Spontaneous decay and emission rates for an atom situated at a distance z0 from a planar surface.
The rate is normalized to the decay rate in vacuum, Γ0=4ω3|d|2/3c3, where d is the transition dipole.
The substrate medium is described by a local dielectric function ε(ω). The surface is allowed to have a surface layer of conductange σ(ω).
The option is given to adopt values of this conductance corresponding to graphene, modeled from the model of L. A. Falkovsky, J. Phys.: Conf. Series 129, 012004 (2008).
See details of the theory in
L. A. Blanco and F. J. García de Abajo, Phys. Rev. B 69, 205414 (2004).