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Condensed matter systems with topological order and metamaterials with left-handed chirality have attracted recently extensive interests in the fields of physics and optics. So far the two fields are independent, and there is no work to address their connection. Here we propose to establish the relation between the topological order in condensed matter systems and the chirality in metamaterials, by mapping explicitly Maxwells equations to the Dirac equation in one dimension. We report an experimental implement of the band inversion in the Dirac equation, which accompanies change of chirality of electromagnetic wave in metamaterials, and the first microwave measurement of topological excitations and topological phases in one dimension. Our finding provides a proof-of-principle example that electromagnetic wave in the metamaterials can be used to simulate the topological order in condensed matter systems and quantum phenomena in relativistic quantum mechanics in a controlled laboratory environment.
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The excitation of toroidal multipoles in metamaterials was investigated for high-Q response at a subwavelength scale. In this study, we explored the optimization of toroidal excitations in a planar metamaterial comprised of asymmetric split ring resonators (ASRRs). It was found that the scattering power of toroidal dipole can be remarkably strengthened by adjusting the characteristic parameter of ASRRs: asymmetric factor. Interestingly, the improvement in toroidal excitation accompanies increment on the Q-factor of the toroidal metamaterial; it is shown that both the scattering power of toroidal dipole and the Q-factor were increased more than one order by changing the asymmetric factor of ASRRs. The optimization in excitation of toroidal multipole provide opportunity to further increase the Q-factor of metamaterial and boost light-matter interactions at the subwavelength scale for potential applications in low-power nonlinear processing, and sensitive photonic applications.
We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {epsilon}/{mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner.
The recent realization of photonic topological insulators has brought the discovery of fundamentally new states of light and revolutionary applications such as non-reciprocal devices for photonic diodes and robust waveguides for light routing. The spatially distinguished layer pseudospin has attracted attention in two-dimensional electronic materials. Here we report layered photonic topological insulators based on all-dielectric bilayer photonic crystal slabs. The introduction of layer pseudospin offers more dispersion engineering capability, leading to the layer-polarized and layer-mixed photonic topological insulators. Their phase transition is demonstrated with a model Hamiltonian by considering the nonzero interlayer coupling. Layer-direction locking behavior is found in layer-polarized photonic topological insulators. High transmission is preserved in the bilayer domain wall between two layer-mixed photonic topological insulators, even when a large defect is introduced. Layered photonic topological insulators not only offer a route towards the observation of richer nontrivial phases, but also open a way for device applications in integrated photonics and information processing by using the additional layer pseudospin.
Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwells equations for a photonic crystal (PhC) and identify quadrupole topological photonic crystals formed through a band inversion process. Unlike prior studies relying on threaded flux, our quadrupole moment is quantized purely by crystalline symmetries, which we confirm using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands, and the expectation value of the quadrupole operator. Furthermore, through the bulk-edge correspondence of Wannier bands, we reveal the boundary manifestations of nontrivial quadrupole phases as quantized polarizations at edges and bound states at corners. Finally, we relate the nontrivial corner states to the emergent phenomena of quantized fractional corner charges and a filling anomaly as first predicted in electronic systems. Our work paves the way to further explore higher-order topological phases in nanophotonic systems and our method of inducing quadrupole phase transitions is also applicable to other wave systems, such as electrons, phonons and polaritons.
To efficiently integrate cutting-edge terahertz technology into compact devices, the highly confined terahertz plasmons are attracting intensive attentions. Compared to plasmons at visible frequencies in metals, terahertz plasmons, typically in lightly doped semiconductors or graphene, are sensitive to carrier density (n) and thus have an easy tunability, which, however, leads to unstable or imprecise terahertz spectra. By deriving a simplified but universal form of plasmon frequencies, here we reveal a unified mechanism for generating unusual n-independent plasmons (DIPs) in all topological states with different dimensions. Remarkably, we predict that terahertz DIPs can be excited in 2D nodal-line and 1D nodal-point systems, confirmed by the first-principles calculations on almost all existing topological semimetals with diverse lattice symmetries. Besides of n independence, the feature of Fermi-velocity and degeneracy-factor dependences in DIPs can be applied to design topological superlattice and multi-walled carbon nanotube metamaterials for broadband terahertz spectroscopy and quantized terahertz plasmons, respectively. Surprisingly, high spatial confinement and quality factor, also insensitive to n, can be simultaneously achieved in these terahertz DIPs. Our findings pave the way to developing topological plasmonic devices for stable terahertz applications.
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