Theory of Self-Trapped Spatially Incoherent Light Beams

Mitchell, Matthew; Segev, Mordechai; Coskun, Tamer H.; Christodoulides, Demetrios N.

doi:10.1103/physrevlett.79.4990

Cited by 237 publications

(147 citation statements)

References 19 publications

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“…The method and, correspondingly, both stability and instability results can be extended to other types of solitary waves, such as multi-component spatial solitons (e.g., incoherent solitons) in non-Kerr (e.g., saturable) media, parametric solitary waves in quadratic (or χ (2) ) optical media, etc. In all such cases, our stability and instability results (i)-(iv) can be readily generalized with a rigorous proof of some of the previously known results of the asymptotic multi-scale expansion theory.…”

Section: Discussionmentioning

confidence: 99%

Stability criterion for multicomponent solitary waves

Pelinovsky

Kivshar

2000

Phys. Rev. E

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We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of N incoherently coupled nonlinear Schrödinger 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 multi-component 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.

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Section: Discussionmentioning

confidence: 99%

Stability criterion for multicomponent solitary waves

Pelinovsky

Kivshar

2000

Phys. Rev. E

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“…Moreover, the full set of the time-dependent HFB equations was used in Ref. [528] to show that the matter flux from the condensate to the thermal cloud may cause the bright matter-wave solitons to split into two solitonic fragments (each of them is a mixture of the condensed and non-condensed particles); these may be viewed as partially incoherent solitons, similar to the ones known in the context of nonlinear optics [529,530]. Partially incoherent lattice solitons at a finite temperature T were also predicted to exist in Ref.…”

Section: Beyond Mean-field Descriptionmentioning

confidence: 99%

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

2008

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Abstract. The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45 • EP: Ermakov-Pinney (Equation)• GP: Gross-Pitaevskii (Equation)• KdV: Korteweg-de Vries (Equation)• LS: Lyapunov-Schmidt (Technique)• MT: Magnetic Trap• NLS: Nonlinear Schrödinger (Equation)• NPSE: Non-polynomial Schrödinger Equation IntroductionThe phenomenon of Bose-Einstein condensation is a quantum phase transition originally predicted by Bose [1] and Einstein [2,3] in 1924. In particular, it was shown that below a critical transition temperature T c , a finite fraction of particles of a boson gas (i.e., whose particles obey the Bose statistics) condenses into the same quantum state, known as the Bose-Einstein condensate (BEC). Although BoseEinstein condensation is known to be a fundamental phenomenon, connected, e.g., to superfluidity in liquid helium and superconductivity in metals (see, e.g., Ref.[4]), BECs were experimentally realized 70 years after their theoretical prediction: this major achievement took place in 1995, when different species of dilute alkali vapors confined in a magnetic trap (MT) were cooled down to extremely low temperatures [5][6][7], and has already been recognized through the 2001 Nobel prize in Physics [8,9]. This first unambiguous manifestation of a macroscopic quantum state in a manybody system sparked an explosion of activity, as reflected by the publication of several thousand papers related to BECs since then. Nowadays there exist more than fifty experimental BEC groups around the world, while an enormous amount of theoretical work has followed and driven the experimental efforts, with an impressive impact on many branches of Physics.From a theoretical standpoint, and for experimentally relevant conditions, the static and dynamical properties of a BEC can be described by means of an effective mean-field equation known as the Gross-Pitaevskii (GP) equation [10,11]. This is a variant of the famous nonlinear Schrödinger (NLS) equation [12] (incorporating an external potential used to confine th...

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“…We note finally, that fully incoherent solitons as recently shown experimentally [10], and analyzed theoretically [11,12], where a beam of incoherent light is self-trapping due to a nonlinearity. The solitons reported here are, however, more similar to the coherent ones [4,5]: only a small incoherent part of the radiation appears due to a scattering of coherent light on the random potential.…”

Section: Discussionmentioning

confidence: 99%

Spatial solitons and Anderson localization

Staliūnas

2003

Phys. Rev. A

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Stochastic (Anderson) localization is the spatial localization of the wave-function of quantum particles in random media. We show, that a corresponding phenomenon can stabilize spatial solitons in optical resonators: spatial solitons in resonators with randomly distorted mirrors are more stable than in perfect mirror resonators. We demonstrate the phenomenon numerically, by investigating solitons in lasers with saturable absorber, and analytically by deriving and analyzing coupled equations of spatially coherent and incoherent field components.

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Theory of Self-Trapped Spatially Incoherent Light Beams

Cited by 237 publications

References 19 publications

Stability criterion for multicomponent solitary waves

Stability criterion for multicomponent solitary waves

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

Spatial solitons and Anderson localization

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