Discrete vortex solitons and parity time symmetry

Leykam, Daniel; Konotop, V. V.; Desyatnikov, Anton S.

doi:10.1364/ol.38.000371

Cited by 49 publications

(66 citation statements)

References 14 publications

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“…In accordance with the expansions (11)- (12), at the points of the bifurcations (ε = 0) one has E =Ẽ 1,2 and U = 0. The modes obeying expansions (19)- (20) have also been found in our numerics. For such modes at ε = 0 one has E =Ẽ 3,4 and U = 4α 2 3,4 with α 3,4 being solutions of the quadratic equation introduced in Sec.…”

Section: B Numerical Resultssupporting

confidence: 82%

“…Another extension of nonlinear dimer activity is related to the inclusion of PTsymmetric defects in discrete nonlinear systems. In the latter context, problems such as nonlinear wave scattering [18] (see also [19]) and the lifting of the degeneracy of discrete vortices [20] were considered. Finally, a nonlinear dimer or more generally the so-called nonlinear "oligomers" (i.e., few site configurations) introduced in [21] (see also [22]), were shown to allow for the existence of continuous families of nonlinear modes [23].…”

Section: Introductionmentioning

confidence: 99%

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PT-symmetric coupler withχ(2)nonlinearity

Zezyulin

Kevrekidis

et al. 2013

Phys. Rev. A

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We introduce the notion of a PT -symmetric dimer with a χ (2) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical timeevolution simulations exploring the evolution of the different configurations, when unstable.

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Section: B Numerical Resultssupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

PT-symmetric coupler withχ(2)nonlinearity

Zezyulin

Kevrekidis

et al. 2013

Phys. Rev. A

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“…5(b) has also been investigated in Ref. [58] (and also discussed in [69]). Although the PT-symmetry breaking threshold for underlying linear system is γ crit = 0, the nonlinear branches of solutions still exist for nonzero values of gain/loss parameter γ .…”

Section: Pt-symmetric Trimermentioning

confidence: 93%

“…12(c)] [69]. One of the important characteristics of the vortex modes is a topological charge m which is equal to the phase winding number in units of 2π around the vortex origin and the sign of m determines the direction of power flow.…”

Section: Multicore Fibersmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

331

259

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One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested ParityTime (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensitydependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

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“…For discrete models that arise due to a discretization of an underlying continuous field, the (discrete) topological charge indicates the total topological charge of the continuous field vortices which are located in the region enclosed by the closed loop. It may thus be of interest to get information about the underlying field 9 , and several works [53][54][55][56] with discrete models have therefore interpolated of the field between the sites, for instance to gain information about where the vortex cores are located, how many they are, and how they interact.…”

Section: Vortices and Charge Flippingmentioning

confidence: 99%

Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

Jason¹

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This thesis is mainly concerned with theoretical studies of two types of models: quantum mechanical Bose-Hubbard models and (semi-)classical discrete nonlinear Schrödinger (DNLS) models.Bose-Hubbard models have in the last few decades been widely used to describe Bose-Einstein condensates placed in periodic optical potentials, a hot research topic with promising future applications within quantum computations and quantum simulations. The Bose-Hubbard model, in its simplest form, describes the competition between tunneling of particles between neighboring potential wells ('sites') and their on-site interactions (can be either repulsive or attractive). We will also consider extensions of the basic models, with additional interactions and tunneling processes.While Bose-Hubbard models describe the behavior of a collection of particles in a lattice, the DNLS description is in terms of a classical field on each site. DNLS models can also be applicable for Bose-Einstein condensates in periodic potentials, but in the limit of many bosons per site, where quantum fluctuations are negligible and a description in terms of average values is valid. The particle interactions of the Bose-Hubbard models become nonlinearities in the DNLS models, so that the DNLS model, in its simplest form, describes a competition between on-site nonlinearity and tunneling to neighboring sites. DNLS models are however also applicable for several other physical systems, most notably for nonlinear waveguide arrays, another rapidly evolving research field.The research presented in this thesis can be roughly divided into two parts: 1) We have studied certain families of solutions to the DNLS model. First, we have considered charge flipping vortices in DNLS trimers and hexamers. Vortices represent a rotational flow of energy, and a charge flipping vortex is one where the rotational direction (repeatedly) changes. We have found that charge flipping vortices indeed exist in these systems, and that they belong to continuous families of solutions located between two stationary solutions.Second, we have studied discrete breathers, which are spatially localized and time-periodic solutions, in a DNLS models with the geometry of a ring coupled to an additional, central site. We found under which parameter values these solutions exist, and also studied the properties of their continuous solution families. We found that these families undergo different bifurcations, and that, for example, the discrete breathers which have a peak on one and two (neighboring) sites, respectively, belong to the same family below a critical value of the ring-to-centralv vi site coupling, but to separate families for values above it.2) Since Bose-Hubbard models can be approximated with DNLS models in the limit of a large number of bosons per site, we studied signatures of certain classical solutions and structures of DNLS models in the corresponding Bose-Hubbard models.These studies have partly focused on quantum lattice compactons. The corresponding classical lattice compac...

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Discrete vortex solitons and parity time symmetry

Cited by 49 publications

References 14 publications

PT-symmetric coupler withχ(2)nonlinearity

PT-symmetric coupler withχ(2)nonlinearity

Nonlinear switching and solitons in PT‐symmetric photonic systems

Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models : Localization, vortices, and quantum-classical correspondence

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