Exact calculation of local density of states in three-dimensional photonic crystals

This paper presents the exact calculation of local density of states in three-dimensional photonic crystals (PCs). Theoretically, the local density of states (LDOS), the so-called generalized LDOS (GLDOS), and the local coupling strength (LCS) have been numerically evaluated, and it is found that these quantities play an extremely important role in quantum electrodynamics of atomic spontaneous emission in PCs. Based from a transform relation derived, a correct expression of calculating the LDOS is presented which satisfies the symmetry of the lattice. The enhancement effect of the LDOS in the PC´s with a diamond structure, compared to the vacuum case is revealed.