Semidiscrete solitons in arrayed waveguide structures with Kerr nonlinearity

Panoiu, Nicolae C.; Malomed, Boris A.; Osgood, Richard M.

doi:10.1103/physreva.78.013801

Cited by 22 publications

(7 citation statements)

References 37 publications

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“…A prototypical model with the Kerr nonlinearity, which does not reduce to the usual discrete one, was introduced by Panoiu, Malomed, and Osgood (2008). It describes a waveguide built in the form of a slab substrate, with an array of guiding ribs either mounted on top of it, or buried into the slab.…”

Section: = 1 Smentioning

confidence: 99%

“…( 4) with and , where and L are the strength and period of the respective NL, and is the delta-function. Similar twocomponent semi-discrete systems were introduced by Panoiu, Malomed, and Osgood, 2008. A prototype of such models is the NLSE with the attractive (alias self-focusing) nonlinearity concentrated at a single point, i.e., Eq. ( 4) with and n x .…”

Section: Discrete Systemsmentioning

confidence: 99%

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Solitons in nonlinear lattices

2011

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This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of 1D solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for the theoretical and experimental studies alike. In both the 1D and 2D cases, the mechanism which creates solitons in NLs is principally different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.Peer ReviewedPostprint (published version

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Section: = 1 Smentioning

confidence: 99%

Section: Discrete Systemsmentioning

confidence: 99%

Solitons in nonlinear lattices

2011

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“…(27)] and twisted SDSs were also investigated. In the course of the imaginary-z propagation, the intersite-centered input spontaneously shifts in either direction, converting into a stable onsite soliton (as might be naturally expected, in view of the well-known instability of intersite-centered solitons in the discrete NLS equation [19]).…”

Section: Surface Solitonsmentioning

confidence: 99%

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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“…Ref. [60]. A remarkable peculiarity of such a system is that the linear coupling mixes completely different types of the asymptotic behavior at |x| → ∞: the trapped component is always confined, in the form of a Gaussian, by the HO potential, while the untrapped one is free to escape.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

Hacker¹,

Malomed²

2021

Preprint

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We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO's ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carry over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas-Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one-and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

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Semidiscrete solitons in arrayed waveguide structures with Kerr nonlinearity

Cited by 22 publications

References 37 publications

Solitons in nonlinear lattices

Solitons in nonlinear lattices

Propagation and collisions of semidiscrete solitons in arrayed and stacked waveguides

Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

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