General electromagnetic density of modes for a one-dimensional photonic crystal

In this paper, we present more general, exact, and concise expressions for calculating the electromagnetic density of modes (EDOM) in one dimension ph otonic crystal (superlattice) for E and H polarizations. The expression is used for numerical computation of the EDOM in the lower-index (dielectric c onstant) layer. We discuss the difference between the EDOM in high- and low -index layers as due to the presence of waveguiding modes and evanescent-ex cited Bloch modes in the higher-index layer. Two methods of computation are presented to compute the EDOM in the lower-index layer. We suggest the pos sibility of using the EDOM to establish population inversion, which may be useful for higher-frequency lasers (e.g., x rays) and control any radiative processes. We also elaborate on the limitations of the results of Alvarado Rodriguez ct al. as due to the approximation used in the evaluation of par tial derivative omega/partial derivativek(y,z) for del (k)omega and comment on the Limitations of the one-dimensional EDOM expression of Bendickson et al.