Photon density of states of a multilayer heterostructure in a rectangular waveguide

We have studied the propagation of the TE and TM modes and the photon density of states (PDOS) for a periodic multilayer heterostructure in a rectangular waveguide. A transfer matrix approach is employed to discretize the dielectric function profile of the dielectric multilayer heterostructures and the transmission functions are calculated by matching the boundary conditions at each interfaces. In order to solve the PDOS, it is necessary to calculate the dispersion relation, and the corresponding band structures are obtained by solving the eigenvalue equations with proper periodic boundary conditions. The PDOS of the quasi-one-dimensional photonic crystal for the TE and TM modes are obtained, respectively. These results are relevant to the spontaneous emission by an atom or to dipole radiation in quasi-one-dimensional periodic structures.