Sub-wavelength resonators:: On the use of metafilms to overcome the λ/2 size limit

Metamaterials - in particular, double negative materials - have been used in the design of electromagnetic resonators as a means to overcome the classical lambda/2 size limitation. The surface equivalent of a metamaterial is a so-called metafilm - a surface distribution of suitably chosen electrically small scatterers. In this paper we illustrate how metafilms can be used to overcome the lambda/2 size limit in order to design resonators of very small dimension. We present expressions that relate the polarisability densities of the scatterers of the metafilm needed to achieve in principle any desired resonator size. To validate the analytical results, comparisons to full-wave simulations of resonators containing various metafilms are shown. The effect of loss is investigated, and it is shown that smaller resonator size is achieved at the expense of lower Q (quality factor). The results can be scaled; that is, the dimensions of the scatterers can range from relatively large to relatively small, depending on the frequencies of interest.