Exact solution for square-wave grating covered with graphene: surface plasmon-polaritons in the terahertz range

We provide an analytical solution to the problem of scattering of electromagnetic radiation by a square-wave grating with a flat graphene sheet on top. We show that for deep groves there is a strong plasmonic response, with light absorption in the graphene sheet reaching more than 45% due to the excitation of surface plasmon-polaritons. The case of a grating with a graphene sheet presenting an induced periodic modulation of the conductivity is also discussed.