Engineering topological corner states in two-dimensional Su-Schrieffer-Heeger analog photonic crystals

Based on two-dimensional (2D) Su-Schrieffer-Heeger (SSH) analog photonic crystals (PCs), we construct photonic topological corner states (TCSs). Then by regulating the unit cells at corners, on edges, or in the bulk of the photonic finite structures, we successfully engineer the frequencies, field localizations, and spatial field distributions of these TCSs. We also demonstrate a new type of trivial corner states (CSs) and present their topological origins, and realize the topological bound states in continuum (BIC) with TCSs in the bulk band. Our results reveal that TCSs are mainly determined by the corner cells and their surrounding conditions. By employing waveguide-cavity coupling structures, we successfully excite these engineered TCSs. Our research provides instructive and effective methods to engineer multi-frequency, multi-mode TCSs in 2D photonic systems, and paves the way for designing multi-mode, multi-channel micro-nano photonic devices with TCSs on demand.