To further characterize the MS’s response, it is of interest to determine its effective material and wave parameters. The method described in ref.50 was used to extract the effective wave impedance Zeff, the effective dielectric constant εeff, and the effective permeability μeff from the S-parameters. These wave and medium parameters are shown in Fig. 7. During the extraction process, the MS was assumed to be homogeneous with an effective thickness equal to that of the substrate upon which the TC-UAJC element resides. Homogenization is justified due to the sub-wavelength nature of the MS inclusions. Owing to the MS’s very thin nature in the direction of propagation, the extraction process was expected to proceed smoothly. Moreover, its thinness led to virtually the same results relative to each port of the unit cell. In order to obtain more complete extraction results, the MS was simulated up to 30 GHz for the TM excitation, well above its TM reflection resonance frequency of 15.8 GHz.Figure 7Extracted parameters of the MS for the TM excitation. (a) Effective impedance. (b) Effective permittivity and effective permeability at the frequencies of interest and (c) across the whole band showing TM resonance at 15.8 GHz.