Three different techniques are applied for accurate constitutive parameters determination of isotropic split-ring resonator (SRR) and SRR with a cut wire (Composite) metamaterial (MM) slabs. The first two techniques use explicit analytical calibration-dependent and calibration-invariant expressions while the third technique is based on Lorentz and Drude dispersion models. We have tested these techniques from simulated scattering (S-) parameters of two classic SRR and Composite MM slabs with various level of losses and different calibration plane factors. From the comparison, we conclude that whereas the extracted complex permittivity of both slabs by the analytical techniques produces unphysical results at resonance regions, that by the dispersion model eliminates this shortcoming and retrieves physically accurate constitutive parameters over the whole analyzed frequency region. We argue that incorrect retrieval of complex permittivity by analytical methods comes from spatial dispersion effects due to the discreteness of conducting elements within MM slabs which largely vary simulated S-parameters in the resonance regions where the slabs are highly spatially dispersive.
2. Lindell, I. V., S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media-media with negative parameters, capable of supporting backward waves," Microw. Opt. Technol. Lett., Vol. 31, 129-133, 2001.
3. Engheta, N., "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability ," IEEE Antennas Wireless Propagat. Lett., Vol. 1, 10-13, 2002.
4. Alu, A. and N. Engheta, "Radiation from a travelling-wave current sheet at the interface between a conventional material and a metamaterial with negative permittivity and permeability," Microw. Opt. Technol. Lett., Vol. 35, No. 6, 460-463, 2002.
5. 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.
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. Cojocaru, E., "Electromagnetic tunneling in lossless trilayer stacks containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 113, 227-249, 2011.
8. Alu, A., "First-principles homogenization theory for periodic metamaterials," Phys. Rev. B, Vol. 84, 075153, 2011.
9. Nicolson, A. M. and G. Ross, "Measurement of the intrinsic properties of materials by time-domain techniques," IEEE Trans. Instrum. Meas., Vol. 19, No. 4, 377-382, 1970.
10. Weir, W. B., "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE, Vol. 62, No. 1, 33-36, 1974.
11. 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, No. 1, 52-57, 1997.
12. 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, No. 2, 471-477, 2009.
13. 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.
14. 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, No. 9, 2257-2267, 2009.
15. 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.
16. Smith, D. R., S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B, Vol. 65, 195104, 2002.
17. 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.
18. Li, Z., K. Aydin, and E. Ozbay, "Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coe±cients ," Phys. Rev. E, Vol. 79, 026610, 2009.
19. Lubkowski, G., R. Schuhmann, and T. Weiland, "Extraction of effective metamaterial parameters by parameter fitting of dispersive models," Microw. Opt. Technol. Lett., Vol. 49, No. 2, 285-288, 2007.
20. Markos, P. and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials ," Opt. Express, Vol. 11, 649-661, 2003.
21. 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.
22. Shelby, R. A., D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett., Vol. 78, No. 4, 489-491, 2001.
23. Mattiucci, N., G. D'Aguanno, N. Akozbek, M. Scalora, and M. J. Blomer, "Homogenization procedure for a metamaterial and local violation of the second principle of thermodynamics," Opt. Commun., Vol. 283, 1613-1620, 2010.
24. 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.
25. 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.
26. Luukkonen, O., S. I. Maslovski, and S. A. Tretyakov, "A stepwise Nicolson-Ross-Weir-based material parameter extraction method," IEEE Antennas Propag. Lett., Vol. 10, 1295-1298, 2011.
27. Hasar, U. C., J. J. Barroso, C. Sabah, and Y. Kaya, "Resolving phase ambiguity in the inverse problem of reflection-only measurement methods ," Progress In Electromagnetics Research, Vol. 129, 405-420, 2012.
28. Sabah, C. and S. Uckun, "Multilayer system of Lorentz/Drude type metamaterials with dielectric slabs and its application to electromagnetic filters," Progress In Electromagnetics Research, Vol. 91, 349-364, 2009.
29. Hasar, U. C., J. J. Barroso, M. Ertugrul, C. Sabah, and B. Cavusoglu, "Application of a useful uncertainty analysis as a metric tool for assessing the performance of electromagnetic properties retrieval methods of bianisotropic metamaterials," Progress In Electromagnetics Research, Vol. 128, 365-380, 2012.
30. Xu, S., L. Yang, L. Huang, and H. Chen, "Experimental measurement method to determine the permittivity of extra thin materials using resonant metamaterials," Progress In Electromagnetics Research, Vol. 120, 327-337, 2011.
31. Hasar, U. C., "A new method for evaluation of thickness and monitoring its variation of medium- and low-loss materials," Progress In Electromagnetics Research, Vol. 94, 403-418, 2009.