Self-Trapping of Partially Spatially Incoherent Light

Mitchell, Matthew; Chen, Zhigang; Shih, Ming-Feng; Segev, Mordechai

doi:10.1103/physrevlett.77.490

Cited by 435 publications

(242 citation statements)

References 17 publications

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“…From physical experiment(cf. [12]), two dimensional photorefractive screening solitons and a two dimensional self-trapped beam were observed. It is natural to believe that there are two dimensional multi-component solitons and self-trapped beams.…”

Section: Introductionmentioning

confidence: 98%

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Lin

Wei

2006

Physica D: Nonlinear Phenomena

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Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrödinger equations (NLSE). Here we consider simultaneous blow-up solutions of two-component system of self-focusing NLSE. By studying the associated self-similar solutions, we prove two components of solutions blow up at the same time. These self-similar solutions may come from solitary wave solutions with multi-bumps forming abundant geometric patterns which cannot be found in one-component self-focusing NLSE. Our results may provide the first step to investigate optical turbulence in two-component system of NLSE.

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Section: Introductionmentioning

confidence: 98%

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Lin

Wei

2006

Physica D: Nonlinear Phenomena

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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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“…The closure is, however, possible noticing that the scattered field components are proportional to the total scattered field, within the limit of smallness used: The system (14) describes the dynamics of the coupled coherent and incoherent parts of the radiation. Its form is completely analogous to the equation system derived for harmonic potential (7.a), (10). The system (14) is straightforwardly extendable to 2D case (by substituting spatial derivatives by Laplace operators).…”

Section: Coherent -Incoherent Field Decompositionmentioning

confidence: 91%

“…In [8] and [9] the original Turing pattern formation mechanism was generalized to diffracting fields, and in general to nonlocal fields, where nonlocality can be caused by diffusion as well as by diffraction, or both. (10) shows that one encounters here the generalized Turing pattern formation mechanism, where the net diffraction of harmonic field components plays the role of a nonlocality.…”

Section: C) Homogeneous (Solid Line) and Harmonic (Dashed And Point mentioning

confidence: 99%

“…The system of coupled equations for homogeneous field component (7.a) and for the harmonic field components (10) gives an interpretation for the stabilization of spatial solitons. The system (7.a), (10) can be identified with the Turing equation system for local activator and lateral inhibitor [7]. A more recent analysis show that a diffusion of the inhibitor field (in particular the diffusion of population inversion field of a laser in [8]), as well as a diffraction of the inhibitor field (in particular the diffraction of the pump field of optical parametric oscillators in [9]) leads to the enhancement of the modulational instability, and consequently, to stabilization of spatial solitons.…”

Section: C) Homogeneous (Solid Line) and Harmonic (Dashed And Point mentioning

confidence: 99%

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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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Self-Trapping of Partially Spatially Incoherent Light

Abstract: We report the first observation of self-trapping of a spatially incoherent optical beam in a nonlinear medium. Self-trapping occurs in both transverse dimensions, when diffraction is exactly balanced by photorefractive self-focusing. [S0031-9007(96)00610-2]

Cited by 435 publications

References 17 publications

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

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

Spatial solitons and Anderson localization

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