In this work, we design and study an optical hyperbolic metamaterial of a few layers (i.e. metasurface), with a specific in-plane dispersion relationship that has a transition from open hyperbolic type I to type II. We will show that although there is no longer a topological transition from a closed curve to an open hyperbola in dispersion relationship, the local photonic density of state (PDOS) still can be significantly enhanced around the transition point, due to epsilon-near-zero (ENZ) modes. We also show a finite-size effect, which leads to the PDOS enhancement that is strongly dependent on the top layer of material. It is found a balance between the ENZ modes and surface plasmon polaritons for PDOS enhancement. Our results provide some insights for enhancing light–matter interactions via hyperbolic metasurfaces.

在这项工作中，我们设计并研究了几层（即超表面）的光学双曲超材料，具有特定的面内色散关系，从开放双曲 I 型过渡到 II 型。我们将证明，虽然在色散关系中不再存在从闭合曲线到开双曲线的拓扑转变，但由于 epsilon-near-zero，局部光子态密度 (PDOS) 在转变点附近仍然可以显着增强(ENZ) 模式。我们还展示了一种有限尺寸效应，这会导致强烈依赖于顶层材料的 PDOS 增强。已发现用于 PDOS 增强的 ENZ 模式和表面等离子体激元之间的平衡。我们的结果为通过双曲超表面增强光-物质相互作用提供了一些见解。