Hasar Ugur Cem, Barroso Joaquim J, Sabah Cumali, Kaya Yunus, Ertugrul Mehmet
Department of Electrical and Electronics Engineering, Ataturk University, 25240 Erzurum, Turkey.
Opt Express. 2012 Dec 17;20(27):29002-22. doi: 10.1364/OE.20.029002.
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.
我们进行了一项文献中未研究过的完整不确定性分析，以研究两个具有单频和双频谐振特性的超材料平板（第一个仅含裂环谐振器（SRR），第二个含SRR和连续导线）的反演电磁特性对测量/模拟散射参数、平板长度和工作频率的依赖性。这种分析对于选择合适的反演方法以及正确检验超材料平板的奇异特性（尤其是在其谐振区域）是必要的。为此分析，开发了一个微分不确定性模型，以监测因变量（超材料平板的电磁特性）随自变量（散射（S -）参数、平板长度和工作频率）的微小变化。利用两种各有优势的互补方法（解析方法和色散模型方法）来反演各种超材料平板的电磁特性，这是不确定性分析应用所必需的。我们从研究中注意到以下重要结果。首先，当电磁特性值缩小到零或接近S参数快速变化的谐振区域时，所分析的超材料平板反演电磁特性的不确定性会急剧增加。其次，由于介质基板不完善或金属有限电导率导致的超材料平板内部的任何低损耗或中等损耗，都可以降低谐振区域附近的这些不确定性，因为这些损耗会阻碍S参数的突变。最后，我们注意到，特别是平板长度和工作频率的精确信息，是准确分析超材料平板（尤其是多频超材料平板）在谐振区域附近奇异电磁特性的先决条件。
