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 polarizations. first, the dominating differential equations of transverse components of electromagnetic fields in each layer are derived. considering the general solution form 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 the layers and reflection and transmission coefficients are calculated. this method is used in analyzing two inhomogeneous planar layers consisting of conventional material and metamaterial in an interesting example. the presented results are useful for constructing general duality between conventional materials and metamaterials.