Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices

Zhu, Xing; Wang, Hong; Zheng, Li-Xian; Li, Huagang; He, Yan

doi:10.1364/ol.36.002680

Cited by 103 publications

(53 citation statements)

References 18 publications

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“…A system of superlattices described by W 0 sin(2x) has been studied in [109]. Parameter ε here controls the relative strength of the superlattices.…”

Section: Solitons In Periodic Potentialsmentioning

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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“…A system of superlattices described by W 0 sin(2x) has been studied in [109]. Parameter ε here controls the relative strength of the superlattices.…”

Section: Solitons In Periodic Potentialsmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

345

263

View full text Add to dashboard Cite

show abstract

“…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 PT -symmetric waveguides [5], couplers [6][7][8][9], oligomers [10,11], and periodic lattices with [12] and without [13][14][15][16][17] transverse refractive-index gradients, and in truncated lattices [18], among other settings. An especially interesting situation occurs when the underlying evolution equations contain only nonlinear PT -symmetric terms [19,20], or mixed linear-nonlinear lattices [21][22][23].…”

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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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“…The NLS equation describing light propagation in optics [11] with real external potentials or/and gain-andloss distributions has been investigated [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] since the refractive index of the optical waveguide can be complex [29,30]. It is surprising to find that if the complex refractive index satisfies the property of the paritytime (PT ) symmetry [31], that is, if the real and imaginary parts of the refractive index are the even and odd functions of spatial position, respectively, then the propagation constant of the light can still be in all-real spectrum range, hence admitting stationary beam transmission [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

“…It is surprising to find that if the complex refractive index satisfies the property of the paritytime (PT ) symmetry [31], that is, if the real and imaginary parts of the refractive index are the even and odd functions of spatial position, respectively, then the propagation constant of the light can still be in all-real spectrum range, hence admitting stationary beam transmission [32][33][34][35]. Moreover, the complex PT -symmetric potentials can also support continuous families of stable solitons [17][18][19][20][21][22][23][24][25][26][27][28] even if the solitons appear in the range of the broken linear PT -symmetric phases (see, e.g., Ref. [18]).…”

Section: Introductionmentioning

confidence: 99%

Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation

Chen

Yan

2017

Phys. Rev. E

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The effect of derivative nonlinearity and parity-time-(PT -) symmetric potentials on the wave propagation dynamics is investigated in the derivative nonlinear Schrödinger equation, where the physically interesting Scarff-II and hamonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken/broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semi-elastic interactions between exact bright solitons and exotic incident waves are illustrated such that we find that exact nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.

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Gap solitons in parity-time complex periodic optical lattices with the real part of superlattices

Cited by 103 publications

References 18 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

Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation

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