Interface States and Interface-Bulk Correspondence of One-dimensional Hyperbolic Metamaterials.

We investigate the interface state on one-dimensional hyperbolic metamaterial (1DHMM). Initially, we analyze the plasmonic band structure of binary 1DHMM and analytically determine its band crossing condition. Then, we scrutinize the existence of an interface state in the plasmonic band gap of 1DHMM on three types of interfaces: dielectric/1DHMM, metal/1DHMM, and 1DHMM/1DHMM. We find that the band crossing dramatically influences the existence of an interface state. We also show a rigorous relation between the existence of the interface state of 1DHMM in the plasmonic band gap and the wave admittance in the plasmonic band region. More importantly, this relation not only holds for binary 1DHMM but also can be generalized to any 1DHMM with inversion symmetry. We also characterize the interface state by the transverse spin angular momentum and reveal the transverse spin flipping of the interface state.