The authors model the optical visibility of monolayer and bilayer graphene deposited on a substrate or thermally annealed on the surface of SiC. Visibility is much stonger in reflection than in transmission, reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.
We take data for the real and imaginary parts of the permittivity of Si from Ref. 10. The imaginary part is substantial only for , so we approximate . The permittivity of is nearly dispersionless in this frequency range (Ref. 11), so we take the dielectric constant as . SiC has some dispersion for these frequencies12 but the imaginary part is negligible so we assume .