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Journal ArticleDOI

Photonic topological insulators

01 Mar 2013-Nature Materials (Nature Publishing Group)-Vol. 12, Iss: 3, pp 233-239
TL;DR: It is shown that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those identified for condensed-matter topological insulators.
Abstract: Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.
Citations
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Journal ArticleDOI
TL;DR: Weyl and Dirac semimetals as discussed by the authors are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry, and they have generated much recent interest.
Abstract: Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

3,407 citations

Journal ArticleDOI
TL;DR: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light as mentioned in this paper, which holds great promise for applications.
Abstract: Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

3,052 citations


Cites background or methods from "Photonic topological insulators"

  • ...Starting with an introduction to the relevant topological concepts, we introduce the 2D quantum Hall phase through the stability of Dirac cones [4, 5], followed by its realizations in gyromagnetic photonic crystals [7, 8, 13], in coupled resonators [9, 10, 16] and waveguides [15], in bianisotropic metamaterials [11] and in quasicrystals [14]....

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  • ...In their inspiring theoretical proposal [11], Khanikaev et al....

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  • ...[11] Alexander B Khanikaev, S Hossein Mousavi, Wang-Kong Tse, Mehdi Kargarian, Allan H MacDonald, and Gennady Shvets, “Photonic topological insulators,” Nature materials 12, 233– 239 (2013)....

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  • ...Edge states of T -invariant topological phases [11, 58] do not have reflection even when the system is reciprocal, thus it might be possible that isolators are unnecessary for photonic circuits consisting of T -invariant topological phases....

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Journal ArticleDOI
11 Apr 2013-Nature
TL;DR: This work proposes and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport—a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges.
Abstract: Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrodinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering.

2,483 citations

Journal ArticleDOI
TL;DR: In this paper, the interplay between parity-time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics has been explored both theoretically and experimentally.
Abstract: In recent years, notions drawn from non-Hermitian physics and parity–time (PT) symmetry have attracted considerable attention. In particular, the realization that the interplay between gain and loss can lead to entirely new and unexpected features has initiated an intense research effort to explore non-Hermitian systems both theoretically and experimentally. Here we review recent progress in this emerging field, and provide an outlook to future directions and developments. This Review Article outlines the exploration of the interplay between parity–time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics.

1,831 citations

Journal ArticleDOI
TL;DR: In this paper, a review of recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems is presented, from the superfluid flow around a defect at low speeds to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles.
Abstract: This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

1,469 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topologically insulators have been observed.
Abstract: Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.

15,562 citations

Journal ArticleDOI
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

11,092 citations


"Photonic topological insulators" refers background in this paper

  • ...The recent discovery of two [ 1, 2] and three [ 3, 4, 5, 6, 7] dimensional topological insulators has stimulated interest in nontrivial topological phases....

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Journal ArticleDOI
TL;DR: The authors' simulations show that a version of the lens operating at the frequency of visible light can be realized in the form of a thin slab of silver, which resolves objects only a few nanometers across.
Abstract: Optical lenses have for centuries been one of scientists’ prime tools. Their operation is well understood on the basis of classical optics: curved surfaces focus light by virtue of the refractive index contrast. Equally their limitations are dictated by wave optics: no lens can focus light onto an area smaller than a square wavelength. What is there new to say other than to polish the lens more perfectly and to invent slightly better dielectrics? In this Letter I want to challenge the traditional limitation on lens performance and propose a class of “superlenses,” and to suggest a practical scheme for implementing such a lens. Let us look more closely at the reasons for limitation in performance. Consider an infinitesimal dipole of frequency v in front of a lens. The electric component of the field will be given by some 2D Fourier expansion,

10,974 citations

Journal ArticleDOI
06 Apr 2001-Science
TL;DR: These experiments directly confirm the predictions of Maxwell's equations that n is given by the negative square root ofɛ·μ for the frequencies where both the permittivity and the permeability are negative.
Abstract: We present experimental scattering data at microwave frequencies on a structured metamaterial that exhibits a frequency band where the effective index of refraction (n) is negative. The material consists of a two-dimensional array of repeated unit cells of copper strips and split ring resonators on interlocking strips of standard circuit board material. By measuring the scattering angle of the transmitted beam through a prism fabricated from this material, we determine the effective n, appropriate to Snell's law. These experiments directly confirm the predictions of Maxwell's equations that n is given by the negative square root of epsilon.mu for the frequencies where both the permittivity (epsilon) and the permeability (mu) are negative. Configurations of geometrical optical designs are now possible that could not be realized by positive index materials.

8,477 citations


"Photonic topological insulators" refers background in this paper

  • ...To achieve the desirable - matched bi-anisotropic metamaterial we propose here a design which is rather traditional for the microwave spectral range [ 45]....

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