Effective Material Property Extraction of a Metamaterial by Taking Boundary Effects Into Account at TE/TM Polarized Incidence

In this paper, we present the extraction for effective material parameters for a metamaterial from TE or TM waveguide measurements with generalized sheet transition conditions (GSTCs) used to provide electric and magnetic surface susceptibilities that approximate boundary effects between the metamaterial and air. The retrieval algorithm determines the effective material properties via scattering data obtained from the metamaterial in a waveguide. The effective refractive index is expressed as a function of S-parameters for two samples of different length. The effective wave impedance is given in terms of $S$-parameters and the refractive index, assuming that GSTCs account for the boundary effects. The effective permittivity and permeability can then be determined through the refractive index and wave impedance. By use of S-parameters generated by commercial three-dimensional (3-D) full-wave simulation software our present equations are tested for two cases of metamaterials: magneto-dielectric (ε=μ) and dielectric (TiO) particles. We also conduct S-parameter measurements on dielectric cubes with an S-band (WR-284) waveguide to compute the effective material properties. Furthermore, our results are compared to those derived from another retrieval method used in the literature, which does not account for boundary effects.