Boundary configured chiral edge states in valley topological photonic crystal.

Chiral edge states (CESs) have been demonstrated at the external boundary of a valley photonic crystal (VPC), with flexibly tunable group velocity and frequency range by adjusting the boundary structure. In this work, we show parallel and antiparallel CESs located at two opposite VPC-air boundaries, which contain wave components belonging to opposite valleys or the same valley. In addition, we design a meta-structure with four types of air-contacted boundary that support CESs in different frequency ranges. The structure also has an internal interface channel supporting the valley edge state that bridges the top and bottom boundaries. We show that the CESs, while excited at a given port, can be exclusively guided to the other three ports, depending on the operating frequency. Our work provides an alternative way to design compact topological devices for optical waveguides and wave splitters.

Square-root topological state of coupled plasmonic nanoparticles in a decorated Su-Schrieffer-Heeger lattice.

The square-root operation can generate systems with new (to the best of our knowledge) topological phases whose topological properties are inherited from the parent Hamiltonian. In this Letter, we introduce the concept of square-root topology in the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model and construct a square-root topological square nanoparticle lattice (SRTL) by inserting additional sites into the original 2D SSH model. We find that the topological states in the SRTL are intriguingly different from those in the corresponding SSH model (with on-site potential) due to the change in symmetrical characteristics. Plasmonic nanoparticle arrays are used to demonstrate this by including both nearest-neighbor and next-nearest-neighbor interactions within the dipole approximation. These unique topological states, such as the single corner mode and multiple topological edge modes, enrich the topological features produced by square-root operation and expand the scope to apply such topological features into photonic systems.

Four dimensional second-order topological insulator based on a synthetic plasmonic metasurface.

It is possible to explore higher dimensional topological properties in lower dimensional structures by introducing additional synthetic dimensions. In this Letter, we construct a four-dimensional (4D) second-order topological insulator using gradient nanoparticle arrays arranged in a periodic lattice. The nanoparticle array has spatially varying inter-particle distance along x and y directions, which can be regarded as two synthetic dimensions. Different from higher-order topological insulators in classical wave systems, the higher-order topological states in this 4D system are protected by a pair of first Chern numbers in two-dimensional (2D) subspaces instead of by the quantized 2D Zak phases. It is shown that there exist (4-1)- and (4-2)-dimensional boundary states for both transverse and longitudinal collective resonant modes, which provides new, to the best of our knowledge, mechanisms for light confinement and control in such a plasmonic superlattice.