Investigation of corner states in second-order photonic topological insulator

Recently, higher-order topological insulators have been investigated as a novel topological phase of matter that obey an extended topological bulk-boundary correspondence principle. In this paper, we study the influence of BNN interaction on photonic higher-order corner states. We find both next-nearest-neighbor (NNN) hopping and perfect electric conductor (PEC) boundaries can solely result in two kinds of corner states which are quite different from the traditional "zero-energy" state. To demonstrate this intuitively, we design a novel all-dielectric structure that can effectively shield the influence of NNN couplings while remain the effect of PEC boundaries, so that we can distinguish the contributions from NNN hopping and PEC boundaries. In addition, we also investigate the total contribution on corner states when NNN couplings and PEC boundaries coexist, and some interesting features are revealed. These findings may expand our understanding of the high-order corner modes in a more general framework.