Title: A novel analytical method for analysis of electromagnetic scattering from inhomogeneous spherical structures using duality principles,
Abstract: In this article, a novel analytical approach is presented for the analysis of
electromagnetic (EM) scattering from radially inhomogeneous spherical
structures (RISSs) based on the duality principle. According to the spherical
symmetry, similar angular dependencies in all the regions are considered using
spherical harmonics. To extract the radial dependency, the system of
differential equations of wave propagation toward the inhomogeneity direction
is equated with the dual planar ones. A general duality between electromagnetic
fields and parameters and scattering parameters of the two structures is
introduced. The validity of the proposed approach is verified through a
comprehensive example. The presented approach substitutes a complicated problem
in spherical coordinate to an easy, well posed, and a previously solved problem
in planar geometry. This approach is valid for all continuously varying
inhomogeneity profiles. One of the major advantages of the proposed method is
the capability of studying two general and applicable types of RISSs. As an
interesting application, a new class of lens antenna based on the physical
concept of the gradient refractive index material is introduced. The approach
is used to analyze the EM scattering from the structure and validate strong
performance of the lens.