Showing papers by "Yuri S. Kivshar published in 2001"
TL;DR: In this paper, the authors consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe its collective modes, a nonlinear generalisation of the Hermite-Gauss eigenmodes of a harmonic oscillator.
169 citations
TL;DR: A physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals is revealed.
Abstract: We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.
135 citations
TL;DR: The existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect are analyzed and a novel type of stable nonlinear band-gap localized state is demonstrated.
Abstract: We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.
111 citations
TL;DR: Novel classes of optical vector solitons that consist of incoherently coupled self-trapped "necklace" beams carrying zero, integer, and even fractional angular momentum are introduced.
Abstract: We introduce novel classes of optical vector solitons that consist of incoherently coupled self-trapped ''necklace'' beams carrying zero, integer, and even fractional angular momentum. Because of the stabilizing mutual attraction between the components, such stationary localized structures exhibit quasistable propagation for much larger distances than the corresponding scalar vortex solitons and expanding scalar necklace beams.
100 citations
TL;DR: In this paper, the intensity distribution in an optical beam carrying a vortex and its helical wave front (color surface) was studied. But the authors focused on the distribution of the intensity in the optical beam.
Abstract: Intensity distribution in an optical beam carrying a vortex (mesh) and its helical wave front (color surface).
57 citations
TL;DR: In this article, a detailed analysis of gray spatial optical solitons in biased photorefractive media is provided, including their transverse velocity, spatial width, and phase profile.
Abstract: We provide a detailed analysis of gray spatial optical solitons in biased photorefractive media. The properties associated with these solitons, such as their transverse velocity, spatial width, and phase profile, are obtained as functions of their normalized intensity and degree of “grayness.” By employing the stability criterion based on the renormalized field momentum, we investigate the stability regions of gray spatial photorefractive solitons. The process of the soliton Y splitting arising from an initially even field depression is quasi-analytically described by use of a Hamiltonian formalism.
46 citations
TL;DR: In this paper, it was shown that the spinor Bose-Einstein condenstate may experience modulational instability of the ground state leading to a fragmentation of the spin domains.
Abstract: We demonstrate, analytically and numerically, that the ferromagnetic phase of the spinor Bose-Einstein condenstate may experience modulational instability of the ground state leading to a fragmentation of the spin domains. Together with other nonlinear effects in the atomic optics of ultracold gases (such as coherent photoassociation and four-wave mixing) this effect provides one more analogy between coherent matter waves and light waves in nonlinear optics.
45 citations
TL;DR: The theoretical and experimental results of the structure, formation, and instability development of the quadrupole vector solitons are presented.
Abstract: We introduce the concept of multipole spatial optical vector solitons associated with higher-order guided modes trapped by a soliton-induced waveguide in a bulk medium. Such stationary localized waves include previously predicted vortex- and dipole-mode vector solitons and also describe new higher-order vector solitons and necklace-type beams. We present the theoretical and experimental results of the structure, formation, and instability development of the quadrupole vector solitons.
41 citations
TL;DR: In this article, a mean-field model of an atomic Bose-Einstein condensate parametrically coupled to a molecular condensor via a Raman photoassociation process is presented.
Abstract: We analyze a mean-field model of an atomic Bose-Einstein condensate parametrically coupled to a molecular condensate via a Raman photoassociation process. We show that an interplay of nonlinear interspecies and intraspecies interactions leads to the formation of mutually trapped states of a hybrid condensate, which are spatially localized and dynamically stable even without a trap.
38 citations
TL;DR: A physical mechanism of fractal soliton scattering associated with multiparticle effects is revealed, and chaotic interaction of two breathers with incommensurable frequencies is demonstrated.
Abstract: We study in detail the interaction of composite solitary waves and consider, as an example, the breather collisions in a weakly discrete sine-Gordon equation. We reveal a physical mechanism of fractal soliton scattering associated with multiparticle effects, and demonstrate chaotic interaction of two breathers with incommensurable frequencies.
38 citations
TL;DR: An analytical stability criterion for the nonlinear localized modes is obtained and the case of a power-law nonlinearity in detail is considered in detail, including the mode decay or switching to a new stable state, and collapse at the impurity site.
Abstract: We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schr\"odinger equation and describe three types of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.
TL;DR: A wave-front splitting of the scattered wave develops into transverse modulational instability, "unzipping" the stripe into trains of vortices with opposite charges.
Abstract: We study linear and nonlinear wave scattering by an optical vortex in a self-defocusing nonlinear Kerr medium. In the linear case, we find a splitting of a plane-wave front at the vortex proportional to its circulation, similar to what occurs in the scattered wave of electrons for the Aharonov-Bohm effect. For larger wave amplitudes, we study analytically and numerically the scattering of a dark-soliton stripe (a nonlinear analog of a small-amplitude wave packet) by a vortex and observe a significant asymmetry of the scattered wave. Subsequently, a wave-front splitting of the scattered wave develops into transverse modulational instability, “unzipping” the stripe into trains of vortices with opposite charges.
TL;DR: It is demonstrated, theoretically and experimentally, that dipole-mode vector solitons created in biased photorefractive media possess a number of anisotropy-driven properties, such as stability of a selected orientation, wobbling, and incomplete rotation, owing to the anisotropic nonlocal response of the photoreFractive non-linearity.
Abstract: We demonstrate, theoretically and experimentally, that dipole-mode vector solitons created in biased photorefractive media possess a number of anisotropy-driven properties, such as stability of a selected orientation, wobbling, and incomplete rotation, owing to the anisotropic nonlocal response of the photorefractive nonlinearity. Such features are found for higher-order (multipole) vector solitons, and they are carefully verified in an experiment.
TL;DR: In this paper, the authors proposed a parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmoric wave that is collinear to the fundamental.
Abstract: We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discuss how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO3 and LiTaO3.
TL;DR: In this paper, the structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates are analyzed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process.
Abstract: The structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates is analyzed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process. New types of topological vortex states are predicted to exist in the coherently coupled two-component condensates even without a trap, and their nontrivial dynamics in the presence of losses is demonstrated.
TL;DR: In this paper, the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations was demonstrated. But the authors did not consider the non-integrable multi-component nonlinear models.
TL;DR: In this paper, the authors present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations.
Abstract: We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations. In particular, we demonstrate that the soliton internal modes are responsible for the appearance of the soliton instability, and outline an analytical approach based an a multi-scale asymptotic technique that allows to analyze the soliton dynamics near the marginal stability point. We also discuss some results of the rigorous linear stability analysis of fundamental solitary waves and nonlinear impurity modes. Finally, we demonstrate that multi-hump vector solitary waves may become stable in some nonlinear models, and discuss the examples of stable (1+1)-dimensional composite solitons and (2+1)-dimensional dipole-mode solitons in a model of two incoherently interacting optical beams.
TL;DR: In this article, a multistep cascading approach is applied to the problem of fourth-harmonic generation in a single quadratic crystal, and a new model of parametric wave mixing is analyzed in detail.
TL;DR: In this paper, a theory of modulational instability of multiparameter solitary waves and analysis of composite (or vector) optical solitons in a saturable nonlinear medium were developed.
Abstract: We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.
TL;DR: In this paper, the authors present numerical simulations for an effectively isotropic model and experimental results for a set of different combinations of a Gaussian beam co-propagating incoherently with a beam of a more complex internal structure, such as a higher order transverse laser mode.
Abstract: We review the generation of the recently predicted multi-component spatial optical solitons in a saturable nonlinear bulk medium. We present numerical simulations for an effectively isotropic model and experimental results for a set of different combinations of a Gaussian beam co-propagating incoherently with a beam of a more complex internal structure, such as a higher order transverse laser mode. We discuss the different formation processes and the general properties of a variety of different dipole-mode composite solitons and expand our investigations to the generation of a quadrupole-mode composite soliton.
TL;DR: A brief overview of the basic concepts of the theory of spatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models, can be found in this article.
Abstract: We present a brief overview of the basic concepts of the theory of spatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.
11 May 2001
TL;DR: It is shown that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discussed how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO(3) and LiTaO (3) .
Abstract: Summary form only given. Quasi-phase matching (QPM) (Fejer et al, 1992) is an established technique for efficient frequency conversion. QPM structures have a uniform refractive index, and a periodic quadratic nonlinearity. The nonlinearity is usually periodic in one direction, and is piecewise constant in strips. A two-dimensional generalization was recently proposed by Berger (Phys. Rev. Lett. vol. 81, p. 4136, 1998) and studied experimentally by Broderick et al (Phys. Rev. Lett. vol. 84, p. 4345, 2000). In Broderick's samples, the refractive index is again uniform, but the periodicity derives from a hexagonal lattice, with a single hexagon in each unit cell in which the nonlinearity is inverted. Using a fundamental wavelength of /spl lambda/=1533 nm, Broderick et al demonstrated efficient second harmonic (SH) generation, and also third and fourth harmonic (FH) generation, the latter of which is of importance here. FH generation occurred stepwise, but was not efficient since not all steps were phase matched. Saltiel et al (2000) proposed a scheme for efficient FH generation, in which, however, the fundamental and FH are not collinear. Other FH generation schemes either involve nonphase matched processes, two separate crystals, or rely on some property of the host's refractive index (Hooper et al, 1994; Pfister et al, 1997). Here, we discuss a scheme that makes use of a single nonlinear crystal, and in which the FH is collinear with the fundamental. The efficiency is also larger than in comparable schemes.
11 May 2001
TL;DR: In this article, a consistent theory of nonlinearity-induced self-trapping effects in 2D reduced-symmetry photonic crystals with a Kerr non-linearity was proposed.
Abstract: Summary form only given. A low-intensity light cannot propagate through a photonic bandgap (PBG) crystal if its frequency falls into a band gap. However, it has been recently suggested, in the framework of the couple-mode theory, that in the case of a two-dimensional (2D) periodic medium with a Kerr-type nonlinear high-intensity light with the frequency inside the gap can propagate in the form of finite energy solitary waves as 2D gap solitons, which are localized in both directions. Employing the technique based on Greens function, we develop a consistent theory of nonlinearity-induced self-trapping effects in 2D photonic crystals with a Kerr nonlinearity. As an example, we consider 2D reduced-symmetry photonic crystals which have recently attracted considerable interest because of their ability to possess larger absolute band gaps.
TL;DR: In this article, the effect of localized modes such as breathers on nonlinear optical properties of finite polyenes has been analyzed within a simple theoretical model and demonstrated analytically.
26 Mar 2001
TL;DR: In this article, the existence and stability of nonlinear guided waves in a periodic medium with a single or periodic array of non-linear layers is analyzed. And the authors describe novel types of stable nonlinear band-gap localized states, and reveal an important physical mechanism of the oscillatory wave instabilities associated with the bandgap resonances.
Abstract: We analyze the existence and stability of nonlinear guided waves in a periodic medium with a single or periodic array of nonlinear layers We describe novel types of stable nonlinear band-gap localized states, and also reveal an important physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances
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TL;DR: In this article, the authors describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability and low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals.
Abstract: We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides Employing the technique based on the Green function, we describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions
12 Apr 2001
TL;DR: In this paper, a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides was developed and employed for investigating the existence and properties of localized defect modes.
Abstract: We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D squarelattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.
TL;DR: In this paper, the existence and stability of nonlinear localized waves in a system described by the Kronig-Penney model with a nonlinear impurity was analyzed and new effects introduced by step-like periodicity of the medium parameters.
Abstract: We analyze the existence and stability of nonlinear localized waves in a system described by the Kronig-Penney model with a nonlinear impurity. First, we study the properties of such waves in a homogeneous medium, and then analyze new effects introduced by step-like periodicity of the medium parameters. In particular, we demonstrate the existence of a novel type of stable nonlinear band-gap localized states, and also reveal an important physical mechanism of the oscillatory wave instabilities of localized modes associated with the band-gap wave resonances.
01 Jan 2001
TL;DR: In this paper, two-step second-order (orχ(2): χ2) cascading provides an efficient way to generate an effective nonlinear phase shift for the purposes of all-optical nonlinear switching.
Abstract: It is well recognized that two-step second-order (orχ(2): χ(2) cascading provides an efficient way to generate an effective nonlinear phase shift for the purposes of all-optical nonlinear switching [1]. Cascading of χ(2) processes allows all-optical switching to be achieved at pump levels substantially lower than those usually available in centrosymmetric media with highest known cubic nonlinearity [2]. A further search for the methods allowing to reduce the switching power is crucial for the future applications of all-optical devices based on cascading of χ(2) processes. The switching intensity is usually connected with the input power density necessary for achieving a nonlinear phase shift (NPS) of the amount of π or π/2, depending of the type of the device. The larger is the efficiency of the NPS generation, the lower is the switching intensity. Some methods for an enhancement of the NPS in quadratic nonlinear media with two-step second-order cascading processes have been recently suggested in [3, 4].