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.

© 2012 OSA

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2012 (3)

U. C. Hasar, J. J. Barroso, C. Sabah, and Y. Kaya, “Resolving phase ambiguity in the inverse problem of reflection-only measurement methods,” Prog. Electromagn. Res. 129, 405–420 (2012).

C. Sabah, “Multi-resonant metamaterial design based on concentric V -shaped magnetic resonators,” J. Electromagn. Waves Appl. 26(8-9), 1105–1115 (2012).
[Crossref]

U. C. Hasar, I. Y. Ozbek, E. A. Oral, T. Karacali, and H. Efeoglu, “The effect of silicon loss and fabrication tolerance on spectral properties of porous silicon Fabry-Perot cavities in sensing applications,” Opt. Express 20(20), 22208–22223 (2012).
[Crossref] [PubMed]

2011 (14)

S. Xu, L. Yang, L. Huang, and H. Chen, “Experimental measurement method to determine the permittivity of extra thin materials using resonating metamaterials,” Prog. Electromagn. Res. 120, 327–337 (2011).

O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A tespwise Nicolson-Ross-Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
[Crossref]

J. J. Barroso and U. C. Hasar, “Resolving phase ambiguity in the inverse problem of transmission/reflection measurement methods,” Int. J. Infrared Millim. Waves 32(6), 857–866 (2011).
[Crossref]

U. C. Hasar and I. Y. Ozbek, “Complex permittivity determination of lossy materials at millimeter and terahertz frequencies using free-space amplitude measurements,” J. Electromagn. Waves Appl. 25(14-15), 2100–2109 (2011).
[Crossref]

U. C. Hasar and A. Abusoglu, “Using millimeter and terahertz frequencies for complex permittivity retrieval of low-loss materials,” J. Electromagn. Waves Appl. 25(17-18), 2389–2398 (2011).
[Crossref]

B. Kapilevich, Y. Pinhasi, and B. Litvak, “Measurement of complex permittivity of lossy materials in free space using matched THz power meter,” Int. J. Infrared Millim. Waves 32(12), 1446–1456 (2011).
[Crossref]

X.-X. Liu, D. A. Powell, and A. Alu, “Correcting the Fabry-Perot artifacts in metamaterial retrieval procedures,” Phys. Rev. B 84(23), 235106 (2011).
[Crossref]

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

W. H. Wee and J. B. Pendry, “Universal evolution of perfect lenses,” Phys. Rev. Lett. 106(16), 165503 (2011).
[Crossref] [PubMed]

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

C. Sabah, “Multiband planar metamaterials,” Microw. Opt. Technol. Lett. 53(10), 2255–2258 (2011).
[Crossref]

Z. H. Jiang, 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. 109(1), 013515 (2011).
[Crossref]

U. C. Hasar and J. J. Barroso, “Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials,” Prog. Electromagn. Res. 112, 109–124 (2011).

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[Crossref]

2010 (8)

U. C. Hasar, “A microwave method for accurate and stable retrieval of constitutive parameters of low- and medium-loss materials,” IEEE Microw. Wirel. Compon. Lett. 20(12), 696–698 (2010).
[Crossref]

U. C. Hasar, “Procedure for accurate and stable constitutive parameters extraction of materials at microwave frequencies,” Prog. Electromagn. Res. 109, 107–121 (2010).
[Crossref]

J. Qi, H. Kettunen, H. Wallen, and A. Sihvola, “Compensation of Fabry-Perot resonances in homogenization of dielectric composites,” IEEE Antennas Wireless Propag. Lett. 9, 1057–1060 (2010).
[Crossref]

D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization? The microstructure of highly anisotropic particles with an SRR-like geometry,” Adv. Funct. Mater. 20(7), 1116–1124 (2010).
[Crossref]

U. C. Hasar, “Unique permittivity determination of low-loss dielectric materials from transmission measurements at microwave frequencies,” Prog. Electromagn. Res. 107, 31–46 (2010).
[Crossref]

Z. Szabo, G.-H. Park, R. Hedge, and E.-P. Li, “Unique extraction of metamaterial parameters based on Kramers-Kronig relationship,” IEEE Trans. Microw. Theory Tech. 58(10), 2646–2653 (2010).
[Crossref]

E. Pshenay-Severin, F. Setzpfandt, C. Helgert, U. Hubner, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, “Experimental determination of the dispersion relation of light in metamaterials by white-light interferometry,” J. Opt. Soc. Am. B 27(4), 660–666 (2010).
[Crossref]

J. J. Barroso and A. L. de Paula, “Retrieval of permittivity and permeability of homogeneous materials from scattering parameters,” J. Electromagn. Waves Appl. 24(11-12), 1563–1574 (2010).
[Crossref]

2009 (11)

K. Chalapat, K. Sarvala, J. Li, and G. S. Paraoanu, “Wideband reference-plane invariant method for measuring electromagnetic parameters of materials,” IEEE Trans. Microw. Theory Tech. 57(9), 2257–2267 (2009).
[Crossref]

U. C. Hasar and C. R. Westgate, “A broadband and stable method for unique complex permittivity determination of low-loss materials,” IEEE Trans. Microw. Theory Tech. 57(2), 471–477 (2009).
[Crossref]

C. Sabah and S. Uckun, “Multilayer system of Lorentz/Drude type metamaterials with dielectric slabs and its application to electromagnetic filters,” Prog. Electromagn. Res. 91, 349–364 (2009).
[Crossref]

G. Lubkowski, B. Bandlow, R. Schuhmann, and T. Weiland, “Effective modeling of double negative metamaterial macrostructures,” IEEE Trans. Microw. Theory Tech. 57(5), 1136–1146 (2009).
[Crossref]

S. Xia, Z. Xu, and X. Wei, “Thickness-induced resonance-based complex permittivity measurement technique for barium strontium titanate ceramics at microwave frequency,” Rev. Sci. Instrum. 80(11), 114703 (2009).
[Crossref] [PubMed]

H. Nemec, P. Kuzel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79, 241108(R) (2009).

R. Melik, E. Unal, N. K. Perkgoz, C. Puttlitz, and H. V. Demir, “Metamaterial-based wireless strain sensors,” Appl. Phys. Lett. 95(1), 011106 (2009).
[Crossref]

L. Jelinek, R. Marques, and M. J. Freire, “Accurate modeling of split ring metamaterial lenses for magnetic resonance imaging applications,” J. Appl. Phys. 105(2), 024907 (2009).
[Crossref]

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tunnermann, F. Lederer, and T. Pertsch, “effective properties of amorphous metamaterials,” Phys. Rev. B 79(23), 233107 (2009).
[Crossref]

K. B. Alici and E. Ozbay, “Oblique response of a split-ring-resonator-based left-handed metamaterial slab,” Opt. Lett. 34(15), 2294–2296 (2009).
[Crossref] [PubMed]

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026610 (2009).
[Crossref] [PubMed]

2008 (1)

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

2007 (6)

K. Aydin, Z. Li, M. Hudlicka, S. A. Tretyakov, and E. Ozbay, “Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions,” New J. Phys. 9(9), 326 (2007).
[Crossref]

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75(11), 115114 (2007).
[Crossref]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

V. V. Varadan and R. Ro, “Unique retrieval of complex permittivity and permeability of dispersive materials from reflection and transmitted fields by enforcing causality,” IEEE Trans. Microw. Theory Tech. 55(10), 2224–2230 (2007).
[Crossref]

B. Kapilevih and B. Litvak, “THz characterization of high-dielectric constant materials using double-layer sample,” Microw. Opt. Technol. Lett. 49(6), 1388–1391 (2007).
[Crossref]

G. Lubkowski, R. Schuhmann, and T. Weiland, “Extraction of effective metamaterial parameters by parameter fitting of dispersive models,” Microw. Opt. Technol. Lett. 49(2), 285–288 (2007).
[Crossref]

2006 (3)

O. Büyüköztürk, 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,” Cement Concr. Compos. 28(4), 349–359 (2006).
[Crossref]

D. R. Smith, D. Schurig, and J. J. Mock, “Characterization of a planar artificial magnetic metamaterial surface,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 036604 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

2005 (3)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005).
[Crossref] [PubMed]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 046610 (2005).
[Crossref] [PubMed]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

2004 (2)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

T. J. Cui and J. A. Kong, “Time-domain electromagnetic energy in a frequency-dispersive left-handed medium,” Phys. Rev. B 70(20), 205106 (2004).
[Crossref]

2003 (2)

A. H. Muqaibel and A. Safaai-Jazi, “A new formulation for characterization of materials based on measured insertion transfer function,” IEEE Trans. Microw. Theory Tech. 51(8), 1946–1951 (2003).
[Crossref]

P. Markos and C. M. Soukoulis, “Transmission properties and effective electromagnetic parameters of double negative metamaterials,” Opt. Express 11(7), 649–661 (2003).
[Crossref] [PubMed]

2002 (2)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002).
[Crossref]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

2001 (4)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

M. Bozzi, L. Perregrini, J. Weinzierl, and C. Winnewisser, “Efficient analysis of quasi-optical filters by a hybrid MoM/Bi-RME method,” IEEE Trans. Antenn. Propag. 49(7), 1054–1064 (2001).
[Crossref]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
[Crossref] [PubMed]

T. Weiland, 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. 90(10), 5419–5424 (2001).
[Crossref]

2000 (3)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998).
[Crossref]

1997 (2)

R. Storn and K. Price, “Differential evaluation–A simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim. 11(4), 341–359 (1997).
[Crossref]

A. H. Boughriet, C. Legrand, and A. Chapoton, “Noniterative stable transmission/reflection method for low-loss material complex permittivity determination,” IEEE Trans. Microw. Theory Tech. 45(1), 52–57 (1997).
[Crossref]

1992 (1)

J. Baker-Jarvis, R. G. Geyer, and P. D. Domich, “A nonlinear least-squares solution with causality constrains applied to transmission line permittivity and permeability determination,” IEEE Trans. Instrum. Meas. 41(5), 646–652 (1992).
[Crossref]

1990 (1)

J. Baker–Jarvis, E. J. Vanzura, and W. A. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory Tech. 38(8), 1096–1103 (1990).
[Crossref]

1974 (1)

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62(1), 33–36 (1974).
[Crossref]

1970 (1)

A. M. Nicolson and G. Ross, “Measurement of the intrinsic properties of materials by time–domain techniques,” IEEE Trans. Instrum. Meas. 19(4), 377–382 (1970).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values ofε and μ, ” Sov. Phys. Uspekhi 10, 509–514 (1968).
[Crossref]

1953 (1)

S. J. Kline and F. A. McClintock, “Describing uncertainties in single−sample experiments,” Mech. Eng. 75, 3 (1953).

Abusoglu, A.

U. C. Hasar and A. Abusoglu, “Using millimeter and terahertz frequencies for complex permittivity retrieval of low-loss materials,” J. Electromagn. Waves Appl. 25(17-18), 2389–2398 (2011).
[Crossref]

Alici, K. B.

Alu, A.

X.-X. Liu, D. A. Powell, and A. Alu, “Correcting the Fabry-Perot artifacts in metamaterial retrieval procedures,” Phys. Rev. B 84(23), 235106 (2011).
[Crossref]

Alù, A.

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84(7), 075153 (2011).
[Crossref]

Aydin, K.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026610 (2009).
[Crossref] [PubMed]

K. Aydin, Z. Li, M. Hudlicka, S. A. Tretyakov, and E. Ozbay, “Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions,” New J. Phys. 9(9), 326 (2007).
[Crossref]

Baker-Jarvis, J.

J. Baker-Jarvis, R. G. Geyer, and P. D. Domich, “A nonlinear least-squares solution with causality constrains applied to transmission line permittivity and permeability determination,” IEEE Trans. Instrum. Meas. 41(5), 646–652 (1992).
[Crossref]

Baker–Jarvis, J.

J. Baker–Jarvis, E. J. Vanzura, and W. A. Kissick, “Improved technique for determining complex permittivity with the transmission/reflection method,” IEEE Trans. Microw. Theory Tech. 38(8), 1096–1103 (1990).
[Crossref]

Bandlow, B.

G. Lubkowski, B. Bandlow, R. Schuhmann, and T. Weiland, “Effective modeling of double negative metamaterial macrostructures,” IEEE Trans. Microw. Theory Tech. 57(5), 1136–1146 (2009).
[Crossref]

Barroso, J. J.

U. C. Hasar, J. J. Barroso, C. Sabah, and Y. Kaya, “Resolving phase ambiguity in the inverse problem of reflection-only measurement methods,” Prog. Electromagn. Res. 129, 405–420 (2012).

J. J. Barroso and U. C. Hasar, “Resolving phase ambiguity in the inverse problem of transmission/reflection measurement methods,” Int. J. Infrared Millim. Waves 32(6), 857–866 (2011).
[Crossref]

U. C. Hasar and J. J. Barroso, “Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials,” Prog. Electromagn. Res. 112, 109–124 (2011).

J. J. Barroso and A. L. de Paula, “Retrieval of permittivity and permeability of homogeneous materials from scattering parameters,” J. Electromagn. Waves Appl. 24(11-12), 1563–1574 (2010).
[Crossref]

Basov, D. N.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75(11), 115114 (2007).
[Crossref]

Bossard, J. A.

Z. H. Jiang, 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. 109(1), 013515 (2011).
[Crossref]

Boughriet, A. H.

A. H. Boughriet, C. Legrand, and A. Chapoton, “Noniterative stable transmission/reflection method for low-loss material complex permittivity determination,” IEEE Trans. Microw. Theory Tech. 45(1), 52–57 (1997).
[Crossref]

Bozzi, M.

M. Bozzi, L. Perregrini, J. Weinzierl, and C. Winnewisser, “Efficient analysis of quasi-optical filters by a hybrid MoM/Bi-RME method,” IEEE Trans. Antenn. Propag. 49(7), 1054–1064 (2001).
[Crossref]

Büyüköztürk, O.

O. Büyüköztürk, 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,” Cement Concr. Compos. 28(4), 349–359 (2006).
[Crossref]

Chalapat, K.

K. Chalapat, K. Sarvala, J. Li, and G. S. Paraoanu, “Wideband reference-plane invariant method for measuring electromagnetic parameters of materials,” IEEE Trans. Microw. Theory Tech. 57(9), 2257–2267 (2009).
[Crossref]

Chapoton, A.

A. H. Boughriet, C. Legrand, and A. Chapoton, “Noniterative stable transmission/reflection method for low-loss material complex permittivity determination,” IEEE Trans. Microw. Theory Tech. 45(1), 52–57 (1997).
[Crossref]

Chen, H.

S. Xu, L. Yang, L. Huang, and H. Chen, “Experimental measurement method to determine the permittivity of extra thin materials using resonating metamaterials,” Prog. Electromagn. Res. 120, 327–337 (2011).

Chen, X.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 046610 (2005).
[Crossref] [PubMed]

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Chipouline, A.

Choi, M.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Cui, T. J.

T. J. Cui and J. A. Kong, “Time-domain electromagnetic energy in a frequency-dispersive left-handed medium,” Phys. Rev. B 70(20), 205106 (2004).
[Crossref]

de Paula, A. L.

J. J. Barroso and A. L. de Paula, “Retrieval of permittivity and permeability of homogeneous materials from scattering parameters,” J. Electromagn. Waves Appl. 24(11-12), 1563–1574 (2010).
[Crossref]

Demir, H. V.

R. Melik, E. Unal, N. K. Perkgoz, C. Puttlitz, and H. V. Demir, “Metamaterial-based wireless strain sensors,” Appl. Phys. Lett. 95(1), 011106 (2009).
[Crossref]

Diduszko, R.

D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization? The microstructure of highly anisotropic particles with an SRR-like geometry,” Adv. Funct. Mater. 20(7), 1116–1124 (2010).
[Crossref]

Domich, P. D.

J. Baker-Jarvis, R. G. Geyer, and P. D. Domich, “A nonlinear least-squares solution with causality constrains applied to transmission line permittivity and permeability determination,” IEEE Trans. Instrum. Meas. 41(5), 646–652 (1992).
[Crossref]

Driscoll, T.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, “Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements,” Phys. Rev. B 75(11), 115114 (2007).
[Crossref]

Du, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Economou, E. N.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

Efeoglu, H.

Etrich, C.

C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tunnermann, F. Lederer, and T. Pertsch, “effective properties of amorphous metamaterials,” Phys. Rev. B 79(23), 233107 (2009).
[Crossref]

Freire, M. J.

L. Jelinek, R. Marques, and M. J. Freire, “Accurate modeling of split ring metamaterial lenses for magnetic resonance imaging applications,” J. Appl. Phys. 105(2), 024907 (2009).
[Crossref]

Gajc, M.

D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization? The microstructure of highly anisotropic particles with an SRR-like geometry,” Adv. Funct. Mater. 20(7), 1116–1124 (2010).
[Crossref]

Geyer, R. G.

J. Baker-Jarvis, R. G. Geyer, and P. D. Domich, “A nonlinear least-squares solution with causality constrains applied to transmission line permittivity and permeability determination,” IEEE Trans. Instrum. Meas. 41(5), 646–652 (1992).
[Crossref]

Greegor, R. B.

T. Weiland, 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. 90(10), 5419–5424 (2001).
[Crossref]

Grzegorczyk, T. M.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(4), 046610 (2005).
[Crossref] [PubMed]

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Hasar, U. C.

U. C. Hasar, J. J. Barroso, C. Sabah, and Y. Kaya, “Resolving phase ambiguity in the inverse problem of reflection-only measurement methods,” Prog. Electromagn. Res. 129, 405–420 (2012).

U. C. Hasar, I. Y. Ozbek, E. A. Oral, T. Karacali, and H. Efeoglu, “The effect of silicon loss and fabrication tolerance on spectral properties of porous silicon Fabry-Perot cavities in sensing applications,” Opt. Express 20(20), 22208–22223 (2012).
[Crossref] [PubMed]

J. J. Barroso and U. C. Hasar, “Resolving phase ambiguity in the inverse problem of transmission/reflection measurement methods,” Int. J. Infrared Millim. Waves 32(6), 857–866 (2011).
[Crossref]

U. C. Hasar and I. Y. Ozbek, “Complex permittivity determination of lossy materials at millimeter and terahertz frequencies using free-space amplitude measurements,” J. Electromagn. Waves Appl. 25(14-15), 2100–2109 (2011).
[Crossref]

U. C. Hasar and A. Abusoglu, “Using millimeter and terahertz frequencies for complex permittivity retrieval of low-loss materials,” J. Electromagn. Waves Appl. 25(17-18), 2389–2398 (2011).
[Crossref]

U. C. Hasar and J. J. Barroso, “Retrieval approach for determination of forward and backward wave impedances of bianisotropic metamaterials,” Prog. Electromagn. Res. 112, 109–124 (2011).

U. C. Hasar, “A microwave method for accurate and stable retrieval of constitutive parameters of low- and medium-loss materials,” IEEE Microw. Wirel. Compon. Lett. 20(12), 696–698 (2010).
[Crossref]

U. C. Hasar, “Procedure for accurate and stable constitutive parameters extraction of materials at microwave frequencies,” Prog. Electromagn. Res. 109, 107–121 (2010).
[Crossref]

U. C. Hasar, “Unique permittivity determination of low-loss dielectric materials from transmission measurements at microwave frequencies,” Prog. Electromagn. Res. 107, 31–46 (2010).
[Crossref]

U. C. Hasar and C. R. Westgate, “A broadband and stable method for unique complex permittivity determination of low-loss materials,” IEEE Trans. Microw. Theory Tech. 57(2), 471–477 (2009).
[Crossref]

Hedge, R.

Z. Szabo, G.-H. Park, R. Hedge, and E.-P. Li, “Unique extraction of metamaterial parameters based on Kramers-Kronig relationship,” IEEE Trans. Microw. Theory Tech. 58(10), 2646–2653 (2010).
[Crossref]

Helgert, C.

Heyman, E.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
[Crossref] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998).
[Crossref]

Huang, L.

S. Xu, L. Yang, L. Huang, and H. Chen, “Experimental measurement method to determine the permittivity of extra thin materials using resonating metamaterials,” Prog. Electromagn. Res. 120, 327–337 (2011).

Hubner, U.

Hudlicka, M.

K. Aydin, Z. Li, M. Hudlicka, S. A. Tretyakov, and E. Ozbay, “Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions,” New J. Phys. 9(9), 326 (2007).
[Crossref]

Jelinek, L.

L. Jelinek, R. Marques, and M. J. Freire, “Accurate modeling of split ring metamaterial lenses for magnetic resonance imaging applications,” J. Appl. Phys. 105(2), 024907 (2009).
[Crossref]

Jiang, Z. H.

Z. H. Jiang, 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. 109(1), 013515 (2011).
[Crossref]

Kadlec, C.

H. Nemec, P. Kuzel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79, 241108(R) (2009).

Kadlec, F.

H. Nemec, P. Kuzel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79, 241108(R) (2009).

Kafesaki, M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005).
[Crossref] [PubMed]

Kang, K. Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Kang, L.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007).
[Crossref]

Kang, S. B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Kapilevich, B.

B. Kapilevich, Y. Pinhasi, and B. Litvak, “Measurement of complex permittivity of lossy materials in free space using matched THz power meter,” Int. J. Infrared Millim. Waves 32(12), 1446–1456 (2011).
[Crossref]

Kapilevih, B.

B. Kapilevih and B. Litvak, “THz characterization of high-dielectric constant materials using double-layer sample,” Microw. Opt. Technol. Lett. 49(6), 1388–1391 (2007).
[Crossref]

Karacali, T.

Kaya, Y.

U. C. Hasar, J. J. Barroso, C. Sabah, and Y. Kaya, “Resolving phase ambiguity in the inverse problem of reflection-only measurement methods,” Prog. Electromagn. Res. 129, 405–420 (2012).

Kettunen, H.

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Figures (24)

Fig. 1
Fig. 1

Schematic view of a single cell of a metamaterial (a) with SRRs only and (b) with SRRs and a wire.

Fig. 2
Fig. 2

Schematic view of a single cell of a metamaterial (a) with concentric open ring resonators only and (b) with concentric open ring resonators and a wire.

Fig. 3
Fig. 3

(a) Magnitude and (b) phase of the simulated S-parameters for the lossy SB&DB SRR MM slabs.

Fig. 4
Fig. 4

(a) Magnitude and (b) phase of the simulated S-parameters for the lossy SB&DB Composite MM slabs.

Fig. 5
Fig. 5

Real and imaginary parts of retrieved refractive index of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the analytical approach.

Fig. 6
Fig. 6

Real and imaginary parts of retrieved wave impedance of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the analytical approach.

Fig. 7
Fig. 7

Real and imaginary parts of retrieved permittivity of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the analytical approach.

Fig. 8
Fig. 8

Real and imaginary parts of retrieved permeability of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the analytical approach.

Fig. 9
Fig. 9

Real and imaginary parts of retrieved refractive index of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the dispersion model approach.

Fig. 10
Fig. 10

Real and imaginary parts of retrieved wave impedance of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the dispersion model approach.

Fig. 11
Fig. 11

Real and imaginary parts of retrieved permittivity of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the dispersion model approach.

Fig. 12
Fig. 12

Real and imaginary parts of retrieved permeability of the lossy SB&DB (a) SRR MM slab and (b) Composite MM slab using the dispersion model approach.

Fig. 13
Fig. 13

Frequency dependence of real and imaginary parts of (a) Δ ε r / ε r and (b) Δ μ r / μ r for the lossy SB&DB SRR MM slabs using the analytical approach.

Fig. 14
Fig. 14

Frequency dependence of real and imaginary parts of (a) Δ ε r / ε r and (b) Δ μ r / μ r for the lossy SB&DB Composite MM slabs using the analytical approach.

Fig. 15
Fig. 15

Frequency dependence of real and imaginary parts of (a) Δ ε r and (b) Δ μ r / μ r for the lossy SB&DB SRR MM slabs using the dispersive model approach.

Fig. 16
Fig. 16

Frequency dependence of real and imaginary parts of (a) Δ ε r / ε r and (b) Δ μ r / μ r for the lossy SB&DB Composite MM slabs using the dispersive model approach.

Fig. 17
Fig. 17

Frequency dependence of Δ μ r ' for lossy SB&DB SRR and Composite MM slabs obtained from (a) the analytical approach and (b) the dispersive model approach.

Fig. 18
Fig. 18

Frequency dependence of real and imaginary parts of (a) Δ ε r / ε r and (b) Δ μ r / μ r for the low-loss and lossy SB Composite MM slabs using the dispersive model approach.

Fig. 19
Fig. 19

Frequency dependence of real and imaginary parts of (a) ε r / d and (b) μ r / d for the lossy SB&DB Composite MM slabs using the analytical approach.

Fig. 20
Fig. 20

Frequency dependence of real and imaginary parts of (a) ε r / f and (b) μ r / f for the lossy SB&DB Composite MM slabs using the analytical approach.

Fig. 21
Fig. 21

Frequency dependence of real and imaginary parts of (a) ε r / d and (b) μ r / d for the lossy SB&DB Composite MM slabs using the dispersive model approach.

Fig. 22
Fig. 22

Frequency dependence of real and imaginary parts of (a) ε r / f and (b) μ r / f for the lossy SB&DB Composite MM slabs using the dispersive model approach.

Fig. 23
Fig. 23

Frequency dependence of real and imaginary parts of (a) ε r / d and (b) μ r / d for the low-loss and lossy SB Composite MM slabs using the dispersive model approach.

Fig. 24
Fig. 24

Frequency dependence of real and imaginary parts of (a) ε r / f and (b) μ r / f for the low-loss and lossy SB Composite MM slabs using the dispersive model approach.

Tables (3)

Tables Icon

Table 1 Optimized Drude/Lorentz Dispersive Parameters for the Lossy SB&DB SRR and Compos. MM Slabs

Tables Icon

Table 2 Important Largest Uncertainty Levels and their Reasons for the Lossy SB&DB SRR MM Slabs (the Number in Parentheses in a Superscript Denotes the Reason of Uncertainty Level)

Tables Icon

Table 3 Important Largest Uncertainty Levels and their Reasons for the Lossy SB&DB Composite MM Slabs (the Number in Parentheses in a Superscript Denotes the Reason of Uncertainty Level)

Equations (15)

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S 11 =| S 11 | e i θ 11 = Γ( 1 T 2 ) 1 Γ 2 T 2 = S 22 , S 21 =| S 21 | e i θ 21 = T( 1 Γ 2 ) 1 Γ 2 T 2 = S 12 ,
Γ= ( z1 ) / ( z+1 ) , T=exp( i k 0 nd ), k 0 = 2πf /c .
z= ( 1+ S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2 , T= S 21 1 S 11 ( z1 ) / ( z+1 ) ,
n= [ ( lnT ) " 2πmi ( lnT ) ' ] / ( k 0 d ) , m=0,1,2,3...
ε r =n/z , μ r =nz.
ε r ( ω )= ε ω ep 2 ω( ω+i δ e ) , μ r ( ω )= μ ( μ s μ ) ω mp 2 ω( ω+i δ m ) ω mp 2 ,
ε r ( ω )= ε t=1 N ω ep(t) 2 ω( ω+i δ e(t) ) , μ r ( ω )= t=1 N [ μ (t) ( μ s(t) μ (t) ) ω mp(t) 2 ω( ω+i δ m(t) ) ω mp(t) 2 ] ,
1 ε 5, 0 δ e , δ m 5, 1 μ s 2.
ω ep + ε ( ω er 2 + δ e 2 ) , ω mp = ω mr 2 ( μ s + μ ) ω mr 4 ( μ s μ ) 2 4 μ μ s δ m 2 ω mr 2 2 μ s ,
Δξ ξ = 1 ξ u [ ( ξ | S u | Δ| S u | ) 2 + ( ξ θ u Δ θ u ) 2 ] + ( ξ d Δd ) 2 + ( ξ f Δf ) 2 ,
ε r | S 11 | = D e i θ 11 ADBC , ε r | S 21 | = B e i θ 21 ADBC , ε r d = DEBF ADBC , ε r f = DGBH ADBC ,
μ r | S 11 | = C D ε r | S 11 | , μ r | S 21 | = A B ε r | S 21 | , μ r d = EA ε r / d B , μ r f = GA ε r / f B ,
ε r θ u =i| S u | ε r | S u | , μ r θ u =i| S u | μ r | S u | , A= S 11 Γ Γ ε r + S 11 T T ε r ,
B= S 11 Γ Γ μ r + S 11 T T μ r , C= S 21 Γ Γ ε r + S 21 T T ε r , D= S 21 Γ Γ μ r + S 21 T T μ r ,
E= S 11 T T d , F= S 21 T T d , G= S 11 T T f , H= S 21 T T f .

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