Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media

Soljačić, Marin; Segev, Mordechai; Coskun, Tamer H.; Christodoulides, Demetrios N.; Vishwanath, Ashvin

doi:10.1103/physrevlett.84.467

Cited by 245 publications

(175 citation statements)

References 32 publications

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“…For a pure Kerr nonlinearity, i.e. d j = 0 for all j, the random phase of the background pulse will give rise to a reduction of the modulational instability growth rate [13,14]. Here we find that the random phase will also contribute to the real part of K, and the imaginary contribution via interactions between the corrections to the Kerr nonlinearity and spectral broadening.…”

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confidence: 73%

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Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

et al. 2006

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The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schrödinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques.

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confidence: 73%

“…The Wigner function represents a generalized distribution function for optical quasi-particles. The Wigner method [13], as well as the equivalent mutual coherence method [14], have been used to analyze the modulational instability in the "standard" nonlinear Schrödinger picture, in which the righthand side of Eq. (1) is identically zero.…”

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confidence: 99%

Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

et al. 2006

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“…The phenomenon of MI has been identified and studied in various physical systems, such as fluids [20], plasma [21], nonlinear optics [22], discrete nonlinear systems [23], waveguide arrays, and Fermi-resonant interfaces [24]. It has been shown that MI is strongly affected by mechanisms such as saturation of the nonlinearity [25], coherence properties of optical beams [26], and linear and nonlinear gratings [27]. The model (2) permits plane wave solutions of the form…”

Section: Modulational Instabilitymentioning

confidence: 99%

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

Królikowski

Bang

Nikolov

et al. 2004

J. Opt. B: Quantum Semiclass. Opt.

397

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“…The dispersion relation (6) generalizes the results of previous modulational instability analysis of the nonlinear Schrödinger equation, where the Wigner formalism [14] as well as the mutual coherence method [15] has been used.…”

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Statistical properties of the continuum Salerno model

et al. 2006

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The statistical properties of the Salerno model is investigated. In particular, a comparison between the coherent and partially coherent wave modes is made for the case of a random phased wave packet. It is found that the random phased induced spectral broadening gives rise to damping of instabilities, but also a broadening of the instability region in quasi-particle momentum space. The results can be of significance for condensation of magnetic moment bosons in deep optical lattices.PACS numbers: 05.45. Yv, 63.20.Ry, 63.20.Pw Nonlinear wave propagation models are of importance in a wide variety of settings, such as in nonlinear optics [1,2], in water wave propagation [3], and in plasma systems [4]. Moreover, also discrete systems show important nonlinear properties that give rise to solitary structures in e.g. lattices (see, e.g. [5] and references therein for a review). The discrete Salerno model [6] combines onsite and intersite nonlinear terms in a lattice in order to encompass the different characteristics of nonlinear integrable and non-integrable lattice models. It has also been discovered as an asymptotic form of the Gross-Pitaevskii equation, with applications to Bose-Einstein condensation of atoms with magnetic moments in deep optical lattice traps [7,8]. Recently, the continuum limit of the Salerno model with focusing onsite and defocusing intersite nonlinearities was investigated [8] and soliton solutions were found.In this Brief Report, we will investigate the modulational instability properties of the general continuum limit of the Salerno model. Furthermore, the effects of random phased wave packets on the stability properties will be studied using the Wigner formalism. Results regarding the effect of random pulse phases will be given.The Salerno model was derived as a quantum modified discrete nonlinear Schrödinger equation, giving the time evolution of the field amplitude on the lattice. The relevant equation takes the form [6]where Φ n = Φ(t, x n ) is the field amplitude on the nth lattice site located at x n and ν and µ are the real parameters determining the strength of the onsite and intersite * Also

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Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media

Cited by 245 publications

References 32 publications

Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

Statistical properties of the continuum Salerno model

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