Density of states and spontaneous emission rates in photonic crystals

A numerical method for the calculation of the local density of states of the classical electromagnetic modes existing within a finite periodic dielectric material is proposed. This information allows for a computation of the modified spontaneous emission rate inside the structure, for weak coupling of a dipole transition to the electromagnetic modes. The approach is based on a calculation of the electric field Green function, and includes the contribution arising from surface guided modes as well as from scattering modes of the system. The required computational effort is enormously reduced if the necessary integration over a 2 dimensional Brillouin zone is deformed into the complex plane. An implementation of the approach utilising a transfer matrix approach for the calculation of the Green function is reported, and used in the calculation of the local density of states within a finite two dimensional periodic structure. The method can also be used to find the spatial distribution of emitted light in both the near and far fields.