Propagating and Localized Graphene Surface Plasmon Polaritons on a Grating Structure

The general dispersion characteristics of the surface plasmon polariton (SPP) modes for graphene on a grating structure are studied. It is shown that the dispersion of the excited SPP modes highly depends on the size of the gap of the grating. The dispersion of the SPP modes for such a complex grating system can be well approximated by using the photonic crystal model, and therefore, a full simulation is not needed. The fact that for a large gap size the dispersion of the SPP modes can be found by regarding the grating structure as a series of Fabry-Pérot cavities suggest strong reflection of propagating plasmons at the gap edges; the excited SPP modes become highly localized in contrast to the propagating SPPs when the gap is small.