Abstract

We present methods for retrieving the effective impedance of metamaterials from the Fresnel reflection coefficients at the interface between two semi-infinite media. The derivation involves the projection of rigorous modal expansions onto the dominant modes of the two semi-infinite media. It is shown that the effective impedance can also be written as a ratio of averaged field quantities. Thus, a number of effective impedance formulas, previously obtained by field averaging techniques, can also be derived from the scattering-based formalism by an appropriate choice of projection. Within the effective medium limit, it is observed that a simple semianalytic modeling technique based on the effective impedance can be used to reliably compute the reflection coefficients of metamaterials over a wide range of incidence angles. We use this technique to model planar metamaterial waveguides or surface modes.

© 2016 Optical Society of America

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