Phase shift on reflection from metallodielectric photonic bandgap materials

This paper reports phase-sensitive studies of the mm-wave reflection from a photonic crystal built from conducting spheres. We compare phase shift upon reflection from external interface to the phase shift on reflection from internal interface, the latter was estimated from the spectrum of Fabry-Perot resonances with photonic crystal mirrors. We show that the frequency-dependent phase shift upon internal reflection is consistent with the phase shift on external reflection from the whole crystal. We develop the analytical model that relates reflectivity of multilayers to admittances and to refractive indices of sublayers and takes account of magnetic permeability. This model yields a simple graphical procedure to determine the resonant frequencies of a Fabry-Perot resonator with photonic crystal mirrors. The model describes our results and results of two other groups fairly well.