All-optical logic gates based on topological edge and corner states in two-dimensional photonic crystals with square dielectric columns

Abstract Recently, with the rapid progress in all-optical networks and optical computing, there is an increasing requirement for more appropriate methods to design all-optical logic gates. Photonic crystals (PCs) can be serving as a versatile platform for manipulating light propagation. The realization of topological edge states (TESs) and topological corner states (TCSs) within high-order topological photonic insulators has attracted extensive attention. In this paper, TESs and TCSs are achieved using honeycomb PCs with square dielectric columns instead of conventional cylindrical ones for obtaining a larger photonic energy band gap due to reduction of dielectric column symmetry. TESs with overlapping frequencies can be attained by different arrangements of combining two PCs with distinct topological properties. A sandwich structure comprising both topologically trivial and non-trivial PCs is proposed, and ‘AND Gate’ and ‘OR Gate’ logic gates are implemented through the coupling between edge state waveguides when controlling the number of coupling layers. Additionally, a triangular-shaped box structure composed of non-trivial PCs enveloped by trivial PCs is constructed. Within this structure, TCSs manifest only around each acute angle, and a ‘NOT Gate’ logic gate is realized through corner state coupling and edge state coupling. This work paves a new way of designing high-performance micro–nano all-optical logic gate devices.