Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays

Meier, Joachim; Hudock, Jared; Christodoulides, Demetrios N.; Stegeman, George I.; Silberberg, Yaron; Morandotti, Roberto; Aitchison, J. S.

doi:10.1103/physrevlett.91.143907

Cited by 99 publications

(71 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, in the case of waveguide arrays, one may consider settings with two orthogonal polarizations of light [7], or two different wavelengths, see e.g., Ref. [8].…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking in linearly coupled dynamical lattices

Herring

Kevrekidis²,

Malomed³

et al. 2007

Phys. Rev. E

View full text Add to dashboard Cite

We examine one-and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the systems with equal powers in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the squared l 2 -norm. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in 2D lattice solitons. This feature has no counterpart in the continuum limit, because of the collapse instability in the latter case.

show abstract

“…For instance, in the case of waveguide arrays, one may consider settings with two orthogonal polarizations of light [7], or two different wavelengths, see e.g., Ref. [8].…”

Section: Introductionmentioning

confidence: 99%

Symmetry breaking in linearly coupled dynamical lattices

Herring

Kevrekidis²,

Malomed³

et al. 2007

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The constants A and B are respectively associated with the cross-phase modulation (XPM) and four-wave mixing (FWM) and were evaluated in [23] to be approximately equal to A ≃ 1 and B ≃ 1/2. Wherever possible, the results obtained in this analysis will be given for general A and B, even though the above values have been used in the specifics of our numerical computations.…”

Section: Model and Setupmentioning

confidence: 99%

“…This work sheds new light on the theoretical investigations of this topic, in that the relevant model for the corresponding AlGaAs waveguide array experiment included four wave mixing (FWM) terms that were rarely included in previous theoretical studies. Subsequent studies (see [25,26]) addressed a number of specific properties of the model system put forward in [23]. Such properties related to switching, instability-induced amplification, modulational instability as well as an analysis of the energy barrier between stable discrete solitary waves centered on a lattice site versus two lattice sites.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solitary waves in discrete media with four-wave mixing

2006

View full text Add to dashboard Cite

In this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear inter-component coupling and four wave mixing. The relevant four branches of solutions consist of two single mode branches (transverse electric and transverse magnetic) and two mixed mode branches, involving both components (linearly polarized and elliptically polarized). These solutions are obtained explicitly and their stability is analyzed completely in the anti-continuum limit (where the nodes of the lattice are uncoupled), illustrating the supercritical pitchfork nature of the bifurcations that give rise to the latter two, respectively, from the former two. Then the branches are continued for finite coupling constructing a full two-parameter numerical bifurcation diagram of their existence. Relevant stability ranges and instability regimes are highlighted and, whenever unstable, the solutions are dynamically evolved through direct computations to monitor the development of the corresponding instabilities. Direct connections to the earlier experimental work of Meier et al. [Phys. Rev. Lett. 91, 143907 (2003)] that motivated the present work are given.

show abstract

“…More recently, a number of variants of this theme of optical waveguide arrays have been studied in detail, notable examples being multi-component models involving multiple polarizations [20,21], waveguides featuring quadratic (socalled χ 2 ) nonlinearities [22,23], the examination of dark-solitonic states [24,25] and the study of binary waveguide arrays [26][27][28]. Here, we focus more specifically on the theme of binary waveguide arrays and their alternating coupling structure.…”

Section: Introductionmentioning

confidence: 99%

Existence, stability and dynamics of discrete solitary waves in a binary waveguide array

Shen¹,

Kevrekidis²,

Srinivasan³

et al. 2016

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Recent work has explored binary waveguide arrays in the long-wavelength, near-continuum limit, here we examine the opposite limit, namely the vicinity of the so-called anti-continuum limit. We provide a systematic discussion of states involving one, two and three excited waveguides, and provide comparisons that illustrate how the stability of these states differ from the monoatomic limit of a single type of waveguide. We do so by developing a general theory which systematically tracks down the key eigenvalues of the linearized system. When we find the states to be unstable, we explore their dynamical evolution through direct numerical simulations. The latter typically illustrate, for the parameter values considered herein, the persistence of localized dynamics and the emergence for the duration of our simulations of robust quasi-periodic states for two excited sites. As the number of excited nodes increase, the unstable dynamics feature less regular oscillations of the solution's amplitude.

show abstract

Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays

Cited by 99 publications

References 26 publications

Symmetry breaking in linearly coupled dynamical lattices

Symmetry breaking in linearly coupled dynamical lattices

Solitary waves in discrete media with four-wave mixing

Existence, stability and dynamics of discrete solitary waves in a binary waveguide array

Contact Info

Product

Resources

About