Vibration modes of a gap soliton in a nonlinear optical medium

Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

Bragg solitons in systems with separated nonuniform Bragg grating and nonlinearity

The existence and stability of quiescent Bragg grating solitons are systematically investigated in a dual-core fiber, where one of the cores is uniform and has Kerr nonlinearity while the other one is linear and incorporates a Bragg grating with dispersive reflectivity. Three spectral gaps are identified in the system, in which both lower and upper band gaps overlap with one branch of the continuous spectrum; therefore, these are not genuine band gaps. However, the central band gap is a genuine band gap. Soliton solutions are found in the lower and upper gaps only. It is found that in certain parameter ranges, the solitons develop side lobes. To analyze the side lobes, we have derived exact analytical expressions for the tails of solitons that are in excellent agreement with the numerical solutions. We have analyzed the stability of solitons in the system by means of systematic numerical simulations. We have found vast stable regions in the upper and lower gaps. The effect and interplay of dispersive reflectivity, the group velocity difference, and the grating-induced coupling on the stability of solitons are investigated. A key finding is that a stronger grating-induced coupling coefficient counteracts the stabilization effect of dispersive reflectivity.

Moving Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity

The existence, stability and collision dynamics of moving Bragg grating solitons in a semilinear dual-core system where one core has the Kerr nonlinearity and is equipped with a Bragg grating with dispersive reflectivity, and the other core is linear are investigated. It is found that moving soliton solutions exist as a continuous family of solutions in the upper and lower gaps of the system's linear spectrum. The stability of the moving solitons are investigated by means of systematic numerical stability analysis, and the effect and interplay of various parameters on soliton stability are analyzed. We have also systematically investigated the characteristics of collisions of counter-propagating solitons. In-phase collisions can lead to a variety of outcomes such as passage of solitons through each other with increased, reduced or unchanged velocities, asymmetric separation of solitons, merger of solitons into a quiescent one, formation of three solitons (one quiescent and two moving ones) and destruction of both solitons. The outcome regions of in-phase collisions are identified in the plane of dispersive reflectivity versus frequency. The effects of coupling coefficient, relative group velocity in the linear core, soliton velocity and dispersive reflectivity and the initial phase difference on the outcomes of collisions are studied.

Moving Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity

The stability and collision dynamics of moving solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are investigated. Two disjoint families of solitons are found on the plane of the coefficient of quintic nonlinearity versus the normalized frequency (η,Ω(norm)). Through numerical stability analysis, we have identified stability regions on the (η,Ω(norm)) plane for various values of dispersive reflectivity parameter (m) and velocity (v). The size of stability regions is found to be dependent on m and v. Collisions of counterpropgating Type 1 and Type 2 solitons have been systematically investigated. It is found that for low to moderate values of dispersive reflectivity, the collisions of Type 1 solitons can result in various outcomes such as separation of solitons with reduced, increased, unchanged, or asymmetric velocities and generation of a quiescent soliton by merger or formation of three solitons. For strong dispersive reflectivity (e.g., m=0.5), the collisions of low-velocity in-phase Type 1 solitons may lead to repulsion of solitons, asymmetric separation, merger into a single soliton, or formation of three solitons (one quiescent and two moving solitons). At higher velocities collisions predominantly lead to the formation of three solitons. For m=0.5, in-phase Type 2 solitons may repel or form a temporary bound state of quiescent Type 1 solitons that subsequently splits into two asymmetrically separating Type 1 solitons. π-out-of-phase Type 2 solitons may also merge to form a quiescent Type 1 soliton.

Double-discrete solitons in fishnet arrays of optical fibers

We demonstrate that crossed arrays of optical fibers support the double-discrete linear and nonlinear propagation of light beams, in which not only the transverse coordinate (the fiber's number) is discrete, but also the longitudinal (propagation) coordinate, i.e., the number of the fiber-crossing site, is effectively discrete too. In the linear limit, this transmission regime features double-discrete self-collimation. The nonlinear fishnet arrays with both focusing and defocusing nonlinearities give rise to double-discrete spatial solitons. Solitons bifurcating from two different branches of the linear dispersion relation feature strong interactions and form composite states. In the continuum limit, the model of the nonlinear fishnet reduces to a system of coupled-mode equations similar to those describing Bragg gratings, but without the cross-phase-modulation terms.

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

Gap solitons in grating superstructures

We report results of the investigation of gap solitons (GSs) in the generic model of a periodically modulated Bragg grating (BG), which includes periodic modulation of the BG chirp or local refractive index, and periodic variation of the local reflectivity. We demonstrate that, while the previously studied reflectivity modulation strongly destabilizes all solitons, the periodic chirp modulation, which is a novel feature, stabilizes a new family of double-peak fundamental BGs in the side bandgap at negative frequencies (gap No. -1), and keeps solitons stable in the central bandgap (No. 0). The two soliton families demonstrate bistability, coexisting at equal values of energy. In addition, stable 4-peak bound states are formed by pairs of fundamental GSs in bandgap -1. Self-trapping and mobility of the solitons are studied too.

Periodic waves in fiber Bragg gratings

We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named "sn" and "cn" waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies (omega<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and, in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and omega>0, is identified. However, the sn waves with omega<0, as well as all cn solutions, are strongly unstable.

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.

Quasisymmetric and asymmetric gap solitons in linearly coupled Bragg gratings with a phase shift

We introduce a model including two linearly coupled Bragg gratings, with a mismatch (phase shift theta) between them. The model may be realized as parallel-coupled fiber Bragg gratings (FBGs), or, in the spatial domain, as two parallel planar waveguides carrying diffraction gratings. The phase shift induced by a shear stress may be used to design a different type of FBG sensor. In the absence of the mismatch, the symmetry-breaking bifurcation of gap solitons (GSs) in this model was investigated before. Our objective is to study how mismatch theta affects families of symmetric and asymmetric GSs, and the bifurcation between them. We find that the system's band gap is always filled with solitons (for theta not equal to 0, the gap's width does not depend on coupling constant lambda if it exceeds some minimum value). The largest velocity of the moving soliton, cmax, is found as a function of theta and lambda (cmax grows with theta). The mismatch transforms symmetric GSs into quasisymmetric (QS) ones, in which the two components are not identical, but their peak powers and energies are equal. The mismatch also breaks the spatial symmetry of the GSs. The QS solitons are stable against symmetry-breaking perturbations as long as asymmetric (AS) solutions do not exist. If theta is small, AS solitons emerge from their QS counterparts through a supercritical bifurcation. However, the bifurcation may become subcritical at larger theta. The condition for the stability against oscillatory perturbations (unrelated to the symmetry breaking) is essentially the same as in the ordinary FBG model: both QS and AS solitons are stable if their intrinsic frequency is positive (i.e., in a half of the band gap).

Stable solitons of even and odd parities supported by competing nonlocal nonlinearities

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of small perturbations, and tested in direct simulations. We find that the stability of the fundamental solitons strictly follows the Vakhitov-Kolokolov criterion, whereas the dipole solitons can be destabilized through a Hamiltonian-Hopf bifurcation. The solitons of both types may be stable in the nonlocal model with only quintic self-attractive nonlinearity, in contrast with the instability of all solitons in the local version of the quintic model.

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.

Gap solitons in a medium with third-harmonic generation

We find two-component optical solitons in a nonlinear waveguide with a Bragg grating, including Kerr effects and third-harmonic generation (THG). The model may be realized in temporal and in spatial domains. Two species of fundamental gap solitons (GSs) are found. The first ("THG-gap soliton") has the bulk of its energy at the fundamental frequency (FF) and a lesser part in the third-harmonic (TH) band. The FF part of the soliton is always single humped; the TH part may be single or double humped. Stability domains for quiescent and moving THG-gap solitons strongly shrink with increase of velocity. The second species is the usual ("simple") GS, sitting entirely in the TH band. More complex solutions are also found, in the form of a bound state of a THG-gap soliton and two simple GSs, with a finite binding energy. When a THG-gap soliton is unstable, the instability is oscillatory. It may ultimately cause the THG-gap soliton to throw off some radiation and evolve into a localized structure with the FF and TH components out of phase, with or without internal oscillations. Stable solitons feature an excited state (i.e., they support a localized eigenmode).

Trapping Bragg solitons by a pair of defects

We study collisions of moving solitons in a fiber Bragg grating with a structure composed of two local defects of the grating, attractive or repulsive. Results are summarized in the form of diagrams showing the share of the trapped energy as a function of the soliton's velocity and defects' strength. The moving soliton can be trapped by a cavity bounded by repulsive defects; a well-defined region of the most efficient trapping is identified. The trapped soliton performs persistent oscillations in the cavity, with the frequency in the GHz range. For attractive defects, essential differences are found from the earlier studied case of the collision of a soliton with a single defect: in this case, too, there appears a well-defined region of the most efficient trapping, and the largest velocity, up to which the soliton can be captured, increases. The findings may be significant for experiments aimed at the creation of "standing-light" pulses in the fiber gratings and for related applications. Collisions between identical solitons moving across the two-defect structure are also studied. On the attractive set, soliton-soliton collisions may give rise to symmetric capture of the solitons by both defects or merger into a single pulse trapped at one defect.

Coupled-mode theory for spatial gap solitons in optically induced lattices

We derive two systems of coupled-mode equations for spatial gap solitons in one-dimensional (1D) and quasi-one-dimensional (Q1D) photonic lattices induced by two interfering optical beams in a nonlinear photorefractive crystal. The models differ from the ordinary coupled-mode system (e.g., for the fiber Bragg grating) by saturable nonlinearity and, if expanded to cubic terms, by the presence of four-wave-mixing terms. In the 1D system, solutions for stationary gap solitons are obtained in an implicit analytical form. For the Q1D model and for tilted ("moving") solitons in both models, solutions are found in a numerical form. The existence of stable tilted solitons in the full underlying model of the photonic lattice in the photorefractive medium is also shown. The stability of gap solitons is systematically investigated in direct simulations, revealing a nontrivial border of instability against oscillatory perturbations. In the Q1D model, two disjointed stability regions are found. The stability border of tilted solitons does not depend on the tilt. Interactions between stable tilted solitons are investigated too. The collisions are, chiefly, elastic, but they may be inelastic close to the instability border.

Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity

We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty. However, in contrast with the situation known in the model combining a periodic potential and the self-focusing Kerr nonlinearity, the solitons fill only a finite zone near the top of the semi-infinite gap, which is a consequence of the saturable character of the CQ nonlinearity. If the potential structure is much deeper, then fundamental and double (both symmetric and antisymmetric) solitons with a flat-top shape are found in the finite gaps. Computation of stability eigenvalues for small perturbations and direct simulations show that all the solitons are stable. In the shallow KP potential, the soliton characteristics, in the form of the integral power Q (or width w) versus the propagation constant k, reveal strong bistability, with two and, sometimes, four different solutions found for a given k (the bistability disappears with the increase of the depth of the potential). Disobeying the Vakhitov-Kolokolov criterion, the solution branches with both dQ/dk > 0 and dQ/dk < 0 are stable. The curve Q(k) corresponding to each particular type of the solution (with a given number of local peaks and definite symmetry) ends at a finite maximum value of Q (breathers are found past the end points). The increase of the integral power gives rise to additional peaks in the soliton's shape, each corresponding to a subpulse trapped in a local channel of the KP structure (a beam-splitting property). It is plausible that these features are shared by other models combining saturable nonlinearity and a periodic substrate.

Symmetric and asymmetric solitons in linearly coupled Bragg gratings

We demonstrate that a symmetric system of two linearly coupled waveguides, with Kerr nonlinearity and resonant grating in both of them, gives rise to a family of symmetric and antisymmetric solitons in an exact analytical form, a part of which exists outside of the bandgap in the system's spectrum, i.e., they may be regarded as embedded solitons (ES's, i.e., the ones partly overlapping with the continuous spectrum). Parameters of the family are the soliton's amplitude and velocity. Asymmetric ES's, unlike the regular (nonembedded) gap solitons (GS's), do not exist in the system. Moreover, ES's exist even in the case when the system's spectrum contains no bandgap. The main issue is the stability of the solitons. We demonstrate that some symmetric ES's are stable, while all the antisymmetric solitons are unstable; an explanation is given to the latter property, based on the consideration of the system's Hamiltonian. We produce a full stability diagram, which comprises both embedded and regular solitons, quiescent and moving. A stability region for ES's is found around the point where the constant of the linear coupling between the two cores is equal to the Bragg-reflectivity coefficient accounting for the linear conversion between the right- and left-traveling waves in each core, i.e., the ES's are the "most endemic" solitary solitons in this system. The stability region quickly shrinks with the increase of the soliton's velocity c, and completely disappears when c exceeds half the maximum velocity. Collisions between stable moving solitons of various types are also considered, with a conclusion that the collisions are always quasielastic.

Standard and embedded solitons in nematic optical fibers

A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wave packets of transverse magnetic modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive a complex modified Korteweg-de Vries equation (CM KdV) which governs the dynamics for the amplitude of the wave packet. In this derivation the dispersion, self-focussing, and diffraction in the nematic fiber are taken into account. It is shown that this CM KdV equation has two-parameter families of bright and dark complex solitons. We show analytically that under certain conditions, the bright solitons are actually double-embedded solitons. We explain why these solitons do not radiate at all, even though their wave numbers are contained in the linear spectrum of the system. We study (numerically and analytically) the stability of these solitons. Our results show that these embedded solitons are stable solutions, which is an interesting property since in most systems the embedded solitons are weakly unstable solutions. Finally, we close the paper by making comments on the advantages as well as the limitations of our approach, and on further generalizations of the model and method presented.

Formation of a standing-light pulse through collision of gap solitons

Results of a systematic theoretical study of collisions between moving solitons in a fiber grating are presented. Various outcomes of the collision are identified, the most interesting one being merger of the solitons into a single zero-velocity pulse, which suggests a way to create pulses of "standing light." The merger occurs with the solitons whose energy takes values between 0.15 and 0.35 of the limit value, while their velocity is limited by approximately 0.2 of the limit light velocity in the fiber. If the energy is larger, another noteworthy outcome is acceleration of the solitons as a result of the collision. In the case of mutual passage of the solitons, inelasticity of the collision is quantified by the energy-loss share. Past the soliton's stability limit, the collision results in strong deformation and subsequent destruction of the solitons. Simulations of multiple collisions of two solitons in a fiber-loop configuration are performed too. In this case, the maximum velocity admitting the merger increases to approximately 0.4 of the limit velocity. The influence of an attractive local defect on the collision is also studied, with the conclusion that the defect does not alter the overall picture, although it traps a small-amplitude pulse. Related effects in single-soliton dynamics are considered too, the most important one being the possibility of slowing down the soliton (reducing its velocity to the above-mentioned values that admit fusion of colliding solitons) by passing it through an apodized fiber grating, i.e., one with a gradually increasing Bragg reflectivity. Additionally, transformation of an input sech signal into a gap soliton (which is quantified by the share of lost energy), and the rate of decay of a quiescent gap soliton in a finite fiber grating, due to energy leakage through loose edges, are also studied.

Discrete vector solitons in two-dimensional nonlinear waveguide arrays: solutions, stability, and dynamics

We identify and investigate bimodal (vector) solitons in models of square-lattice arrays of nonlinear optical waveguides. These vector self-localized states are, in fact, self-induced channels in a nonlinear photonic-crystal matrix. Such two-dimensional discrete vector solitons are possible in waveguide arrays in which each element carries two light beams that are either orthogonally polarized or have different carrier wavelengths. Estimates of the physical parameters necessary to support such soliton solutions in waveguide arrays are given. Using Newton relaxation methods, we obtain stationary vector-soliton solutions, and examine their stability through the computation of linearized eigenvalues for small perturbations. Our results may also be applicable to other systems such as two-component Bose-Einstein condensates trapped in a two-dimensional optical lattice.

Interaction of a soliton with a localized gain in a fiber Bragg grating

A model of a lossy nonlinear fiber grating with a "hot spot," which combines a local gain and an attractive perturbation of the refractive index, is introduced. A family of exact solutions for pinned solitons is found in the absence of loss and gain. In the presence of the loss and localized gain, an instability threshold of the zero solution is found. If the loss and gain are small, it is predicted what soliton is selected by the energy-balance condition. Direct simulations demonstrate that only one pinned soliton is stable in the conservative model, and it is a semiattractor: solitons with a larger energy relax to it via emission of radiation, while those with a smaller energy decay. The same is found for solitons trapped by a pair of repulsive inhomogeneities. In the model with the loss and gain, stable pinned pulses demonstrate persistent internal vibrations and emission of radiation. If these solitons are nearly stationary, the prediction based on the energy balance underestimates the necessary gain by 10-15% (due to radiation loss). If the loss and gain are larger, the intrinsic vibrations of the pinned soliton become chaotic. The local gain alone, without the attractive perturbation of the local refractive index, cannot maintain a stable pinned soliton. For collisions of moving solitons with the "hot spot," passage and capture regimes are identified, the capture actually implying splitting of the soliton.

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, gives rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s=2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

Interaction of N solitons in the massive Thirring model and optical gap system: the complex Toda chain model

Using the Karpman-Solov'ev quasiparticle approach for soliton-soliton interaction we show that the train propagation of N well-separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalized (nonintegrable) complex Toda chain is derived for description of the train propagation of well-separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.

Solitary waves in systems with separated Bragg grating and nonlinearity

The existence and stability of solitons in a dual-core optical waveguide, in which one core has Kerr nonlinearity while the other one is linear with a Bragg grating written on it, are investigated. The system's spectrum for the frequency omega of linear waves always contains a gap. If the group velocity c in the linear core is zero, it also has two other, upper and lower (in terms of omega) gaps. If c not equal to 0, the upper and lower gaps do not exist in the rigorous sense, as each overlaps with one branch of the continuous spectrum. When c=0, a family of zero-velocity soliton solutions, filling all the three gaps, is found analytically. Their stability is tested numerically, leading to a conclusion that only solitons in an upper section of the upper gap are stable. For c not equal to 0, soliton solutions are sought for numerically. Stationary solutions are only found in the upper gap, in the form of unusual solitons, which exist as a continuous family in the former upper gap, despite its overlapping with one branch of the continuous spectrum. A region in the parameter plane (c,omega) is identified where these solitons are stable; it is again an upper section of the upper gap. Stable moving solitons are found too. A feasible explanation for the (virtual) existence of these solitons, based on an analytical estimate of their radiative-decay rate (if the decay takes place), is presented.

Bragg-grating solitons in a semilinear dual-core system

We investigate the existence and stability of gap solitons in a double-core optical fiber, where one core has the Kerr nonlinearity and the other one is linear, with the Bragg grating (BG) written on the nonlinear core, while the linear one may or may not have a BG. The model considerably extends the previously studied families of BG solitons. For zero-velocity solitons, we find exact solutions in a limiting case when the group-velocity terms are absent in the equation for the linear core. In the general case, solitons are found numerically. Stability borders for the solitons are found in terms of an internal parameter of the soliton family. Depending on the frequency omega, the solitons may remain stable for large values of the group velocity in the linear core. Stable moving solitons are also found. They are produced by interaction of initially separated solitons, which shows a considerable spontaneous symmetry breaking in the case when the solitons attract each other.

From parametric gap solitons to chaos by means of second-harmonic generation in Bragg gratings

We review the theory of light localization due to the combined action of single or double Bragg coupling between dichromatic counterpropagating envelopes and parametric mixing nonlinearities. We discuss existence, stability, and excitation of such localized envelopes. We also investigate the link between stationary gap solitons and input-output response of nonlinear quadratic Bragg gratings. Frustrated transmission and multistable switching is expected to occur under suitable integrable (cascading) limits. Substantial deviations from these conditions lead to the onset of spatial chaos. (c) 2000 American Institute of Physics.

Dark and bright solitons in resonantly absorbing gratings

We consider an optical medium consisting of a periodic refractive-index grating and a periodic set of thin layers of two-level systems resonantly interacting with the electromagnetic field. Recently, it has been shown that such a system gives rise to a vast variety of stable bright solitons. In this work, we demonstrate that the system has another very unusual property: stable bright solitons can coexist with stable continuous-wave (cw) states and stable dark solitons (DS's). Depending on the parameters' values, a DS frequency band coexists (without overlap) with one or two bright-soliton bands. Quiescent (standing) DS's are found in an analytical form, and moving ones are obtained numerically. Simulations show that a considerable part of the DS solutions are completely stable against arbitrary small perturbations. The fact that this system supports both stable bright and dark solitons for the same parameters values may find interesting applications in photonics.