Showing papers by "Yuri S. Kivshar published in 1997"
TL;DR: In this paper, the authors characterize dark-type vector optical solitons of arbitrary polarization in isotropic, Kerr-type media by applying Hirota's method to the integrable Manakov model with a defocusing nonlinearity.
Abstract: We characterize dark-type vector optical solitons of arbitrary polarization in isotropic, Kerr-type media by applying Hirota's method to the integrable Manakov model with a defocusing nonlinearity We find that nonuniformly polarized solitons comprise a rich solution family that can be divided into two categories: dark-dark and dark-bright vector solitons We consider the propagation dynamics and the interactions of these vector solitons by deriving multisoliton solutions, and show the existence of stationary bound states, a phenomenon not observed for scalar dark solitons
180 citations
TL;DR: In this article, the authors provided a comprehensive experimental and theoretical study of incoherently coupled photorefractive spatial-soliton pairs in all three possible realizations: bright-bright, dark-dark, and dark-bright.
Abstract: We provide a comprehensive experimental and theoretical study of incoherently coupled photorefractive spatial-soliton pairs in all three possible realizations: bright–bright, dark–dark, and dark–bright. We also show that when the total intensity of two coupled solitons is much lower than the effective dark irradiance, the coupled soliton pair is reduced to Manakov solitons. In all cases, mutual trapping of both components in the coupled soliton pair is verified by analyzing, experimentally and numerically, the beam evolution after decoupling.
138 citations
TL;DR: In this article, it was shown that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic medium is strongly influenced by induced Kerr effects, such as self-and cross-phase modulation.
Abstract: We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or ${\ensuremath{\chi}}^{(2)}$) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog of the guided-center soliton) supported by the quadratic and induced cubic nonlinearities.
119 citations
TL;DR: It is shown that resonant wave mixing that is due to quadratic non linearity can support stable bright spatial solitons, even in the most counterintuitive case of a bulk medium with defocusing Kerr nonlinearity.
Abstract: We show that resonant wave mixing that is due to quadratic nonlinearity can support stable bright spatial solitons, even in the most counterintuitive case of a bulk medium with defocusing Kerr nonlinearity We analyze the structure and stability of such self-guided beams and demonstrate that they can be generated from a Gaussian input beam, provided that its power is above a certain threshold
47 citations
TL;DR: In this paper, the authors reveal that three-wave parametric mixing in a diffractive quadratic medium can lead to multistability of self-guided beams, and that switching between different stable states of these multivalued spatial solitary waves is also demonstrated.
Abstract: We reveal that three-wave parametric mixing in a diffractive quadratic (or {chi}{sup (2)}) medium can lead to multistability of self-guided beams. Switching between different stable states of these multivalued spatial solitary waves is also demonstrated. {copyright} {ital 1997} {ital The American Physical Society}
38 citations
TL;DR: In this paper, a comparison between the experimental data on the structure and motion of vortex solitons created as localized structures in a diffracting Gaussian beam and the theory based on the generalized nonlinear Schrodinger equation is made.
Abstract: We present a brief overview of recent experimental and theoretical results on optical vortex solitons (in particular, those recently obtained at the Australian National University). Special attention is paid to a direct comparison between the experimental data on the structure and motion of vortex solitons created as localized structures in a diffracting Gaussian beam and the theory based on the generalized nonlinear Schrodinger equation. We also analyze, for the first time to our knowledge, the effect of strong nonlinearity saturation on the transverse (or snake-type) instability of a dark-soliton stripe and show that saturation leads to a drastic suppression of the instability.
35 citations
TL;DR: In this paper, the authors consider a generalized Frenkel-Kontorova model, describing the dynamics of a chain of particles in a periodic substrate potential, and analyze the effect of discreteness on the existence and properties of internal modes of kinks, topological excitations of the chain.
Abstract: We consider a generalized Frenkel-Kontorova model, describing the dynamics of a chain of particles in a periodic substrate potential, and analyze the effect of discreteness on the existence and properties of internal ~or shape! modes of kinks, topological excitations of the chain. In particular, we show that kink’s internal modes can appear not only below but also above the phonon spectrum band and, in the latter case, the localized mode describes out-of-phase oscillations of the kink’s shape. For the sinusoidal on-site potential, when the model is described by the discrete sine-Gordon equation, we reveal, in sharp contrast with the continuum limit, the existence of the kink’s internal mode in a narrow region of the discreteness parameter. We apply two different analytical techniques to describe the cases of weak and strong coupling between particles, explaining qualitatively and even quantitatively the main features of the kink oscillations observed in numerical simulations. We also discuss the effect of nonlinearity on the existence and properties of kink’s internal modes and show, in particular, that a nonlinearity-induced frequency shift of the lattice vibrations can lead to the creation of the nonlinear kink’s internal modes, which, however, slowly decay due to a generation of radiation through higher-order harmonics. @S1063-651X~97!11010-8#
34 citations
TL;DR: In this paper, the authors give a comprehensive summary of the results on self-guided beams, bright spatial solitary waves, emphasizing the most recent advances and emphasizing that all spatial solitons are generically the same, independent of the type of nonlinear medium, and such free-propagating beams can execute interesting dynamics, including spiraling around one another, self-tapering, periodically changing their shape, cross section, or polarization, and inelastically colliding to annihilate one another.
Abstract: We give a comprehensive summary of the results on self-guided beams, bright spatial solitary waves, emphasizing the most recent advances. To be stable in a bulk medium, such beams should propagate in a non-Kerr medium. It is emphasized that all spatial solitons are generically the same, independent of the type of nonlinear medium, and such free-propagating beams can execute interesting dynamics, including spiraling around one another, self-tapering, periodically changing their shape, cross section, or polarization, and inelastically colliding to annihilate one another, fuse, or create a new beam. Most of these types of solitary-wave dynamics have recently been confirmed experimentally for self-guided beams propagating in different non-Kerr materials. Significantly, there exists no temporal analog (e.g., for pulse propagation in fibers) even for stationary spatial solitons of a bulk medium.
30 citations
TL;DR: It is shown that one-dimensional parametric spatial solitons undergo temporal instability that leads to their breakup into spatiotemporal patterns with a characteristic snakelike shape.
Abstract: We show that one-dimensional parametric spatial solitons undergo temporal instability that leads to their breakup into spatiotemporal patterns with a characteristic snakelike shape.
28 citations
TL;DR: In this article, the authors analyze (1+1)-and (2+1-) self-guided beams (spatial solitons) due to three-wave parametric mixing (or type II second-harmonic generation) in diffractive optical materials with χ(2) nonlinearity.
Abstract: We analyze (1+1)- and (2+1)-dimensional self-guided beams (spatial solitons) due to three-wave parametric mixing (or type II second-harmonic generation) in diffractive optical materials with χ(2) nonlinearity We also discuss the optimal conditions for observing self-trapping in different experimental geometries
27 citations
TL;DR: The concept of soliton internal mode is introduced to explain quantitatively the long-lived oscillations of self-guided beams, or breathing spatial solitons, and it is shown that the existence of the internal mode affects strongly the beam propagation in non-Kerr media, leading to oscillatory dependence of the output width of the beam versus its input power.
Abstract: The concept of soliton internal mode is introduced to explain quantitatively the long-lived oscillations of self-guided beams, or breathing spatial solitons. Cubic–quintic nonlinearity is considered in detail, and it is shown that the existence of the internal mode affects strongly the beam propagation in non-Kerr media, leading to oscillatory dependence of the output width of the beam versus its input power.
TL;DR: In this article, stable nonlinear localized modes can exist not only at a light-mass isotopic impurity, but also at a heavy-mass impurity due to an interplay between discreteness and nonlinearity.
Abstract: We demonstrate that stable nonlinear localized modes can exist not only at a light-mass isotopic impurity, but also at a heavy-mass impurity, due to an interplay between discreteness and nonlinearity. This is in sharp contrast to the theory of linear lattice vibrations that an impurity mode is possible only at a light-mass defect. We determine the structure of the nonlinear impurity modes analytically using a four-particle approximation, and confirm the stability by direct numerical simulations.
TL;DR: A power threshold for the existence of two-frequency spatial solitons is found, and the multistability of solitary waves in a Kerr medium owing to a higher-order nonlinear phase shift caused by cascaded third-order processes is revealed.
Abstract: The effect of phase-matched third-harmonic generation on the structure and stability of spatial solitary waves is investigated. A power threshold for the existence of two-frequency spatial solitons is found, and the multistability of solitary waves in a Kerr medium owing to a higher-order nonlinear phase shift caused by cascaded third-order processes is revealed.
TL;DR: In this article, the stability of one-parameter families of ground-state planar SHG solitons has been investigated, and it is shown that the development of the instability leads either to the formation of lattices of higher dimensions, or to the complete disintegration of the soliton.
Abstract: For three decades optical spatial solitons confined in the transverse plane were commonly believed to be a prerogative of media with cubiclike nonlinearities @1#. A remarkable exception is the work carried out in Ref. @2#, where the possibility to achieve diffraction-free propagation via threephoton interactions in quadratic media ~henceforth, parametric solitons! was first pointed out. The field of quadratic solitons has acquired importance only recently @3#, also stimulated by experiments in second-harmonic generation ~SHG! in bulk media ~211 dimensions! and planar waveguides ~111 dimensions! @4#. Since the parametric solitons are strictly speaking solitary waves ~the model equations are not integrable!, a crucial issue is their stability. Two main types of instabilities can be distinguished: ~i! longitudinal instability against perturbations that share the soliton symmetry @5#; ~ii! symmetrybreaking instabilities ~reminiscent of modulational instabilities of plane-waves @6#!, that take place whenever the solitons are embedded in a higher dimensional ‘‘space’’ with respect to the subspace in which they are localized @7,8#. For the former type of problem, stability criteria have been recently developed @5#, through asymptotic techniques @9#: both ~111!and ~211!-dimensional parametric solitons are stable in the largest portion of their existence domain in the parameter space. Moreover, the global stability ~no collapse! of ~211!and ~311!-dimensional parametric solitons and bullets is supported by the Liapunov-type stability analysis @10#. Conversely, the symmetry breaking of parametric solitons is still an open issue, even though the problem has been widely studied for cubic media @7#. Here we investigate the stability of the whole one-parameter families of ground-state planar SHG solitons. We anticipate that the development of the instability leads either to the formation of lattices of higher dimensional solitons, or to the complete disintegration ~radiative decay! of the soliton. The transverse instability of soliton stripes belongs to the former case, whereas the dynamics of temporal instabilities of both ~111!and ~211!dimensional solitons depends on the dispersive regime. Our results are of great importance for recent experiments in transverse pattern formation occurring via SHG @11,12#. In particular, the filamentation of beams with strongly elliptical cross sections ~i.e., pseudostripe! was already observed @11#, using nonsoliton input conditions ~i.e., SHG from the funda-
10 Nov 1997
TL;DR: In this paper, phase-matched third-harmonic generation in a Kerr medium leads to a power threshold for the existence of two-frequency spatial solitons while cascading of third-order processes causes a higher-order phase shift and multistability of solitary waves.
Abstract: We show that phase-matched third-harmonic generation in a Kerr medium leads to a power threshold for the existence of two-frequency spatial solitons while cascading of third-order processes causes a higher-order phase shift and multistability of solitary waves.