Three-Dimensional Spiraling of Interacting Spatial Solitons

Shih, Ming-Feng; Segev, Mordechai; Salamo, Greg

doi:10.1103/physrevlett.78.2551

Cited by 184 publications

(124 citation statements)

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“…Recently, experiments demonstrating non-planar interaction and spiraling of spatial solitons in a photorefractive medium have been reported [3]. However, in spite of earlier predictions of non-planar soliton interactions [4], the experimental results [3] have not been explained theoretically so far.…”

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confidence: 61%

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Induced Coherence and Stable Soliton Spiraling

et al. 1999

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We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.Self-guided optical beams (or spatial solitons) have attracted substantial research interest in the last three decades [1].Although interactions between twodimensional (2D) solitons in Kerr and non-Kerr media have been studied extensively, only the recent discoveries of stable three-dimensional (3D) solitons in different nonlinear bulk media In this Letter we develop, for the first time to our knowledge, a theory of soliton spiraling in a photorefractive-type nonlinear bulk medium. We derive an analytical model describing stable soliton spiraling and predict a number of new effects in soliton interactions, such as an induced coherence and control over 3D interactions, which we verify here experimentally, using experimental setup similar to that reported earlier [3]. Importantly, our analytical model and numerical simulations show that interacting-spiraling solitons conserve angular momentum. We believe that this result is a core foundation for future research on 3D soliton control, resembling the conservation of linear momentum in the interaction of more conventional (1+1)-dimensional solitons [6].We consider incoherent beam interaction in an isotropic saturable nonlinear medium described by two coupled normalized nonlinear Schrödinger (NLS) equationswhere u and w are the beam envelopes, z is the propagation distance; ∇ 2 ⊥ ≡ ∂ 2 /∂x 2 + ∂ 2 /∂y 2 accounts for the diffraction in the transverse (x, y) plane. This system, in the 2D case (i.e., for ∇ 2 ⊥ ≡ ∂ 2 /∂x 2 ), gives rise to incoherently-coupled soliton pairs [7] and to incoherent collisions [8] which have both been demonstrated with photorefractive screening solitons [9].We look for solitary waves of Eqs. (1) in the form u = U (r) exp (iβ u z), w = W (r) exp (iβ w z), where the envelopes U and W satisfy the equationsHere r ≡ x 2 + y 2 is the radial coordinate, and β u and β w are nonlinearity-induced shifts of the propagation constants. System (2) has two families of soliton solutions: U = G u (β u , r), W = 0 and U = 0, W = G w (β w , r), which can be found numerically by solving the equation, where α = {u, w}. These solutions can be characterised by the soliton powers P (β α ) ≡ 2π ∞ 0 G 2 α (β α , r) rdr. In addition to the one-component solitons, at β u = β v ≡ β there exists a family of two-component (vector) solitons defined as: U = G(β, r) cos θ, W = G(β, r) sin θ, where the variable θ characterises a power distribution between the components. Moving solitons of Eqs. (1) can be obtained by a well-known gauge transformation.

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confidence: 61%

“…The experiments are carried out using the photorefractive screening nonlinearity [3,9]. In essence, the photorefractive nonlinearity is anisotropic [13], which makes it non-ideal to test our model.…”

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confidence: 99%

Induced Coherence and Stable Soliton Spiraling

et al. 1999

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“…Two-dimensional (2D) optical bright solitons [13] and three-dimensional (3D) light bullets [14] have been reported in non-local media. In addition, nonlocal interactions significantly influence inter-soliton collisions [4,7,15,16] and may lead to the formation of soliton complexes [17,18].…”

Section: Introductionmentioning

confidence: 99%

“…Last two decades have witnessed intensive investigations, both theoretical and experimental, on multi-dimensional solitons, especially in systems possessing nonlocal nonlinearity (NLNL) [1][2][3] such as Bose-Einstein condensates (BECs) of particles with permanent [4,5] or induced dipole moments [6] (dipolar BECs), photo refractive materials [7], nematic liquid crystals [8,9] and others [10][11][12]. Two-dimensional (2D) optical bright solitons [13] and three-dimensional (3D) light bullets [14] have been reported in non-local media.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional bright solitons in dipolar Bose-Einstein condensates with tilted dipoles

et al. 2015

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The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate-plane. The tilting angle constitutes an additional tuning parameter, which help us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon-instability in a homogeneous 2D condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach, involving the tuning of tilting angle.

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“…[13][14][15][16] Optical solitons have been shown to attract, repel, breakup, merge, orbit each-other or even annihilate. 5,[17][18][19][20][21] As in various other media, soliton interactions can be either shortrange, occurring when the tails of neighbouring solitons overlap, 6,17,22,23 or long range, through a coupling with a non-local response, be it optical radiation, charge carriers, or thermal waves. [24][25][26][27] The weakest soliton interactions reported are long range, 24,25 but their observation is typically limited by the duration or propagation length over which the solitons can be maintained.…”

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Ultraweak long-range interactions of solitons observed over astronomical distances

et al. 2013

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We report what we believe is the weakest interaction between solitons ever observed. Our experiment involves temporal optical cavity solitons recirculating in a coherently-driven passive optical fibre ring resonator. We observe two solitons, separated by up to 8,000 times their width, changing their temporal separation by a fraction of an attosecond per round-trip of the 100 m-long resonator, or equivalently 1/10,000 of the wavelength of the soliton carrier wave per characteristic dispersive length. The interactions are so weak that, at the speed of light, they require an effective propagation distance of the order of an astronomical unit to fully develop, i.e. tens of millions of kilometres. The interaction is mediated by transverse acoustic waves generated in the optical fibre by the propagating solitons through electrostriction.Solitons are self-localized wave packets that do not spread, the dispersion of the supporting medium being cancelled by a nonlinear effect. 1-4 They are universal, and in many respects behave like particles. 2 They exert forces on each other and can interact in various ways, elastically or inelastically. 2,5,6 Here we report what we believe is by far the weakest form of soliton interaction ever observed. Using recirculating optical cavity solitons, we report interactions so weak that the solitons shift their positions by only about 10 −7 of their width -amounting to 1/10,000 of the wavelength of the soliton carrier wave -per characteristic dispersive length. At the speed of light, these interactions require effective propagation distances of the order of an astronomical unit (AU) to be revealed, i.e. tens of millions of kilometres. The sheer fact that we can actually observe such ultra-weak interactions in a noisy laboratory environment highlights the robustness and stability of solitons as never-before.Solitons occur in media as diverse as water, DNA, plasma, or ultra-cold gases, 1,7-12 but over the last 20 years optics has led the way in our understanding of soliton interactions because of the ease with which optical solitons can be studied experimentally. [13][14][15][16] Optical solitons have been shown to attract, repel, breakup, merge, orbit each-other or even annihilate. 5,17-21 As in various other media, soliton interactions can be either shortrange, occurring when the tails of neighbouring solitons overlap, 6,17,22,23 or long range, through a coupling with a non-local response, be it optical radiation, charge carriers, or thermal waves. 24-27 The weakest soliton interactions reported are long range, 24,25 but their observation is typically limited by the duration or propagation length over which the solitons can be maintained. In optics, this is often simply dictated by the size of a nonlinear crystal or the length of an optical fibre. To overcome this restriction, our experiment involves solitons recirculating in an optical fibre loop.More specifically, we consider temporal cavity solitons (CSs) propagating in a coherently-driven passive nonlinear fibre ring resonator. 28 Not...

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Three-Dimensional Spiraling of Interacting Spatial Solitons

Cited by 184 publications

References 19 publications

Induced Coherence and Stable Soliton Spiraling

Induced Coherence and Stable Soliton Spiraling

Two-dimensional bright solitons in dipolar Bose-Einstein condensates with tilted dipoles

Ultraweak long-range interactions of solitons observed over astronomical distances

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