Abstract

Metamaterials (MMs) are artificial materials that have received attention recently because their built-in features create collective electromagnetic effects that are otherwise impossible, such as negative refraction, and because of their exotic electromagnetic applications, namely, perfect lens and invisibility cloaks. Depending on wave propagation characteristics, MMs possessing normally weak magneto-electric coupling coefficients start to exhibit stronger bianisotropic effects. Therefore, accurate electromagnetic characterization of these MMs is important. In this study, we adapt a stepwise method based on the Nicolson–Ross–Weir technique for accurate and unique retrieval of electromagnetic properties of bianisotropic MM slabs. For this goal, we have derived explicit expressions for unique retrieval of electromagnetic properties of these slabs and compared these expressions with those in the literature in the retrieval process. From the comparison, we note that derived expressions are appropriate for unique determination of electromagnetic properties of bianisotropic MM slabs. In the performance analysis of the stepwise method for different measurement scenarios, we considered different bianisotropic MM cell configurations (split-ring and Omega-shaped resonators as well as the same resonators with wire strips) and extracted their electromagnetic properties when measured/simulated scattering parameters have some thermal noise. We note that for most of the frequencies, the stepwise method retrieves correct electromagnetic properties even when a relatively higher normally distributed noise with zero mean value and with standard deviations of 0.015 is present. In addition to the influence of thermal noise on performance of the stepwise method, we also analyzed the effect of both increasing length slab and the frequency band on retrieved electromagnetic properties of the analyzed various bianisotropic MM slabs.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  3. R. A. Shelby, D. R. Smith, and S. Shultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef]
  4. 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, 369–373 (2011).
    [CrossRef]
  5. J. B. Pendry, D. Schuring, and D. R. Smith, “Controlling electromagnetic waves,” Science 312, 1780–1782 (2006).
    [CrossRef]
  6. R. E. Collin, Field Theory of Guided Waves (Wiley-IEEE, 1990).
  7. 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, 326 (2007).
    [CrossRef]
  8. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low-frequency plasmons in thin-wire structures,” J. Phys. 10, 4785–4809 (1998).
    [CrossRef]
  9. 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, 2075–2084 (1999).
    [CrossRef]
  10. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
    [CrossRef]
  11. Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
    [CrossRef]
  12. C. Sabah, “Multi-resonant metamaterial design based on concentric V-shaped magnetic resonators,” J. Electromagn. Waves Appl. 26, 1105–1115 (2012).
    [CrossRef]
  13. C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles,” Phys. Lett. 311, 254–263 (2003).
    [CrossRef]
  14. J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
    [CrossRef]
  15. L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
    [CrossRef]
  16. V. V. Varadan, R. Ro, and S. Penumarthy, “Switching of electrical and magnetic resonances in omega structures by a reflection operation–experimental studies,” Microw. Opt. Technol. Lett. 48, 2624–2629 (2006).
    [CrossRef]
  17. E. Lheurette, O. Vanbeisen, and D. Lippens, “Double negative media using interconnected Ω-type metallic particles,” Microw. Opt. Technol. Lett. 49, 84–90 (2007).
    [CrossRef]
  18. K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
    [CrossRef]
  19. Z. Li, K. Aydin, and E. Ozbay, “Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions,” Photon. Nanostr. 10, 329–336 (2012).
    [CrossRef]
  20. C. Sabah, ““Multiband planar metamaterials,” Microw. Opt. Technol. Lett. 53, 2255–2258 (2011).
    [CrossRef]
  21. C. Sabah, “Multiband metamaterials based on multiple concentric open ring resonators topology,” IEEE J. Sel. Top. Quantum Electron. 19, 8500808 (2012).
    [CrossRef]
  22. 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, 233107 (2009).
    [CrossRef]
  23. J. B. Pendry, “Metamaterials in the sunshine,” Nat. Mater. 5, 599–600 (2006).
    [CrossRef]
  24. 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, 011112 (2007).
    [CrossRef]
  25. 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).
    [CrossRef]
  26. D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
    [CrossRef]
  27. Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79, 026610 (2009).
    [CrossRef]
  28. H. Ouyang, C. C. Striemer, and P. M. Fauchet, “Quantitative analysis of the sensitivity of porous silicon optical biosensors,” Appl. Phys. Lett. 88, 163108 (2006).
    [CrossRef]
  29. T. L. Kelly, A. G. Sega, and M. J. Sailor, “Identification and quantification of organic vapors by time-resolved diffusion in stacked mesoporous photonic crystals,” Nano Lett. 11, 3169–3173 (2011).
    [CrossRef]
  30. 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, 22208–22223 (2012).
    [CrossRef]
  31. R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65, 144440 (2002).
    [CrossRef]
  32. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
    [CrossRef]
  33. A. Alu, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84, 075153 (2011).
    [CrossRef]
  34. 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, 195104 (2002).
    [CrossRef]
  35. X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
    [CrossRef]
  36. A. M. Nicolson and G. Ross, “Measurement of the intrinsic properties of materials by time–domain techniques,” IEEE Trans. Instrum. Meas. 19, 377–382 (1970).
    [CrossRef]
  37. W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).
    [CrossRef]
  38. 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 70, 016608 (2004).
    [CrossRef]
  39. X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71, 046610 (2005).
    [CrossRef]
  40. 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).
  41. C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” Phys. Rev. B 86, 085146 (2012).
    [CrossRef]
  42. F.-J. Hsieh and W.-C. Wang, “Full extraction methods to retrieve effective refractive index and parameters of a bianisotropic metamaterial based on material dispersion models,” J. Appl. Phys. 112, 064907 (2012).
    [CrossRef]
  43. O. Luukkonen, S. I. Maslovski, and S. A. Tretyakov, “A stepwise Nicolson–Ross–Weir-based material parameter extraction method,” IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011).
    [CrossRef]
  44. 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, 2224–2230 (2007).
    [CrossRef]
  45. J. J. Barroso and U. C. Hasar, “Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method,” J. Infrared Millim. Terahertz Waves 33, 237–244 (2012).
    [CrossRef]
  46. 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).
  47. 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, 5419–5424 (2001).
    [CrossRef]
  48. G. Lubkowski, B. Bandlow, R. Schuhmann, and T. Weiland, “Effective modeling of double negative metamaterial macrostructures,” IEEE Trans. Microw. Theory Tech. 57, 1136–1146 (2009).
    [CrossRef]
  49. S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
    [CrossRef]
  50. S. Zu, L. Yang, L. Huang, and H. Chen, “Experimental measurement method to determine the permittivity of extra thin materials using resonant metamaterials,” Prog. Electromagn. Res. 120, 327–337 (2011).
  51. U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).
  52. U. C. Hasar, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
    [CrossRef]
  53. I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
    [CrossRef]
  54. F. Bilotti and L. Sevgi, “Metamaterials: definitions, properties, applications, and FDTD-based modeling and simulation (invited paper),” Int. J. RF Microw. CAE 22, 422–438 (2012).
    [CrossRef]
  55. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

2012 (12)

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

Z. Li, K. Aydin, and E. Ozbay, “Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions,” Photon. Nanostr. 10, 329–336 (2012).
[CrossRef]

C. Sabah, “Multiband metamaterials based on multiple concentric open ring resonators topology,” IEEE J. Sel. Top. Quantum Electron. 19, 8500808 (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, 22208–22223 (2012).
[CrossRef]

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” Phys. Rev. B 86, 085146 (2012).
[CrossRef]

F.-J. Hsieh and W.-C. Wang, “Full extraction methods to retrieve effective refractive index and parameters of a bianisotropic metamaterial based on material dispersion models,” J. Appl. Phys. 112, 064907 (2012).
[CrossRef]

J. J. Barroso and U. C. Hasar, “Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method,” J. Infrared Millim. Terahertz Waves 33, 237–244 (2012).
[CrossRef]

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, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).

U. C. Hasar, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
[CrossRef]

I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
[CrossRef]

F. Bilotti and L. Sevgi, “Metamaterials: definitions, properties, applications, and FDTD-based modeling and simulation (invited paper),” Int. J. RF Microw. CAE 22, 422–438 (2012).
[CrossRef]

2011 (7)

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).

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

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

T. L. Kelly, A. G. Sega, and M. J. Sailor, “Identification and quantification of organic vapors by time-resolved diffusion in stacked mesoporous photonic crystals,” Nano Lett. 11, 3169–3173 (2011).
[CrossRef]

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

C. Sabah, ““Multiband planar metamaterials,” Microw. Opt. Technol. Lett. 53, 2255–2258 (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, 369–373 (2011).
[CrossRef]

2009 (4)

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, 233107 (2009).
[CrossRef]

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).
[CrossRef]

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

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

2008 (1)

K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
[CrossRef]

2007 (6)

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, 011112 (2007).
[CrossRef]

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, 326 (2007).
[CrossRef]

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

E. Lheurette, O. Vanbeisen, and D. Lippens, “Double negative media using interconnected Ω-type metallic particles,” Microw. Opt. Technol. Lett. 49, 84–90 (2007).
[CrossRef]

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (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, 2224–2230 (2007).
[CrossRef]

2006 (4)

V. V. Varadan, R. Ro, and S. Penumarthy, “Switching of electrical and magnetic resonances in omega structures by a reflection operation–experimental studies,” Microw. Opt. Technol. Lett. 48, 2624–2629 (2006).
[CrossRef]

J. B. Pendry, D. Schuring, and D. R. Smith, “Controlling electromagnetic waves,” Science 312, 1780–1782 (2006).
[CrossRef]

J. B. Pendry, “Metamaterials in the sunshine,” Nat. Mater. 5, 599–600 (2006).
[CrossRef]

H. Ouyang, C. C. Striemer, and P. M. Fauchet, “Quantitative analysis of the sensitivity of porous silicon optical biosensors,” Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

2005 (3)

D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

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

2004 (5)

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 70, 016608 (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

2003 (1)

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles,” Phys. Lett. 311, 254–263 (2003).
[CrossRef]

2002 (2)

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, 195104 (2002).
[CrossRef]

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

2001 (2)

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

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, 5419–5424 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (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, 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. 10, 4785–4809 (1998).
[CrossRef]

1974 (1)

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 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, 377–382 (1970).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).

Alu, A.

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

Aydin, K.

Z. Li, K. Aydin, and E. Ozbay, “Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions,” Photon. Nanostr. 10, 329–336 (2012).
[CrossRef]

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

K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
[CrossRef]

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, 326 (2007).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Bandlow, B.

G. Lubkowski, B. Bandlow, R. Schuhmann, and T. Weiland, “Effective modeling of double negative metamaterial macrostructures,” IEEE Trans. Microw. Theory Tech. 57, 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).

U. C. Hasar, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
[CrossRef]

U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).

J. J. Barroso and U. C. Hasar, “Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method,” J. Infrared Millim. Terahertz Waves 33, 237–244 (2012).
[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).

Bilge, S.

K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
[CrossRef]

Bilotti, F.

F. Bilotti and L. Sevgi, “Metamaterials: definitions, properties, applications, and FDTD-based modeling and simulation (invited paper),” Int. J. RF Microw. CAE 22, 422–438 (2012).
[CrossRef]

Cavusoglu, B.

U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).

Chen, H.

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

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

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 71, 046610 (2005).
[CrossRef]

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

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 70, 016608 (2004).
[CrossRef]

Chirvony, V.

I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
[CrossRef]

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, 369–373 (2011).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (Wiley-IEEE, 1990).

Dong, Z.-G.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (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, 011112 (2007).
[CrossRef]

Economou, E. N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

Efeoglu, H.

Ertugrul, M.

U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).

U. C. Hasar, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
[CrossRef]

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, 233107 (2009).
[CrossRef]

Fauchet, P. M.

H. Ouyang, C. C. Striemer, and P. M. Fauchet, “Quantitative analysis of the sensitivity of porous silicon optical biosensors,” Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

Fietz, C.

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” Phys. Rev. B 86, 085146 (2012).
[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, 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 71, 046610 (2005).
[CrossRef]

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

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

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 70, 016608 (2004).
[CrossRef]

Hasar, U. C.

J. J. Barroso and U. C. Hasar, “Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method,” J. Infrared Millim. Terahertz Waves 33, 237–244 (2012).
[CrossRef]

U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (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, 22208–22223 (2012).
[CrossRef]

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, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
[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).

He, S.

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles,” Phys. Lett. 311, 254–263 (2003).
[CrossRef]

Helgert, 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, 233107 (2009).
[CrossRef]

Hill, D.

I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
[CrossRef]

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, 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. 10, 4785–4809 (1998).
[CrossRef]

Hsieh, F.-J.

F.-J. Hsieh and W.-C. Wang, “Full extraction methods to retrieve effective refractive index and parameters of a bianisotropic metamaterial based on material dispersion models,” J. Appl. Phys. 112, 064907 (2012).
[CrossRef]

Huang, L.

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

Huangfu, J.

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

Hudlicka, M.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
[CrossRef]

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, 326 (2007).
[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).
[CrossRef]

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).
[CrossRef]

Kafesaki, M.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

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, 369–373 (2011).
[CrossRef]

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, 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, 369–373 (2011).
[CrossRef]

Karacali, T.

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

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).

U. C. Hasar, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
[CrossRef]

Kelly, T. L.

T. L. Kelly, A. G. Sega, and M. J. Sailor, “Identification and quantification of organic vapors by time-resolved diffusion in stacked mesoporous photonic crystals,” Nano Lett. 11, 3169–3173 (2011).
[CrossRef]

Kim, 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, 369–373 (2011).
[CrossRef]

Kley, E.-B.

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, 233107 (2009).
[CrossRef]

Kong, J. A.

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

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

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

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 70, 016608 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

Koschhy, T.

D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Koschny, T.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

Kuzel, P.

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).
[CrossRef]

Kwak, M. H.

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, 369–373 (2011).
[CrossRef]

Lederer, F.

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, 233107 (2009).
[CrossRef]

Lee, S. H.

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, 369–373 (2011).
[CrossRef]

Lee, Y-.H.

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, 369–373 (2011).
[CrossRef]

Lei, S.-Y.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Lheurette, E.

E. Lheurette, O. Vanbeisen, and D. Lippens, “Double negative media using interconnected Ω-type metallic particles,” Microw. Opt. Technol. Lett. 49, 84–90 (2007).
[CrossRef]

Li, 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, 011112 (2007).
[CrossRef]

Li, Q.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Li, T.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Li, Y.

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

Li, Z.

Z. Li, K. Aydin, and E. Ozbay, “Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions,” Photon. Nanostr. 10, 329–336 (2012).
[CrossRef]

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

K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
[CrossRef]

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, 326 (2007).
[CrossRef]

Liang, X.

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, 011112 (2007).
[CrossRef]

Lippens, D.

E. Lheurette, O. Vanbeisen, and D. Lippens, “Double negative media using interconnected Ω-type metallic particles,” Microw. Opt. Technol. Lett. 49, 84–90 (2007).
[CrossRef]

Liu, H.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Lubkowski, G.

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

Luukkonen, O.

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

Markos, P.

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, 195104 (2002).
[CrossRef]

Marques, R.

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

Maslovski, S. I.

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

Matrinez-Pastor, J.

I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
[CrossRef]

Medina, F.

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

Menzel, 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, 233107 (2009).
[CrossRef]

Min, 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, 369–373 (2011).
[CrossRef]

Mounaix, P.

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).
[CrossRef]

Nemec, H.

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).
[CrossRef]

Nicolson, A. M.

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

Oral, E. A.

Ouyang, H.

H. Ouyang, C. C. Striemer, and P. M. Fauchet, “Quantitative analysis of the sensitivity of porous silicon optical biosensors,” Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

Ozbay, E.

Z. Li, K. Aydin, and E. Ozbay, “Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions,” Photon. Nanostr. 10, 329–336 (2012).
[CrossRef]

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

K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
[CrossRef]

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, 326 (2007).
[CrossRef]

Ozbek, I. Y.

Pacheco, J.

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 70, 016608 (2004).
[CrossRef]

Parazzoli, C. G.

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, 5419–5424 (2001).
[CrossRef]

Park, N.

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, 369–373 (2011).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schuring, and D. R. Smith, “Controlling electromagnetic waves,” Science 312, 1780–1782 (2006).
[CrossRef]

J. B. Pendry, “Metamaterials in the sunshine,” Nat. Mater. 5, 599–600 (2006).
[CrossRef]

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

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, 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. 10, 4785–4809 (1998).
[CrossRef]

Penumarthy, S.

V. V. Varadan, R. Ro, and S. Penumarthy, “Switching of electrical and magnetic resonances in omega structures by a reflection operation–experimental studies,” Microw. Opt. Technol. Lett. 48, 2624–2629 (2006).
[CrossRef]

Pertsch, T.

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, 233107 (2009).
[CrossRef]

Rafii-El-Idrissi, R.

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

Ran, L.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

Ro, R.

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, 2224–2230 (2007).
[CrossRef]

V. V. Varadan, R. Ro, and S. Penumarthy, “Switching of electrical and magnetic resonances in omega structures by a reflection operation–experimental studies,” Microw. Opt. Technol. Lett. 48, 2624–2629 (2006).
[CrossRef]

Robbins, D. 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, 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. 10, 4785–4809 (1998).
[CrossRef]

Rockstuhl, 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, 233107 (2009).
[CrossRef]

Ross, G.

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

Sabah, C.

U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).

C. Sabah, “Multiband metamaterials based on multiple concentric open ring resonators topology,” IEEE J. Sel. Top. Quantum Electron. 19, 8500808 (2012).
[CrossRef]

U. C. Hasar, J. J. Barroso, C. Sabah, Y. Kaya, and M. Ertugrul, “Differential uncertainty analysis for evaluating the accuracy of S-parameter retrieval methods for electromagnetic properties of metamaterial slabs,” Opt. Express 20, 29002–29022 (2012).
[CrossRef]

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

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

Sailor, M. J.

T. L. Kelly, A. G. Sega, and M. J. Sailor, “Identification and quantification of organic vapors by time-resolved diffusion in stacked mesoporous photonic crystals,” Nano Lett. 11, 3169–3173 (2011).
[CrossRef]

Schuhmann, R.

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

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, 5419–5424 (2001).
[CrossRef]

Schultz, S.

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, 195104 (2002).
[CrossRef]

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, 5419–5424 (2001).
[CrossRef]

Schuring, D.

J. B. Pendry, D. Schuring, and D. R. Smith, “Controlling electromagnetic waves,” Science 312, 1780–1782 (2006).
[CrossRef]

Sega, A. G.

T. L. Kelly, A. G. Sega, and M. J. Sailor, “Identification and quantification of organic vapors by time-resolved diffusion in stacked mesoporous photonic crystals,” Nano Lett. 11, 3169–3173 (2011).
[CrossRef]

Sevgi, L.

F. Bilotti and L. Sevgi, “Metamaterials: definitions, properties, applications, and FDTD-based modeling and simulation (invited paper),” Int. J. RF Microw. CAE 22, 422–438 (2012).
[CrossRef]

Shelby, R. A.

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

Shin, J.

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, 369–373 (2011).
[CrossRef]

Shultz, S.

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

Simovski, C. R.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
[CrossRef]

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles,” Phys. Lett. 311, 254–263 (2003).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schuring, and D. R. Smith, “Controlling electromagnetic waves,” Science 312, 1780–1782 (2006).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[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, 195104 (2002).
[CrossRef]

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, 5419–5424 (2001).
[CrossRef]

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

Soukoulis, C. M.

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” Phys. Rev. B 86, 085146 (2012).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[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, 195104 (2002).
[CrossRef]

Stewart, W. 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, 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. 10, 4785–4809 (1998).
[CrossRef]

Striemer, C. C.

H. Ouyang, C. C. Striemer, and P. M. Fauchet, “Quantitative analysis of the sensitivity of porous silicon optical biosensors,” Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

Suarez, I.

I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
[CrossRef]

Tang, H.

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, 011112 (2007).
[CrossRef]

Tretyakov, S. A.

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

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, 326 (2007).
[CrossRef]

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
[CrossRef]

Tunnermann, A.

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, 233107 (2009).
[CrossRef]

Vanbeisen, O.

E. Lheurette, O. Vanbeisen, and D. Lippens, “Double negative media using interconnected Ω-type metallic particles,” Microw. Opt. Technol. Lett. 49, 84–90 (2007).
[CrossRef]

Varadan, V. V.

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, 2224–2230 (2007).
[CrossRef]

V. V. Varadan, R. Ro, and S. Penumarthy, “Switching of electrical and magnetic resonances in omega structures by a reflection operation–experimental studies,” Microw. Opt. Technol. Lett. 48, 2624–2629 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).

Vetter, A. M.

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, 5419–5424 (2001).
[CrossRef]

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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, 5419–5424 (2001).
[CrossRef]

Wang, F.-M.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Wang, W.-C.

F.-J. Hsieh and W.-C. Wang, “Full extraction methods to retrieve effective refractive index and parameters of a bianisotropic metamaterial based on material dispersion models,” J. Appl. Phys. 112, 064907 (2012).
[CrossRef]

Weiland, T.

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

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, 5419–5424 (2001).
[CrossRef]

Weir, W. B.

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

Wu, B.-I.

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

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

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 70, 016608 (2004).
[CrossRef]

Xu, M.-X.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Yahiaoui, R.

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).
[CrossRef]

Yang, L.

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

Zhang, 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, 011112 (2007).
[CrossRef]

Zhang, X.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

Zhao, Q.

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, 011112 (2007).
[CrossRef]

Zhou, J.

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, 011112 (2007).
[CrossRef]

Zhu, S.-N.

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

Zu, S.

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

Appl. Phys. Lett. (4)

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Omega-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[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, 011112 (2007).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004).
[CrossRef]

H. Ouyang, C. C. Striemer, and P. M. Fauchet, “Quantitative analysis of the sensitivity of porous silicon optical biosensors,” Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

C. Sabah, “Multiband metamaterials based on multiple concentric open ring resonators topology,” IEEE J. Sel. Top. Quantum Electron. 19, 8500808 (2012).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

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

IEEE Trans. Microw. Theory Tech. (3)

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, 2075–2084 (1999).
[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, 2224–2230 (2007).
[CrossRef]

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

Int. J. RF Microw. CAE (1)

F. Bilotti and L. Sevgi, “Metamaterials: definitions, properties, applications, and FDTD-based modeling and simulation (invited paper),” Int. J. RF Microw. CAE 22, 422–438 (2012).
[CrossRef]

J. Appl. Phys. (3)

F.-J. Hsieh and W.-C. Wang, “Full extraction methods to retrieve effective refractive index and parameters of a bianisotropic metamaterial based on material dispersion models,” J. Appl. Phys. 112, 064907 (2012).
[CrossRef]

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, 5419–5424 (2001).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Metamaterial exhibiting left-handed properties over multiple frequency bands,” J. Appl. Phys. 96, 5338–5340 (2004).
[CrossRef]

J. Electromagn. Waves Appl. (1)

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

J. Infrared Millim. Terahertz Waves (1)

J. J. Barroso and U. C. Hasar, “Constitutive parameters of a metamaterial slab retrieved by the phase unwrapping method,” J. Infrared Millim. Terahertz Waves 33, 237–244 (2012).
[CrossRef]

J. Phys. (1)

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

Microw. Opt. Technol. Lett. (3)

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

V. V. Varadan, R. Ro, and S. Penumarthy, “Switching of electrical and magnetic resonances in omega structures by a reflection operation–experimental studies,” Microw. Opt. Technol. Lett. 48, 2624–2629 (2006).
[CrossRef]

E. Lheurette, O. Vanbeisen, and D. Lippens, “Double negative media using interconnected Ω-type metallic particles,” Microw. Opt. Technol. Lett. 49, 84–90 (2007).
[CrossRef]

Nano Lett. (1)

T. L. Kelly, A. G. Sega, and M. J. Sailor, “Identification and quantification of organic vapors by time-resolved diffusion in stacked mesoporous photonic crystals,” Nano Lett. 11, 3169–3173 (2011).
[CrossRef]

Nat. Mater. (1)

J. B. Pendry, “Metamaterials in the sunshine,” Nat. Mater. 5, 599–600 (2006).
[CrossRef]

Nature (1)

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, 369–373 (2011).
[CrossRef]

New J. Phys. (1)

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, 326 (2007).
[CrossRef]

Opt. Express (2)

Photon. Nanostr. (3)

I. Suarez, V. Chirvony, D. Hill, and J. Matrinez-Pastor, “Simulation of surface-modified porous silicon photonic crystals for biosensing applications,” Photon. Nanostr. 10, 304–311 (2012).
[CrossRef]

K. Aydin, Z. Li, S. Bilge, and E. Ozbay, “Experimental and numerical study of omega type bianisotropic metamaterials combined with a negative permittivity medium,” Photon. Nanostr. 6, 116–121 (2008).
[CrossRef]

Z. Li, K. Aydin, and E. Ozbay, “Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions,” Photon. Nanostr. 10, 329–336 (2012).
[CrossRef]

Phys. Lett. (1)

C. R. Simovski and S. He, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting Ω particles,” Phys. Lett. 311, 254–263 (2003).
[CrossRef]

Phys. Rev. B (9)

L. Ran, J. Huangfu, H. Chen, Y. Li, X. Zhang, K. Chen, and J. A. Kong, “Microwave solid-state left-handed material with a broad bandwidth and an ultralow loss,” Phys. Rev. B 70, 073102 (2004).
[CrossRef]

Z.-G. Dong, S.-Y. Lei, Q. Li, M.-X. Xu, H. Liu, T. Li, F.-M. Wang, and S.-N. Zhu, “Non-left-handed transmission and bianisotropic effect in a π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007).
[CrossRef]

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

A. Alu, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84, 075153 (2011).
[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, 195104 (2002).
[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, 233107 (2009).
[CrossRef]

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).
[CrossRef]

C. Fietz and C. M. Soukoulis, “Scattering matrix of the boundary of a nonlocal metamaterial,” Phys. Rev. B 86, 085146 (2012).
[CrossRef]

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75, 153104 (2007).
[CrossRef]

Phys. Rev. E (5)

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 70, 016608 (2004).
[CrossRef]

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

D. R. Smith, D. C. Vier, T. Koschhy, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

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

Phys. Rev. Lett. (1)

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

Proc. IEEE (1)

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

Prog. Electromagn. Res. (4)

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, 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).

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

U. C. Hasar, 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 of retrieval methods of bianisotropic metamaterials,” Prog. Electromagn. Res. 128, 365–380 (2012).

Science (2)

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

J. B. Pendry, D. Schuring, and D. R. Smith, “Controlling electromagnetic waves,” Science 312, 1780–1782 (2006).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).

Other (2)

R. E. Collin, Field Theory of Guided Waves (Wiley-IEEE, 1990).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1.
Fig. 1.

(a) Bianisotropic unit cell composed of only split-ring resonators (SRRs) and (b) bianisotropic composite unit cell composed of SRRs and wire strip.

Fig. 2.
Fig. 2.

(a) Bianisotropic unit cell composed of only Omega resonator and (b) bianisotropic composite unit cell composed of Omega resonator and wire strip.

Fig. 3.
Fig. 3.

(a) Magnitude and (b) phase of S-parameters of the bianisotropic SRR slab with L=8.8mm.

Fig. 4.
Fig. 4.

(a) Magnitude and (b) phase of S-parameters of the bianisotropic Composite-I slab with L=8.8mm.

Fig. 5.
Fig. 5.

(a) Magnitude and (b) phase of S-parameters of the bianisotropic Omega slab with L=5.0mm.

Fig. 6.
Fig. 6.

(a) Magnitude and (b) phase of S-parameters of the bianisotropic Composite-II slab with L=5.0mm.

Fig. 7.
Fig. 7.

(a) Retrieved Re{zw+} of the bianisotropic Composite-II slab using different methods, and (b) its closer view between 8.9 GHz and 9.4 GHz. Blue curve (our method) is coincident with the red curve (positive sign) of [19,27].

Fig. 8.
Fig. 8.

Retrieved (a) n and zw+, (b) zw and εz, and (c) μy and ξ0 of the bianisotropic SRR MM slab with L=8.8mm by the stepwise method.

Fig. 9.
Fig. 9.

Retrieved (a) n and zw+, (b) zw and εz, and (c) μy and ξ0 of the bianisotropic Composite-I MM slab with L=8.8mm by the stepwise method.

Fig. 10.
Fig. 10.

Retrieved (a) n and zw+, (b) zw and εz, and (c) μy and ξ0 of the bianisotropic Omega MM slab with L=5.0mm by the stepwise method.

Fig. 11.
Fig. 11.

Retrieved (a) n and zw+, (b) zw and εz, and (c) μy and ξ0 of the bianisotropic Composite-II MM slab with L=5.0mm by the stepwise method.

Fig. 12.
Fig. 12.

Retrieved (a) n and zw+, (b) zw and εz, and (c) μy and ξ0 of the bianisotropic SRR MM slab with L=8.8mm by the method in [19,27].

Fig. 13.
Fig. 13.

Retrieved (a) εz, (b) μy, and (c) ξ0 of the bianisotropic SRR MM slab with L=8.8mm by the stepwise method when uncorrelated random noise with ρ=0 and various σ are introduced.

Fig. 14.
Fig. 14.

Retrieved (a) εz, (b) μy, and (c) ξ0 of the bianisotropic Composite-II MM slab with L=5.0mm by the stepwise method when uncorrelated random noise with ρ=0 and various σ are introduced.

Fig. 15.
Fig. 15.

Retrieved (a) εz, (b) μy, and (c) ξ0 of the bianisotropic SRR MM slab with L=10.0mm by the stepwise method when uncorrelated random noise with ρ=0 and various σ are introduced.

Fig. 16.
Fig. 16.

Retrieved (a) εz, (b) μy, and (c) ξ0 of the bianisotropic Composite-II MM slab with L=7.5mm by the stepwise method when uncorrelated random noise with ρ=0 and various σ are introduced.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

S11=Γ1(1T2)1Γ1Γ2T2,S22=Γ2(1T2)1Γ1Γ2T2,
S21=(1Γ1Γ2)T1Γ1Γ2T2,Γ1(2)=zw+()1zw+()+1,
zw=μyniξ0,T=eik0nL,n=εzμyξ02.
zw+=Λ2Λ224Λ1Λ32Λ1,zw=Λ4zw++1zw++Λ4,
Λ1=S212(1S11)(1S22),Λ2=2(S11S22),
Λ3=(1+S11)(1+S22)S212,Λ4=S11+S22S11S22.
T=Γ1(1Γ1Γ2)S21(1Γ1Γ2)(Γ1S11Γ1Γ2),
n=[Im(lnT) ∓ 2πmiRe(lnT)]/(k0L),
θr+1=θr+Im[ln(Tr+1/Tr)],
n(r+1)=Im[lnTr+1Tr]+θr2πm0iln|Tr+1|k0(r+1)L,
Tr=ek0rnrLe+i(k0rnrL2πm0)=|Tr|e+iθr,
ξ0=n(Γ2Γ1)i(1Γ1Γ2),εz=n2+ξ02μy,
μy=(1Γ1Γ2)(n2+ξ02)n(1+Γ1Γ2)2nΓ1iξ0(1Γ1Γ2).
n=1k0LRe{cos1[1S11S22+S2122S21]}+2πmk0L.

Metrics