Directive Surface Plasmons on Tunable Two-Dimensional Hyperbolic Metasurfaces and Black Phosphorus: Green's Function and Complex Plane Analysis

摘要

We study the electromagnetic response of two- and quasi-two-dimensionalhyperbolic materials, on which a simple dipole source can excite awell-confined and tunable surface plasmon polariton (SPP). The analysis isbased on the Green's function for an anisotropic two-dimensional surface, whichnominally requires the evaluation of a two-dimensional Sommerfeld integral. Weshow that for the SPP contribution this integral can be evaluated efficientlyin a mixed continuous-discrete form as a continuous spectrum contribution(branch cut integral) of a residue term, in distinction to the isotropic case,where the SPP is simply given as a discrete residue term. The regime of strongSPP excitation is discussed, and complex-plane singularities are identified,leading to physical insight into the excited SPP. We also present a stationaryphase solution valid for large radial distances. Examples are presented usinggraphene strips to form a hyperbolic metasurface, and thin-film blackphosphorus. The Green's function and complex-plane analysis developed allowsfor the exploration of hyperbolic plasmons in general 2D materials.