Thin films versus 2D sheets in layered structures: graphene and 2D metallic sheets

We study an interface between two media separated by a strictly 2D sheet. We show how the amplitude reflection coefficient can be modeled by that for an interface where the 2D sheet has been replaced by a film of small but finite thickness. We give the relationship between the 3D dielectric function of the thin film and the 2D dielectric function of the sheet. We choose graphene and a 2D metallic sheet as illustrative examples. This approach turns out to be very useful when treating graphene or graphene like sheets in non-planar structures