Complex dispersion relation of 1D dielectric photonic crystal with thin metallic layers
We have carried out the analytical and numerical analysis of metallic insets embedded in a dielectric photonic crystal (DPC). The corresponding one-dimensional metallo-dielectric photonic crystal (MDPC) is studied in relation to the substratum DPC. We describe the complex MDPC dispersion relation curves and the transmission coefficient at the different propagation regimens trough the finite stack. While in the DPC, the band gap argument corresponds to undefined complex solutions of a real dispersion relation, in a MDPC corresponds to a definite complex solution, function of the metal thickness; and analytic continuation of the dispersion curve on the imaginary K plane. The metal absorption is described by the Drude model, and as a result of the absorption in the inset metallic films, complex Bloch vectors are produced for all frequencies as evanescent waves that differ from the straightforward metal absorption.
dispersion relation photonic crystal metallic layers band structure transfer matrix