  The use of graphene in surface plasmon resonance sensors, covering a metallic
(plasmonic) film, has a number of demonstrated advantages, such protecting the
film against corrosion/oxidation and facilitating the introduction of
functional groups for selective sensing. Recently, a number of works have
claimed that few-layer graphene can also increase the sensitivity of the
sensor. However, graphene was treated as an isotropic thin film, with an
out-of-plane refractive index that is identical to the in-plane index. Here, we
critically examine the role of single and few layers of graphene in the
sensitivity enhancement of surface plasmon resonance sensors. Graphene is
introduced over the metallic film via three different descriptions: as an
atomic-thick two-dimensional sheet, as a thin effective isotropic material
(same conductivity in the three coordinate directions), and as an non-isotropic
layer (different conductivity in the perpendicular direction to the
two-dimensional plane). We find that only the isotropic layer model, which is
known to be incorrect for the optically modelling of graphene, provides
sizeable sensitivity increases, while the other, more accurate, models lead to
negligible contribution to the sensitivity.
