Graphene as a tunable plasmonic metasurface with transformation optics

Graphene can be biased by electrical gating or by chemical doping, which modifies its Fermi level and enables the existence of surface plasmons propagating along graphene. These surface plasmons, because of the two-dimensional (2D) nature of this material, have very short wavelengths and extreme out-of-plane confinement. Graphene plasmons feature in the THz regime with relatively low losses, where the plasmonic response of metals is weak. These facts, added to the important ingredient of tunability with external bias, make graphene a very suitable platform for the design of plasmonic metasurfaces in the THz regime. Metasurfaces, which are the 2D counterpart of metamaterials, consist of a planar arrangement of resonant subwavelengthsize building blocks. By appropriately them, metasurfaces provide an ultrathin platform for manipulating electromagnetic waves, and they have shown novel phenomena and applications as from broadband light bending and anomalous reflection and refraction. In this contribution we demonstrate a tunable meta-surface by inducing a periodic conductivity modulation in a graphene sheet. The conductivity modulation acts as a subwavelength grating that allows for external terahertz radiation to couple into the surface plasmons supported by the graphene layer. The coupling to highly confined plasmons provides a dramatic enhancement of the interaction of electromagnetic radiation with graphene. Making use of transformation optics we derive analytical expressions for the optical response of the system, and find the optimal configuration for coupling into plasmons. These graphene conductivity gratings are tunable plasmonic metasurfaces characterized by an effective surface conductivity, which is derived from a sheet retrieval method. In addition, for the case of conductivity modulations along two directions we find that the graphene metasurface responds isotropically under electromagnetic fields incident at any angle. Thus, the modulated graphene can be used for fast switching and tuning of THz radiation of arbitrary polarisation and orientation.