Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media

Buccoliero, Daniel; Desyatnikov, Anton S.; Królikowski, Wiesław; Kivshar, Yuri S.

doi:10.1103/physrevlett.98.053901

Cited by 280 publications

(207 citation statements)

References 25 publications

(38 reference statements)

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“…This repulsion is a direct consequence of the nonlocal nature of the nematic response, combined with the intricate dependence of the response on the specific properties of the boundaries. In general, boundaries affect not only the position, but also the internal dynamics [20] of more complex soliton of different symmetries [32].…”

Section: B 2d Soliton Bouncing In a Rectangular Cellmentioning

confidence: 99%

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

et al. 2009

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Section: B 2d Soliton Bouncing In a Rectangular Cellmentioning

confidence: 99%

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

et al. 2009

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“…1(a-c)), in similarity to higher-order localized modes in saturable media [36] and recently observed fundamental modes of multimode fibers [37]. Mathematical model.…”

mentioning

confidence: 72%

Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

et al. 2018

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We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization. [3,4]. Wave collapse (also known as blow-up or selffocusing) occurs in a range of physical systems including nonlinear optics, plasmas, fluid dynamics, physics of atmosphere and ocean, and solid state physics [5]. Typically, wave collapse is associated with multidimensional physical problems [3][4][5][6][7][8][9][10][11][12][13]. From a broader perspective, wave collapse is the process of the singularity formation in a finite time (or at a finite distance), which is typically arrested by higher-order effects not accounted for in the original model. Effect of wave collapse can be exploited for compression of optical pulses [8][9][10][11] and optical pulse fusion [11,12]. An arrest of wave collapse and emergence of stable coherent structures in higher-dimensional systems have been studied in various physical contexts (see, e.g. the review paper [14] and references therein). Solitons localized in time and one transverse spatial dimension have been observed in quadratic media [15], and such solitons suffer from modulation instability which breaks elliptical beams into filaments. Three-dimensional spatiotemporal solitons were demonstrated in arrays of weakly coupled optical waveguides [16,17], but such solitons are largely controlled by the lattice discreteness being stable for a weak coupling.For long time, the use of single-mode optical fibers was the solution of choice for long-haul communication systems, allowing to avoid spatial scattering of light for delivering optical signals without spatial-mode dispersion over thousands of kilometers. However, a fast-growing demands on capacity of fiber systems and challenges imposed by nonlinear signal interaction attracted the recent attention to the technology of spatial-division multiplexing (SDM) for future high-capacity optical communications (see, e.g. Refs. [18,19] and references therein). A solution based on the use of multiple systems over parallel fibres while always possible, is not attractive due to linearly scaled (with growing capacity) transmission costs and power consumption. Potentially, the SDM technology might offer a cost-per-bit reduction and improved energy efficiency. One of the considered possibilities for implementing the SDM technology is the use of multimode fibers (MMFs) for parallel communication channels. In MMFs optical pathways are defined by different spatial modes, and spatial signal pr...

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“…In this case, the nonlocal nonlinear Schrödinger equation (NNLSE), which governs the propagation of an optical beam in a nonlocal nonlinear medium can be simplified to a linear equation, as suggested by A. W. Snyder and D. J. Mitchell [4]. Various solitons and breather solutions in the strongly nonlocal nonlinear media have been found [5][6][7][8]. Most of these studies focus on the shapes of optical beams invariant during propagation in linear and nonlinear media [6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Evolution of Cos-Gaussian Beams in a Strongly Nonlocal Nonlinear Medium

Guan¹,

Zhong²,

Chew³

et al. 2013

PIER

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Abstract-The dynamical properties of cos-Gaussian beams in strongly nonlocal nonlinear (SNN) media are theoretically investigated. Based on the moments method, the analytical expression for the rootmean-square (RMS) of the cos-Gaussian beam propagating in a SNN medium is derived. The critical powers that keep the RMS beam widths invariant during propagation in a SNN medium are discussed. The RMS beam width tends to evolve periodically when the initial power does not equal to the critical power. The analytical solution of the cos-Gaussian beams in SNN media is obtained by the technique of variable transformation. Despite the difference in beam profile symmetries and initial powers, a cos-Gaussian beam always transforms periodically into a cosh-Gaussian beam during propagation and the transformation between the two beams revives after a propagation distance.

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Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media

Cited by 280 publications

References 25 publications

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

Evolution of Cos-Gaussian Beams in a Strongly Nonlocal Nonlinear Medium

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