Surface defect gap solitons in two-dimensional optical lattices

We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.     

Solitons supported by defects of PT-invariant potentials with real part of dual-frequency lattices

The existence and stability of defect solitons in defective PT potentials with real part of dual-frequency lattices are reported. For positive defects, fundamental solitons are always stable in the semi-infinite gap and nonexistent in the first gap. While for negative defects, in the semi-infinite gap, fundamental solitons are stable in most of their existence region apart from low power region, but all the fundamental solitons are stable in the first gap. Dipole solitions are unstable in the whole semi-infinite gap regardless of defects, but in the first gap they can be stable in the low power region for positive defects.     

Surface defect gap solitons in superlattices with self-defocusing nonlinearity

We put forward the existence and stability of defect surface gap solitons at the interface between uniform media and an superlattice with self-defocusing nonlinearity. We reveal that the defect plays the significant role in controlling the region of solitons existing. Various solitons are found to be existed in different gaps for different defects. For positive defects, fundamental solitons can exist stably in the semi-infinite gap, and dipole solitons can exist stably in the first gap but they are unstable in the second gap. For zero or negative defects, fundamental and dipole solitons can exist stably in the first gap and the second gap, respectively.     

Defect solitons supported by the interface between simple lattices and superlattices

We study surface defect solitons (SDSs) at an interface between superlattices and simple lattices with focusing saturable nonlinearity. The properties of the SDSs formed in such kinds of mixed structures are obviously different from those in single superlattices or single ordinary lattices. Research results show that surface solitons with a zero defect or a positive defect are stable in the semi-infinite gap and cannot exist in the first gap. For the case of a negative defect, the stable region of surface solitons will be narrower in the semi-infinite gap with the increase of the defect depth. Surface gap solitons (SGSs) can stably exist in the first gap for a deeper negative defect depth.     

The contrast between defect solitons in parityben time symmetric superlattice and simple-lattice complex potentials

The existence and stability of defect superlattice solitons in parity-time (PT) symmetric superlattice and simple-lattice complex potentials are reported. Compared with defect simple-lattice solitons in similar potentials, the defect soliton in superlattice has a wider stable range than that in simple-lattice. The solitons' power increases with increasing propagation constant. For the positive defect, the solitons are stable in the whole region where solitons exist in the semi-infinite gap. For the zero defect, the solitons are unstable at the edge of the band. For the negative defect, the solitons propagate with the shape of Y at low propagation constant and propagate stably at the large one.     

中心对称光折变晶体中Kagome光子晶格内带隙孤子的研究

研究了中心对称光折变晶体中Kagome光子晶格内带隙孤子的存在及其稳定性。结果表明:带隙孤子只存在于半无限带隙内,中功率的带隙孤子是稳定的,高功率和低功率的带隙孤子是不稳定的。在高功率和中功率区域内,带隙孤子的功率随传播常数的增加而减小。在低功率区域内,带隙孤子的功率随传播常数的增加而变大。     

Surface superlattice gap solitons

We demonstrate that specific surface superlattice gap solitons can be supported at an interface between a one-dimensional photonic superlattice and a uniform medium with saturable nonlinearity. The solitons are stable in the semi-infinite gap but do not exist in the first gap. With the decrease of the power, the solitons jump from the surface site to the next one, and they may continue the motion into the lattices, which offers potential applications for the routing of optical signals.     

Defect solitons supported by parity-time symmetric defects in superlattices

The existence and stability of defect solitons supported by parity-time (PT) symmetric defects in superlattices are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive defects, zero defects, and negative defects. In the first gap, out-of-phase solitons are stable for positive defects or zero defects, whereas in-phase solitons are stable for negative defects. For both the in-phase and out-of-phase solitons with the positive defect and in-phase solitons with negative defect in the first gap, there exists a cutoff point of the propagation constant below which the defect solitons vanish. The value of the cutoff point depends on the depth of defect and the imaginary parts of the PT symmetric defect potentials. The influence of the imaginary part of the PT symmetric defect potentials on soliton stability is revealed.     

Surface defect gap solitons in one-dimensional dual-frequency lattices

We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region of semi-finite gap, and the semi-finite gap exists not only in the positive and zero defects but also in the negative defect; unlike in the regular lattices, the semi-finite gap exists in the positive and zero defects but does not exist in the negative defect. In particular, stable solitons exist almost in the whole semi-finite gap for the positive and zero defects. These properties are different from other lattices with defects. In addition, it is found that the existence of surface dual-frequency lattice solitons does not need a threshold power.     

Fundamental and multipole solitons supported by one-dimensional multilayer photonic crystals potentials

The existence and stability of solitons in one-dimensional multilayer photonic crystals potentials are reported. For all of the solitons, there exist cutoff points of the propagation constant below which the solitons vanish in the semi-infinite gap. The fundamental solitons are stable in the whole range where solitons exist. The antisymmetric dipole solitons can be stable when the propagation constant closes to the cutoff point. The range of stability for symmetric tripole solitons is changed with modulation depth and width of the multilayer photonic crystals potentials. The power of solitons increases with increasing of propagation constant and modulation width or decreasing of modulation depth of the potentials.     

Two-dimensional stationary nonlinear surface solitons in nonlocal nonlinear media

We address two-dimensional surface solitons occurring at the interface between a semi-infinite linear medium and a semi-infinite nonlocal nonlinear medium. We find that there exist stable single and dipole surface solitons. The properties of the surface solitons can be affected by the degree of nonlocality. Interestingly, only when the degree of nonlocality is greater than a critical value, the surface solitons can exist.     

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrödinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.     

Interface kink solitons in defocusing saturable nonlinear media

We report on the dynamics of semi-localized nonlinear optical modes supported by an interface separating a uniform defocusing saturable medium and an imprinted semi-infinite photonic lattice. Out-of-phase and in-phase kink solitons composed by dark-soliton-like pedestals and oscillatory tails are found. Two branches of out-of-phase kink solitons exist in shallow lattices. Saturable nonlinearity enhances the pedestal height and renormalized energy flow of kink solitons evidently. While in-phase kink solitons are always unstable, out-of-phase kink solitons will be completely stable provided that lattice depth exceeds a critical value. Furthermore, stable kink solitons in the higher band gaps are also possible. Our results may give a helpful hint for understanding the dynamics of kink solitons with high pedestals in other fields.     

Solitons in a system of three linearly coupled fiber gratings

We introduce a model of three parallel-coupled nonlinear waveguiding cores equipped with Bragg gratings (BGs), which form an equilateral triangle. The most promising way to create multi-core BG configuration is to use inverted gratings, written on internal surfaces of relatively broad holes embedded in a photonic-crystal-fiber matrix. The objective of the work is to investigate solitons and their stability in this system. New results are also obtained for the earlier investigated dual-core system. Families of symmetric and antisymmetric solutions are found analytically, extending beyond the spectral gap in both the dual- and tri-core systems. Moreover, these families persist in the case (strong coupling between the cores) when there is no gap in the systems linear spectrum. Three different types of asymmetric solitons are found (by means of the variational approach and numerical methods) in the tri-core system. They exist only inside the spectral gap, but asymmetric solitons with nonvanishing tails are found outside the gap as well. Stability of the solitons is explored by direct simulations, and, for symmetric solitons, in a more rigorous way too, by computation of eigenvalues for small perturbations. The symmetric solitons are stable up to points at which two types of asymmetric solitons bifurcate from them. Beyond the bifurcation, one type of the asymmetric solitons is stable, and the other is not. Then, they swap their stability. Asymmetric solitons of the third type are always unstable. When the symmetric solitons are unstable, their instability is oscillatory, and, in most cases, it transforms them into stable breathers. In both the dual- and tri-core systems, the stability region of the symmetric solitons extends far beyond the gap, persisting in the case when the system has no gap at all. The whole stability region of antisymmetric solitons (a new type of solutions in the tri-core system) is located outside the gap. Thus, solitons in multi-core BGs can be observed experimentally in a much broader frequency band than in the single-core one, and in a wider parameter range than it could be expected. Asymmetric delocalized solitons, found outside the spectral gap, can be stable too.Received: 13 August 2003PACS: 42.81.Dp Propagation, scattering, and losses; solitons - 42.65.Tg Optical solitons; nonlinear guided waves - 05.45.Yv Solitons     

Gap solitons supported by optical lattices in biased centrosymmetric photorefractive crystals

We analyze the existence and stability of gap solitons supported by optical lattices with self-focusing nonlinearity in biased centrosymmetric photorefractive crystals. It is shown that, in first finite bandgap, gap solitons are symmetric in transverse dimension, single humped, entirely positive and linearly stable, while these solitons are antisymmetric with similar profiles, the stable and unstable intervals of the gap solitons are intertwined in the second finite bandgap.     

Surface defect kink solitons

We reveal the existence of dynamically stable nonlinear defect kink modes at an interface separating a defocusing Kerr medium and an imprinted semi-infinite lattice with a positive or negative defect covering single or several lattice sites. Increasing the number of defect sites equivalently results in a band-gap shift of lattice which in return alters the existence domains and stability properties of defect solitons. Comparing with the uniform semi-infinite lattice, the instability of kink soliton in lattice with a negative defect is significantly suppressed, especially for in-phase soliton. Our results provide an effective way for the realization of stable in-phase kink solitons.     

Existence, bistability, and instability of Kerr-like parametric gap solitons in quadratic media

We investigate the existence and stability of parametric gap solitons in chi((2)) media in the limit of Kerr-equivalent nonlinearities. We reveal soliton branching (bistability) described by an explicit criterion. Unlike in other optical solitons, both branches of gap solitons can be unstable owing to oscillatory instabilities. Despite these mechanisms stable gap solitons do exist.     

Solitons in a linearly coupled system with separated dispersion and nonlinearity

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not "mixed" in a single nonlinear Schrodinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton's components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad "pedestal." This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.     

Surface gap solitons

We put forward the existence of surface gap solitons at the interface between uniform media and an optical lattice with defocusing nonlinearity. Such new type of solitons forms when the incident and reflected waves at the interface of the lattice experience Bragg scattering, and feature a combination of the unique properties of both surface waves and gap solitons. We discover that gap surface solitons exist only when the lattice depth exceeds a threshold value, that they can be made completely stable, and that they can form stable bound states.     

Defect modes supported by optical lattices in photovoltaic-photorefractive crystals

We study defect modes in optically induced one-dimensional lattices in photovoltaic-photorefractive crystals. These defect modes exist in different bandgaps due to the change of defect intensity. For a positive defect, defect mode branches exist not only in the semi-infinite bandgap, but also in the first and second bandgaps. When the defect mode branch is fixed, the confinement of defect modes increases with the defect strength parameter. For a negative defect, defect mode branches exist only in the first and second bandgaps. For a given defect mode branch, the strongest confinement of the defect modes appears when the lattice intensity at the defect site is not the smallest in its branch. On the other hand, when the defect strength parameter is fixed, the most localized defect modes arise in the semi-infinite bandgap for the positive defect and in the first bandgap for the negative defect.