Graphene plasmons and retardation: Strong light-matter coupling

We study the retardation regime of doped graphene plasmons, given by the nominal crossing of the unretarded plasmon and light-cone. In addition to modifications in the plasmon dispersion relation, retardation implies strong coupling between propagating light and matter, even for homogeneous graphene, which opens up the possibility of efficient plasmonics in simple graphene devices. We exemplify this enhancement in a double-layer configuration that exhibits perfect (if lossless) light transmissions across a classically forbidden region, providing a simpler analog of the corresponding phenomenon in perforated metal sheets. We also show that (broad) Fabry-Pérot resonances present without graphene turn into sharply peaked, quasi-discrete modes in the presence of graphene where graphene's response function is given by the typical Fano lineshape.