Solitons supported by singular modulation of the cubic nonlinearity

Lutsky, Vitaly; Malomed, Boris A.

doi:10.1364/oe.25.012967

Cited by 4 publications

(2 citation statements)

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“…Lutsky and Malomed introduce a model of the optical media with a spatially structured Kerr nonlinearity modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. They investigate the properties of solitons supported by such singular modulation [15].…”

Section: Nonlinear Singular Opticsmentioning

confidence: 99%

Focus issue introduction: synergy of structured light and structured materials

Omatsu¹,

Litchinitser²,

Brasselet³

et al. 2017

Opt. Express

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Structured light beams, such as optical vortices, vector beams, and non-diffracting beams, have been recently studied in a variety of fields, such as optical manipulations, optical telecommunications, nonlinear interactions, quantum physics, and 'super resolution' microscopy.. Their unique physical properties, such as annular intensity profile, helical wavefront and orbital angular momentum, give rise to a plethora of new, fundamental light-matter interactions and device applications. Recent progress in nanostructured materials, including metamaterials and metasurfaces, opened new opportunities for structured light generation on the microscale that exceed the capabilities of bulk-optics approaches such as computer generated holography and diffractive optics. Furthermore, structured optical fields may interact with matters on the subwavelength scale to yield new physical effects, such as spin-orbital momentum coupling. This special issue of Optics Express focuses on the state-of-the-art fundamental research and emerging technologies and applications enabled by the interplay of "structured light" and "structured materials".

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Section: Nonlinear Singular Opticsmentioning

confidence: 99%

Focus issue introduction: synergy of structured light and structured materials

Omatsu¹,

Litchinitser²,

Brasselet³

et al. 2017

Opt. Express

View full text Add to dashboard Cite

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“…This phenomenon has been emphasized at the first time in 1979 by E. B. Davies [1] for atomic, molecular systems and analyzed intensively by B. A. Malomed's group since more than two decades [2][3][4][5][6][7][8][9][10][11][12][13][14]. In optics, the SSB occurs as a result of the interplay between the nonlinearity and waveguiding structures, when the strong nonlinearity partly suppresses the linear coupling between parallel guiding cores, for example in self-focusing Kerr medium [15].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous Symmetry Breaking of Solitons Trapped in a Double-Gauss Potentials

Nguyen¹,

Dinh²,

Cao³

et al. 2018

Comm. in Phys.

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We consider an extended model of the model considered before with double-square potential, namely one-dimensional (1D) nonlinear Schrödinger equation (NLSE) with self-focusing nonlinearity and a 1D double-gauss potential. Spontaneous symmetry breaking has been presented in terms of the control parameter which is propagation constant in the case of optics and chemical potential in the of Bose-Einstein Condensate (BEC), correspondingly. The numerical simulations predict a bifurcation breaking the symmetry of 1D trapped in the double-gauss potential of the supercritical type as in the case of double-square potential. Furthermore we have constructed bifurcation diagrams considering the stability of solitons with three methods: the method using Vakhitov–Kolokolov (V-K) Stability Criterion, Pseudospectral Method and Method for Linear-Stability Eigenvalues. It will be shown that for our model the results obtained are the same for these three methods but the third one is the fastest.

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Multi-soliton states under triangular spatial modulation of the quadratic nonlinearity

Lutsky

Malomed

2018

Eur. Phys. J. Spec. Top.

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We introduce multi-soliton sets in the two-dimensional medium with the χ (2) nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are constructed, and their stability is investigated. Stable symmetric patterns may be built of 1, 4, or 7 individual solitons, while stable asymmetric ones contain 1, 2, or 3 solitons. Symmetric and asymmetric patterns may demonstrate mutual bistability. The shift of the asymmetric single-soliton state from the central position is accurately predicted analytically. Vortex rings composed of three solitons are produced too. possibility to generalize the study of the onset of collapse in nonlinear media [12,13], as well as to emulate the nonlinear dynamics in a sub-1D space, with the effective dimension D = 2 (1 − α) / (2 − α) < 1 [11]. The singular modulation can be emulated by means of above-mentioned techniques, tuning them to the exact resonance in a narrow layer.Another possibility is to consider spatial modulation of the local interaction strength in media with the quadratic (χ (2) ) nonlinearity, which has well-known realizations in optics [14]- [17]. Experimental realizations of such settings are possible, in particular, using the well-elaborated technique of the quasi-phasematching [18]- [20], which can be implemented in a spatially nonuniform form, in 1D and 2D geometries alike, thus helping one to create a required profile of the χ (2) coefficient [21]-[23]. In the theoretical analysis, singular modulation of the quadratic nonlinearity in the 1D system, accounted for by a delta-function,, and localized modes (solitons) pinned to it, were introduced in Ref. [24], and a pair of modulating delta-functions was considered in Ref. [25]. A discrete version of the localized quadratic nonlinearity was elaborated in the form of a linear lattice with one or two χ (2) -nonlinear sites embedded in it [26].While the delta-like modulation of the local χ (2) coefficient may not be easily realized in the experiment, a more realistic case of the 1D singular modulation, with χ (2) ∼ |x| −α and positive α, was introduced in Ref. [27]. It was found that this modulation format supports quadratic solitons, pinned to the singular peak, for α < 1 (the pinned modes vanish at α = 1), and they are chiefly stable. A natural extension of that setting is a symmetric pair of two peaks (similar to the above-mentioned symmetric set of two delta-functions multiplying the nonlinear terms [25]). The consideration of the twin peaks has made it possible to predict effects of the spontaneously symmetry breaking [28] and formation of asymmetric two-soliton states pinned to the two peaks [27]. These results may be used for the design of steering optical beams in the form of spatial solitons.An essential advantage of using the quadratic nonlinearity with this type of the local modulation is that it may be extended to the 2D geometry, by choosing χ (2) (r) ∼ r −α (r is the radial coordinate), while any 2D singular modulation of the self...

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Solitons supported by singular modulation of the cubic nonlinearity

Cited by 4 publications

References 50 publications

Focus issue introduction: synergy of structured light and structured materials

Focus issue introduction: synergy of structured light and structured materials

Spontaneous Symmetry Breaking of Solitons Trapped in a Double-Gauss Potentials

Multi-soliton states under triangular spatial modulation of the quadratic nonlinearity

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