Trislab refractive index retrieval for nearly-homogenized periodic or homogenized media

Abstract A method for refractive index retrieval of periodic media showing nearly-homogeneous behavior is proposed. Given the scattering parameters of three electrically thick slabs with a constantly increasing electrically small thickness difference, effective refractive index of periodic nearly-homogenized linear medium is found. Here we consider the medium as a combination of two interfaces and the inner part of the medium. Each part is represented by its own (unknown) generalized scattering parameter matrix. We construct the scattering parameter matrix of the electrically thick medium parametrically using signal-flow diagrams. Using the parameterized scattering parameters, and their numerical values for three different thickness values (obtained either by numerical simulation or experiment), we come up with a second-degree polynomial equation. The physically-correct root corresponds to the complex exponential affecting on the fields due to propagation. The phase and magnitude of the corresponding complex exponential for the given thickness increment is found, and the effective complex refractive index can be deduced. We believe that we provide researchers a clear and concise way for refractive index retrieval of periodic mediums such as metamaterials and photonic crystals. The method is also applicable to perfectly homogenized media.