Multimode One-Way Waveguides of Large Chern Numbers

Skirlo, Scott A.; Lü, Ling; Soljačić, Marin

doi:10.1103/physrevlett.113.113904

Cited by 276 publications

(201 citation statements)

References 31 publications

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“…More recently, and of more direct interest here, there has been a lot of work on various photonic systems that demonstrate non-trivial Berry properties, both for periodic and continuum materials [40]- [42]. The principal interest in these systems is because at the interface between two regions with different Berry curvatures, a backscatteringimmune (i.e., unidirectional) surface plasmon-polariton (SPP) can propagate.…”

Section: Arxiv:161101670v2 [Quant-ph] 14 Jan 2017mentioning

confidence: 99%

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Gangaraj

Silveirinha

Hanson

2017

IEEE J. Multiscale Multiphys. Comput. Tech.

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Abstract-The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical Schrödinger equation, writing both in Hamiltonian form. However, the aforementioned quantities are not necessarily quantum in nature, and for photonic systems they can be explained using only classical concepts. Here we provide a derivation and description of PTI quantities using classical Maxwell's equations, we demonstrate how an electromagnetic mode can acquire Berry phase, and we discuss the ramifications of this effect. We consider several examples, including wave propagation in a biased plasma, and radiation by a rotating isotropic emitter. These concepts are discussed without invoking quantum mechanics, and can be easily understood from an engineering electromagnetics perspective.Index Terms-Berry Phase, surface wave, photonic topological insulator.

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Section: Arxiv:161101670v2 [Quant-ph] 14 Jan 2017mentioning

confidence: 99%

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Gangaraj

Silveirinha

Hanson

2017

IEEE J. Multiscale Multiphys. Comput. Tech.

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“…DOI: 10.1103/PhysRevLett.115.104302 PACS numbers: 46.40.Cd, 46.40.Ff, 73.43.-f Topological states in electronic materials, including the quantum Hall effect [1] and topological insulators [2,3], have inspired a number of recent developments in photonics [4,5], phononics [6][7][8][9], and mechanical metamaterials [10][11][12][13]. In particular, in analogy to the quantum anomalous Hall effect [14], one-way electromagnetic waveguides in two-dimensional systems have been realized by breaking time-reversal symmetry [15][16][17][18].Very recently, unidirectional edge channels have been proposed for elastic waves using Coriolis force in a noninertial reference frame [19], but such a rotating frame is very difficult to implement in solid state devices. Moreover, one-way propagation of scalar acoustic waves has also been proposed by introducing rotating fluids [20][21][22].…”

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Topological Phononic Crystals with One-Way Elastic Edge Waves

2015

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We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging. DOI: 10.1103/PhysRevLett.115.104302 PACS numbers: 46.40.Cd, 46.40.Ff, 73.43.-f Topological states in electronic materials, including the quantum Hall effect [1] and topological insulators [2,3], have inspired a number of recent developments in photonics [4,5], phononics [6][7][8][9], and mechanical metamaterials [10][11][12][13]. In particular, in analogy to the quantum anomalous Hall effect [14], one-way electromagnetic waveguides in two-dimensional systems have been realized by breaking time-reversal symmetry [15][16][17][18].Very recently, unidirectional edge channels have been proposed for elastic waves using Coriolis force in a noninertial reference frame [19], but such a rotating frame is very difficult to implement in solid state devices. Moreover, one-way propagation of scalar acoustic waves has also been proposed by introducing rotating fluids [20][21][22]. However, it is important to recognize that elastic waves in solids have both transverse and longitudinal polarizations, while acoustic waves in fluids are purely longitudinal. As a result, it is challenging to achieve topological protection for elastic waves on an integrated platform.Here, we present a robust strategy to create topologically nontrivial edge modes for both longitudinal and transverse polarizations in a solid medium. In particular, we introduce gyroscopic phononic crystals, where each lattice site is coupled with a spinning gyroscope that breaks timereversal symmetry in a well-controlled manner. In both hexagonal and square lattices, gyroscopic coupling opens band gaps that are characterized by Chern numbers of 1 and 2. As a result, at the edge of these lattices both single-mode and multimode one-way elastic waves are observed to propagate around arbitrary defects without backscattering.To start, we consider a hexagonal phononic crystal with equal masses (m 2 ¼ m 1 ) connected by linear springs [red and black rods in Figs. 1(a) and 1(b)]. The resulting unit cell has 4 degrees of freedom specified by the displacements of m 1 and m 2 (U ¼ ½u for wave vectors μ within the first Brillouin zone. Here, ω denotes the angular frequency of the propagating wave and M ¼ diagfm 1 ; m 1 ; m 2 ; m 2 g is the mass matrix. Moreover, K is the 4 × 4 stiffness matrix and is a functi...

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“…For example, a chirality-based robust transport was first observed in timereversal (TR) invariant photonic crystals 11 that are topologically 'trivial'. Non-trivial bandgap characterized by non-zero Chern numbers has been achieved in TR broken photonic systems with either external magnetic field [12][13][14][15] or dynamical modulation 16 . Coupled helical waveguide array 17 and hyperbolic metamaterial 18 were utilized to explore topological state by breaking z-reversal symmetry.…”

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confidence: 99%

Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide

et al. 2014

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Photonic analogue of topological insulator was recently predicted by arranging e/m (permittivity/permeability)-matched bianisotropic metamaterials into two-dimensional superlattices. However, the experimental observation of such photonic topological insulator is challenging as bianisotropic metamaterial is usually highly dispersive, so that the e/mmatching condition can only be satisfied in a narrow frequency range. Here we experimentally realize a photonic topological insulator by embedding non-bianisotropic and non-resonant metacrystal into a waveguide. The cross coupling between transverse electric and transverse magnetic modes exists in metacrystal waveguide. Using this approach, the e/m-matching condition is satisfied in a broad frequency range which facilitates experimental observation. The topologically non-trivial bandgap is confirmed by experimentally measured transmission spectra and calculated non-zero spin Chern numbers. Gapless spin-filtered edge states are demonstrated experimentally by measuring the magnitude and phase of the fields. The transport robustness of the edge states is also observed when an obstacle was introduced near the edge.

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Multimode One-Way Waveguides of Large Chern Numbers

Cited by 276 publications

References 31 publications

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Topological Phononic Crystals with One-Way Elastic Edge Waves

Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide

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