We applied a useful uncertainty model, ignored in most metamaterials retrieval studies, to monitor the accuracy of retrieved electromagnetic properties of bianisotropic metamaterial (MM) slabs composed of split-ring resonators and cut wires. Two different MM slab structures are considered to make the analysis complete. As uncertaintymaking factors, we took into consideration of uncertainties in scattering (S-) parameters of bianisotropic MM slabs as well as the length of these slabs. The applied uncertainty model is based upon considering the effect of minute change (differential) in uncertainty factors on the retrieved electromagnetic properties of bianisotropic MM slabs. The significant results concluded from the analysis are: 1) any abrupt changes in the phase of S-parameters of bianisotropic MM slabs remarkably influence the retrieved electromagnetic properties; 2) any small-scale loss (i.e., the loss of the substrate) in the bianisotropic MM slabs improves the accuracy of the retrieved electromagnetic properties of these slabs; and 3) precise knowledge of bianisotropic MM slab lengths are required for correct analysis of exotic properties of these slabs. The presented uncertainty analysis can be utilized as a metric tool for evaluating various retrieval methods of MM slabs in the literature.
2. Pendry, J. B., "Negative refraction makes a perfect lens," Phys.Rev. Lett., Vol. 85, 3966-3969, 2000.
3. Shelby, R. A., D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
4. Duan, Z., B.-I. Wu, S. Xi, H. Chen, and M. Chen, "Research progress in reversed Cherenkov radiation in double-negative metamaterials," Progress In Electromagnetics Research, Vol. 90, 75-87, 2009.
5. Cojocaru, E., "Electromagnetic tunneling in lossless trilayer stacks containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 113, 227-249, 2011.
6. Oraizi, H., A. Abdolali, and N. Vaseghi, "Application of double zero metamaterials as radar absorbing materials for the reduction of radar cross section," Progress In Electromagnetics Research, Vol. 101, 323-337, 2010.
7. Jiang, Z. H., J. A. Bossard, X. Wang, and D. H. Werner, "Synthesizing metamaterials with angularly independent effective medium properties based on an anisotropic parameter retrieval technique coupled with a genetic algorithm," J. Appl. Phys., Vol. 109, 013515, 2011.
8. Collin, R. E., Field Theory of Guided Waves, Wiley-IEEE Press, 1990.
9. Koschny, T., M. Kafesaki, E. N. Economou, and C. M. Soukolis, "Effective medium theory of left-handed materials," Phys. Rev. Lett., Vol. 93, 107402, 2004.
10. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coeffcients," Phys. Rev. B, Vol. 65, 195104, 2002.
11. Li, Z., K. Aydin, and E. Ozbay, "Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coeffcients," Phys. Rev. E, Vol. 79, 026610, 2009.
12. Smith, D. R., D. C. Vier, T. Koschhy, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E, Vol. 71, 036617,2005.
13. Chen, X., B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E, Vol. 71, 046610,2005.
14. Hasar, U. C. and J. J. Barroso, "Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials," Progress In Electromagnetics Research, Vol. 112, 109-124, 2011.
15. Marques, R., F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B, Vol. 65, 144440, 2002.
16. Katsarakis, N., T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett., Vol. 84, 2943-2945, 2004.
17. Alu, A., "First-principles homogenization theory for periodic metamaterials," Phys. Rev. B, Vol. 84, 075153, 2011.
18. Lubrowski, G., R. Schuhmann, and T. Weiland, "Extraction of effective metamaterial parameters by parameter fitting of dispersive models," Microw. Opt. Technol. Lett., Vol. 49, 285-288, 2007.
19. Markos, P. and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials," Opt. Express, Vol. 11, 649-661, 2003.
20. Ziolkowski, R. W., "Design, fabrication, and testing of double negative metamaterials," IEEE Trans. Antennas Propag., Vol. 51, 1516-1529, 2003.
21. Chen, X., T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E, Vol. 70, 016608, 2004.
22. Andryieuski, A., R. Malureanu, and A. V. Lavrinenko, "Wave propagation retrieval method for chiral metamaterials," Opt. Express, Vol. 18, No. 15, 15498-15503, 2010.
23. Andryieuski, A., C. Menzel, C. Rockstuhl, R. Malureanu,F. Lederer, and A. Lavrinenko, "Homogenization of resonant chiral metamaterials," Phys. Rev. B, Vol. 82, 235107, 2010.
24. Nicolson, A. M. and G. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Trans. Instrum. Meas., Vol. 19, 377-382, 1970.
25. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE, Vol. 62, 33-36, 1974.
26. Baker-Jarvis, J., E. J. Vanzura, and W. A. Kissick, "Improved technique for determining complex permittivity with the transmission/reflection method," IEEE Trans. Microw. Theory Tech., Vol. 38, 1096-1103, 1990.
27. Boughriet, A. H., C. Legrand, and A. Chapoton, "Noniterative stable transmission/reflection method for low-loss material complex permittivity determination," IEEE Trans. Microw. Theory Tech., Vol. 45, 52-57, 1997.
28. Hasar, U. C. and C. R. Westgate, "A broadband and stable method for unique complex permittivity determination of low-loss materials," IEEE Trans. Microw. Theory Tech., Vol. 57, 471-477, 2009.
29. Barroso, J. J. and A. L. de Paula, "Retrieval of permittivity and permeability of homogeneous materials from scattering parameters," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 11-12, 1563-1574, 2010.
30. Chalapat, K., K. Sarvala, J. Li, and G. S. Paraoanu, "Wideband reference-plane invariant method for measuring electromagnetic parameters of materials," IEEE Trans. Microw. Theory Tech., Vol. 57, 2257-2267, 2009.
31. Hasar, U. C. and Y. Kaya, "Reference-independent microwave method for constitutive parameters determination of liquid materials from measured scattering parameters," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 11-12, 1708-1717, 2011.
32. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE, Vol. 62, 33-36, 1974.
33. Muqaibel, A. H. and A. Safaai-Jazi, "A new formulation for characterization of materials based on measured insertion transfer function," IEEE Trans. Microw. Theory Tech., Vol. 51, 1946-1951, 2003.
34. Xia, S., Z. Xu, and X. Wei, "Thickness-induced resonance-based complex permittivity measurement technique for barium strontium titanate ceramics at microwave frequency," Rev. Sci. Instrum., Vol. 80, 114703,2009.
35. Buyukozturk, O., T.-Y. Yu, and J. A. Ortega, "A methodology for determining complex permittivity of construction materials based on transmission-only coherent, wide-bandwidth free-space measurements," Cem. Concr. Compos., Vol. 28, 349-359, 2006.
36. Szabo, Z., G.-H. Park, R. Hedge, and E.-P. Li, "Unique extraction of metamaterial parameters based on Kramers-Kronig relationship," IEEE Trans. Microw. Theory Tech., Vol. 58, 2646-2653, 2010.
37. Varadan, V. V. and R. Ro, "Unique retrieval of complex permittivity and permeability of dispersive materials from re°ection and transmitted fields by enforcing causality," IEEE Trans. Microw. Theory Tech., Vol. 55, 2224-2230, 2007.
38. Barroso, J. J. and U. C. Hasar, "Resolving phase ambiguity in the inverse problem of transmission/reflection measurement methods," Int. J. Infrared Milli. Waves, Vol. 32, 857-866, 2011.
39. Weiland, T., R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: Comparison of calculations and experiments," J. Appl. Phys., Vol. 90, 5419-5424, 2001.
40. Lubkowski, G., B. Bandlow, R. Schuhmann, and T. Weiland, "Effective modeling of double negative metamaterial macrostructures," IEEE Trans. Microw. Theory Tech., Vol. 57, 1136-1146, 2009.
41. Kline, S. J. and F. A. McClintock, "Describing uncertainties in single-sample experiments," Mech. Eng., Vol. 75, 3, 1953.
42. Baker-Jarvis, J., M. D. Janezic, J. H. Grosvenor, Jr., and R. G. Geyer, "Transmission/reflection and short-circuit line methods for measuring permittivity and permeability,", Tech. Note 1355, NIST, Boulder, CO, 1992.