Abstract

This work presents experimental measurements of two square split resonant ring and metal wire (SSRR-MW) samples with different cell sizes at microwave frequencies. The geometrical sizes of the metamaterial cells are found to play an important role in the resonant frequency. Cells with different geometrical sizes are chosen to stack into a two-layer or three-layer metamaterial unit to realize the multiple negative passbands. The effective parameters of three separate SSRR-MW models (a one-layer unit, a two-layer unit, and a three-layer unit) are retrieved from the simulation data. The composed models exhibit two or three negative bands by overlapping the passbands of original cells and broadening the overall bandwidth. The recovered parameters show good agreement with the theoretical analysis.

© 2013 Optical Society of America

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Errata

Peng Gao, Chunmin Zhang, Zongwei Jia, and Yongqiang Kang, "Multiple frequency bands of square split resonant rings and metal wire metamaterial: erratum," Appl. Opt. 52, 7523-7523 (2013)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-31-7523

References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

X. F. Zhang, P. F. Guan, and X. L. Dong, “Transform between the permeability and permittivity in the close-packed Ni nanoparticles,” Appl. Phys. Lett. 97, 033107 (2010).
[CrossRef]

Z. Szabó, G. H. Park, R. Hedge, and E. P. Li, “A unique extraction of metamaterial parameters based on Kramers–Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58, 2646–2653 (2010).
[CrossRef]

C. M. Zhang, P. Gao, M. Z. Sun, and T. K. Mu, “Analysis of the resonant frequency of the octagonal split resonant rings with metal wires,” Appl. Opt. 49, 5638–5644 (2010).
[CrossRef]

2007

2006

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

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

2005

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

2004

X. D. 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]

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

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

2003

C. R. Simovskia 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. A 311, 254–263 (2003).
[CrossRef]

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

2002

D. R. Smith and S. Schultz, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. E 65, 195104 (2002).

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed metamaterials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, “Numerical studies of left-handed materials and arrays of split ring resonators,” Phys. Rev. E 65, 036622 (2002).
[CrossRef]

2001

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

2000

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

Cai, W. S.

Chen, H.

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

Chen, H. S.

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

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

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

Chen, K. S.

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

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

Chen, X. D.

X. D. 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]

Chettiar, U. K.

Dong, X. L.

X. F. Zhang, P. F. Guan, and X. L. Dong, “Transform between the permeability and permittivity in the close-packed Ni nanoparticles,” Appl. Phys. Lett. 97, 033107 (2010).
[CrossRef]

Drachev, V. P.

Gao, P.

Grzegorczyk, T. M.

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

X. D. 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]

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

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed metamaterials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Guan, P. F.

X. F. Zhang, P. F. Guan, and X. L. Dong, “Transform between the permeability and permittivity in the close-packed Ni nanoparticles,” Appl. Phys. Lett. 97, 033107 (2010).
[CrossRef]

He, S.

C. R. Simovskia 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. A 311, 254–263 (2003).
[CrossRef]

Hedge, R.

Z. Szabó, G. H. Park, R. Hedge, and E. P. Li, “A unique extraction of metamaterial parameters based on Kramers–Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58, 2646–2653 (2010).
[CrossRef]

Huangfu, J. T.

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

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

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

Huangpu, J.

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

Jiang, Q.

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

Kildishev, A. V.

Kong, J. A.

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

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

X. D. 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]

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

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed metamaterials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Koschny, T.

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

Li, E. P.

Z. Szabó, G. H. Park, R. Hedge, and E. P. Li, “A unique extraction of metamaterial parameters based on Kramers–Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58, 2646–2653 (2010).
[CrossRef]

Markos, P.

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

P. Markos and C. M. Soukoulis, “Numerical studies of left-handed materials and arrays of split ring resonators,” Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Moss, C. D.

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed metamaterials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Mu, T. K.

Nemat-Nasser, S. C.

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

Pacheco, J.

X. D. 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, “A composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Park, G. H.

Z. Szabó, G. H. Park, R. Hedge, and E. P. Li, “A unique extraction of metamaterial parameters based on Kramers–Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58, 2646–2653 (2010).
[CrossRef]

Ran, L. X.

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

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

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

Schultz, S.

D. R. Smith and S. Schultz, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. E 65, 195104 (2002).

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

Schulz, S.

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

Shalaev, V. M.

Shelby, R. A.

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

Simovskia, C. R.

C. R. Simovskia 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. A 311, 254–263 (2003).
[CrossRef]

Smith, D. R.

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

D. R. Smith and S. Schultz, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. E 65, 195104 (2002).

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

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

Soukoulis, C. M.

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

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

P. Markos and C. M. Soukoulis, “Numerical studies of left-handed materials and arrays of split ring resonators,” Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Sun, M. Z.

Szabó, Z.

Z. Szabó, G. H. Park, R. Hedge, and E. P. Li, “A unique extraction of metamaterial parameters based on Kramers–Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58, 2646–2653 (2010).
[CrossRef]

Vier, D. C.

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

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

Wang, D.

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

Wu, B. I.

X. D. 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]

Xiao, S. M.

Yuan, H. K.

Zhang, C. M.

Zhang, X. F.

X. F. Zhang, P. F. Guan, and X. L. Dong, “Transform between the permeability and permittivity in the close-packed Ni nanoparticles,” Appl. Phys. Lett. 97, 033107 (2010).
[CrossRef]

Zhang, X. M.

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

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

Zhang, Y.

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed metamaterials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

X. F. Zhang, P. F. Guan, and X. L. Dong, “Transform between the permeability and permittivity in the close-packed Ni nanoparticles,” Appl. Phys. Lett. 97, 033107 (2010).
[CrossRef]

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

H. Chen, D. Wang, J. Huangpu, Q. Jiang, and J. A. Kong, “Metamaterial with randomized patterns for negative refraction of electromagnetic wave,” Appl. Phys. Lett. 88, 031908 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

Z. Szabó, G. H. Park, R. Hedge, and E. P. Li, “A unique extraction of metamaterial parameters based on Kramers–Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58, 2646–2653 (2010).
[CrossRef]

J. Appl. Phys.

L. X. Ran, J. T. Huangfu, H. S. Chen, X. M. Zhang, K. S. Chen, T. M. Grzegorczyk, and J. A. Kong, “Beam shifting experiment for the characterization of left-handed properties,” J. Appl. Phys. 95, 2238–2241 (2004).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phys. Lett. A

C. R. Simovskia 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. A 311, 254–263 (2003).
[CrossRef]

Phys. Rev. E

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

P. Markos and C. M. Soukoulis, “Numerical studies of left-handed materials and arrays of split ring resonators,” Phys. Rev. E 65, 036622 (2002).
[CrossRef]

X. D. 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]

D. R. Smith and S. Schultz, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. E 65, 195104 (2002).

Phys. Rev. Lett.

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

Prog. Electromagn. Res.

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed metamaterials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Science

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

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Figures (10)

Fig. 1.
Fig. 1.

SSRR cell composed with copper strips.

Fig. 2.
Fig. 2.

Single cell used in the work and the definition of the parameters characterizing the unit cell of the SSRR metamaterial. (a) and (b) Constructional drawing. (c) Side view.

Fig. 3.
Fig. 3.

Prism-shaped metamaterial sample formed of crossed three-layer SSRR-MW units.

Fig. 4.
Fig. 4.

Experimental principle of the beam-refraction instrument, including the generating device, the signal supplying and collecting instrument, and the data.

Fig. 5.
Fig. 5.

3D results of the beam-refraction experiment on a prism of the metamaterial indicated in Fig. 2. (a) Big SSRR-MW and (b) small SSRR-MW periodic structure samples. The horizontal axis represents frequency in gigahertz, the vertical axis represents the refractive angle in degrees, and the color represents the detected power. The insert picture realizes its detailed experimental description.

Fig. 6.
Fig. 6.

Extracted effective parameters. (a) Electric permittivity and magnetic permeability and (b) effective negative index. Note that the effective parameters are dependent on the size of the unit cell.

Fig. 7.
Fig. 7.

Theoretical result of double resonant frequencies of the permeability.

Fig. 8.
Fig. 8.

(a) Two-layer SSRR-MW unit. (b) Three-layer SSRR-MW unit.

Fig. 9.
Fig. 9.

S parameter and retrieval parameters as a function of frequency for a two-layer SSRR-MW unit. (a) Magnitude, (b) phase of the simulated S parameters, (c) impedance, (d) index, (e) permittivity, and (f) permeability recovered from the simulative results.

Fig. 10.
Fig. 10.

S parameter and retrieval parameters as a function of frequency for a three-layer SSRR-MW unit. (a) Magnitude, (b) phase of the simulated S parameters, (c) impedance, (d) index, (e) permittivity, and (f) permeability recovered from the simulative results.

Tables (1)

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Table 1. Parameters of Three SSRR Cells

Equations (10)

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L=BSI=4μ0S2aπ.
C=QU=QEd=σSEd=4πε0ln(a+a2+a22a+a2+a22a+a2+a12a+a2+a12)Sc.
ωm0=1LC,ωmp=ωm01F,
Zeff=±(1+S11)2S212(1S11)2S212,
Neff=k0deff{Im[ln(X±i1X2)]+2mπi[ln(X±i1X2)]},
X=1S112+S2122S21,
εeff=neffzeff,μeff=neffzeff.
ε(ω)ε0=1ωp2ω2+iγω,
μ(ω)μ0=1ωmp2ωmo2ω2ωmo2+iγω,
μ(ω)μ0=i=1n1ωmpi2ωmoi2ω2ωmoi2+iγiω.

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