Theory of Incoherent Self-Focusing in Biased Photorefractive Media

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

doi:10.1103/physrevlett.78.646

Cited by 319 publications

(159 citation statements)

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“…For a deeper understanding of the stabilizing effect of partial coherence in nonlinear media, the modal expansion was proposed [6], similarly to the statistical description of partially correlated fields. In this approach, an optical field is composed of infinitely many components ψ k , which propagate at slightly different angles and form the coherence spectrum.…”

Section: Introductionmentioning

confidence: 99%

Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations

2008

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Abstract. A Hamiltonian system of incoherently coupled nonlinear Schrödinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.

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Section: Introductionmentioning

confidence: 99%

Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations

2008

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“…(1, 2-5), and to determine the corresponding dispersion relation, it is necessary to linearize Eqns. (2)(3)(4)(5), noting that up to first order…”

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confidence: 99%

“…random phase plates in inertial confinement fusion (ICF)). Recent theoretical work in nonlinear optics, triggered by the work of Segev and co-workers [1], led to the development of techniques capable of describing the propagation and the modulation instability of partially coherent/incoherent "white" light in nonlinear media [3]. The critical underlying assumption of all these models is the paraxial wave approximation, valid in transparent media for radiation beams not tightly focused, which reduces the problem of electromagnetic wave propagation in dispersive (and diffractive) nonlinear media to the search of a forward propagating solution, formally described by the nonlinear Schrödinger equation.…”

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confidence: 99%

White-Light Parametric Instabilities in Plasmas

Santos¹,

Silva²,

Bingham

2007

Phys. Rev. Lett.

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Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for Stimulated Raman Scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width σ of the radiation field, scaling with 1/σ for backscattering (three-wave process), and with 1/σ 1/2 for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.Parametric instabilities are pervasive in many fields of science, associated with the onset of nonlinear and collective effects such as solitons, vortices, self-organization, and spontaneous ordering. Recent developments in light sources and laser technology continue to reveal novel features of the parametric instabilities, for instance in nonlinear optics, with the recent experimental discovery of white light solitons [1], or in plasma physics, in the realm of relativistic nonlinear optics [2]. The standard theoretical approach to study parametric instabilities is based on a coherent wave description which is clearly limited because, in most systems, waves are only partially coherent, with incoherence either inherently induced by fluctuations, or induced by external passive systems (e.g. random phase plates in inertial confinement fusion (ICF)). Recent theoretical work in nonlinear optics, triggered by the work of Segev and co-workers [1], led to the development of techniques capable of describing the propagation and the modulation instability of partially coherent/incoherent "white" light in nonlinear media [3]. The critical underlying assumption of all these models is the paraxial wave approximation, valid in transparent media for radiation beams not tightly focused, which reduces the problem of electromagnetic wave propagation in dispersive (and diffractive) nonlinear media to the search of a forward propagating solution, formally described by the nonlinear Schrödinger equation. While in nonlinear optics, and for the conditions studied so far, such approximation is clearly valid, in plasma physics it is not. The instabilities associated with the partially reflected backscattered radiation [4] are critical in many laser-plasma and astrophysical scenarios [5], and the paraxial approximation has limited applicability even in the description of forward scattering instabilities driven by ultra intense lasers in underdense/transparent plasmas [6].Inclusion of bandwidth/incoherence effects in laser driven parametric instabilities in plasmas and in three-wave processes is a long-standing problem [7,8], because incoherent pumps can decrease the growth of the laser driven instabilities in ICF, Fast Ignition, or novel laser amplification schemes [9]. The difficulty resides in the lack of an appropriate theoretical framework...

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“…For the statement (21), we use the interpolation inequality, Sobolev inequality, (19) and (20) to find…”

Section: Hencementioning

confidence: 99%

“…Finally we would to recall that system of type (S) can describe other physical phenomena, such as Kerr-like photorefractive media in optics, (cf. [1,20,21,22]), Hartree-Fock theory for double condensate [25]. See [31] and [37] for more applications in physical and chemical phenomenas.…”

Section: Introductionmentioning

confidence: 99%