We present numerical and analytical results for the lifetime of emitters in close proximity to graphene sheets. Specifically, we analyze the contributions from different physical channels that participate in the decay processes. Our results demonstrate that measuring the emitters' decay rates provides an efficient route for sensing graphene's optoelectronic properties, notably the existence and size of a potential band gap in its electronic band structure.

We investigate the dispersion relations of TE resonances in different graphene-dielectric structures. Previous work has shown that when a graphene layer is brought into contact with a dielectric material, a gap can appear in its electric band structure. This allows for the formation of TE-plasmons with unusual dispersion relations. In addition, if the dielectric has a finite thickness, graphene strongly modifies the behavior of the waveguiding modes by introducing dissipation above a well-defined cutoff frequency, thus providing the possibility of mode filtering.

We describe the treatment of thin conductive sheets within the Discontinuous Galerkin Time-Domain (DGTD) method for solving the Maxwell equations and apply this approach to the efficient computation of the optical properties of graphene-based systems. In particular, we show that a thin conductive sheet can be handled by incorporating the associated jump conditions of the electromagnetic field into the numerical flux of the DGTD approach. This results in a flexible and efficient numerical scheme that can be applied to a number of systems.