Scattering of surface plasmon-polaritons in a graphene multilayer   photonic crystal with inhomogeneous doping
  The propagation of a surface plasmon-polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum; (ii) the scattering at an interface where there is a sudden change of the electronic doping. The formalism is then extended to the {\it barrier problem}. In this system rich physics is found for the plasmonic mode, showing: total reflection, total transmission, Fabry-P\'erot oscillations, and coupling to photonic modes. 
Yu. V. Bludov, N. M. R. Peres, G. Smirnov, M. I. Vasilevskiy
cond-mat.mes-hall physics.optics