  We investigate the propagation of surface waves along a spatially dispersive
graphene sheet, including substrate effects. The proposed analysis derives the
admittances of an equivalent circuit of graphene able to handle spatial
dispersion, using a non-local model of graphene conductivity. Similar to
frequency selective surfaces, the analytical admittances depend on the
propagation constant of the waves traveling along the sheet. Dispersion
relations for the supported TE and TM modes are then obtained by applying a
transverse resonance equation. Application of the method demonstrates that
spatial dispersion can dramatically affect the propagation of surface plasmons,
notably modifying their mode confinement and increasing losses, even at
frequencies where intraband transitions are the dominant contribution to
graphene conductivity. These results show the need for correctly assessing
spatial dispersion effects in the development of plasmonic devices at the low
THz band.

Mesoscale and Nanoscale Physics