Experimental demonstration of the robust edge states in a split-ring-resonator chain

Jiang, Jun; Guo, Zhiwei; Ding, Yaqiong; Sun, Yipeng; Li, Yunhui; Jiang, Haitao; Chen, Hong

doi:10.1364/oe.26.012891

Cited by 41 publications

(32 citation statements)

References 48 publications

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“…The eigenfunctions of these modes identify them as edge states. Similarly appearing edge states have been observed in one-dimensional photonic systems previously [7]. Figure 3E shows how the edge state branches off as an isolated state separated from the two semicontinuous energy bands (blue arrow).…”

Section: Numerical Simulations Of Large Resonator Arrayssupporting

confidence: 77%

“…Radiofrequency resonator arrays offer intriguing possibilities for the creation and study of topological modes due not only to the number of geometries and topologies that can be easily realized, but also because they are based upon convenient, readily fabricated and manipulated substrates that can be easily translated into working devices at a range of length scales [6,7,9,[11][12][13][14][15][16]. Perhaps the most common application of bulk modes of radiofrequency resonators is in medical magnetic resonance imaging [17].…”

Section: Topological Modesmentioning

confidence: 99%

“…This discovery has not only led to observations of new properties of periodic systems observed in nature, but also to new materials in the quantum and classical regimes. Many of these systems are relatively simple, and include chains of massspring oscillators [3], magnetically coupled spinners [2], plasmonic nanoparticles [4,5], dielectric resonator chains [6,7], planar metasurface architectures [8], microwave arrays [9], and acoustic systems [10].…”

Section: Topological Modesmentioning

confidence: 99%

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Topological modes in radiofrequency resonator arrays

Voss

Ballon

2020

Physics Letters A

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Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an experimental and an accompanying numerical toolbox to create and analyze topological states in coupled radiofrequency resonator arrays. The arrays are coupled harmonic oscillator systems that are very easily constructed, offer a variety of geometric configurations, and whose eigenfunctions and eigenvalues are amenable to detailed analysis. These systems offer well defined analogs to coupled oscillator systems in general in that they are characterized by resonances whose frequency spectra depend on the individual resonators, the interactions between them, and the geometric and topological symmetries and boundary conditions. In particular, we describe an experimental analog of a small one-dimensional system, with excellent agreement with theory. The numerical part of the toolbox allows for simulations of larger mesoscopic systems with a semi-continuous band structure, in which all resonators still exhibit individual signatures. Systematic parameter variation yields an astonishing richness of band structures in this simple linear system, allowing for further explorations into novel phenomena of topological modes.

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Section: Numerical Simulations Of Large Resonator Arrayssupporting

confidence: 77%

Section: Topological Modesmentioning

confidence: 99%

Section: Topological Modesmentioning

confidence: 99%

See 1 more Smart Citation

Topological modes in radiofrequency resonator arrays

Voss

Ballon

2020

Physics Letters A

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“…Topology is at the heart of modern condensed matter physics [1][2][3][4] and photonics [5][6][7][8]. It can be found in electronic [9,10], photonic [11][12][13][14][15][16], acoustic [17][18][19], and mechanical [20] systems, just to give four examples. Topology in physics refers to generic electronic properties of a condensed system (or photonic system if photons are concerned), which are unchanged by continuous deformations of the Hamiltonian parameters, as long as the gaps in the spectrum remain open.…”

Section: Introductionmentioning

confidence: 99%

Topological photonic Tamm states and the Su-Schrieffer-Heeger model

et al. 2020

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In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed. arXiv:2001.10628v1 [cond-mat.mes-hall]

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“…1 The experimental results for the spinner systems presented here have broad implications for other metamaterials, particularly for a large class of metamaterials experimentally shown to realize the 1D SSH model and its edge or antiphase boundary states. It includes photonic [19,[25][26][27][28][29], electronic [30], plasmonic [31], acoustic [23], and microwave [32] metamaterials, and lattices of the Bose-Einstein condensates [33], circuit elements [34][35][36][37], and split-ring-resonators [38]. In particular, flat bands and localized modes have significant technological applications in photonics.…”

Section: (G))mentioning

confidence: 99%

Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials

Qian,

Zhu,

Ahn

et al. 2020

Preprint

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Motivated by the recent theoretical studies on a two-dimensional (2D) chiral Hamiltonian based on the Su-Schrieffer-Heeger chains [L. Zhu, E. Prodan, and K. H. Ahn, Phys. Rev. B 99, 041117(R) (2019)], we experimentally and computationally demonstrate that topological flat frequency bands can occur at open edges of 2D planar metamaterials and at antiphase boundary seams of ring-shaped or tubular metamaterials. Specifically, using mechanical systems made of magnetically coupled spinners, we reveal that the presence of the edge or seam bands that are flat in the entire projected reciprocal space follows the predictions based on topological winding numbers. The edge-to-edge distance sensitively controls the flatness of the edge bands and the localization of excitations. The analogue of the fractional charge state is also observed. Possible realizations of flat bands in a large class of metamaterials, including photonic crystals and electronic metamaterials, are discussed.

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Experimental demonstration of the robust edge states in a split-ring-resonator chain

Cited by 41 publications

References 48 publications

Topological modes in radiofrequency resonator arrays

Topological modes in radiofrequency resonator arrays

Topological photonic Tamm states and the Su-Schrieffer-Heeger model

Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials

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