Comprehensive and analytical investigation of topological interface states in one-dimensional photonic systems

Abstract

Topological interface states (TISs) have attracted considerable interest due to their exceptional impact on enhancing light-matter interactions in photonic systems. We investigate the TISs in a one-dimensional photonic heterostructure incorporating a cap layer. The behavior of TISs is examined using the transfer matrix method, varying the physical parameters of the cap layer. An analytical expression for TISs is derived using a direct matching approach based on the Kronig-Penney model. The analytical results acquired for TIS have been simulated across several configurations, and the outcomes indicate full consistency. Our findings indicate that TISs are highly sensitive to the thickness of the cap layer, exhibiting a periodic dependency on its variation. While the cap layer’s permittivity affects the position of TISs, its influence is weaker compared to that of the thickness. Additionally, we analyzed the impact of nonlinearity by adding a thin nonlinear layer at the interface and found that TISs are extremely responsive to the cap layer’s nonlinearity. These results could support the integration of TISs into future topological cavity and laser applications.