Homogenization of a Multilayer Coating: Application to Model-Order Reduction

We consider the time-harmonic scattering problem from a 3-D object coated with isotropic layers and solved via a full-wave method. The computational burden increases with the number of unknowns that depends on the density of the volume [finite element method (FEM)] or surface (MoM) mesh. Therefore, it is of interest to replace the whole structure, or some part of it only, by a homogeneous one with, if possible, a small optical index, and whose scattered field is as close as possible to the exact one. First, an infinite planar structure is considered. Three methods are proposed to calculate the isotropic homogenized dielectric permittivity and magnetic permeability that approximate accurately the reflection coefficient of the stratified structure for propagative and evanescent waves. One of them offers the possibility to include various constraints, such as minimization of the homogeneous index. Also, the potentialities of an anisotropic homogeneous material are investigated, and partial homogenization of the multilayer is considered. These results are then applied to a coated 3-D object modeled with the FEM. Numerical examples are presented that demonstrate the efficiency of these techniques.