Abstract

The theory of surface homogenization aims at replacing subwavelength metasurfaces consisting of a periodic arrangement of particles by effective transition conditions. In this work, we extend this framework to the case of electromagnetic metasurfaces consisting of a periodic collection of subwavelength resonant Mie particles. These particles exhibit a strong contrast in their permittivity properties and produce subwavelength resonances that are a key ingredient for wave manipulation by metasurface. We show that Mie scattering can be accounted for in the homogenized model by frequency-dependent effective parameters using a two-scale homogenization approach combined with a matched asymptotic analysis. We study in particular the cases of TE and TM polarizations which surprisingly require a different theoretical treatment. We validate our approach by comparing the semi-analytical results provided by the effective model with direct numerical simulations.