Multidimensional solitons in fiber arrays

Aceves, Alejandro B.; Angelis, Costantino De; Rubenchik, Alexander M.; Turitsyn, Sergei K.

doi:10.1364/ol.19.000329

Cited by 157 publications

(116 citation statements)

References 14 publications

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“…It was known [21,22,24,40] are strongly localized in the transverse direction, is a noteworthy finding, as, in the limit when almost all the energy is trapped in the central core, one might expect completely elastic collisions governed by the usual NLSE. Collisions between solitons centered at two adjacent cores, rather than in the same one, have been considered too.…”

Section: Resultsmentioning

confidence: 93%

“…Solitons of this type in planar fiber arrays had been studied theoretically some time ago, starting from Ref. [21], with expected applications to the collapse-effect compression of the solitons [22] (in the fully continuous limit, the SDSs go over into the Townes solitons [23] of the 2D NLSE, which are subject to the critical collapse in 2D) and all-optical switching and steering in the arrays [24].…”

Section: Introduction and The Modelmentioning

confidence: 99%

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Propagation and collisions of semidiscrete solitons in arrayed and stacked waveguides

Blit

Malomed

2012

Phys. Rev. A

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We consider shapes and dynamics of semi-discrete solitons (SDSs) in the known model of the set of linearly-coupled waveguides with the intrinsic cubic nonlinearity. The model applies to the description of a planar array of optical fibers, or of a stack of parallel planar waveguides, in the temporal and spatial domains, respectively, as well as to the selfattractive Bose-Einstein condensate (BEC) loaded into an array of parallel tunnel-coupled cigar-shaped traps. It was found previously that the interplay of the group-velocity dispersion, discrete diffraction (in the longitudinal and transverse directions, respectively) and intrinsic self-focusing gives rise to SDSs in the array. We here develop the variational approximation (VA) and additional analytical methods for the description of the SDSs, and study their mobility and collisions by means of systematic simulations. The VA and an exact solution of the linearized equation in the cores adjacent to the central one produce an accurate description for the family of stable fundamental onsite-centered SDS solutions, as well of surface SDSs in the semi-infinite array. The VA is also presented for transversely unstable intersite-centered solitons. In simulations, the solitons are not mobile in the discrete direction (non-soliton semi-discrete modes may be mobile across the array). Collisions between SDSs traveling in the longitudinal direction feature a threshold separating the passage and merger or destruction. The exact shape of the threshold, considered as a function of the solitons' energy, features irregularities, while its average form is explained analytically. "Shifted" collisions between SDSs centered at adjacent cores are studied too.

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Section: Resultsmentioning

confidence: 93%

Section: Introduction and The Modelmentioning

confidence: 99%

Propagation and collisions of semidiscrete solitons in arrayed and stacked waveguides

Blit

Malomed

2012

Phys. Rev. A

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“…The spatiotemporal optical solitons in fiber arrays were studied in the Ref. 45, and the corresponding spatiotemporal optical vortices were studied theoretically in the Refs. 46,47 and experimentally in the Ref.…”

Section: Introductionmentioning

confidence: 99%

Stable optical vortices in nonlinear multicore fibers

et al. 2015

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The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF. Keywords: coherent energy propagation; multicore fibers; nonlinear vortices INTRODUCTION Vortex structures are widespread in nature and are found in both macroscopic atmospheric phenomena, such as tornadoes and the Great Red Spot of Jupiter, and microscopic-scale objects in quantum physics. Mathematically, vortices are related to topological defects, the accumulation of geometrical phases, and the phase singularity of a complex linear or nonlinear field (see, e.g., Refs. 1-8 and references therein).Optical vortices present a fascinating and expanding area of research that combines fundamental theoretical and mathematical science and maturing applied technologies (see recent review 4 ). Optical vortices are characterized by a wave field with zero intensity, an undefined phase in the vortex center (pivot point) and the presence of a screw dislocation of the wave front 5,6 . All transmutations of vortices in linear and nonlinear fields obey the conservation of the topological charge S, which is defined as the total change of the phase along a closed curve surrounding the pivotal point of the vortex divided by 2p. The special behavior of the phase and amplitude near the vortex pivot point results in the circular flow of energy in optical vortices [7][8][9][10] . This property is closely related to the ability of optical vortices to carry orbital angular momentum and energy [11][12][13][14] . This property is interesting for various applications, such as in optical traps [15][16][17] , information transmission 18-20 , astrophysics 21,22 , microscopy 23,24 , and laser micromachining 25,26 .In nonlinear media, optical vortices are treated as (topological) vortex solitons 4,27,28 . Such topologically stable pulses can act as information carriers 4,[29][30][31] . It is important that continuum vortex solitons are highly sensitive to azimuthal instability. Stabilization is possible by applying optically induced photonic lattices, which lead to a discrete optical vortex field. Different types of discrete lattice vortex solitons were theoretically predicted in the Refs. 32-35 and experimentally demonstrated in the Refs. 36,37. Discrete vortex solitons can also be created in photonic crystal fibers and other types of photonic lattices 38,39 . Discrete vortex solitons are frequently associated with soliton clusters, which feature interesting mobility properties and

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“…The concept of surface solitons has been recently extended to cover spatiotemporal surface solitons [35,36] described by the continuous-discrete nonlinear equations similar to those investigated earlier for cubic [37][38][39][40] and quadratic [41] nonlinear optical media, but with the properties strongly affected by the presence of the surface in the form of the lattice truncation.…”

Section: Introductionmentioning

confidence: 99%

Collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices

2009

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Abstract:Systematic results of collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices are reported. The generic outcomes are identified for (i) the collision of two identical solitons located in the corner, at the edge, and in the center of the photonic lattice, and for (ii) the collision of two non-identical corner and edge solitons located at different distances from the boundaries of the photonic lattice. Depending on the values of the kick (collision momentum) and of the nonlinear (cubic) gain, the collision scenarios include soliton merging, creation of an extra soliton, soliton bouncing, soliton spreading, and quasi-elastic (symmetric) interactions. 05.45.Yv, 42.65.Tg, 42.65.Sf, 47.20 PACS (2008):

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Multidimensional solitons in fiber arrays

Cited by 157 publications

References 14 publications

Propagation and collisions of semidiscrete solitons in arrayed and stacked waveguides

Propagation and collisions of semidiscrete solitons in arrayed and stacked waveguides

Stable optical vortices in nonlinear multicore fibers

Collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices

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