Optical mesh lattices with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>symmetry

Miri, Mohammad‐Ali; Regensburger, Alois; Peschel, Ulf; Christodoulides, Demetrios N.

doi:10.1103/physreva.86.023807

Cited by 109 publications

(81 citation statements)

References 70 publications

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“…This model can be treated as the bi-layer model with alternating gain/loss sites, thus creating the structure belonging to the class of PT-symmetric models revealing quite unexpected properties of scattering see, for example, [13,15,18,24,30,31]). …”

Section: The Modelmentioning

confidence: 99%

“…In other words, this symmetry demands that the refractive index profile must be an even function of position while the gain/loss spatial distribution should be antisymmetric. As pointed out in several studies [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], PT-symmetry can lead to a number of intriguing processes. These include for example band-merging effects in PT-symmetric lattices [8], abrupt phase transitions [12], power oscillations and double refraction, and unidirectional invisibility [14,16,24].…”

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confidence: 99%

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Gain- or loss-induced localization in one-dimensionalPT-symmetric tight-binding models

et al. 2014

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We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of PT-symmetry in energy transport problems occurring in such PT-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples.

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Section: The Modelmentioning

confidence: 99%

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confidence: 99%

Gain- or loss-induced localization in one-dimensionalPT-symmetric tight-binding models

et al. 2014

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“…[200], they investigated a class of optical mesh periodic structures that are discretized in both the transverse and longitudinal directions, which is equivalent to the above ones in the temporal domain. The mesh arrangements are composed of an array of waveguides with each one being discretely and periodically coupled to its adjacent neighbors.…”

Section: Mesh Latticesmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

338

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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“…Guided by the tight-binding analogy above, we apply the so-called Floquet-Bloch ansatz for the eigenstates 32,33 …”

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confidence: 99%

Experimental measurement of the Berry curvature from anomalous transport

et al. 2017

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The geometric properties of energy bands underlie fascinating phenomena in many systems, including solid-state, ultracold gases and photonics. The local geometric characteristics such as the Berry curvature 1 can be related to global topological invariants such as those classifying the quantum Hall states or topological insulators. Regardless of the band topology, however, any non-zero Berry curvature can have important consequences, such as in the semi-classical evolution of a coherent wavepacket. Here, we experimentally demonstrate that the wavepacket dynamics can be used to directly map out the Berry curvature. To this end, we use optical pulses in two coupled fibre loops to study the discrete time evolution of a wavepacket in a one-dimensional geometric 'charge' pump, where the Berry curvature leads to an anomalous displacement of the wavepacket. This is both the first direct observation of Berry curvature e ects in an optical system, and a proof-ofprinciple demonstration that wavepacket dynamics can serve as a high-resolution tool for mapping out geometric properties.The Berry curvature is a geometrical property of an energy band, which plays a key role in many physical phenomena as it encodes how eigenstates evolve as a local function of parameters 1 . In a twodimensional (2D) quantum Hall system, for example, the integral of the Berry curvature over the 2D Brillouin zone determines the Chern number: a global topological invariant that underlies the quantization of Hall transport for a 2D filled energy band 2 . As first explained by Thouless 3 , there can be an analogous topological quantization of particle transport in a 1D band insulator, when the lattice potential is 'pumped' , that is, is slowly and periodically modulated in time. Also in this case, the geometrical and topological properties are defined for an effective 2D parameter space, but now one spanned by the 1D Bloch momentum and the external periodic pumping parameter.A local non-zero Berry curvature can have striking physical effects in both 2D systems and 1D pumps, regardless of whether the global topological Chern number is non-trivial. In the simplest case, a semi-classical wavepacket moves as a coherent object governed by classical equations of motion with an additional 'anomalous' Hall velocity due to the geometrical Berry curvature at its centre-ofmass, as an external force is applied or as the control parameter is pumped 1,4 . As highlighted further below, this anomalous transport can be understood physically as the Berry curvature acting like a magnetic field in parameter space [5][6][7] .In recent years, there have been many landmark experiments to engineer and study geometrical and topological energy bands in ultracold gases and photonics . In photonics, for example, topological edge states have been studied in a wide variety of (effectively) 1D set-ups, such as quantum walks 14 and pumping in optical quasicrystals 13,29,30 , as well as in 2D quantum Hall-like systems of photonic crystals 9-11 , propagating waveguides 12 and silico...

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Optical mesh lattices withPTsymmetry

Cited by 109 publications

References 70 publications

Gain- or loss-induced localization in one-dimensionalPT-symmetric tight-binding models

Gain- or loss-induced localization in one-dimensionalPT-symmetric tight-binding models

Nonlinear switching and solitons in PT‐symmetric photonic systems

Experimental measurement of the Berry curvature from anomalous transport

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