Direct observation of valley-polarized topological edge states in designer surface plasmon crystals

Wu, Xiaoxiao; Meng, Yan; Tian, Jingxuan; Huang, Yingzhou; Xiang, Hong; Han, Dezhuan; Wen, Weijia

doi:10.1038/s41467-017-01515-2

Cited by 345 publications

(298 citation statements)

References 57 publications

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“…According to k·p method, the effective Hamiltonian around K/K′ valley can be expressed as H K/K′ ( δ k ) = ±( v D δk x σ x + v D δk y σ y ) ± mv D 2 σ z , where δ k = k − k K/K′ is the displacement of wave vector k to K/K′ valley in the reciprocal space, v D is the group velocity, m is the effective mass term, and σ i = ( i = x, y, z ) are elements in the Pauli matrices . Solving the effective Hamiltonian, we can obtain the Berry curvature at K/K′ valley,

Ω_{K / {normalK}^{'}} (δ k) = \pm \frac{m v_{normalD}}{2 {(δ k^{2} + m^{2} v_{normalD}^{2})}^{3 / 2}}

. In order to consolidate the above theoretical analysis, we calculate the Berry curvatures of the four bands near K valley by performing first‐principle simulations of the practical structure in the COMSOL Multiphysics, as shown in Figure e.…”

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confidence: 99%

Valley‐Hall Photonic Topological Insulators with Dual‐Band Kink States

Chen

Zhang

et al. 2019

Advanced Optical Materials

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Extensive researches have revealed that valley, a binary degree of freedom (DOF), can be an excellent candidate of information carrier. Recently, valley DOF is introduced into photonic systems, and several valley‐Hall photonic topological insulators (PTIs) are experimentally demonstrated. However, in the previous valley‐Hall PTIs, topological kink states only work at a single frequency band, which limits potential applications in multiband waveguides, filters, communications, and so on. To overcome this challenge, here a valley‐Hall PTI, where the topological kink states exist at two separated frequency bands, is experimentally demonstrated in a microwave substrate‐integrated circuitry. Both the simulated and experimental results demonstrate the dual‐band valley‐Hall topological kink states are robust against the sharp bends of the internal domain wall with negligible intervalley scattering. This work may pave the way for multichannel substrate‐integrated photonic devices with high efficiency and high capacity for information communications and processing.

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Ω_{K / {normalK}^{'}} (δ k) = \pm \frac{m v_{normalD}}{2 {(δ k^{2} + m^{2} v_{normalD}^{2})}^{3 / 2}}

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confidence: 99%

Valley‐Hall Photonic Topological Insulators with Dual‐Band Kink States

Chen

Zhang

et al. 2019

Advanced Optical Materials

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“…Due to the high efficiency of the coupling between the topological modes and free space modes, we anticipate many practical applications for directional antennas, lasers, and other communication devices across the electromagnetic spectrum. During preparation of this work, two related reports 29,30 of experimental realizations of photonic valley edge states were brought to our attention. The fundamental difference of our work is the demonstration of topologically protected refraction.…”

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confidence: 99%

Topologically protected refraction of robust kink states in valley photonic crystals

et al. 2017

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Recently discovered1,2 valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials [3][4][5][6][7][8][9] . Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states [3][4][5][6][7][8][9] at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling e ciency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an e ective spin-orbit coupling in one of the VPC domains. This also constitutes the first realization of spin-valley locking for topological valley transport.

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“…This map proves that the wave is indeed guided by the interface line between the two inverted dual‐metasurfaces with good localization and negligible scattering losses at the bends. Note that the edge modes are also robust against 90° bends, as demonstrated in Figure d, since they could also occur along the armchair edge of the hexagonal metasurface, unlike the so‐called valley topological insulators …”

Section: Resultsmentioning

confidence: 96%

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

Bisharat

Sievenpiper

2019

Laser & Photonics Reviews

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The discovery of topological insulators was rapidly followed by the advent of their photonic analogues, motivated by the prospect of backscattering‐immune light propagation. So far, however, implementations have mainly relied on engineering bulk modes in photonic crystals and waveguide arrays in two‐dimensional (2D) systems, which closely mimic their electronic counterparts. In addition, metamaterials‐based implementations subject to electromagnetic duality and bianisotropy conditions suffer from intricate designs and narrow operating bandwidths. Here, it is shown that symmetry‐protected topological states akin to the quantum spin‐Hall effect can be realized in a straightforward manner by coupling surface modes over metasurfaces of complementary electromagnetic responses. Specifically, stacking unit cells of such metasurfaces directly results in double Dirac cones of degenerate transverse‐electric (TE) and transverse‐magnetic (TM) modes, which break into a wide nontrivial bandgap at small interlayer separation. Consequently, the ultrathin structure supports robust gapless edge states, which are confined along a one‐dimensional (1D) line rather than a surface interface, as demonstrated at microwave frequencies by near‐field imaging. The simplicity and versatility of the proposed approach proves attractive as a tabletop platform for the study of classical topological phases, as well as for applications benefiting the compactness of metasurfaces and the potential of topological insulators.

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Direct observation of valley-polarized topological edge states in designer surface plasmon crystals

Cited by 345 publications

References 57 publications

Valley‐Hall Photonic Topological Insulators with Dual‐Band Kink States

Valley‐Hall Photonic Topological Insulators with Dual‐Band Kink States

Topologically protected refraction of robust kink states in valley photonic crystals

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

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