Green-function theory of spontaneous emission and cooperative effects in a superlattice of thin metal layers

Real-space electric-field Green functions are derived for a superlattice structure composed of a regular array of thin metal films immersed in a dielectric. The derivation makes use of the jump condition on the magnetic field due to the areal conductivity of the metal and conforms with Bloch's theorem on the one-dimensional periodicity of the structure along the growth direction. The initial steps lead to mixed (real-space-reciprocal-space) Green functions. We show how the desired all-space Green functions are obtainable from these by Fourier transformation to real space, making use of the symmetry properties of the system. The emission rate for a dipole of a given orientation follows directly from the imaginary part of the appropriate equal-spare Green function. The results are investigated for different electron densities and different periodicity lengths and compared with the results appropriate for a single sheet and various asymptotic limits. Also using the same set of Green functions, we determine pair cooperative effects for dipoles embedded in the structure. Interesting features are pointed out when the dipoles have different orientations and/or are situated in different unit cells of the superlattice.