Transverse-average field approach for the characterization of thin metamaterial slabs

The objective of this work is to investigate in which circumstances the scattering of electromagnetic waves by a thin metamaterial slab can be characterized using known effective parameters of the associated unbounded periodic bulk medium. It is proved that the classical approach or classical boundary conditions may become less accurate or incomplete if the size of inclusions is not significantly smaller than the wavelength. To circumvent this problem we demonstrate that the interaction of waves with metamaterial structures may in many cases with practical interest be conveniently described using a transverse averaged-field technique, and that this approach can be very accurate even for wide incident angles, evanescent waves, and for large and moderately large wavelengths.