Interplay of disorder and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>symmetry in one-dimensional optical lattices

Mejía-Cortés, Cristian; Molina, Mario I.

doi:10.1103/physreva.91.033815

Cited by 41 publications

(25 citation statements)

References 45 publications

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“…The nonlinear effects in PT-symmetric systems can be utilized for an efficient control of light including all-optical low-threshold switching and unidirectional invisibility [24,56,57]. The possibility to engineer PT-symmetric oligomers, which may include nonlinearity, triggers a broad variety of studies on both the few-site systems and entire PT-symmetric lattices, including onedimensional PT-symmetric dimer [35,58], trimer [58,59], quadrimer [58,60], 2D PT-symmetric plaquettes [60,61], PT-symmetric finite/infinite chains [62][63][64][65], necklaces [66] and multicore fibers [67].…”

Section: Discrete Pt-symmetric Oligomersmentioning

confidence: 99%

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: Discrete Pt-symmetric Oligomersmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

352

263

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“…Thus questions about localization and PT -symmetry breaking in a disordered PT -symmetric system appear moot. 31,32 In this report, we show that the PT -symmetric phase in a disordered system is not always fragile, and that it is protected against random tunneling or on-site potential disorder if the disorder has specific periodicities. We elucidate an underlying symmetry that is critical for the said protection.…”

Section: Introductionmentioning

confidence: 62%

“…We note that in this regime, the intensity I d (k,t) does not reach a steady state value. 4,31,32 Figure 3 (c)-(e) encapsulates the effects of correlated disorder on the disorder-averaged site-and time-dependent intensity I d (k,t). The results are for an N = 39 site lattice with on-site potential disorder with periodicity p = 10, number of disorder realizations M = 10 3 , and an initial state localized at the center of the lattice, k 0 = 20.…”

Section: Disorder Induced Pt Threshold Distribution and Localizationmentioning

confidence: 99%

Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization

Harter

Onanga

Joglekar

2018

Sci Rep

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Open, non-equilibrium systems with balanced gain and loss, known as parity-time ()-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the -symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials ±iγ at reflection-symmetric sites. Contrary to the popular belief, we show that the -symmetric phase is protected in the presence of a periodic disorder which leads to a positive -symmetry breaking threshold. We uncover a veiled symmetry of such disordered systems that is instrumental for the said protection, and show that this symmetry leads to new localization behavior across the -symmetry breaking transition. We elucidate the interplay between such localization and the -symmetry breaking phenomena in disordered -symmetric lattices, with Hermitian disorder or gain-loss disorder, and support our conclusions with a beampropagation- method analysis. Our theoretical predictions provide avenues for experimental realizations of -symmetric systems with engineered disorder.

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“…The eigenvalues of matrix C -1 are pairs of two purely real numbers for γ < 0.107, coincide at an EP for γ = 0.107, and then split into a complex conjugate pair ( Figure 6D). This eigenvalue behavior is equivalent to the transition of PT-symmetric Hamiltonians in quantum mechanics from the PT-symmetric phase to the PT-broken phase [11,13,88,89]. The EP of the constitutive matrix C -1 is actually the EP of the S matrix, which leads to the unidirectional reflectionless behavior shown in Figure 6B and C.…”

Section: Unidirectional Reflectionless Propagation In Pt-symmetric Symentioning

confidence: 96%

Unidirectional reflectionless light propagation at exceptional points

et al. 2017

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Abstract:In this paper, we provide a comprehensive review of unidirectional reflectionless light propagation in photonic devices at exceptional points (EPs). EPs, which are branch point singularities of the spectrum, associated with the coalescence of both eigenvalues and corresponding eigenstates, lead to interesting phenomena, such as level repulsion and crossing, bifurcation, chaos, and phase transitions in open quantum systems described by non-Hermitian Hamiltonians. Recently, it was shown that judiciously designed photonic synthetic matters could mimic the complex non-Hermitian Hamiltonians in quantum mechanics and realize unidirectional reflection at optical EPs. Unidirectional reflectionlessness is of great interest for optical invisibility. Achieving unidirectional reflectionless light propagation could also be potentially important for developing optical devices, such as optical network analyzers. Here, we discuss unidirectional reflectionlessness at EPs in both parity-time (PT)-symmetric and non-PT-symmetric optical systems. We also provide an outlook on possible future directions in this field.

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Interplay of disorder andPTsymmetry in one-dimensional optical lattices

Cited by 41 publications

References 45 publications

Nonlinear switching and solitons in PT‐symmetric photonic systems

Nonlinear switching and solitons in PT‐symmetric photonic systems

Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization

Unidirectional reflectionless light propagation at exceptional points

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