Causality and passivity properties of effective parameters of electromagnetic multilayered structures

Effective properties of periodic structures are investigated at all frequencies. It is shown that a simple dielectric multilayer with arbitrary low contrast can display artificial magnetoelectric coupling and magnetism. Effective parameters, as functions of the complex frequency, possess all the analytic properties required by the causality principle. The theoretical expression of the effective index and surface impedance are numerically tested; the former is shown to reduce to the mean refractive index at infinite frequency, just like the refractive index in the x-ray regime. We stress that periodic multilayers, with frequency-independent (noncausal) dielectric constants, make effective media with artificial causality.