Electromagnetic properties of periodic multilayers of ultrathin metallic films from dc to ultraviolet frequencies

Ultrathin metallic films have an interesting electromagnetic behavior as the frequency of the incident field is varied over several orders of magnitude, because of the dramatic dispersion exhibited by the metal permittivity. We study a finite multilayer of periodically placed planar conducting films for frequencies varying from the dc limit to the far ultraviolet. We provide the optimized reflectivity and transmittivity of the system for the various frequency regimes involved. Further, we produce the dispersion diagrams of the corresponding photonic bandgap structures, which clearly show the transition of the system from a metallic (low frequencies) to a dielectric (optical frequencies) behavior. In addition, simple design formulas for maximum reflectivity of finite film number N are presented in terms of film thickness and film spacing in each of the representative frequency ranges.