-converter working either in low gain limit or under large gain. We present explicit analytical results for the measure of entanglement in terms of the logarithmic negativity for a variety of input states. We also address the effect of loss on entanglement dynamics of waveguide modes. Our results indicate that the waveguide structures are reasonably robust against the effect of loss and thus quite appropriate for quantum architectures as well as for the study of coherent phenomena like random walks. Our analysis is based on realistic structures used currently.

Competing nonlinearities in quadratic nonlinear waveguide arrays

We demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double-resonant system with quadratic nonlinear response. We use an array of periodically poled coupled optical waveguides and observe inhibition of the nonlinear beam self-action independent on power. This inhibition is demonstrated in both regimes of normal and anomalous beam diffraction.

Observation of discrete solitons in lattices with second-order interaction

We present what we believe to be the first experimental demonstration of discrete solitons under the influence of first- and second-order lattice site interaction in zigzag femtosecond laser-written waveguide arrays. We show how the formation of these entities is affected by different ratios of the interaction strength. Increasing the second-order coupling between the lattices sites yields an almost linear increase of the input power required for soliton formation.

Spatial-spectral vortex solitons in quadratic lattices

We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase gradients at the fundamental frequency and second-harmonic fields and the parametric frequency conversion between the spectral components. The linear stability analysis shows that such modes are stable in a broad parameter region.

Parametric solitons in two-dimensional lattices of purely nonlinear origin

We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.

Mobility of discrete solitons in quadratically nonlinear media

We study the mobility of solitons in lattices with quadratic (chi(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (chi(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes: staying put, persistent motion, or destruction. On the 2D lattice, the solitons survive the largest kick and attain the largest speed along the diagonal direction.

Shaping and control of polychromatic light in nonlinear photonic lattices

<p> <a href="http://oe.osa.org/virtual_issue.cfm?vid=36">Focus Serial: Frontiers of Nonlinear Optics</a> </p>We overview our recent results on spatio-spectral control, diffraction management, broadband switching, and self-trapping of polychromatic light in periodic photonic lattices in the form of rainbow gap solitons, polychromatic surface waves, and multigap color breathers. We show that an interplay of wave scattering from a periodic structure and interaction of multiple colors in media with slow nonlinear response can be used to selectively separate or combine different spectral components. We use an array of optical waveguides fabricated in a LiNbO(3) crystal to actively control the output spectrum of the supercontinuum radiation and generate polychromatic gap solitons through a sharp transition from spatial separation of spectral components to the simultaneous spatio-spectral localization of supercontinuum light. We also show that by introducing specially optimized periodic bending of waveguides in the longitudinal direction, one can manage the strength and type of diffraction in an ultra-broad spectral region and, in particular, realize the multicolor Talbot effect.

Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media

Solitary waves bifurcated from edges of Bloch bands in two-dimensional periodic media are determined both analytically and numerically in the context of a two-dimensional nonlinear Schrödinger equation with a periodic potential. Using multiscale perturbation methods, the envelope equations of solitary waves near Bloch bands are analytically derived. These envelope equations reveal that solitary waves can bifurcate from edges of Bloch bands under either focusing or defocusing nonlinearity, depending on the signs of the second-order dispersion coefficients at the edge points. Interestingly, at edge points with two linearly independent Bloch modes, the envelope equations lead to a host of solitary wave structures, including reduced-symmetry solitons, dipole-array solitons, vortex-cell solitons, and so on-many of which have not been reported before to our knowledge. It is also shown analytically that the centers of envelope solutions can be positioned at only four possible locations at or between potential peaks. Numerically, families of these solitary waves are directly computed both near and far away from the band edges. Near the band edges, the numerical solutions spread over many lattice sites, and they fully agree with the analytical solutions obtained from the envelope equations. Far away from the band edges, solitary waves are strongly localized, with intensity and phase profiles characteristic of individual families.

Spatial solitons in nematic liquid crystals: from bulk to discrete

We review theoretical and experimental results on spatial solitons in nematic liquid crystalline cells, including two-dimensional solitons in bulk and discrete solitons in one-dimensional waveguide arrays. In bulk we describe the propagation of continuous solitons in the presence of adjustable walk-off, their interaction with light-induced defects and refraction-reflection at a voltage-tunable interface. In optical lattices we address the transition from discrete diffraction to localization, as well as all-optical beam steering.

Tamm oscillations in semi-infinite nonlinear waveguide arrays

We demonstrate the existence of nonlinear Tamm oscillations at the interface between a substrate and a one-dimensional waveguide array with either cubic or saturable, self-focusing or self-defocusing nonlinearity. Light is trapped in the vicinity of the array boundary due to the interplay between the repulsive edge potential and Bragg reflection inside the array. In the special case when this potential is linear these oscillations reduce themselves to surface Bloch oscillations.

Discrete X-wave formation in nonlinear waveguide arrays

We present experimental evidence for the spontaneous formation of discrete X waves in AlGaAs waveguide arrays. This new family of optical waves has been excited, for the first time, by using the interplay between discrete diffraction and normal temporal dispersion, in the presence of Kerr nonlinearity. Our experimental results are in good agreement with theoretical predictions.

Ultrafast laser waveguide writing: Lithium niobate and the role of circular polarization and picosecond pulse width

For the first time to our knowledge, ultrafast laser writing has generated room-temperature stable guided-wave optics in bulk lithium niobate for the telecommunication spectrum. Among a seven-dimensional parameter space for waveguide optimization, two frequently overlooked parameters, pulse duration and polarization, were found to be key in overcoming undesired nonlinear optical responses imposed by this material. Single-mode waveguides were best formed with circularly polarized light having a relatively long pulse duration of approximately 1.0 ps. The waveguides were highly polarization dependent and guided in both telecommunication bands near 1300 and 1550 nm, exhibiting losses as low as 0.7 dB/cm.

Prism coupling method to excite and analyze Floquet-Bloch modes in linear and nonlinear waveguide arrays

We demonstrate an experimental method for the direct measurement of band structures of one-dimensional periodic optical media. With the help of a prism coupler that is used in a retroreflective scheme, the allowed bands of a waveguide array in lithium niobate are determined and the results are compared with numerical calculations. Furthermore, we demonstrate the suitability of this method to measure propagation constants of extended nonlinear modes inside the forbidden gap.

Surface lattice solitons

We study theoretically nonlinear surface waves in optical lattices and show that solitons can exist at the heterointerface between two different semi-infinite 1D waveguide arrays, as well as at the boundaries of a 2D nonlinear lattice. The existence and properties of these surface soliton solutions are investigated in detail.

Observation of discrete quadratic surface solitons

We report the first observation of discrete quadratic surface solitons in self-focusing and defocusing periodically poled lithium niobate waveguide arrays. By operating on either side of the phase-matching condition and using the cascading nonlinearity, both in-phase and staggered discrete surface solitons were observed. This represents the first experimental demonstration of staggered/gap surface solitons at the interface of a semi-infinite nonlinear lattice. The experimental results were found to be in good agreement with theory.

Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides

We demonstrate that an array of discrete waveguides on a slab substrate, both featuring chi2 nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite soliton are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found, too. In contrast with the usual systems, the intersite-centered fundamental solitons and bound states with the twisted continuous components are stable over almost the entire domain of their existence.

Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices

We report the first experimental demonstration of ring-shaped photonic lattices by optical induction and the formation of discrete solitons in such radially symmetric lattices. The transition from discrete diffraction to single-channel guidance or nonlinear self-trapping of a probe beam is achieved by fine-tuning the lattice potential or the focusing nonlinearity. In addition to solitons trapped in the lattice center and in different lattice rings, we demonstrate controlled soliton rotation in the Bessel-like ring lattices.

Method of images in optical discrete systems

We show that optical wave propagation in discrete boundary geometries can be effectively analyzed using the method of images. Such semi-infinite and finite discrete systems include, for example, waveguide arrays as well as coupled resonator optical waveguides. In the linear domain, the diffraction properties of one- and two-dimensional bounded array structures are considered in detail. The possibility of using the method of images to numerically investigate nonlinear semi-infinite lattices is also discussed.

Observation of discrete surface solitons

We report the first observation of discrete optical surface solitons at the interface between a nonlinear self-focusing waveguide lattice and a continuous medium. The effect of power on the localization process of these optical self-trapped states at the edge of an AlGaAs waveguide array is investigated in detail. Our experimental results are in good agreement with theoretical predictions.

Defect solitons in photonic lattices

Nonlinear defect modes (defect solitons) and their stability in one-dimensional photonic lattices with focusing saturable nonlinearity are investigated. It is shown that defect solitons bifurcate out from every infinitesimal linear defect mode. Low-power defect solitons are linearly stable in lower bandgaps but unstable in higher bandgaps. At higher powers, defect solitons become unstable in attractive defects, but can remain stable in repulsive defects. Furthermore, for high-power solitons in attractive defects, we found a type of Vakhitov-Kolokolov (VK) instability which is different from the usual VK instability based on the sign of the slope in the power curve. Lastly, we demonstrate that in each bandgap, in addition to defect solitons which bifurcate from linear defect modes, there is also an infinite family of other defect solitons which can be stable in certain parameter regimes.

Mobility of discrete cavity solitons

We investigate the mobility of discrete cavity solitons in arrays of coupled quadratic nonlinear resonators driven by an inclined holding beam. Unlike in transversely homogeneous cavities the inherent discreteness hinders or even prevents the soliton motion. As a consequence for the same system parameters one type of soliton may still be at rest, whereas others already move. This feature gives rise to collisions between these different types. To study the soliton dynamics in more detail we take advantage of a perturbation theory and derive soliton velocities semianalytically.

Discrete surface solitons

It is theoretically shown that discrete nonlinear surface waves are possible in waveguide lattices. These self-trapped states are located at the edge of the array and can exist only above a certain power threshold. The excitation characteristics and stability properties of these surface waves are systematically investigated.

Two-color discrete localized modes and resonant scattering in arrays of nonlinear quadratic optical waveguides

We analyze the properties and stability of two-color discrete localized modes in arrays of channel waveguides where tunable quadratic nonlinearity is introduced as a nonlinear defect by periodic poling of a single waveguide in the array. We show that, depending on the value of the phase mismatch and the input power, such two-color defect modes can be realized in three different localized states. We also study resonant light scattering in the arrays with the defect waveguide.

Spectral renormalization method for computing self-localized solutions to nonlinear systems

A new numerical scheme for computing self-localized states--or solitons--of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrödinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme from diverging. The nonlinear guided mode is then determined from a convergent fixed point iteration scheme. This spectral renormalization method can find wide applications in nonlinear optics and related fields such as Bose-Einstein condensation and fluid mechanics.

Observation of second-band vortex solitons in 2D photonic lattices

We demonstrate second-band bright vortex-array solitons in photonic lattices. This constitutes the first experimental observation of higher-band solitons in any 2D periodic system. These solitons possess complex intensity and phase structures, yet they can be excited by a simple highly localized vortex-ring beam. Finally, we show that the linear diffraction of such beams exhibits preferential transport along the lattice axes.

Defect modes in one-dimensional photonic lattices

Linear defect modes in one-dimensional photonic lattices are studied theoretically. For negative (repulsive) defects, various localized defect modes are found. The strongest confinement of the defect modes appears when the lattice intensity at the defect site is nonzero rather than zero. When launched at small angles into such a defect site of the lattice, a Gaussian beam can be trapped and undergo snake oscillations under appropriate conditions.

Discrete quadratic cavity solitons

We predict the existence of various types of discrete solitons in arrays of coupled optical cavities endowed with a quadratic nonlinearity. We derive mean-field equations and determine their range of validity by comparing results with those from the original round-trip model. By using an analytical approach we identify domains in parameter space where solitons can potentially exist and describe their asymptotic behavior. Taking advantage of these results, we numerically find discrete solitons of different topologies. Some of them are unique to discrete models. Ultimately, we study the stability of these soliton solutions and find that discreteness appreciably influences this behavior.

Highly localized discrete quadratic solitons

We observe highly localized solitons in periodically poled lithium niobate waveguide arrays close to phase matching for second-harmonic generation. With fundamental and second-harmonic input in one channel the response indicates two distinguishable propagation schemes. Depending on the relative phase between the two input waves, a self-trapped beam emerges, resembling closely either the in- or the out-of-phase quadratic eigenmode of a single waveguide. A stable soliton propagates when the input waves are in phase.

Beam interactions with a blocker soliton in one-dimensional arrays

We investigate experimentally and numerically the interaction of a highly localized, single-channel discrete soliton (blocker) with a wide, tilted beam in a one-dimensional AlGaAs array. In agreement with theory the blocker is observed to discretely shift its position by multiple channels, depending on the intensity and relative phase of the tilted beam.

Fano resonance in quadratic waveguide arrays

We study resonant light scattering in arrays of channel optical waveguides in which tunable quadratic non-linearity is introduced as nonlinear defects by periodic poling of single (or several) waveguides in the array. We describe novel features of wave scattering that can be observed in this structure and show that it is a good candidate for observation of Fano resonance in nonlinear optics.

X - waves in nonlinear normally dispersive waveguide arrays

We theoretically demonstrate that optical discrete X-waves are possible in normally dispersive nonlinear waveguide arrays. We show that such X-waves can be effectively excited for a wide range of initial conditions and in certain occasions can be generated in cascade. The possibility of observing this family of waves in AlGaAs array systems is investigated in terms of pertinent examples.

Discrete light propagation and self-trapping in liquid crystals

We investigate light propagation and self-localization in a voltage-controlled array of channel waveguides realized in undoped nematic liquid crystals. We report on discrete diffraction and solitons, as well as all-optical angular steering and the formation of multiband vector breathers. The results and are in excellent agreement with both coupled mode theory and full numerical simulations.

Multicolor vortex solitons in two-dimensional photonic lattices

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.

Spatiotemporal discrete multicolor solitons

We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even, and twisted stationary solutions are thoroughly characterized and their stability against perturbations is investigated. We show that the twisted and even solitons display instability, while most of the odd solitons show remarkable stability upon evolution.