Anomaly of Transmission Properties in Pre-Cantor Dielectric Multilayers

摘要

Using the transmission-line theory, we investigate wave propagation in a pre-Cantor multilayer. Transmission spectra of the low stages of pre-Cantor media show good agreement with those of numerical calculation of Maxwell's equations using the FDTD method. Numerical results obtained using the FDTD method show that the electric field at the midpoint of the nth stage pre-Cantor medium has sharp resonance and broad attenuation at transmission bands that are newly generated in attenuation bands of the (n?1)th stage. Using an expression of transmittance of the high stage of pre-Cantor multilayer, we show that the transmittance t becomes a two-valued function of t = 0/1 and the collection of points for t = 1 is a power set of positive integers whose cardinal number is 30.