Eigenwaves and leaky waves on a lattice of small scatterers

Previously, the quantum mechanical Bloch waves in a cubic crystal were analyzed by a cavity or structure constant approach by J. Korringa, W. Kohn and N. Rostoker, et al. In the present report, the above method is reformulated to permit the analysis of electromagnetic Bloch waves in artificial dielectrics as well as electromagnetic surface waves and leaky waves on open periodic structures. The analysis, which is particularly appropriate for "small scatterers," proceeds as follows. It is shown that a "lossless" scatterer embedded in a "lossless" medium can be characterized by a Hermitian matrix R. The lattice structure is then characterized by a "structure constant" matrix
\Gamma
which is Hermitian in the eigenwave region and non-Hermitian in the leaky wave region. A dispersion relation is then obtained from the condition that the determinant of the matrix (
R-\Gamma
) vanishes.