Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis

Duanmu, M.; Li, K.; Horne, Rudy L.; Kevrekidis, P. G.; Whitaker, N.

doi:10.1098/rsta.2012.0171

Cited by 49 publications

(52 citation statements)

References 38 publications

(84 reference statements)

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“…More complicated structure of PT-symmetric trimer including competing nonlinear gain with linear loss in the first waveguide and vise versa in the third waveguide has also been studied in [34]. The introduced nonlinear gain and loss give rise to rich features of asymmetric modes not observed in linear gain/loss profile systems.…”

Section: Pt-symmetric Trimermentioning

confidence: 99%

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Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

352

263

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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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Section: Pt-symmetric Trimermentioning

confidence: 99%

“…PT-symmetric trimer, first discussed in [58] and revisited in [34,68] PT-symmetric interposition of these waveguides with nonzero PT-symmetry breaking threshold: equal gain and loss parameters, i.e. …”

Section: Pt-symmetric Trimermentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

352

263

View full text Add to dashboard Cite

show abstract

“…Refs. [22][23][24]. Extensions beyond the dimer case to oligomers and eventually to lattices would also be particularly interesting to consider [15,16,18,19].…”

Section: Discussionmentioning

confidence: 99%

“…The inclusion of the Kerr nonlinearity into the conservative part of the system suggests that its gain-and-loss part can be made nonlinear too, by adopting mutually balanced cubic gain and loss terms [22][23][24]. Effects of combined linear and nonlinear PT terms on the existence and stability of solitons were studied in [25].…”

Section: Introduction and The Modelmentioning

confidence: 99%

Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems

D'Ambroise

Malomed

Kevrekidis

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the PT symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac) forcing is applied through periodic modulation of the coefficient accounting for the coupling of the two degrees of freedom. The system may be realized in optics as a dual-core waveguide with the gain and loss applied to different cores, and the thickness of the gap between them subject to a periodic modulation. The onset and development of the parametric instability for a small forcing amplitude (V1) is studied in an analytical form. The full dynamical chart of the system is generated by systematic simulations. At sufficiently large values of the forcing frequency, ω, tongues of the parametric instability originate, with the increase of V1, as predicted by the analysis. However, the tongues following further increase of V1 feature a pattern drastically different from that in usual (non-PT ) parametrically driven systems: instead of bending down to larger values of the dc coupling constant, V0, they maintain a direction parallel to the V1 axis. The system of the parallel tongues gets dense with the decrease of ω, merging into a complex small-scale structure of alternating regions of stability and instability. The cases of ω → 0 and ω → ∞ are studied analytically by means of the adiabatic and averaging approximation, respectively. The cubic nonlinearity, if added to the system, alters the picture, destabilizing many originally robust dynamical regimes, and stabilizing some which were unstable. Recently, a great deal of interest has been drawn to systems featuring the PT (parity-time) symmetry. Originally, they were introduced as quantum systems with spatially separated and symmetrically placed linear gain and loss. A fundamental property of non-Hermitian PT -symmetric Hamiltonians is the fact that their spectra remain purely real, like in the case of the usual Hermitian Hamiltonians, provided that the strength of the non-Hermitian part of the Hamiltonian, γ, does not exceed a certain critical value, γ cr , at which the PT symmetry breaks down. Such linear systems were recently implemented experimentally in optics, due to the fact that the paraxial propagation equation for electromagnetic waves can emulate the quantum-mechanical Schrödinger equation. In particular, the PT -symmetric quantum system may be emulated by waveguides with spatially separated mutually balanced gain and loss elements. Additional interest to the optical realizations of the PT symmetry has been drawn by the possibility to implement this setting in nonlinear waveguides. Unlike the ordinary models of nonlinear dissipative systems, where stable modes exist as isolated attractors, in PT -symmetric systems they emerge in continuous families, similar to what is commonly known about conservative nonlinear systems. However, the increase of the gain-loss coefficient, γ, leads to the shrinkage of existence and stability region...

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“…Since then, numerous phenomena have been reported in the field of parity time symmetric optics. To cite, some of them include: onset of chaos in optomechanical systems [5], optical mesh lattices [6][7][8], modulational invisibility in complex media [9], Peregrine soliton dynamics [10], plasmon excitation [11,12], unidirectional reflectionlessness, invisibility and non-reciprocity in periodic structures [13][14][15][16][17], whispering gallery modes [18], microring resonators [19][20][21], optical oligomers [22][23][24][25] and so on.…”

Section: Introductionmentioning

confidence: 99%

Highly amplified light transmission in a parity-time symmetric multilayered structure

Deka

Sarma

2018

Appl. Opt.

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We propose a parity-time symmetric dielectric-nanofilm-dielectric multilayered structure that could facilitate highly amplified transmission of optical power in the infrared spectrum. We have theoretically studied our model using the transfer matrix formalism. The reflection and the transmission coefficients of the S-matrix are evaluated. The theoretical results are validated by FDTD numerical simulation. We have shown how the thickness of the layers and the gain/loss coefficient of the active layers could generate spectral singularities in the S-matrix and how these singularities could be exploited to achieve amplified transmission of a single wavelength through the structure.

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Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis

Cited by 49 publications

References 38 publications

Nonlinear switching and solitons in PT‐symmetric photonic systems

Nonlinear switching and solitons in PT‐symmetric photonic systems

Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems

Highly amplified light transmission in a parity-time symmetric multilayered structure

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