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

TL;DR

This paper analyzes the excitation and behavior of surface plasmon polaritons on tunable hyperbolic 2D materials like black phosphorus and graphene, providing a Green's function and complex-plane approach for understanding their electromagnetic response.

Contribution

It introduces an efficient method to evaluate the Green's function for anisotropic 2D hyperbolic materials, revealing new insights into SPP excitation and complex-plane singularities.

Findings

Efficient evaluation of Green's function via mixed integral form.

Identification of complex-plane singularities affecting SPP excitation.

Application to graphene strips and black phosphorus demonstrating tunable hyperbolic plasmons.

Abstract

We study the electromagnetic response of two- and quasi-two-dimensional hyperbolic materials, on which a simple dipole source can excite a well-confined and tunable surface plasmon polariton (SPP). The analysis is based on the Green's function for an anisotropic two-dimensional surface, which nominally requires the evaluation of a two-dimensional Sommerfeld integral. We show that for the SPP contribution this integral can be evaluated efficiently in 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 strong SPP excitation is discussed, and complex-plane singularities are identified, leading to physical insight into the excited SPP. We also present a stationary phase solution valid for large radial distances. Examples are presented using graphene strips to form a hyperbolic metasurface, and thin-film black phosphorus. The Green's function and complex-plane analysis developed allows for the exploration of hyperbolic plasmons in general 2D materials.