Two-dimensional Green tensor and local density of states in finite-sized two-dimensional photonic crystals

The two-dimensional Green tensor for two-dimensional photonic crystals, consisting of clusters of circular cylinders of infinite length, is constructed using the exact theory of multipole expansions. On the basis of this Green tensor, the local density of states for both polarizations is calculated, showing how the density of states depends on the position inside the crystal. We include results for clusters with a waveguide, obtained by removing a line of cylinders, and a cavity, obtained by forming a localized defect.