An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimallythin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity σ = σ ′ + jσ ′′ , a proper transverse-electric (TE) surface wave exists if and only if σ ′′ > 0 (associated with interband conductivity), and a proper transverse-magnetic (TM) surface wave exists for σ ′′ < 0 (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of σ ′′ can be varied, allowing for some control over surface wave properties.

No abstract

Motivated by the recent emergence of a new class of anisotropic 2D materials, we examine their electromagnetic modes and demonstrate that a broad class of the materials can host highly directional hyperbolic plasmons. Their propagation direction can be manipulated on the spot by gate doping, enabling hyperbolic beam reflection, refraction, and bending. The realization of these natural 2D hyperbolic media opens up a new avenue in dynamic control of hyperbolic plasmons not possible in the 3D version.

A model is developed for a parallel-plate waveguide formed by graphene. The graphene is represented by an infinitesimally thin, local two-sided surface characterized by a surface conductivity obtained from the Kubo formula. Maxwell’s equations are solved for the model fields guided by the graphene layers. It is shown that despite the extreme thinness of its walls, a graphene parallel-plate waveguide can guide quasi-transverse electromagnetic modes with attenuation similar to structures composed of metals, while providing some control over propagation characteristics via the charge density or chemical potential. Given the interest in developing graphene electronics, such waveguides may be of interest in future applications.

No abstract