Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light.