General Formulation to Investigate Scattering from Multilayer Lossy Inhomogeneous Metamaterial Planar Structures

This paper presents a general formulation to investigate the scattering from Multilayer Lossy Inhomogeneous Metamaterial Planar Structure (MLIMPS) with arbitrary number of layers and polarization. First, the dominating differential equation of transverse components of electromagnetic fields in each layers derived. Considering the general form of solution of the differential equations and the boundary conditions of the problem; a set of linear equations is obtained. By solving these equations, the electromagnetic fields in all layers and reflection and transmission coefficients are calculated. This method is applied in an interesting example for two bi-layered structures with inhomogeneous conventional material and metamaterial profile for constitutive parameters. Results which are presented in example are useful for constructing general duality between conventional material and metamaterials.