Abstract

A waveguide-based retrieval method for measuring complex permittivity and permeability tensors of metamaterials is presented. In the proposed scheme, multiple independent sets of scattering data for the material under test with different orientations are measured in the frequency range corresponding to the dominant TE10 mode. The method is applied to various metamaterials and shows its effectiveness in the effective parameters extraction.

© 2006 Optical Society of America

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  1. 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, 4184 (2000).
    [CrossRef] [PubMed]
  2. 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]
  3. L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
    [CrossRef]
  4. P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 5 (2002).
    [CrossRef]
  5. H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
    [CrossRef]
  6. H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
    [CrossRef]
  7. J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
    [CrossRef]
  8. S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
    [CrossRef]
  9. A. Sihvola, "Metamaterials and depolarization factors," Progress In Electromagnetics Research, PIER 51, 65 (2005).
    [CrossRef]
  10. D. R. Smith, and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett.,  90, 077405 (2003).
    [CrossRef] [PubMed]
  11. H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
    [CrossRef]
  12. S.-W. Lee, Y. Kuga, and A. Ishimaru, "Quasi-static analysis of materials with small tunable stacked split ring resonators," Progress in Electromagnetics Research-PIER 51, 219, (2005).
    [CrossRef]
  13. T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
    [CrossRef]
  14. Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express  14, 2220 (2006).
    [CrossRef] [PubMed]
  15. Q. Sui, C. Li, and F. Li, "The experimental study of /4 monopole antennas in meta-material," Progress In Electromagnetics Research, PIER 51, 281, (2005).
    [CrossRef]
  16. N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas and Wireless Propagation Letters 1, 10 (2002).
    [CrossRef]
  17. B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).
  18. A.K. Hamid, "Axially slotted antenna on a circular or elliptic cylinder coated with metamaterials," Progress In Electromagnetics Research, PIER 51, 329, (2005).
    [CrossRef]
  19. L. Chen, C. K. Ong, and B. T. G. Tan, "Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics," IEEE Trans. Instrum. Meas. 48, 6 (1999).
  20. N. B. Tahar, and A. F.-Lamer, "Broad-band simultaneous measurement of the complex permittivity tensor for uniaxial materials using a coaxial discontinuity," IEEE Trans. Microw. Theory Tech. 39, 10 (1991).
  21. D. Ghodgaonkar, V. Varadan, and V. Varadan, "Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas. 39, 387 (1990).
    [CrossRef]
  22. N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).
  23. A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (2004).
    [CrossRef]
  24. M. J. Akhtar, L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. Microw. Theory Tech. 54, 5 (2006).
    [CrossRef]
  25. 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]
  26. J. A. Kong, Electromagnetic Wave Theory (Wiley and Sons, 1986, 1990, EMW Publishing, 2000, 2005)
  27. T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
    [CrossRef]
  28. X. Chen, T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab of general bianisotropic medium," Progress in Electromagnetics Research-PIER 60, 1 (2006).
    [CrossRef]
  29. 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]
  30. 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]
  31. J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [CrossRef]
  32. H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
    [CrossRef]
  33. T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (2005).
    [CrossRef]

2006 (5)

M. J. Akhtar, L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. Microw. Theory Tech. 54, 5 (2006).
[CrossRef]

X. Chen, T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab of general bianisotropic medium," Progress in Electromagnetics Research-PIER 60, 1 (2006).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[CrossRef]

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express  14, 2220 (2006).
[CrossRef] [PubMed]

2005 (12)

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

A. Sihvola, "Metamaterials and depolarization factors," Progress In Electromagnetics Research, PIER 51, 65 (2005).
[CrossRef]

H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
[CrossRef]

S.-W. Lee, Y. Kuga, and A. Ishimaru, "Quasi-static analysis of materials with small tunable stacked split ring resonators," Progress in Electromagnetics Research-PIER 51, 219, (2005).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (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]

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
[CrossRef]

Q. Sui, C. Li, and F. Li, "The experimental study of /4 monopole antennas in meta-material," Progress In Electromagnetics Research, PIER 51, 281, (2005).
[CrossRef]

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

A.K. Hamid, "Axially slotted antenna on a circular or elliptic cylinder coated with metamaterials," Progress In Electromagnetics Research, PIER 51, 329, (2005).
[CrossRef]

2004 (4)

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (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. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
[CrossRef]

J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
[CrossRef]

2003 (1)

D. R. Smith, and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett.,  90, 077405 (2003).
[CrossRef] [PubMed]

2002 (4)

P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 5 (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, 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]

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas and Wireless Propagation Letters 1, 10 (2002).
[CrossRef]

2000 (1)

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, 4184 (2000).
[CrossRef] [PubMed]

1999 (2)

J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

L. Chen, C. K. Ong, and B. T. G. Tan, "Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics," IEEE Trans. Instrum. Meas. 48, 6 (1999).

1990 (1)

D. Ghodgaonkar, V. Varadan, and V. Varadan, "Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas. 39, 387 (1990).
[CrossRef]

1984 (1)

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

Akhtar, M. J.

M. J. Akhtar, L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. Microw. Theory Tech. 54, 5 (2006).
[CrossRef]

Baena, J. D.

J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
[CrossRef]

Basov, D. N.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

Chen, H.

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express  14, 2220 (2006).
[CrossRef] [PubMed]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
[CrossRef]

Chen, J.

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
[CrossRef]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
[CrossRef]

Chen, L.

L. Chen, C. K. Ong, and B. T. G. Tan, "Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics," IEEE Trans. Instrum. Meas. 48, 6 (1999).

Chen, X.

X. Chen, T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab of general bianisotropic medium," Progress in Electromagnetics Research-PIER 60, 1 (2006).
[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]

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
[CrossRef]

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

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]

Damascos, N. J.

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

Driscoll, T.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

Economou, E. N.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (2005).
[CrossRef]

Engheta, N.

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas and Wireless Propagation Letters 1, 10 (2002).
[CrossRef]

Feher, L. E.

M. J. Akhtar, L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. Microw. Theory Tech. 54, 5 (2006).
[CrossRef]

Gay-Balmaz, P.

P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 5 (2002).
[CrossRef]

Ghodgaonkar, D.

D. Ghodgaonkar, V. Varadan, and V. Varadan, "Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas. 39, 387 (1990).
[CrossRef]

Grzegorczyk, T.

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab of general bianisotropic medium," Progress in Electromagnetics Research-PIER 60, 1 (2006).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[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]

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (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]

Hamid, A.K.

A.K. Hamid, "Axially slotted antenna on a circular or elliptic cylinder coated with metamaterials," Progress In Electromagnetics Research, PIER 51, 329, (2005).
[CrossRef]

Holten, A. J.

J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Huangfu, J.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[CrossRef]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express  14, 2220 (2006).
[CrossRef] [PubMed]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
[CrossRef]

Ikonen, P.

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

Ishimaru, A.

S.-W. Lee, Y. Kuga, and A. Ishimaru, "Quasi-static analysis of materials with small tunable stacked split ring resonators," Progress in Electromagnetics Research-PIER 51, 219, (2005).
[CrossRef]

Kaunisto, M.

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

Kolmakov, I.

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

Kong, J. A.

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express  14, 2220 (2006).
[CrossRef] [PubMed]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[CrossRef]

X. Chen, T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab of general bianisotropic medium," Progress in Electromagnetics Research-PIER 60, 1 (2006).
[CrossRef]

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (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]

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (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]

Koschny, T.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (2005).
[CrossRef]

Kuga, Y.

S.-W. Lee, Y. Kuga, and A. Ishimaru, "Quasi-static analysis of materials with small tunable stacked split ring resonators," Progress in Electromagnetics Research-PIER 51, 219, (2005).
[CrossRef]

Lee, S.-W.

S.-W. Lee, Y. Kuga, and A. Ishimaru, "Quasi-static analysis of materials with small tunable stacked split ring resonators," Progress in Electromagnetics Research-PIER 51, 219, (2005).
[CrossRef]

Li, C.

Q. Sui, C. Li, and F. Li, "The experimental study of /4 monopole antennas in meta-material," Progress In Electromagnetics Research, PIER 51, 281, (2005).
[CrossRef]

Li, F.

Q. Sui, C. Li, and F. Li, "The experimental study of /4 monopole antennas in meta-material," Progress In Electromagnetics Research, PIER 51, 281, (2005).
[CrossRef]

Li, L. W.

H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
[CrossRef]

Mack, R. B.

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

Maffett, A. L.

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

Markos, P.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (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]

Marques, R.

J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
[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]

Martel, J.

J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
[CrossRef]

Martin, O. J. F.

P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 5 (2002).
[CrossRef]

Maslovski, S.

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

Medina, F.

J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
[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]

Nemat-Nasser, S.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (2004).
[CrossRef]

Nemat-Nasser, S. C.

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, 4184 (2000).
[CrossRef] [PubMed]

Ong, C. K.

L. Chen, C. K. Ong, and B. T. G. Tan, "Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics," IEEE Trans. Instrum. Meas. 48, 6 (1999).

Pacheco, J.

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
[CrossRef]

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

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]

Padilla, W. J.

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, 4184 (2000).
[CrossRef] [PubMed]

Parmon, W.

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

Pendry, J. B.

J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[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.

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express  14, 2220 (2006).
[CrossRef] [PubMed]

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Rye, P. M.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (2004).
[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]

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, 4184 (2000).
[CrossRef] [PubMed]

Schurig, D.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

D. R. Smith, and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett.,  90, 077405 (2003).
[CrossRef] [PubMed]

Shen, L.

Sihvola, A.

A. Sihvola, "Metamaterials and depolarization factors," Progress In Electromagnetics Research, PIER 51, 65 (2005).
[CrossRef]

Smith, D. R.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (2005).
[CrossRef]

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (2004).
[CrossRef]

D. R. Smith, and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett.,  90, 077405 (2003).
[CrossRef] [PubMed]

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]

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, 4184 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (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]

Starr, A. F.

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (2004).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Sui, Q.

Q. Sui, C. Li, and F. Li, "The experimental study of /4 monopole antennas in meta-material," Progress In Electromagnetics Research, PIER 51, 281, (2005).
[CrossRef]

Tan, B. T. G.

L. Chen, C. K. Ong, and B. T. G. Tan, "Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics," IEEE Trans. Instrum. Meas. 48, 6 (1999).

Thumm, M.

M. J. Akhtar, L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. Microw. Theory Tech. 54, 5 (2006).
[CrossRef]

Tretyakov, S.

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

Uslenghi, P. L. E.

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

Varadan, V.

D. Ghodgaonkar, V. Varadan, and V. Varadan, "Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas. 39, 387 (1990).
[CrossRef]

D. Ghodgaonkar, V. Varadan, and V. Varadan, "Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas. 39, 387 (1990).
[CrossRef]

Vier, D. C.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (2005).
[CrossRef]

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, 4184 (2000).
[CrossRef] [PubMed]

Wang, W.

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

Wu, B.-I.

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (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]

Wu, Q.

H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
[CrossRef]

Yao, H. Y.

H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
[CrossRef]

Yuan, Y.

Zhang, X. M.

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 5 (2002).
[CrossRef]

T.  Driscoll, D. N.  Basov, A. F.  Starr, P. M.  Rye, S.  Nemat-Nasser, D.  Schurig, and D. R.  Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett.  88, 081101 (2006).
[CrossRef]

IEEE Antennas and Wireless Propagation Letters (1)

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas and Wireless Propagation Letters 1, 10 (2002).
[CrossRef]

IEEE Trans. Instrum. Meas (1)

L. Chen, C. K. Ong, and B. T. G. Tan, "Cavity perturbation technique for the measurement of permittivity tensor of uniaxially anisotropic dielectrics," IEEE Trans. Instrum. Meas. 48, 6 (1999).

IEEE Trans. Instrum. Meas. (1)

D. Ghodgaonkar, V. Varadan, and V. Varadan, "Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies," IEEE Trans. Instrum. Meas. 39, 387 (1990).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

M. J. Akhtar, L. E. Feher, and M. Thumm, "A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials," IEEE Trans. Microw. Theory Tech. 54, 5 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. MTT (1)

N. J. Damascos, R. B. Mack, A. L. Maffett, W. Parmon, and P. L. E. Uslenghi, "The inverse problem for biaxial materials," IEEE Trans. Microw. Theory Tech. MTT- 32, 4 (1984).

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holten, D. J. Robbins, and W. J. Stewart, "Magnetism from Conductors and Enhanced Non-Linear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

J. Appl. Phys. (1)

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915, (2006).
[CrossRef]

Opt. Express (1)

Phys. Rev B. (2)

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. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization of a negative-refractive-index composite metamaterial," Phys. Rev B. 70, 113102 (2004).
[CrossRef]

Phys. Rev. B (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]

J. D. Baena, R. Marques, F. Medina, and J. Martel, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev. B 69, 014402 (2004).
[CrossRef]

Phys. Rev. E. (3)

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left-handed materials composed of only S-shaped resonators," Phys. Rev. E. 70, 057605 (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]

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. (2)

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, 4184 (2000).
[CrossRef] [PubMed]

D. R. Smith, and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett.,  90, 077405 (2003).
[CrossRef] [PubMed]

Phys. Rev.B. (1)

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev.B. 71, 245105 (2005).
[CrossRef]

Progress In Electromagnetics Research, PIER (8)

Q. Sui, C. Li, and F. Li, "The experimental study of /4 monopole antennas in meta-material," Progress In Electromagnetics Research, PIER 51, 281, (2005).
[CrossRef]

T. M. Grzegorczyk, X. Chen, J. Pacheco, J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and goos-hanchen shifts in anisotropic and bianisotropic left-handed metamaterials," Progress In Electromagnetics Research, PIER 51, 83, (2005).
[CrossRef]

B.-I. Wu, W. Wang, J. Pacheco, X. Chen, T. Grzegorczyk, and J. A. Kong, "A study of using metamaterials as antenna substrate to enhance gain," Progress In Electromagnetics Research, PIER 51, 395, (2005).

A.K. Hamid, "Axially slotted antenna on a circular or elliptic cylinder coated with metamaterials," Progress In Electromagnetics Research, PIER 51, 329, (2005).
[CrossRef]

S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, "Artificial magnetic materials based on the new magnetic particle: metasolenoid," Progress In Electromagnetics Research, PIER 54, 61 (2005).
[CrossRef]

A. Sihvola, "Metamaterials and depolarization factors," Progress In Electromagnetics Research, PIER 51, 65 (2005).
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed matamaterials," Progress In Electromagnetics Research, PIER 51, 249 (2005).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. M. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Magnetic properties of s-shaped split-ring resonators," Progress In Electromagnetics Research, PIER 51, 231 (2005).
[CrossRef]

Progress in Electromagnetics Research-PIER (3)

H. Y. Yao, L. W. Li, Q. Wu, and J. A. Kong, "Macroscopic performance analysis of metamaterials synthesized from micrsocopic 2-D isotropic cross split-ring resonator array," Progress in Electromagnetics Research-PIER 51, 197 (2005).
[CrossRef]

S.-W. Lee, Y. Kuga, and A. Ishimaru, "Quasi-static analysis of materials with small tunable stacked split ring resonators," Progress in Electromagnetics Research-PIER 51, 219, (2005).
[CrossRef]

X. Chen, T. M. Grzegorczyk, and J. A. Kong, "Optimization approach to the retrieval of the constitutive parameters of slab of general bianisotropic medium," Progress in Electromagnetics Research-PIER 60, 1 (2006).
[CrossRef]

Other (2)

N. B. Tahar, and A. F.-Lamer, "Broad-band simultaneous measurement of the complex permittivity tensor for uniaxial materials using a coaxial discontinuity," IEEE Trans. Microw. Theory Tech. 39, 10 (1991).

J. A. Kong, Electromagnetic Wave Theory (Wiley and Sons, 1986, 1990, EMW Publishing, 2000, 2005)

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Figures (5)

Fig. 1.
Fig. 1.

Experimental scheme for the S parameters measurement in waveguide.

Fig. 2.
Fig. 2.

Comparison of the analytical (markers) and the retrieved results (Solid lines: real part; dashed lines: imaginary part) for a loss homogeneous medium.

Fig. 3.
Fig. 3.

Measured ε r and µ r for the Teflon and FR4 substrate.

Fig. 4.
Fig. 4.

(a) The dimensions of the SRR unit, (b) (c) two measurements corresponding to two different orientations of the SRR in the waveguide.

Fig. 5.
Fig. 5.

Measured constitutive parameters of the SRR structure.

Equations (9)

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z = ± { [ ( 1 + S 11 ) 2 S 21 2 ] [ ( 1 S 11 ) 2 S 21 2 ] } 1 2
e i n k 0 z d = X ± i ( 1 X 2 ) 1 2
n a = ( k 0 2 ε 3 μ 1 k x 2 μ 1 μ 2 ) 1 2 ( k 0 2 k x 2 ) 1 2
z a = μ 1 ( k 0 2 k x 2 ) 1 2 ( k 0 2 ε 3 μ 1 k x 2 μ 1 μ 2 ) 1 2
n b = ( k 0 2 ε 3 μ 2 k x 2 μ 2 μ 1 ) 1 2 ( k 0 2 k x 2 ) 1 2
z b = μ 2 ( k 0 2 k x 2 ) 1 2 ( k 0 2 ε 3 μ 2 k x 2 μ 2 μ 1 ) 1 2
μ 1 = n a z a , μ 2 = n b z b
ε 3 a = ( n a 2 k 0 z 2 + k x 2 μ 1 μ 2 ) ( k 0 2 μ 1 )
ε 3 b = ( n b 2 k 0 z 2 + k x 2 μ 2 μ 1 ) ( k 0 2 μ 2 )

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