Previous studies on the propagation direction of valley topological edge states mainly focus on the matching between orbital angular momentum of the excitation source and specific pseudo-spin state of valley edge mode at certain frequency that falls in the bandgap of the topologically distinct bulk components. In this work, we propose topological photonic crystals (PCs) hosting two topological protected bandgaps. It is shown that by constructing the interface between different PC structures with distinct topological phase, edge states can be engineered inside these two bandgaps, which provides a convenient way to achieve flexible wave routing. Particularly, we study three types of meta-structures consisting of these PCs in which the valley edge states routing path highly depends on the operating frequency and inputting port of the excitation source. Our study provides an alternative way in designing topological devices such as wave splitters and frequency division devices.

Photonic topological insulators protected by the lattice spatial symmetry (e.g., inversion and rotation symmetry) mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate theoretically, numerically, and experimentally that a type of judiciously designed two-dimensional Kekulé photonic crystal with time reversal symmetry can possess topological valley and pseudo-spin edge states in different frequency bands. Topologically robust transportation of both the valley and pseudo-spin edge states was confirmed by measuring the transmission of straight and z-shaped interface supported edge mode and comparing with bulk modes in the microwave frequency regime. In addition, we show that due to the distinct topological origins, valley and pseudo-spin edge states can be distinguished by examining their end-scattering into the free space. Our system provides an alternative way in manipulating electromagnetic waves with additional degree-of-freedom, which has potential applications for robust and high-capacity waveguiding and multi-mode dividing.

The resonance based strong light-matter interaction in metamaterials offers unprecedented opportunities to manipulate polarization of electromagnetic waves. In this work, we fabricate a three-dimensional (3D) metamaterial consisting of 90-degreetwisted split-tube resonators using a 3D printing technique and demonstrate the corresponding asymmetric transmission for linearly polarized electromagnetic waves in the Ku band with near-unity polarization conversion efficiency. Experimental results reveal a 90-degree polarization rotation and an incident polarization angle dependent asymmetric transmission at a frequency around 15.2 GHz. The experimental results are in good agreement with simulations. Possessing the merits of both flexibility of response tailoring and ease of fabrication, the proposed 3D-printed metamaterials have a great potential for compact polarization-control devices exhibiting unidirectional transmission at both microwave and terahertz frequencies.

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.