In this work we design and experimentally realize a photonic kagome metasurface exhibiting a Wannier-type higher-order topological phase. We demonstrate and visualize the emergence of a topological transition and opening of a Dirac cone by directly exciting the bulk modes of the HOTI metasurface via solid-state immersion spectroscopy. The open nature of the metasurface is then utilized to directly image topological boundary states. We show that, while the domain walls host 1D edge states, their bending induces 0D higher-order topological modes confined to the corners. The demonstrated metasurface hosting topological boundary modes of different dimensionality paves the way to a new generation of universal and resilient optical devices which can controllably scatter, trap and guide optical fields in a robust way.
we demonstrate 2D photonic HOTI (PHOTI) with topological states two dimensions lower than the one of the host system. We consider a photonic metacrystal of distorted Kagome lattice geometry that exhibits topological bulk polarization, leading to the emergence of 1D topological edge states and of higher order 0D states confined to the corners of the structure. Interestingly, in addition to corner states due to the nearest neighbour interactions and protected by generalized chiral symmetry 1, we discover and take advantage of a new class of topological corner states sustained by long-range interactions, available in wave-based systems, such as in photonics. Our findings demonstrate that photonic HOTIs possess richer physics compared to their condensed matter counterparts, offering opportunities for engineering novel designer electromagnetic states with unique topological robustness.
Higher-order topological (HOT) states are topological states localized in more than one dimension of a D-dimensional system. In the recent years, HOT states have been shown to exist in classical wave-systems such as photonics and acoustics and have been used to explore a host of topological phenomena that have typically been associated with condensed matter systems. In our work, we construct the 3D acoustic metamaterial with HOT states through a rapid prototyping process and manufacture the individual metaatoms and metamolecules, which can then be snapped together to form 3D metamaterials with complex geometries. The assembled 3D topological metamaterial represents the acoustic analogue of the pyrochlore lattice with acoustic modes strongly bound to the individual resonant cavities and a design that only allows for nearest neighbor coupling. This provides us with the framework to explore the topological nature of the structure in a semi-analytical way (tight-binding model) while comparing it to the first-principles finite element method (FEM) model, and then comparing both theoretical results to the experiment. Consistent with the models, we observe the third-order (0-D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of HOT states in three dimensions. Additionally, we experimentally measure the field profile of each topological mode, which are in excellent agreement with the numerically calculated profiles of the HOT states.
We demonstrate that the distorted Kagome lattice formed by two-dimensional(2d) array of dielectric rods embedded in
air exhibits a new class of topological states characterized by a topological invariant number in Pauli vector space. The
Kagome lattice can be considered as a 2d analogue of the Su-Schrieffer–Heeger (SSH) model, which displays a phase
transition by detuning the relative amplitudes of the inter-cell and intra-cell hopping terms. The phase transition is
accompanied by the opening of a complete band gap in the Brillouin zone, which may host topological edge states on
either the truncated end of the lattice or at the domain walls between topological nontrivial and trivial domains. To
further reveal the connection between the bulk invariance and edge states, polarizations of shrunken and expanded
effects are calculated. Our first-principles simulations based on finite element method (FEM) are used to design the
lattice and confirm the analytic prediction.
Bulk spectrum and edge modes of 2D photonic crystals with parity and time-reversal symmetries broken in a different way are investigated. It is shown that for specific values of parameter of the symmetry reduction the bulk modes exhibit a peculiar one-way Dirac-like dispersion. The domain wall formed by two crystals with the symmetry reduction parameter reversed is shown to exhibit an edge mode which coexists with the one-way bulk Dirac regime. In addition, we demonstrate that parity-time symmetric interfaces between photonic crystals with gain and loss support a new class of dissipation-less surface modes.