Abstract

Left-handed metamaterials always gain the electromagnetic properties from the structure rather than inherit them directly from the materials they are composed of. In this article, a metamaterial was made using split-ring resonators and slabs of ferroelectric materials, where negative permittivity was realized by intrinsic properties of ferroelectric materials. Using a waveguide-based retrieval method, the permittivity and permeability of the metamaterials were experimentally retrieved, showing successfully the left-handed behaviors of the metamaterial over certain frequency band.

© 2007 Optical Society of America

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References

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. D. R. Smith, W. J. Padilla, and D. C. Vier, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
    [CrossRef] [PubMed]
  4. 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]
  5. P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 939 (2002).
    [CrossRef]
  6. 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]
  7. 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]
  8. J. D. Baena, R. Marques, and F. Medina, "Artificial magnetic metamaterial design by using spiral resonators," Phys. Rev B. 69, 014402 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. 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 (1999).
    [CrossRef]
  13. A. Pimenov, A. Loidl, P. Przyslupski, and B. Dabrowski, "Negative refraction in ferromagnet-superconductor superlattices," Phys. Rev. Lett. 95, 247009 (2005).
    [CrossRef] [PubMed]
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  15. A. L. Pokrovsky, and A. L Efros, "Electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett. 89, 093901 (2002).
    [CrossRef] [PubMed]
  16. R. Marques, and D. R. Smith, "Comment on electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett. 92, 059401 (2004).
    [CrossRef] [PubMed]
  17. X. Cai, X. Zhou, and G. Hu, "Numerical study on left-handed materials made of ferrite and metallic wires," Chinese Phys. Lett. 23, 348 (2006).
    [CrossRef]
  18. G. Dewar, "A thin wire array and magnetic host structure with n <0," J. Appl. Phys. 97, 10Q101 (2005).
    [CrossRef]
  19. J. S. Guerra, and J. A. Eiras, "Dielectric anomalies in La modified PbTiO3 ferroelectric ceramics in the microwave frequency region," Ferroelectrics 294, 25 (2003).
    [CrossRef]
  20. M. P. McNeal, S. Jang, and R. E. Newnham, "The effect of grain and particle size on the microwave properties of barium titanate BaTiO3," J. Appl. Phys. 83, 3288 (1998).
    [CrossRef]
  21. H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and Jin Au Kong, "Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  24. W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proceeding of IEEE 62, 1 (1974).
    [CrossRef]
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    [CrossRef]
  26. 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]
  27. T. C. Choy, Effective medium theory: principles and applications, (Oxford science publications 1999).

2006

2005

A. Pimenov, A. Loidl, P. Przyslupski, and B. Dabrowski, "Negative refraction in ferromagnet-superconductor superlattices," Phys. Rev. Lett. 95, 247009 (2005).
[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]

2004

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

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

R. Marques, and D. R. Smith, "Comment on electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett. 92, 059401 (2004).
[CrossRef] [PubMed]

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E. 70, 016608 (2004).
[CrossRef]

2003

J. S. Guerra, and J. A. Eiras, "Dielectric anomalies in La modified PbTiO3 ferroelectric ceramics in the microwave frequency region," Ferroelectrics 294, 25 (2003).
[CrossRef]

2002

A. L. Pokrovsky, and A. L Efros, "Electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett. 89, 093901 (2002).
[CrossRef] [PubMed]

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]

P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 939 (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]

J. A. Kong, "Electromagnetic wave interaction with stratified negative isotropic media," Prog. Electromagn. Res. 35, 1 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padilla, and D. C. Vier, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

1999

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 (1999).
[CrossRef]

1998

M. P. McNeal, S. Jang, and R. E. Newnham, "The effect of grain and particle size on the microwave properties of barium titanate BaTiO3," J. Appl. Phys. 83, 3288 (1998).
[CrossRef]

1996

J. B. Pendry, A. J. Holden, W. J. Stewart, and S. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

1974

W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proceeding of IEEE 62, 1 (1974).
[CrossRef]

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Appl. Phys. Lett.

P. Gay-Balmaz, and O. J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 939 (2002).
[CrossRef]

Chinese Phys. Lett.

X. Cai, X. Zhou, and G. Hu, "Numerical study on left-handed materials made of ferrite and metallic wires," Chinese Phys. Lett. 23, 348 (2006).
[CrossRef]

Ferroelectrics

J. S. Guerra, and J. A. Eiras, "Dielectric anomalies in La modified PbTiO3 ferroelectric ceramics in the microwave frequency region," Ferroelectrics 294, 25 (2003).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

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 (1999).
[CrossRef]

J. Appl. Phys.

M. P. McNeal, S. Jang, and R. E. Newnham, "The effect of grain and particle size on the microwave properties of barium titanate BaTiO3," J. Appl. Phys. 83, 3288 (1998).
[CrossRef]

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

Opt. Express

Phys. Rev B.

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]

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

Phys. Rev. B.

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]

Phys. Rev. E.

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]

Phys. Rev. Lett.

D. R. Smith, W. J. Padilla, and D. C. Vier, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and S. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

A. Pimenov, A. Loidl, P. Przyslupski, and B. Dabrowski, "Negative refraction in ferromagnet-superconductor superlattices," Phys. Rev. Lett. 95, 247009 (2005).
[CrossRef] [PubMed]

A. L. Pokrovsky, and A. L Efros, "Electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett. 89, 093901 (2002).
[CrossRef] [PubMed]

R. Marques, and D. R. Smith, "Comment on electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett. 92, 059401 (2004).
[CrossRef] [PubMed]

Proceeding of IEEE

W. B. Weir, "Automatic measurement of complex dielectric constant and permeability at microwave frequencies," Proceeding of IEEE 62, 1 (1974).
[CrossRef]

Prog. Electromagn. Res.

J. A. Kong, "Electromagnetic wave interaction with stratified negative isotropic media," Prog. Electromagn. Res. 35, 1 (2002).
[CrossRef]

Progress In Electromagnetics Research, PIER

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]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other

J. Pacheco, "Theory and application of left-handed metamaterials," Ph. D. thesis, Massachusetts Institute of Technology, (2004).

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

G. Dewar, "A thin wire array and magnetic host structure with n <0," J. Appl. Phys. 97, 10Q101 (2005).
[CrossRef]

T. C. Choy, Effective medium theory: principles and applications, (Oxford science publications 1999).

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Figures (7)

Fig. 1.
Fig. 1.

Sample of the metamaterial with SRR embedded in ferroelectric medium. The inset shows the unit cell of the SRR structure.

Fig. 2.
Fig. 2.

Experimental setup for the scattering parameters measurement in rectangular waveguide

Fig. 3.
Fig. 3.

Measured εr and μr for the FR4 substrate. (′) and (″) denote the real part and the imaginary part of the parameters, respectively.

Fig. 4.
Fig. 4.

Real part of the measured effective ε3 [dashed line, left-hand scale] and μ1 [solid line, right-hand scale] for the three kinds of materials: SRR only, FE only and SRR/FE. In the legend, (′) denote the real part of the parameters.

Fig. 5.
Fig. 5.

The measured permittivity of the FE material around the dielectric resonance.

Fig. 6.
Fig. 6.

Retrieved ε3 and μ1 for the three materials where the permittivity of FE only material is around -10 at 2.8 GHz. In the legend (′) denote the real part of the parameters.

Fig. 7.
Fig. 7.

Electric field E3 in the mid-plane when the structure has reached steady state. The wave is incident onto the slab from the left. The magnitude of field is in log scale.

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