Effective models of metasurface/metainterface made of three-dimensional Helmholtz resonators

We study a reflective metasurface made of 3D subwavelength Helmholtz resonators. We provide an effective model in the time domain obtained by using a three-scale asymptotic approach. The metasurface is reduced to an homogenized boundary condition involving a resonant, frequency dependant impedance. Our effective model takes into account boundary layer effects near the neck opening, and we provide a precise method to calculate the " added length ". The study is extended to meta-interface in transmission, where the set of effective boundary conditions are replaced by effective jump conditions, and the results are discussed in frequency domain with comparison with direct numerical simulations.