We calculated the local density of state for various positions in a photonic crystal of honeycomb lattice to study how the spontaneous emission rate of a radiating dipole is altered in the presence of the photonic crystal. The local density of states is found to be position-sensitive and its value can be enhanced or depressed relative to the density of states, depending on the location of the dipole. Our study shows that the density of states tends to underestimate the effect of a photonic crystal on the prohibition of light propagation, while on the contrary tends to overestimate the effect on the enhancement of light emission. The calculations also indicate that it is possible to tailor the spontaneous emission of an active medium by careful selecting its location in the photonic crystal. The results are helpful in determining the insertion location of the active medium and in evaluating the efficiency of active photonic crystal devices such as light-emitting diodes or lasers.
