Abstract

The author investigates the characteristics of magnetic resonance band gaps for split ring structures. Resonance band gap width is related to the discrepancy of resonance frequency at two different Bloch wavelength scales. Large band gaps are achieved by lowering the resonance frequency on one hand, and raising the dissimilarity between two respective resonant modes on the other. By increasing the internal fraction of ring area, large resonance band gaps are obtained. The band gap features alter as the plasmonic effect becomes significant, where the kinetic inductance outweighs the geometric one and the magnetic resonance attenuates.

© 2008 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  2. D. R. Smith and N. Kroll, "Negative Refractive Index in Left-HandedMaterials," Phys. Rev. Lett. 85, 2933-2936 (2000).
    [CrossRef] [PubMed]
  3. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
    [CrossRef] [PubMed]
  4. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
    [CrossRef] [PubMed]
  5. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
  6. H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024,915 (2006).
    [CrossRef]
  7. A. B. Movchan and S. Guenneau, "Split-ring resonators and localized modes," Phys. Rev. B 70, 125,116 (2004).
    [CrossRef]
  8. Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
    [CrossRef] [PubMed]
  9. A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens.Matter 11, 2503-2512 (1999).
    [CrossRef]
  10. R. L. Chern, C. C. Chang, and C. C. Chang, "Interfacial operator approach to computing band structures for photonic crystals of polar materials," Phys. Rev. B 73, 235,123 (2006).
    [CrossRef]
  11. R. L. Chern, C. C. Chang, and C. C. Chang, "Surface and bulk modes for periodic structures of negative index materials," Phys. Rev. B 74, 155,101 (2006).
    [CrossRef]
  12. R. L. Chern, "Surface plasmon modes for periodic lattices of plasmonic hole waveguides," Phys. Rev. B 77, 045,409 (2008).
    [CrossRef]
  13. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
    [CrossRef]
  14. S. O’Brien and J. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys.-Condes. Matter 14, 6383-6394 (2002).
    [CrossRef]
  15. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
    [CrossRef]
  16. R. L. Chern, "Magnetic and surface plasmon resonances for periodic lattices of plasmonic split-ring resonators," Phys. Rev. B 78, 085,116.

2008

R. L. Chern, "Surface plasmon modes for periodic lattices of plasmonic hole waveguides," Phys. Rev. B 77, 045,409 (2008).
[CrossRef]

2006

R. L. Chern, C. C. Chang, and C. C. Chang, "Interfacial operator approach to computing band structures for photonic crystals of polar materials," Phys. Rev. B 73, 235,123 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Surface and bulk modes for periodic structures of negative index materials," Phys. Rev. B 74, 155,101 (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, 024,915 (2006).
[CrossRef]

2005

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

2004

A. B. Movchan and S. Guenneau, "Split-ring resonators and localized modes," Phys. Rev. B 70, 125,116 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

2002

S. O’Brien and J. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys.-Condes. Matter 14, 6383-6394 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

2000

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-HandedMaterials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

1999

A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens.Matter 11, 2503-2512 (1999).
[CrossRef]

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

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Chan, C. T.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Chang, C. C.

R. L. Chern, C. C. Chang, and C. C. Chang, "Interfacial operator approach to computing band structures for photonic crystals of polar materials," Phys. Rev. B 73, 235,123 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Interfacial operator approach to computing band structures for photonic crystals of polar materials," Phys. Rev. B 73, 235,123 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Surface and bulk modes for periodic structures of negative index materials," Phys. Rev. B 74, 155,101 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Surface and bulk modes for periodic structures of negative index materials," Phys. Rev. B 74, 155,101 (2006).
[CrossRef]

Chen, H.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024,915 (2006).
[CrossRef]

Chern, R. L.

R. L. Chern, "Surface plasmon modes for periodic lattices of plasmonic hole waveguides," Phys. Rev. B 77, 045,409 (2008).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Surface and bulk modes for periodic structures of negative index materials," Phys. Rev. B 74, 155,101 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Interfacial operator approach to computing band structures for photonic crystals of polar materials," Phys. Rev. B 73, 235,123 (2006).
[CrossRef]

R. L. Chern, "Magnetic and surface plasmon resonances for periodic lattices of plasmonic split-ring resonators," Phys. Rev. B 78, 085,116.

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Grzegorczyk, T. M.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024,915 (2006).
[CrossRef]

Guenneau, S.

A. B. Movchan and S. Guenneau, "Split-ring resonators and localized modes," Phys. Rev. B 70, 125,116 (2004).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (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, 024,915 (2006).
[CrossRef]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

Kong, J. A.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024,915 (2006).
[CrossRef]

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Kroll, N.

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-HandedMaterials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Liu, Z.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Mao, Y.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Moroz, A.

A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens.Matter 11, 2503-2512 (1999).
[CrossRef]

Movchan, A. B.

A. B. Movchan and S. Guenneau, "Split-ring resonators and localized modes," Phys. Rev. B 70, 125,116 (2004).
[CrossRef]

Nemat-Nasser, S. C.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

O’Brien, S.

S. O’Brien and J. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys.-Condes. Matter 14, 6383-6394 (2002).
[CrossRef]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Pendry, J.

S. O’Brien and J. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys.-Condes. Matter 14, 6383-6394 (2002).
[CrossRef]

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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

Ran, L.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024,915 (2006).
[CrossRef]

Robbins, D. J.

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

Schultz, S.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

Sheng, P.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-HandedMaterials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

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

Tip, A.

A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens.Matter 11, 2503-2512 (1999).
[CrossRef]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Yang, Z.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Zhu, Y. Y.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, "Microwave transmission through a twodimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

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

J. Appl. Phys.

H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024,915 (2006).
[CrossRef]

J. Phys. Condens.Matter

A. Moroz and A. Tip, "Resonance-induced effects in photonic crystals," J. Phys. Condens.Matter 11, 2503-2512 (1999).
[CrossRef]

J. Phys.-Condes. Matter

S. O’Brien and J. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys.-Condes. Matter 14, 6383-6394 (2002).
[CrossRef]

Phys. Rev. B

A. B. Movchan and S. Guenneau, "Split-ring resonators and localized modes," Phys. Rev. B 70, 125,116 (2004).
[CrossRef]

R. L. Chern, "Magnetic and surface plasmon resonances for periodic lattices of plasmonic split-ring resonators," Phys. Rev. B 78, 085,116.

R. L. Chern, C. C. Chang, and C. C. Chang, "Interfacial operator approach to computing band structures for photonic crystals of polar materials," Phys. Rev. B 73, 235,123 (2006).
[CrossRef]

R. L. Chern, C. C. Chang, and C. C. Chang, "Surface and bulk modes for periodic structures of negative index materials," Phys. Rev. B 74, 155,101 (2006).
[CrossRef]

R. L. Chern, "Surface plasmon modes for periodic lattices of plasmonic hole waveguides," Phys. Rev. B 77, 045,409 (2008).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith and N. Kroll, "Negative Refractive Index in Left-HandedMaterials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the Magnetic Response of Split-Ring Resonators at Optical Frequencies," Phys. Rev. Lett. 95, 223,902 (2005).
[CrossRef]

Science

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, "Locally Resonant Sonic Materials," Science 289, 1734-1736 (2000).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic Response of Metamaterials at 100 Terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Dispersion diagram for a square SRR structure with s/a=0.8, t/a=0.04, d/a=0.2. Yellow region is the resonance band gap and dashed lines are results for a closed ring structure (d=0) with the same s and t. The unit cell and geometric parameters are shown on the right.

Fig. 2.
Fig. 2.

Magnetic field contours (Re[H]) of the eigenmodes for a square SRR structure with s/a=0.5, t/a=0.04, and d/a=0.1. Red and green colors correspond to positive and negative values, respectively. (a) the upper band edge: point G on the resonance branch with ωa/2πc=0.304. (b) the lower band edge: point M on the acoustical branch with ωa/2πc=0.256. The band gap width is 0.048(2πc/a) and the gap to mid-gap ratio is 17%.

Fig. 3.
Fig. 3.

Magnetic field contours (Re[H]) of the eigenmodes for a square SRR structure with s/a=0.8, t/a=0.04, d/a=0.2 at (a) the upper band edge with ωa/2πc=0.261, and (b) the lower band edge with ωa/2πc=0.151. The band gap width is 0.11(2πc/a) and the gap to mid-gap ratio is 53.4%.

Fig. 4.
Fig. 4.

Dispersion diagrams for the square SRR structures with s/a=0.95 and t/a=0.01. (a) the optimal band gap width 0.252(2πc/a) at d/a=0.85, (b) the optimal gap to mid-gap ratio 109% at d/a=0.2.

Fig. 5.
Fig. 5.

Band gap widths and gap to mid-gap ratios of the SRR structures with t/a=0.01 for various d/a and s/a.

Fig. 6.
Fig. 6.

Magnetic field contours (Re[H]) of the eigenmodes for the SRR structure in Fig. 3 with δ p /a = 1 at (a) the upper band edge and (b) the lower band edge.

Equations (1)

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μ eff = 1 F ω 2 ω 2 ω 0 2 ,

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