An Exact Method for the Extraction of Effective Bulk and Surface Parameters of Periodic Artificial Media

A new method is presented for the extraction of the bulk and surface parameters of a periodic artificial medium which uses the eigenvectors of the generalized transfer matrix of a unit layer. These eigenvectors correspond to the Bloch modes of the periodic structure. The eigenvector related to the propagating Bloch mode directly yields an expression for the effective, intrinsic wave impedance of the medium. Moreover, the interface between the artificial material and a surrounding, conventional (dielectric) region is described by an interface impedance matrix which accounts for the excitation of higher order, nonpropagating Bloch modes at the interface. Although these modes do not propagate into the bulk of the artificial material, they affect the reflection and transmission coefficients of incident waves. From the bulk and surface impedances derived, and with the aid of a simple transmission line model, the scattering parameters of a slab of an artificial medium are computed. Results are in excellent agreement with those of exact full-wave simulations.