Abstract

We consider the hybridization of the resonance of a SRR metamaterial with the gyromagnetic material resonance of yittrium iron garnet (YIG) inclusions. The combination of an artificial structural resonance and natural material resonance generates a unique hybrid resonance that can be harnessed to make tunable metamaterials and further extend the range of achievable electromagnetic materials. A predictive analytic model is applied that accurately describes the characteristics of this SRR/YIG hybridization. We suggest that this hybridization has been observed in experimental data presented by Kang et al. [Opt. Express, 16, 8825 (2008)] and present numerical simulations to support this assertion. In addition, we investigate a design for optimizing the SRR/YIG structure that shows strong hybridization with a minimum amount of YIG material.

© 2009 Optical Society of America

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  1. L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonantors and ferrite rods," Opt. Express 16, 8825-8834 (2008).
    [CrossRef] [PubMed]
  2. 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] [PubMed]
  3. N. Seddon and T. Bearpark, "Observation of the Inverse Doppler Effect," Science 302, 1537 (2003).
    [CrossRef] [PubMed]
  4. V. G. Veselago, "The electrodynamics of substances with simultaneously negative ∑ and μ," Soviet Physics Uspekhi 10, 509-514 (1964).
    [CrossRef]
  5. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
    [CrossRef] [PubMed]
  6. I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
    [CrossRef]
  7. S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004).
    [CrossRef]
  8. T. Hand and S. Cummer, "Frequency Tunable Electromagnetic Metamaterial Using Ferroelectric Loaded Split Rings," J. Appl. Phys. 103, 066105 (2007).
    [CrossRef]
  9. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
    [CrossRef] [PubMed]
  10. Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
    [CrossRef]
  11. V. B. Bregar, "Effective-medium approach to the magnetic susceptibility of composites with ferromagnetic inclusions," Phys. Rev. B 71, 174418 (2005).
    [CrossRef]
  12. Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
    [CrossRef]
  13. J. N. Gollub, D. R. Smith, and J. D. Baena, "Hybrid resonant phenomenon in a metamaterial structure with integrated resonant magnetic material," arXiv:0810.4871 (2008).
  14. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  15. R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
    [CrossRef]
  16. 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]

2008 (1)

2007 (4)

T. Hand and S. Cummer, "Frequency Tunable Electromagnetic Metamaterial Using Ferroelectric Loaded Split Rings," J. Appl. Phys. 103, 066105 (2007).
[CrossRef]

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[CrossRef]

2006 (2)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

2005 (1)

V. B. Bregar, "Effective-medium approach to the magnetic susceptibility of composites with ferromagnetic inclusions," Phys. Rev. B 71, 174418 (2005).
[CrossRef]

2004 (2)

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004).
[CrossRef]

2003 (1)

N. Seddon and T. Bearpark, "Observation of the Inverse Doppler Effect," Science 302, 1537 (2003).
[CrossRef] [PubMed]

2002 (1)

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]

2000 (1)

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] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1964 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative ∑ and μ," Soviet Physics Uspekhi 10, 509-514 (1964).
[CrossRef]

Averitt, R. D.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Bearpark, T.

N. Seddon and T. Bearpark, "Observation of the Inverse Doppler Effect," Science 302, 1537 (2003).
[CrossRef] [PubMed]

Bonache, J.

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

Bregar, V. B.

V. B. Bregar, "Effective-medium approach to the magnetic susceptibility of composites with ferromagnetic inclusions," Phys. Rev. B 71, 174418 (2005).
[CrossRef]

Caloz, C.

S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004).
[CrossRef]

Chen, H.-T.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[CrossRef]

Cummer, S.

T. Hand and S. Cummer, "Frequency Tunable Electromagnetic Metamaterial Using Ferroelectric Loaded Split Rings," J. Appl. Phys. 103, 066105 (2007).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

Du, B.

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Garcia, J. G.

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

Gil, I.

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Hand, T.

T. Hand and S. Cummer, "Frequency Tunable Electromagnetic Metamaterial Using Ferroelectric Loaded Split Rings," J. Appl. Phys. 103, 066105 (2007).
[CrossRef]

Harris, V. G.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

He, P.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

He, Y.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Huang, D.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[CrossRef]

Itoh, T.

S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

Kang, L.

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonantors and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Li, B.

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Lim, S.

S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004).
[CrossRef]

Liu, R.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[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.

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

Martin, F.

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

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] [PubMed]

Padilla, W. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Parimi, P. V.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Rachford, F. J.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[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. Microwave Theory Tech. 47, 2075-2084 (1999).
[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, "A Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

Seddon, N.

N. Seddon and T. Bearpark, "Observation of the Inverse Doppler Effect," Science 302, 1537 (2003).
[CrossRef] [PubMed]

Smith, D. R.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[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, "A Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Sorolla, M.

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

Soukoulis, C. M.

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.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). http://www.sciencemag.org/cgi/reprint/314/5801/977.pdf.
[CrossRef] [PubMed]

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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Tayor, A. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative ∑ and μ," Soviet Physics Uspekhi 10, 509-514 (1964).
[CrossRef]

Vier, D. 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] [PubMed]

Vittoria, C.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

Yoon, S. D.

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

Zhao, B.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[CrossRef]

Zhao, H.

Zhao, Q.

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonantors and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zhou, J.

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonantors and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Q. Zhao, L. Kang, B. Du, B. Li, and J. Zhou, "Electrically tunable negative permeability metamaterials based on nematic liquid crystals," Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Electron. Lett. (1)

I. Gil, J. G. Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Appl. Phys. (1)

T. Hand and S. Cummer, "Frequency Tunable Electromagnetic Metamaterial Using Ferroelectric Loaded Split Rings," J. Appl. Phys. 103, 066105 (2007).
[CrossRef]

J. Magn. Magn. Mater. (1)

Y. He, P. He, S. D. Yoon, P. V. Parimi, F. J. Rachford, V. G. Harris, and C. Vittoria, "Tunable negative index metamaterial using yttrium iron garnet," J. Magn. Magn. Mater. 313, 187-191 (2007).
[CrossRef]

Nature (1)

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Tayor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. B (2)

V. B. Bregar, "Effective-medium approach to the magnetic susceptibility of composites with ferromagnetic inclusions," Phys. Rev. B 71, 174418 (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]

Phys. Rev. E (1)

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description and explanation of electromagnetic behavior in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

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).
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J. N. Gollub, D. R. Smith, and J. D. Baena, "Hybrid resonant phenomenon in a metamaterial structure with integrated resonant magnetic material," arXiv:0810.4871 (2008).

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Figures (5)

Fig. 1.
Fig. 1.

(a) The SRR/YIG unit cell structure is shown. The characteristic dimensions of the structure are d 3 = 2.4 mm, a 2 = 0.6 mm, a 3 = 0.04 mm, g = 0.4 mm, substrate thickness of s 2 = 0.2 mm, and a unit cell size of 3 mm. (b) The extracted permittivity and permeability of the structure.

Fig. 2.
Fig. 2.

(a)The Transmission simulation of the combined SRR/YIG structure and Isolated YIG structure and the analytic hybridization theory are shown for a biasing field of H0 = 3 kG structure. (b) The extracted permeability over the range of biasing field, H 0 = 1.7 – 4.5 kG, with steps of 0.1 kG is shown.

Fig. 3.
Fig. 3.

Numerical simulations of the transmission for a one unit cell thick SRR/YIG meta-material structure and the analytic theory are shown for a range of biasing fields. The position of the YIG resonance is noted by a vertical arrow and the splitting of the 1st and 2nd SRR resonances are noted for each bias field. The extracted permeability and permittivity of the SRR/YIG metamaterial are also shown.

Fig. 4.
Fig. 4.

(a) The characteristic dimensions of the SRR/YIG rod unit cell structure experimentally investigated by Yang et al. are shown with d 1 = 2.2 mm, d 1 =1.2 mm, c = 0.2 mm, g = 0.4 mm, and a 1 = 0.8 mm, a substrate thickness of S 2 = 0.9 mm, and a unit cell size of 5 mm. (b) The numerically extracted permeability and permittivity of the structure are shown.

Fig. 5.
Fig. 5.

The numerically calculated transmission for the combined SRR/YIG structure investigated by Kang et al. is shown along with the analytically determined transmission determined through Eqs. (4–11). Also shown, is the numerically calculated transmission for the YIG rod structure only

Equations (11)

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μ ̅ ( ω ) = A ( 1 ) ( 1 F ( 1 ) ω 2 ω 2 ( ω 0 SRR ( 1 ) ) 2 + Γ SRR ( 1 ) ) ,
ε ̅ ( ω ) = A ( 2 ) ( 1 F ( 2 ) ω 2 ω 2 ( ω 0 SRR ( 2 ) ) 2 + Γ SRR ( 2 ) ) ,
ω 0 SRR = 1 LC .
sin ( θ ( ω ) / 2 ) = k ( ω ) d 2 μ ̅ ( ω ) ε ̅ ( ω ) ,
η = { μ ̅ ( ω ) / ε ̅ ( ω ) cos ( θ ( ω ) / 2 ) , electric resonance μ ̅ ( ω ) / ε ̅ ( ω ) csc ( θ ( ω ) / 2 ) , magnetic resonance
n = θ ( ω ) / k ( ω ) d .
μ ( ω ) = μ 0 ( μ 1 ( ω ) i μ 2 ( ω ) 0 i μ 2 ( ω ) μ 1 ( ω ) 0 0 0 1 ) ,
μ 1 ( ω ) = ω 0 YIG γ μ 0 M s ( ω 0 YIG ) 2 ω 2 ,
μ 2 ( ω ) = ω γ μ 0 M s ( ω 0 YIG ) 2 ω 2 ,
L = μ 0 ( μ 1 ( ω ) μ 1 ( ω ) ( 1 q ) + q ) g geom ,
ω′ 0 SRR ( j ) = 1 μ 1 ( ω ) μ 1 ( ω ) ( 1 q ) + q ω 0 SRR ( j ) .

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