Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs

Abstract

We apply a complete uncertainty analysis, not studied in the literature, to investigate the dependences of retrieved electromagnetic properties of two MM slabs (the first one with only split-ring resonators (SRRs) and the second with SRRs and a continuous wire) with single-band and dual-band resonating properties on the measured/simulated scattering parameters, the slab length, and the operating frequency. Such an analysis is necessary for the selection of a suitable retrieval method together with the correct examination of exotic properties of MM slabs especially in their resonance regions. For this analysis, a differential uncertainty model is developed to monitor minute changes in the dependent variables (electromagnetic properties of MM slabs) in functions of independent variables (scattering (S-) parameters, the slab length, and the operating frequency). Two complementary approaches (the analytical approach and the dispersion model approach) each with different strengths are utilized to retrieve the electromagnetic properties of various MM slabs, which are needed for the application of the uncertainty analysis. We note the following important results from our investigation. First, uncertainties in the retrieved electromagnetic properties of the analyzed MM slabs drastically increase when values of electromagnetic properties shrink to zero or near resonance regions where S-parameters exhibit rapid changes. Second, any low-loss or medium-loss inside the MM slabs due to an imperfect dielectric substrate or a finite conductivity of metals can decrease these uncertainties near resonance regions because these losses hinder abrupt changes in S-parameters. Finally, we note that precise information of especially the slab length and the operating frequency is a prerequisite for accurate analysis of exotic electromagnetic properties of MM slabs (especially multiband MM slabs) near resonance regions.

Stepwise technique for accurate and unique retrieval of electromagnetic properties of bianisotropic metamaterials

“…Therefore, the situation Imfε z g < 0 and/or Imfμ y g < 0 in Figs. 8-11 is nonphysical and attributed to spatial dispersion effects arising from the discreteness of conducting elements [26,27,48,52]. On the other hand, while the maximum absolute of extracted negative Imfμ y g of the bianisotropic SRR MM slab is nearly 13, that of the bianisotropic Omega MM slab is around 1.…”

“…This change in a resonance frequency (either to lower frequencies or higher frequencies) could also be an indication of bianisotropic property of the analyzed MM slab for the following reasons. First, any additional loss (wire strip) present inside a resonating structure, such as MM slabs decreases resonance frequency as well as quality factor of the resonating structure [50][51][52]. Second, a wire strip is effective in producing additional electric resonances [9] to the analyzed MM slab at microwave frequencies (see Figs.…”

“…1 and 2. However, in an actual measurement scenario, measured S-parameters by the measurement equipment such as a vector network analyzer have some uncertainty associated with it [51,52]. To reflect this uncertainty (noise) into the analysis, we added a random uncorrelated noise to real and imaginary parts of the S-parameters [46], since these parts are independent from each other.…”

Calculation and Analysis of the Effective Electromagnetic Parameters of Periodic Structural Radar Absorbing Material Using Simulation and Inversion Methods

“…However, in all the methods mentioned above, the interactions between two adjacent cells were usually ignored. The last type is the study on EEPs of the double negative materials [12][13][14]. To obtain their EEPs values, scattering coefficients which are related to the interaction of two neighbor cells, are usually calculated using the simulation software.…”

Determining the Effective Electromagnetic Parameters of Bianisotropic Metamaterials With Periodic Structures

“…Smith et al first applies the technique to materials composed of SRRs and finite rods [5] and then discusses the retrieval of inhomogeneous materials [6]. Some improved retrieval schemes based on the initial approach are also presented in recent years [7][8][9][10][11]. The parameters of a material can also be obtained by experiments based on the measurement of the S parameters using waveguide method [12].…”