An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

Barashenkov, I. V.; Gianfreda, Mariagiovanna

doi:10.1088/1751-8113/47/28/282001

Cited by 64 publications

(104 citation statements)

References 76 publications

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“…Nonlinearity can provide an important mechanism to balance gain and loss on average [30,38,39]. Such situation can arise even when linear PT symmetry is absent, in particular when the coupling between the waveguides is nonconservative and provides gain or loss depending on the relative phase between the guided modes [38,40] (it was shown experimentally that coupling between waveguides is generally complex, i.e.…”

Section: Actively Coupled Waveguidesmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

345

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: Actively Coupled Waveguidesmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

345

263

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“…Without the rapidly growing defocusing nonlinearity, the PT symmetry of the system considered in this Letter is always broken; in the presence of the nonlinearity modulation the symmetry may be said to become unbreakable, as it holds at arbitrarily large strengths of the balanced gain and loss. Recently, unbreakable symmetry was demonstrated for a dimer, but it was a very special case of a PT -symmetric Hamiltonian system [29].We address the propagation of a laser beam along the ξ axis of a medium with a transverse modulation of the gain-loss and defocusing nonlinearity, obeying the paraxial nonlinear Schrödinger equation for scaled amplitude q of the electromagnetic fieldwhere the propagation distance ξ is normalized to the diffraction length kx 2 0 ; the transverse coordinate η is …”

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confidence: 99%

mentioning

confidence: 99%

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

2014

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We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a parity-time (PT ) symmetry in the form of a purely real spectrum of modes, we show that the PT symmetry is never broken in the present system, and that the system always supports stable bright solitons, i.e., fundamental and multipole ones. This fact is connected to the nonlinearizability of the underlying evolution equation. The high current interest in parity-time (PT )-symmetric systems with complex potentials is partially motivated by the remarkable behavior of the corresponding linear spectrum, which remains purely real until the strength of the imaginary part of the potential attains a certain PTsymmetry breaking threshold, above which it becomes complex [1]. The effect has been experimentally observed in optics, where the similarity of the paraxial evolution equation, governing the propagation of light beams in media with an even spatial profile of the refractive-index modulation and an odd gain-loss profile, with the Schrö-dinger equation governing the evolution of the quantummechanical wave function in a complex potential, enables visualization of the PT symmetry and its breakup at a critical point [2]. While eigenmodes of linear PT -symmetric potentials are well-understood [1,3,4], the evolution of nonlinear excitations in them remains a subject of active research. In particular, the properties of solitons and discrete nonlinear modes have been studied in free-standing As mentioned previously, a generic property of PT -symmetric structures is that they support stable excitations only if the spectrum of the associated linear system is real, i.e., the symmetry is not broken. As a result, the stability domain of nonlinear excitations, if defined in terms of the gain-loss strength, often coincides with the domain of the unbroken PT symmetry in the respective linear system. However, systems may be prepared to be nonlinearizable, i.e., the nonlinear terms in the underlying evolution equation cannot be omitted even for the decaying tails of localized nonlinear excitations. Under such conditions, no direct link can be drawn between the spectra of the nonlinear system and its linear counterpart.In this Letter, we address that case in a system with an odd gain-loss profile and defocusing nonlinearity, whose local strength grows toward the periphery. In the absence of gain and loss, such a system supports bright solitons in all three dimensions [24][25][26][27][28]. Existence of bright solitons in spite of the self-defocusing nature of the nonlinearity is at first counterintuitive, but actually it is a consequence of the nonlinearizability of the respective nonlinear Schrödinger equation on the soliton tails. In this Letter, we show that a system of this type, with an even profile of the growing no...

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“…This is particularly true in semiconductor-based systems where saturation effects strongly influence both gain and loss, to the point that a reversal in PT -symmetry breaking can occur [25]. Clearly, of importance will be to understand at a fundamental level, the role such nonlinear processes play in the dynamics of PT -symmetric arrangements [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Integrable nonlinear parity-time-symmetric optical oscillator

et al. 2016

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The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.

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An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

Cited by 64 publications

References 76 publications

Nonlinear switching and solitons in PT‐symmetric photonic systems

Nonlinear switching and solitons in PT‐symmetric photonic systems

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

Integrable nonlinear parity-time-symmetric optical oscillator

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