Topological states in Penrose-square photonic crystals.

Topological edge states (TESs) and topological corner states (TCSs) in photonic crystals (PCs) provide an effective way to control the propagation and localization of light. The topological performance of integrated photonic devices can be improved by introducing the basic structural unit of photonic quasicrystals (PQCs) into PCs. However, the previous works arranged the basic structural unit of Stampfli-type and 12-fold Penrose-type photonic quasicrystals into triangular lattices, which have a complex structure and allow light to only propagate around 60° or 120° corners, limiting their applications. In this paper, a Penrose-square PC is proposed, which realizes both TESs and TCSs, and light successfully propagates around 90° corners. This work may reduce the difficulties encountered in the preparation of topological photonic crystals (TPCs) structured by arranging the basic structural units of PQCs periodically. It also provides a new, to the best of our knowledge, platform for studying TPCs and new ideas for improving the performance of integrated photonic devices.