Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs

Chen, Xiao; Deng, Wei; Shi, Fu‐Long; Zhao, Fuli; Chen, Min; Dong, Jian‐Wen

doi:10.1103/physrevlett.122.233902

Cited by 488 publications

(219 citation statements)

References 49 publications

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“…Note added: Independent of this work, other photonic realisations of corner states were simultaneously reported, albeit in two-dimensional setups [29,30,31,32], which are entirely different from ours using three-dimensional coupled waveguides.…”

Section: Resultsmentioning

confidence: 86%

Corner states of light in photonic waveguides

Hassan¹,

Kunst²,

Moritz³

et al. 2019

Nat. Photonics

442

244

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The recently established paradigm of higher-order topological states of matter has shown that not only, as previously thought, edge and surface states but also states localised to corners can have robust and exotic properties. Here we report on the experimental realisation of novel corner states made out of classical light in three-dimensional photonic structures inscribed in glass samples using femtosecond (fs) laser technology. By creating and analysing waveguide arrays forming two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localised at the corners in a finite frequency range in complete analogy with a theoretical model of the breathing kagome. Here, the measurements reveal that light can be "fractionalised", corresponding to simultaneous localisation to each corner of a triangular sample, even in the presence of defects. The fabrication method applied in this work exposes the advantage of using fs-laser writing for producing compact three-dimensional devices thus paving the way for technological applications by simulating novel higher-order states of matter. arXiv:1812.08185v3 [cond-mat.mes-hall]

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Section: Resultsmentioning

confidence: 86%

Corner states of light in photonic waveguides

Hassan¹,

Kunst²,

Moritz³

et al. 2019

Nat. Photonics

442

244

View full text Add to dashboard Cite

show abstract

“…[26][27][28] Such a dipole field related to the Zak phase is used to design topological materials, i.e., topological electrides 29,30 and A 3 B atomic sheet such as C 3 N. 31,32 Recently, this idea is extended to an electric quadrapole moment which induces topological corner states. [33][34][35][36][37][38][39][40] In addition, since topological design on the basis of Zak phase does not demand the spin-orbit couplings, this approach is useful to apply to nonelectronic systems such as topological photonic, [41][42][43][44][45] accoustic crystals [46][47][48][49] and topological circuit. 50 One of the most simple models to demonstrate the topological phase transition owing to Zak phase associated with zero Berry curvature is Su-Schrieffer-Heeger (SSH) model 51,52 on two-dimensional (2D) square lattice.…”

Section: Introductionmentioning

confidence: 99%

Topological edge states in the Su-Schrieffer-Heeger model

2019

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Su-Schrieffer-Heeger (SSH) model on two-dimensional square lattice exhibits a topological phase transition, which is related to the Zak phase determined by bulk band topology. The strong modulation of electron hopping causes nontrivial charge polarization even in the presence of inversion symmetry. The energy band structures and topological edge states have been calculated numerically in previous studies. Here, however, full energy spectrum and explicit form of wave functions for two-dimensional bulk and one-dimensional ribbon geometries of SSH model are analytically derived using wave mechanics approach. Explicit analytic representations of wave functions provide the information of parity for each subband, localization length and critical point of topological phase transition in SSH ribbon. It is also shown that the dimensional crossover of topological transition point for SSH model from one to two-dimension.

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“…Owing to the experimental advantages compared to other classical wave systems (such as easy implementations in macro scale [13,14] and direct measurements [15,16]), nowadays, acoustics is intensively used as a test-bed for topological wave physics.…”

Section: Introductionmentioning

confidence: 99%

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

et al. 2020

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In this work, we study the propagation of sound waves in a honeycomb waveguide network loaded with Helmholtz resonators (HRs). By using a plane wave approximation in each waveguide we obtain a first-principle modeling of the network, which is an exact mapping to the graphene tight-binding Hamiltonian. We show that additional Dirac points appear in the band diagram when HRs are introduced at the network nodes. It allows to break the inversion (sub-lattice) symmetry by tuning the resonators, leading to the appearence of edge modes that reflect the configuration of the zigzag boundaries. Besides, the dimerization of the resonators also permits the formation of interface modes located in the band gap, and these modes are found to be robust against symmetry preserving defects. Our results and the proposed networks reveal the additional degree of freedom bestowed by the local resonance in tuning the properties of not only acoustical graphene-like structures but also of more complex systems.

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Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs

Cited by 488 publications

References 49 publications

Corner states of light in photonic waveguides

Corner states of light in photonic waveguides

Topological edge states in the Su-Schrieffer-Heeger model

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

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