We present an approach for the description of fluorescence from optically active materials embedded in layered periodic structures. Based on an exact electromagnetic Green's tensor analysis, we determine the radiative properties of emitters such as the local photonic density of states, Lamb shifts, linewidths, etc. for a finite or infinite sequence of thin alternating plasmonic and dielectric layers. In the effective-medium limit, these systems may exhibit hyperbolic dispersion relations so that the large wave-vector characteristics of all constituents and processes become relevant.

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.

Multiple time-stepping (MTS) algorithms allow to efficiently integrate large systems of ordinary differential equations, where a few stiff terms restrict the timestep of an otherwise non-stiff system. In this work, we discuss a flexible class of MTS techniques, based on multistep methods. Our approach contains several popular methods as special cases and it allows for the easy construction of novel and efficient higher-order MTS schemes. In addition, we demonstrate how to adapt the stability contour of the non-stiff time-integration to the physical system at hand.