Topological Photonics
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.
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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
TL;DR: In this paper, the authors provide an overview of the fundamental origins and important applications of the main spin-orbit interaction phenomena in modern optics that play a crucial role at subwavelength scales, including spin-Hall effects in inhomogeneous media and at optical interfaces, spindependent effects in non-paraxial (focused or scattered) fields, spin-controlled shaping of light using anisotropic structured interfaces (metasurfaces).
Abstract: This Review article provides an overview of the fundamental origins and important applications of the main spin–orbit interaction phenomena in modern optics that play a crucial role at subwavelength scales. Light carries both spin and orbital angular momentum. These dynamical properties are determined by the polarization and spatial degrees of freedom of light. Nano-optics, photonics and plasmonics tend to explore subwavelength scales and additional degrees of freedom of structured — that is, spatially inhomogeneous — optical fields. In such fields, spin and orbital properties become strongly coupled with each other. In this Review we cover the fundamental origins and important applications of the main spin–orbit interaction phenomena in optics. These include: spin-Hall effects in inhomogeneous media and at optical interfaces, spin-dependent effects in nonparaxial (focused or scattered) fields, spin-controlled shaping of light using anisotropic structured interfaces (metasurfaces) and robust spin-directional coupling via evanescent near fields. We show that spin–orbit interactions are inherent in all basic optical processes, and that they play a crucial role in modern optics.
1,642 citations
TL;DR: This work obtains the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by theNon-Bloch winding number instead of the Bloch-Hamiltonian-based topological number.
Abstract: The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone. The resultant phase diagrams dramatically differ from the usual Bloch theory. Specifically, we obtain the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by the non-Bloch winding number instead of the Bloch-Hamiltonian-based topological number. Our work settles the issue of the breakdown of conventional bulk-boundary correspondence and introduces the non-Bloch bulk-boundary correspondence.
1,326 citations
TL;DR: In this article, a review of the design and properties of active acoustic metamaterials can be found, as well as an overview of future directions in the field of sound manipulation.
Abstract: Acoustic metamaterials can manipulate and control sound waves in ways that are not possible in conventional materials. Metamaterials with zero, or even negative, refractive index for sound offer new possibilities for acoustic imaging and for the control of sound at subwavelength scales. The combination of transformation acoustics theory and highly anisotropic acoustic metamaterials enables precise control over the deformation of sound fields, which can be used, for example, to hide or cloak objects from incident acoustic energy. Active acoustic metamaterials use external control to create effective material properties that are not possible with passive structures and have led to the development of dynamically reconfigurable, loss-compensating and parity–time-symmetric materials for sound manipulation. Challenges remain, including the development of efficient techniques for fabricating large-scale metamaterial structures and converting laboratory experiments into useful devices. In this Review, we outline the designs and properties of materials with unusual acoustic parameters (for example, negative refractive index), discuss examples of extreme manipulation of sound and, finally, provide an overview of future directions in the field. Acoustic metamaterials can be used manipulate sound waves with a high degree of control. Their applications include acoustic imaging and cloaking. This Review outlines the designs and properties of these materials, discussing transformation acoustics theory, anisotropic materials and active acoustic metamaterials.
1,299 citations
TL;DR: In this article, a broad range of resonant electromagnetic effects by using two effective coupled oscillators, including the Fano resonance, electromagnetically induced transparency, Kerker and Borrmann effects, and parity-time symmetry breaking, are reviewed.
Abstract: The importance of the Fano resonance concept is recognized across multiple fields of physics. In this Review, Fano resonance is explored in the context of optics, with particular emphasis on dielectric nanostructures and metasurfaces. Rapid progress in photonics and nanotechnology brings many examples of resonant optical phenomena associated with the physics of Fano resonances, with applications in optical switching and sensing. For successful design of photonic devices, it is important to gain deep insight into different resonant phenomena and understand their connection. Here, we review a broad range of resonant electromagnetic effects by using two effective coupled oscillators, including the Fano resonance, electromagnetically induced transparency, Kerker and Borrmann effects, and parity–time symmetry breaking. We discuss how to introduce the Fano parameter for describing a transition between two seemingly different spectroscopic signatures associated with asymmetric Fano and symmetric Lorentzian shapes. We also review the recent results on Fano resonances in dielectric nanostructures and metasurfaces.
1,234 citations
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TL;DR: In this paper, the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations, are discussed.
Abstract: This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
20,824 citations
"Topological Photonics" refers background in this paper
...This is exactly the band structure of graphene (Neto et al., 2009; Wallace, 1947) exhibiting Dirac cones - conical touchings between bands at the Brillouin zone corners....
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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
"Topological Photonics" refers background in this paper
...Analogously, edge states around a generic topologically nontrivial system can be understood as interface states between the system and the topologically trivial vacuum (Hasan and Kane, 2010)....
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...been intense investigation in condensed-matter physics into what different topological phases of matter are possible under various symmetries, and what are the physical consequences of this physics (Bernevig and Hughes, 2013; Chiu et al., 2016; Hasan and Kane, 2010; Qi and Zhang, 2011)....
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..., 2011): topological band theory (Bansil et al., 2016; Hasan and Kane, 2010; Qi and Zhang, 2011) directly applies to the Bloch bands associated with the...
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TL;DR: If a three-dimensionally periodic dielectric structure has an electromagnetic band gap which overlaps the electronic band edge, then spontaneous emission can be rigorously forbidden.
Abstract: It has been recognized for some time that the spontaneous emission by atoms is not necessarily a fixed and immutable property of the coupling between matter and space, but that it can be controlled by modification of the properties of the radiation field. This is equally true in the solid state, where spontaneous emission plays a fundamental role in limiting the performance of semiconductor lasers, heterojunction bipolar transistors, and solar cells. If a three-dimensionally periodic dielectric structure has an electromagnetic band gap which overlaps the electronic band edge, then spontaneous emission can be rigorously forbidden.
12,787 citations
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
"Topological Photonics" refers background in this paper
...Topological ideas in photonics branch from exciting developments in solid-state materials, along with the discovery of new phases of matter called topological insulators [1, 2]....
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...[2] Xiao-Liang Qi and Shou-Cheng Zhang, “Topological insulators and superconductors,” Rev....
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TL;DR: A new mechanism for strong Anderson localization of photons in carefully prepared disordered dielectric superlattices with an everywhere real positive dielectrics constant is described.
Abstract: A new mechanism for strong Anderson localization of photons in carefully prepared disordered dielectric superlattices with an everywhere real positive dielectric constant is described. In three dimensions, two photon mobility edges separate high- and low-frequency extended states from an intermediate-frequency pseudogap of localized states arising from remnant geometric Bragg resonances. Experimentally observable consequences are discussed.
9,067 citations
"Topological Photonics" refers background in this paper
...Most of the early literature on photonic crystals focused on the possibility of realizing a complete photonic band gap (John, 1987; Yablonovitch, 1987) that could, e....
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