Characterization of Surface Waves in a Multilayer Coating—Application to Far-Field Control

Surface waves (SWs) may propagate in a material coating made up of homogeneous layers. They affect antenna performances or the far-field scattered from an object. Also, they must be accounted for in various numerical methods, such as impedance boundary conditions (IBCs), or transmission conditions used in a domain decomposition method. This work is focused on the control of the far-field radiated by SWs from a 3-D object. First, the standard problem of an infinite planar coating backed by an IBC is considered, the waves outside the coating satisfying the boundary condition at infinity. It is well known that the SWs wavenumbers are solutions of a transcendental equation that is obtained here via a very simple numerical method. Analytical results are presented for a lossless monolayer, some of which being, as far as we know, original. Then, from the known properties of the radiation operator, it is shown how these results can be used to control the far-field radiated by SWs on 3-D objects. Numerical experiments performed on a coated sphere and a cone-sphere demonstrate the pertinence of this analysis, even when small losses are present.