We report on the experimental observation of two-dimensional solitons located in a defect channel at the surface of a hexagonal waveguide array. The threshold power for the excitation of defect surface solitons existing due to total internal reflection grows with decrease of the refractive index in negative defects and vanishes for sufficiently strong positive defects. Negative defects can also support linear surface modes existing due to Bragg-type reflections.
The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero defects, fundamental and dipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For negative defects, fundamental solitons can be stable in both the semi-infinite gap and the first gap, whereas dipole solitons are unstable in the first gap. There exist a maximum degree of nonlocal nonlinearity, above which the fundamental sol…
Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the nonlinearity, while dark defect modes are supported by a local decrease of the nonlinearity. Dark solitons exist for both types of the defect, although in the case of weak nonlinearity they feature side bright humps making the total energy propagating through the system larger than the energy transferred by the constant background. All considered defect modes ar…
Defects due to growth fluctuations in broad-area semiconductor lasers induce pinning and frequency shifts of spatial laser solitons. The effects of defects on the interaction of two solitons are considered in lasers with frequency-selective feedback both theoretically and experimentally. We demonstrate frequency and phase synchronization of paired laser solitons as their detuning is varied. In both theory and experiment the locking behavior is well described by the Adler model for the synchronization of coupled oscillators.
We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such configuration represents a line defect, in the lattice plane, which is periodically modulated along the propagation direction. In the linear limit, such a system sustains line defect modes, whose number coincides with the number of tilted layers. In the presence of nonlinearity the branches of defect solitons propagating along the defect line bifurcate from each of the linear defect modes. Dependin…
We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them,is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of t…
We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schrödinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anti-continuum limit and also using the variational approximation (VA), which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below…
Discrete fundamental and dipole solitons are constructed, in an exact analytical form, in an array of linear waveguides with an embedded $\mathcal{PT}$-symmetric dimer, which is composed of two nonlinear waveguides carrying equal gain and loss. Fundamental solitons in tightly knit lattices, as well as all dipole modes, exist above a finite threshold value of the total power. However, the threshold vanishes for fundamental solitons in loosely knit lattices. The stability of the discrete solitons is investigated analytically by means of the Vakhitov-Kolokolov (VK) criterion, and, in the full for…
The existence and stability of defect solitons supported by parity-time (PT) symmetric superlattices with nonlocal nonlinearity are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive or zero defects, but can not exist in the presence of negative defects with strong nonlocality. In the first gap, out-of-phase solitons are stable for positive or zero defects, whereas in-phase solitons are stable for negative defects. The dependence of soliton stabilities on modulation depth of the PT potentials is studied. It is interesting that solitons can exist st…
It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of "holes" in two-dimensional (2D) lattices support continuous families of 2D solitons \textit{embedded} into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the \texti…
We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear-Schrödinger (DNLS) lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in the uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long d…
We construct families of discrete solitons (DSs) in an array of self-defocusing waveguides with an embedded $\mathcal{PT}$ (parity-time)-symmetric dimer, which is represented by a pair of waveguides carrying mutually balanced gain and loss. Four types of states attached to the embedded defect are found, namely, staggered and unstaggered bright localized modes and gray or anti-gray DSs. Their existence and stability regions expand with the increase of the strength of the coupling between the dimer-forming sites. The existence of the gray and staggered bright DSs is qualitatively explained by di…
The resonant scattering of gap solitons (GS) of the periodic nonlinear Schrödinger equation with a localized defect which is symmetric under the parity and the time-reversal (PT) symmetry, is investigated. It is shown that for suitable amplitudes ratios of the real and imaginary parts of the defect potential the resonant transmission of the GS through the defect becomes possible. The resonances occur for potential parameters which allow the existence of localized defect modes with the same energy and norm of the incoming GS. Scattering properties of GSs of different band-gaps with effective ma…
We address the properties of optical solitons in thermal nonlinear media with a local refractive index defect that is capable to trap solitons launched even close to the sample boundary despite the boundary-mediated forces that tend to deflect all beams toward the center of the sample. We show that while such forces become more pronounced with increasing the input beam power the defect can trap only light below a critical power above which solitons are ejected. The dynamics of soliton ejection and the subsequent propagation may be controlled.
The physical mechanism underlying scattering properties of matter wave gap-solitons by linear optical lattice defects is investigated. The occurrence of repeated reflection, transmission and trapping regions for increasing strengths of an optical lattice defect are shown to be due to impurity modes inside the defect potential with chemical potentials and numbers of atoms matching corresponding quantities of an incoming gap-soliton. For gap-solitons with chemical potentials very close to band edges, the number of resonances observed in the scattering coincides with the number of bound states wh…
Recently, optical soliton propagation in an intrinsic nonlinear graphene monolayer configuration has been discovered. However, optical soliton behavior in a free-standing graphene monolayer with defects has not yet been studied. The objective of this article is to employ the generalized finite- difference time-domain (G-FDTD) method to efficiently simulate bright optical solitons, illustrating propagation of the electric field distribution in a free-standing nonlinear layer with variation in nonlinearity along its width. These variations of nonlinearity along the width represent graphene impur…
Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect mo…
A ring dark soliton is a dark soltion occurring in higher dimensions. It is still unknown in microcavity-polariton condensates due to its instability. We find that a stable RDS cannot exist in a MPC without a defect. We then propose a way to create a stable RDS in a MPC by adding a defect with a ring structure to the system. A RDS pinned by the defect potential becomes stable. For various pump powers, we also investigate the stable regime of the RDS by tuning the strength and width of the defect potential. We conclude that the stable RDSs can be obtained.
We study the effect of lifting the degeneracy of vortex modes with a PT symmetric defect, using discrete vortices in a circular array of nonlinear waveguides as an example. When the defect is introduced, the degenerate linear vortex modes spontaneously break PT symmetry and acquire complex eigenvalues, but nonlinear propagating modes with real propagation constants can still exist. The stability of nonlinear modes depends on both the magnitude and the sign of the vortex charge, thus PT symmetric systems offer new mechanisms to control discrete vortices.
We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on existence and stability of surface modes, and find novel classes of two-color twisted surface solitons which are stable in a large domain of their existence.
We address the properties of surface solitons supported by optical lattices imprinted in photorefractive media with asymmetric diffusion nonlinearity. Such solitons exist only in finite gaps of lattice spectrum. In contrast to latticeless geometries, where surface waves exist only when nonlinearity deflects light towards the material surface, the surface lattice solitons exist in settings where diffusion would cause beam bending against the surface.
The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the condition for which is obtained. Studies on scattering of the soliton by an attractive defect potential reveal the existence of total reflection and transmission windows which become very narrow with increasing initial soliton amplitude. Transmission regions disappear beyond the small-amplitude limit. The regions of complete reflection and partial capture co…
We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a -phase difference between neighboring spots. It is shown that the multipole-mode solitons can rotate steadily upon propagation, and the existence domain is strongly affected by the rotation frequency. The rotation may enhance the stabilization of surface multipole-mode solitons.
We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components associated with different spectral gaps. We find numerically discrete surface modes in semi-infinite binary waveguide arrays which can support simultaneously two types of discrete solitons, and analyze different multi-gap states including the soliton-induced waveguides with the guided modes from different gaps and composite vector solitons.
We address surface solitons supported by the interface of optical lattices imprinted in saturable media with surface-localized gain. The nonlinearity saturation puts restrictions on the maximal energy flow carried by surface solitons. As a consequence, the presence of thin amplifying layer near the surface results in the controllable emission of solitons towards the lattice at angles depending on the amplification rate and on lattice depth.
We investigate light beam propagation along the interface between linear and nonlinear media with parity-time PT symmetry, and derive an equation governing the beam propagation. A novel class of two-dimensional PT surface solitons are found analytically and numerically, and checked to be stable over a wide range of PT potential structures and parameters. These surface solitons do not require a power threshold. The transverse power flow across beam is examined within the solitons and found to be caused by the nontrivial phase structure of the solitons. PT surface solitons are possibly observed …
We elucidate the properties of mixed-gap vector surface solitons supported by the interface between a uniform medium and an optical lattice imprinted in a Kerr-type nonlinear media. The components of such mixed-gap solitons emerge from different gaps of lattice spectrum and their mutual trapping results in the formation of stable vector states. The unstable soliton component is stabilized by the cross-coupling with the stable component. We show that vector mixed-gap surface solitons exhibit a new combination of properties of vectorial surface waves and gap solitons.
We predict the existence of surface dark solitons at the interface between a self-defocusing nonlocal nonlinear medium and a linear medium. The fundamental and higher-order surface dark solitons can exist when the linear refractive index of the self-defocusing media is much larger than that of the linear media. The fundamental solitons are stable and the stabilities of higher-order solitons depend on both nonlocality degree and propagation constant.
We discover the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. Such solitons can feature strongly noncanonical profiles, and we found that their properties are dictated by the location of the vortex core relative to the surface. The refractive index modulation forming the lattices at both sides of the interface results in complete stability of the vortex solitons in wide domains of their existence, thus introducing the first known example of stable topological solitons supported by a surface.
We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on the domains of existence and stability of the surface solitons, focusing on new types of dipole solitons residing partially inside the optical lattice. We find that such solitons feature strongly asymmetric shapes and that they are stable in large parts of their existence domain.
We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons fo…
We address soliton formation at the edge of chirped optical lattices imprinted in Kerr-type nonlinear media. We find families of power thresholdless surface waves that do not exist at other types of lattice interfaces. Such solitons form due to combined action of internal reflection at the interface, distributed Bragg-type reflection, and focusing nonlinearity. Remarkably, we discover that surfaces of chirped lattices are soliton attractors: Below an energy threshold, solitons launched well within the lattice self-bend toward the interface, and then stick to it.
We discover multipole-mode solitons supported by the surface between two distinct periodic lattices imprinted in Kerr-type nonlinear media. Such solitons are possible because the refractive index modulation at both sides of the interface glues together their out-of-phase individual constituents. Remarkably, we find that the new type of solitons may feature highly asymmetric shapes and yet they are stable over wide domains of their existence, a rare property to be attributed to their surface nature.
We discover that at the edge of optical lattice imprinted in saturable nonlinear media one-dimensional surface solitons exist only within a band of light intensities, and that they cease to exist when the lattice depth exceeds an upper threshold. We also reveal the generation of arrays of two-dimensional surface solitons mediated by transverse modulational instability of one-dimensional solitons, a process that is found to exhibit specific features associated to properties of the optical lattice.
We report the first experimental observation of vector surface solitons, which form at the edge and in the corner of two-dimensional laser-written waveguide arrays. These elliptically polarized vector states are composed of two orthogonally polarized components. They exist only above a power threshold and bifurcate from scalar surface solitons. The components of a vector soliton may have substantially different degrees of localization in certain parameter ranges.
We reveal the existence of the surface plasmonic lattice solitons (surface PLSs) at the boundary of a semi-infinite metallic-dielectric periodic nano-structure. We find that the truncation of the periodic structure imposes a threshold power for the existence of surface PLSs, and enhances significantly the modal localization. The propagation and excitation of surface PLSs as well as their potential application in the all-optical subwavelength switching are also demonstrated.
Dissipative Kerr solitons in optical microresonators provide a unifying framework for nonlinear optical physics with photonic-integrated technologies and have recently been employed in a wide range of applications from coherent communications to astrophysical spectrometer calibration. Dissipative Kerr solitons can form a rich variety of stable states, ranging from breathers to multiple-soliton formations, among which, the recently discovered soliton crystals stand out. They represent temporally-ordered ensembles of soliton pulses, which can be regularly arranged by a modulation of the continuo…
We report the observation of surface solitons in chirped semi-infinite waveguide arrays whose waveguides exhibit exponentially decreasing refractive indices. We show that the power threshold for surface wave formation decreases with an increase of the array chirp and that for sufficiently large chirp values linear surface modes are supported.
We report on the experimental observation of corner surface solitons localized at the edges joining planar interfaces of hexagonal waveguide array with uniform nonlinear medium. The face angle between these interfaces has a strong impact on the threshold of soliton excitation as well as on the light energy drift and diffraction spreading.
We report on the first observation of surface gap solitons, recently predicted to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity [Ya.V. Kartashov et al., Phys. Rev. Lett. 96, 073901 (2006). We demonstrate strong self-trapping at the edge of a LiNbO_3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap m…
Here, we experimentally generated photonic graphene by resonance of inhomogeneously strained one dimensional lattices of triangular solitons. Where mildly twisted solitons are considered as north and south monopoles, while strongly twisted solitons are considered as defect north monopoles. Weak bounding is observed between the opposite monopoles. Strong bounding occurred between the monopoles with same polarity. Where a defect north monopole is transformed into a flux-like tube. Which generated an optical analogue of the torus sublattice. Bogomolny's vortice-like symmetry is remained intact in…
The properties of vector vortex beams in vertical-cavity-surface emitting lasers with frequency-selective feedback is investigated. They are interpreted as high-order vortex solitons with a spatially non-uniform, but locally linear polarization state. In contrast to most schemes to obtain vector vortex beams relying on imprinting the polarization structure, vector vortex solitons form spontaneously due to the near polarization degeneracy in vertical-cavity devices. We observe radially, hyperbolic and spiral polarization configurations depending on small residual anisotropies in the system and …
Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band-structures. Three-dimensional topological objects of localized particle-like nature attract broad interest across discipline boundaries from elementary particle physics and cosmology to condensed matter physics. Here we show how simple structured light beams can be transformed into optical excitations of atoms with considerably more complex topologies representing three-dimensional particle-like Skyrmions. This construction ca…
We present a theoretical study of the hydrodynamic properties of a quantum gas of exciton-polaritons in a semiconductor microcavity under a resonant laser excitation. The effect of a spatially extended defect on the superfluid flow is investigated as a function of the flow speed. The processes that are responsible for the nucleation of vortices and solitons in the wake of the defect are characterized, as well as the regimes where the superfluid flow remains unperturbed. Specific features due to the non-equilibrium nature of the polariton fluid are put in evidence.
Scenarios for controllable creation, trapping and holding of single and multiple solitons in a specially designed nonlinear Bragg grating (BG) are proposed. The setting includes a chirped BG segment, which is linked via a local defect to a uniform BG with a built-in array of defects. A parabolic relation between the trapping position of the incident soliton and its power is obtained. Simultaneous trapping of two and three solitons at different locations is demonstrated too.
We find that a surface soliton in nonlocal nonlinear media can be regarded as a half of a bulk soliton with an antisymmetric amplitude distribution. The analytical solutions for the surface solitons and breathers in strongly nonlocal media are obtained, and the critical power and breather period are gotten analytically and confirmed by numerical simulations. In addition, the oscillating propagation of nonlocal surface solitons launched away from the stationary position is considered as the interaction between the soliton and its out-of-phase image beam. Its trajectory and oscillating period ob…
Analytical solutions for (1+1)D surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using this analytical solutions. The analytical solutions are verified by numerical simulations. The solutions for surface breathers and their breathing period, and solutions for surface dipole and tripole solitons are also given.
We address the properties of surface-wave solitons on the interface between a semi-infinite homogeneous linear medium and a semi-infinite homogeneous nonlinear nonlocal medium. The stability, energy flow and FWHM of the surface wave solitons can be affected by the degree of nonlocality of the nonlinear medium. We find that the refractive index difference affects the power distribution of the surface solitons in two media. We show that the different boundary values at the interface can lead to the different peak position of the surface solitons, but it can not influence the solitons stability w…
A gap soliton is a solitonic state existing inside the band gap of an infinite-periodic exciton-polariton condensate (EPC). The combination of surface states and gap solitons forms the so named surface gap solitons (SGSs). We analyze the existence of SGSs near the interface between uniform and semi-infinite periodic EPCs. We find that SGSs exist only when the system is excited by a pump with low power and small width. As the pump power or width increases, SGSs become unstable.
We show that surface solitons in the one-dimensional nonlinear Schrödinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of surface solitons shrink with increase of the amplitude of imaginary part of complex potential.
We address formation of stable dissipative surface solitons in the exciton-polariton condensate in one-dimensional array of microcavity pillars under the action of localized resonant pump acting in the edge resonator. We show that localization degree and peak amplitudes of surface solitons can be effectively controlled by the pump frequency and that the allowed energy gap of periodic structure determines the energy range, where surface solitons can form. One observes bistability at sufficiently large pump amplitudes and nonlinearity-induced shift of the position of resonance peak from the allo…
