Showing papers by "Yuri S. Kivshar published in 2000"
TL;DR: In this article, the authors discuss self-focusing of spatial optical solitons in diffractive nonlinear media due to either transverse (one more unbounded spatial dimension) or modulational (induced by temporal wave dispersion) instabilities, in the framework of the cubic nonlinear Schrodinger equation and its generalizations.
356 citations
07 May 2000
TL;DR: In this paper, the authors consider the Bose-Einstein condensate (BEC) dynamics in a harmonic double-well potential, and derive the dynamical coupled-mode equations, valid for any value of the well separation.
Abstract: Summary form only given. A system of interacting bosons confined within an external potential at zero temperature can be described by a macroscopic wave function having the meaning of an order parameter and satisfying the nonlinear Gross-Pitaevskii (GP) equation. In such a system, single-particle states form a set of nonlinear collective modes corresponding to the ground and higher-order (excited) macroscopic states of the Bose-Einstein condensate (BEC) in a trap. We analyse the mode coupling and intermodal population exchange in trapped BECs. We consider the BEC dynamics in a harmonic double-well potential, and derive the dynamical coupled-mode equations, valid for any value of the well separation. Our model can describe both the Josephson tunneling between weakly interacting condensates and effective Rabi oscillations in two component BECs.
155 citations
TL;DR: This work reports on the first experimental observation of a two-dimensional dipole-mode vector solitons and demonstrates a decay of an unstable vortex-mode soliton into a robust Dipole- mode soliton in a SBN crystal.
Abstract: We report on the first experimental observation of a novel type of optical vector soliton, a dipole-mode soliton, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.
97 citations
TL;DR: Different geometries of the waveguides created by an array of nonlinear dielectric rods embedded into an otherwise perfect linear 2D photonic crystal are considered, and it is demonstrated that the effective interaction in such waveguide is nonlocal.
Abstract: We develop the theory of nonlinear localized modes (intrinsic localized modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods embedded into an otherwise perfect linear 2D photonic crystal, and demonstrate that the effective interaction in such waveguides is nonlocal, being described by a nonlinear lattice model with long-range coupling and nonlocal nonlinearity. We reveal the existence of different types of nonlinear guided mode that are also localized in the waveguide direction, and describe their unique properties, including bistability.
93 citations
TL;DR: New type of optical vector soliton that originates from trapping of a dipole mode by the soliton-induced waveguides is found and represents a new type of extremely robust nonlinear vector structure.
Abstract: We find a new type of optical vector soliton that originates from trapping of a dipole mode by the soliton-induced waveguides. These solitons, which appear as a consequence of the vector nature of the two-component system, are more stable than the previously found optical vortex solitons and represent a new type of extremely robust nonlinear vector structure.
92 citations
TL;DR: In this article, a new advanced space and time-resolved Brillouin light scattering (BLS) technique is used to study diffraction of two-dimensional beams and pulses of dipolar spin waves excited by strip-line antennas in tangentially magnetized garnet films.
Abstract: A new advanced space- and time-resolved Brillouin light scattering (BLS) technique is used to study diffraction of two-dimensional beams and pulses of dipolar spin waves excited by strip-line antennas in tangentially magnetized garnet films. The new technique is an effective tool for investigations of two-dimensional spin wave propagation with high spatial and temporal resolution. Linear effects, such as the unidirectional exci-tation of magnetostatic surface waves and the propagation of backward volume magnetostatic waves (BVMSW) in two preferential directions due to the non-collinearity of their phase and group velocities are investigated in detail. In the nonlinear regime stationary and non-stationary self-focusing effects are studied. It is shown, that non-linear diffraction of a stationary BVMSW beam, having a finite transverse aperture, leads to self-focusing of the beam at one spatial point. Diffraction of a finite-duration (non-stationary) BVMSW pulse leads to space-time self-focusing and formation of a strongly localized two-dimensional wave packet (spin wave bullet). Numerical modeling of the diffraction process by using a variational approach and direct numerical integration of the two-dimensional non-linear Schrodinger equation provides a good qualitative description of the observed phenomena.
74 citations
TL;DR: A new type of photonic structure is suggested to achieve simultaneous generation of several harmonics and both general analytical results and design parameters for 2D periodically poled LiNbO(3) structures are presented.
Abstract: We analyze harmonic generation in a two-dimensional (2D) χ2 photonic crystal and demonstrate the possibility of multiple phase matching and multicolor parametric frequency conversion. We suggest a new type of photonic structure to achieve simultaneous generation of several harmonics; we also present both general analytical results and design parameters for 2D periodically poled LiNbO3 structures.
69 citations
TL;DR: For a periodic lattice of nonlinear interfaces, an effective discrete model is derived for the amplitudes of the fundamental and second-harmonic waves at the interfaces and the spatially localized solutions are found--discrete gap solitons.
Abstract: We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or ${\ensuremath{\chi}}^{(2)})$ nonlinear interfaces embedded in a linear layered structure---a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete ${\ensuremath{\chi}}^{(2)}$ equations) and find, numerically and analytically, the spatially localized solutions---discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media.
42 citations
TL;DR: Both fundamental and first-order guided modes are analyzed, as well as cases of effective defocusing and focusing nonlinearity.
Abstract: We study, numerically and analytically, linear and nonlinear waveguides induced by optical vortex solitons in a Kerr medium. Both fundamental and first-order guided modes are analyzed, as well as cases of effective defocusing and focusing nonlinearity.
42 citations
TL;DR: In this article, a general stability criterion is derived for the ground states of the Gross-Pitaevskii equation, which describes attractive Bose-Einstein condensates confined in a magnetic trap.
Abstract: A general stability criterion is derived for the ground states of the Gross-Pitaevskii equation, which describes attractive Bose-Einstein condensates confined in a magnetic trap. These ground states are shown to avoid the collapse in finite time and are proven to be stable in two and three spatial dimensions. Experimental observation of Bose-Einstein condensation ~BEC! in ultracold atomic clouds @1# has stimulated a new direction in the study of macroscopic quantum phenomena. Basically, the interaction between two confined bosons in a condensate is determined by the s-wave scattering length a and it can be either repulsive ( a.0) or attractive ( a,0). Although first BEC experiments were commonly realized with gases promoting a positive scattering length, trapped 7 Li atom gases, which are characterized by a negative scattering length, have raised an increasing interest @2# justified by the rich and complex dynamics mixing instability and generation of solitonlike structures, which substantially alters the formation of condensates. Furthermore, experimental results @3# suggested the possibility of using so-called Feshbach resonances to continuously detune a from positive to negative values by means of an external magnetic field, which brings insight into the experimental realization of BEC’s with attractive interactions.
39 citations
TL;DR: The most general matrix criterion for stability and instability of multicomponent solitary waves is obtained by considering a system of N incoherently coupled nonlinear Schrodinger equations and it is proved that unstable eigenvalues of the linear stability problem for multicomponents solitary waves are connected with negative eigen values of the Hessian matrix.
Abstract: We obtain the most general matrix criterion for stability and instability of multicomponent solitary waves by considering a system of N incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained variational problem which is reduced to finite-dimensional linear algebra. We prove that unstable (all real and positive) eigenvalues of the linear stability problem for multicomponent solitary waves are connected with negative eigenvalues of the Hessian matrix. The latter is constructed for the energetic surface of N-component spatially localized stationary solutions.
TL;DR: Experimental observation of bound states formed by two well-separated vector spatial solitons as the result of a force balance between vector-soliton components and a link between such soliton bound states and two-hump, two-modesolitons is demonstrated.
Abstract: We report experimental observation of bound states formed by two well-separated vector spatial solitons as the result of a force balance between vector-soliton components. We also demonstrate a link between such soliton bound states and two-hump, two-mode solitons, along with the induced coherence effect observed for incoherently interacting solitons.
TL;DR: This work identifies families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describes their properties analytically and numerically.
Abstract: We address the problem of the existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of 2+1-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.
07 May 2000
TL;DR: A multiscale asymptotic theory is developed to predict the main effect of the interaction of an optical vortex soliton with a dark-soliton stripe in a bulk nonlinear defocusing medium and is tested experimentally, observing vortex-induced stripe bending, development of the transverse instability, and stripe breakup.
Abstract: Summary form only given. Recently, different types of the soliton transverse instabilities have been observed experimentally for photorefractive, saturable gaseous, and quadratic media. In particular, Tikhonenko et al. reported the observation of pairs of optical vortex solitons generated due to the transverse instability of a dark-soliton stripe. Here, we study a different scenario of the soliton instabilities and put the following question: What is a result of interaction of dark solitons of different dimensions, i.e. a (1+1)-dimensional dark soliton (dark-soliton stripe) and a (2+1)-dimensional dark soliton of radial symmetry (vortex soliton)?.
TL;DR: In this article, the analytical theory of multikinks for strongly dispersive nonlinear systems was developed for weakly discrete sine-Gordon models and generalized Frenkel-Kontorova models.
Abstract: We develop the analytical theory of multikinks for strongly dispersive nonlinear systems, considering the examples of the weakly discrete sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise parabolic potential We reveal that there are no $2\ensuremath{\pi}$ kinks for this model, but there exist discrete sets of $2\ensuremath{\pi}N$ kinks for all $Ng1$ We also show their bifurcation structure in driven damped systems
TL;DR: Predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-v vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.
Abstract: We analyze two-component spatial optical vortex solitonssupported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a ‘‘halo-vortex,’’ consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a ‘‘ring-vortex’’ soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.
TL;DR: In this article, the authors discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics and describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high-performance computer networks, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase matching in Fibonacci optical superlattices.
Abstract: We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high-performance computer networks, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices.
TL;DR: In Ref. as mentioned in this paper, the formula for k 2 should be k 2 2pn 2 ͞l 2, and on p. 1205, f irst column, first paragraph, d should be d ͒ ͓͑p 2 1 q 2 1 pq͒͞3͔ 1͞2, Dk 2 ǫ jk 2 2 2k 1 j.
Abstract: In Ref. 1: 1. On p. 1204, second column, last paragraph, the formula for k 2 should be k 2 2pn 2 ͞l 2. 2. On p. 1205, f irst column, first paragraph, the formula for d should be d ͑4p͞Dk 2 ͒ ͓͑p 2 1 q 2 1 pq͒͞3͔ 1͞2 , Dk 2 jk 2 2 2k 1 j .
TL;DR: In this article, a cascading parametric interaction for generating a nonlinear phase shift in dielectric media with a quadratic nonlinear response based on two-frequency wave mixing of the fundamental and second-harmonic waves was proposed.
Abstract: We propose a novel type of cascading parametric interaction for generating a nonlinear phase shift in dielectric media with a quadratic nonlinear response based on two-frequency wave mixing of the fundamental and second-harmonic waves. Self-phase modulation of the fundamental wave results from a cascading process consisting of four second-order subprocesses, the direct and reverse subprocesses of Type I second-harmonic generation (SHG) and the direct and reverse subprocesses of Type II SHG. It is found analytically and numerically that the fundamental wave passing through a quadratic medium, tuned for simultaneous near phase matching for these two processes, collects 60% more nonlinear phase shift than does the corresponding two-step cascading. We also obtain the conditions for stationary waves (nonlinear modes) supported by such multistep cascading processes.
06 Aug 2000
TL;DR: In this paper, the first experimental observation of a two-dimensional dipole-mode vector solitons was reported, where a decay of an unstable vortex-mode soliton into a robust dipole mode vector soliton in a SBN crystal was demonstrated.
Abstract: We report on the first experimental observation of a two-dimensional dipole-mode vector solitons We demonstrate a decay of an unstable vortex-mode soliton into a robust dipole-mode soliton in a SBN crystal
01 Jan 2000
TL;DR: In this article, the authors discuss several physical systems where the nonlinear dynamics of topological defects is described by quasi-one-dimensional kink solutions of the generalized Frenkel-Kontorova model and its continuous approximations (the sine-Gordon equation).
Abstract: We discuss several physical systems, where the nonlinear dynamics of topological defects is described by quasi-one-dimensional kink solutions of the generalized Frenkel-Kontorova model and its continuous approximations (the sine-Gordon equation). This includes dislocations, long Josephson junctions, magnetic chains, adsorbed layers of atoms, hydrogen-bonded chains, DNA-type chains, etc.We briefly review different properties of kinks and describe experimental verifications of kink dynamics.
01 Jan 2000
TL;DR: In this paper, a brief overview of different methods for simultaneous phase-matching of several parametric optical processes (the so-called multistep cascading) in engineered structures with the modulated second-order nonlinear susceptibility is presented.
Abstract: We present a brief overview of different methods for simultaneous phase-matching of several parametric optical processes (the so-called multistep cascading) in engineered structures with the modulated second-order nonlinear susceptibility. In particular, we discuss the possibility of double phase-matching in both uniform and non-uniform quasi-phase-matched (QPM) periodic optical superlattices and also in the recently fabricated two-dimensional nonlinear photonic crystals. We include also some original results demonstrating the possibility to achieve double-phase-matching with phase-reversed and periodically chirped QPM structures and also with uniform QPM structures in non-collinear geometry. 2 χ ) intensity-dependent response of a transparent dielectric medium are usually associated with p arametric frequency conversion such as the second- harmonic generation (SHG). However, recent theoretical and experimental results demonstrate that quadratic nonlinearities can also produce many of the effects attributed to non resonant Kerr nonlinearities via ca scading of several second-order parametric processes. Such second-order cascading (SOC) effects can simulate the e ffective third-order processes and, in p articular, those associated with the intensity-dependent change of the medium refractive index (1). Importantly, the effective (or induced) cubic nonlinearity resulting from SOC in a quadratic medium can b e of the several orders of magnitude higher than that usually measured in centrosymmetric Kerr-like nonlinear media, and it i s practically instantaneous. The simplest t ype of SOC is based on the simultaneous action of two second-order parametric sub-processes that belong to a single second-order interaction. For example, the so-called two-step cascading associated with type I second-harmonic generation includes the generation of the second harmonic (SH),
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TL;DR: In this article, the scattering properties of optical dipole-mode vector solitons were investigated and it was shown that such a radially asymmetric composite self-trapped state resembles a molecule of light, which is extremely robust, survives a wide range of collisions, and displays new phenomena such as the transformation of a linear momentum into an angular momentum.
Abstract: We study the scattering properties of optical dipole-mode vector solitons recently predicted theoretically and generated in a laboratory. We demonstrate that such a radially asymmetric composite self-trapped state resembles ``a molecule of light'' which is extremely robust, survives a wide range of collisions, and displays new phenomena such as the transformation of a linear momentum into an angular momentum, etc.We present also experimental verifications of some of our predictions.
07 May 2000
TL;DR: In this paper, a detailed analysis of the properties of gray photorefractive solitons involved in this Y-junction formation is provided, which requires an in-depth understanding of the underlying soliton Y-splitting process.
Abstract: Summary form only given. Recently, soliton splitting has been successfully used to write permanent Y-waveguide structures (3-dB splitters) in the bulk of a photorefractive crystal. Such Y-junctions can then be employed to guide other intense beams at less photosensitive wavelengths (/spl sim/1.5 /spl mu/m) or can be permanently impressed (fixed) into the crystalline lattice. An investigation of the properties of these Y-junction waveguides requires an in-depth understanding of the underlying soliton Y-splitting process. During this process two gray photorefractive solitons are emitted in opposite transverse directions so as to conserve the overall linear momentum of the system. In what follows we provide a detailed analysis of the properties of gray photorefractive solitons involved in this Y-junction formation.
01 Jan 2000
TL;DR: A brief overview of the recent advances in the theoretical and experimental study of self-focusing and self-trapping of light is given in this paper, where different types of solitons and their stability are discussed.
Abstract: A brief overview of the recent advances in the theoretical and experimental study of self-focusing and self-trapping of light is given. Physical mechanisms of self-trapping and different types of self-trapped beams, spatial optical solitons, and their stability are discussed including solitons of non-Kerr media, self-trapped beams and their spiralling in photorefractive crystals, multi-hump solitons and solitonic gluons, discrete solitons in wave guide arrays, etc. A brief summary of the earlier and more recent experimental observations of spatial solitons, transverse instabilities, and soliton interactions is included as well.
23 Mar 2000
TL;DR: In this paper, the authors analyze the properties of vortex solitons generated in Kerr and non-Kerr nonlinear optical media, including the vortex drift and rotation into a diffracting Gaussian beam.
Abstract: We analyze the properties of vortex solitons generated in Kerr and non-Kerr nonlinear optical media, including the vortex drift and rotation into a diffracting Gaussian beam. We also present our recent analytical and experimental results on the vortex-induced break-up of a dark-soliton stripe, and discuss a connection of this phenomenon with the well-known Aharonov-Bohm effect in solids.
06 Aug 2000
TL;DR: In this article, a novel type of extremely robust optical vector soliton originates from trapping of a dipole (HG/sub 01/-type) mode by a soliton-induced waveguide.
Abstract: We predict theoretically a novel type of an extremely robust optical vector soliton that originates from trapping of a dipole (HG/sub 01/-type) mode by a soliton-induced waveguide. As a specific example, we consider two incoherently interacting optical beams propagating along the direction z in a bulk saturable medium. The model describes, in the isotropic approximation, solitons in photorefractive materials.
07 May 2000
TL;DR: In this paper, the authors analyzed the stationary localised pulses of the WDM model and provided a deep insight into the physics of the shepherding effect, where the two co-propagating pulses are widely separated, each pulse propagates independently as if without the presence of the other pulse.
Abstract: Summary form only given.The successful design of low-loss dispersion-shifted and dispersion-flattened optical fibers with low dispersion over a relatively large wavelength range can be used to reduce or completely eliminate the group-velocity mismatch for the multi-channel WDM systems. If the two co-propagating pulses are widely separated, each pulse propagates independently as if without the presence of the other pulse. However, they can be brought significantly closer to each other by the launching of another pulse on a separate wavelength with the proper magnitude and at the proper time. This pulse is called the shepherd pulse because of its shepherding behavior on the other pulses. We analyse these nonlinear modes, the stationary localised pulses of the WDM model, and provide a deep insight into the physics of the shepherding effect.