Electromagnetic Green's tensor and local density of states calculations for collections of spherical scatterers

A Green's tensor formalism of the electromagnetic field for a single scatterer as well as for a cluster of finite number of scatterers is presented. The formalism, based on the multiple-scattering theory for classical waves, provides a means to calculate the number of states, the density of states, as well as the local density of states of the electromagnetic field. The last quantity determines the spontaneous emission rate of atoms embedded within a cluster of spherical bodies. As a case study, density of states functions for a finite planar photonic-crystal slab of titania spheres in air are calculated.