Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles

In recent work, we derived generalized sheet transition conditions (GSTCs) for the average (or "macroscopic") electromagnetic fields across a metafilm, which, when properly designed, can have certain desired reflection and transmission properties. A metafilm is the two-dimensional equivalent of a metamaterial, and is essentially a surface distribution of electrically small scatterers characterized by electric- and magnetic-polarizability densities. In this paper, the GSTC is used to calculate the reflection and transmission coefficients of the metafilm. These coefficients are derived for both TM and TE polarized plane waves with arbitrary incidence angles. We show that the reflection and transmission properties of the metafilm are expressed in terms of the electric and magnetic polarizabilities of the scatterers themselves, and we derive conditions on the polarizabilities of the scatterers required to obtain total transmission and/or total reflection. We show various examples to illustrate the validity of the GSTC for the analysis of a metafilm. By controlling the polarization densities of the scatterers in the metafilm, a "smart" and/or "controllable" surface can be realized. We propose a metafilm composed of spherical magneto-dielectric particles for achieving such a controllable surface. To validate the results for the spherical particle metafilm, we show comparisons with a full-wave computation obtained from a mode-matching technique applied to the doubly infinite array of spherical scatterers. The results in this paper are in principle scalable; that is, the dimensions of the scatterers can range from relatively large to relatively small depending on the frequencies of interest.