Abstract

We present a systematic numerical study, validated by accompanied experimental data, of individual and coupled split ring resonators (SRRs) of a single rectangular ring with one, two and four gaps. We discuss the behavior of the magnetic resonance frequency, the magnetic field and the currents in the SRRs, as one goes from a single SRR to strongly interacting SRR pairs in the SRR plane. We show that coupling of the SRRs along the E direction results to shift of the magnetic resonance frequency to lower or higher values, depending on the capacitive or inductive nature of the coupling. Strong SRR coupling along propagation direction usually results to splitting of the single SRR resonance into two distinct resonances, associated with peculiar field and current distributions.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ," Sov. Phys. Usp. 10, 509-514 (1968)
    [CrossRef]
  2. C. M.  Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
    [CrossRef]
  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. "Focus Issue: Negative Refraction and Metamaterials," Opt. Express 11, 639−755 (2003).
    [PubMed]
  5. R. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  6. R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
    [CrossRef]
  7. T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
    [CrossRef]
  8. H. Danithe, S. Foteinopoulou, and C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photon. Nanostruct. 4, 123-131 (2006).
    [CrossRef]
  9. N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
    [CrossRef]
  10. A. J. Holden, "Towards some real applications for negative materials," Photon. Nanostruct. 3, 96-99 (2005).
    [CrossRef]
  11. S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
    [CrossRef]
  12. A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).
  13. J. B.  Pendry, A.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
    [CrossRef]
  14. 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]
  15. R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials,' Phys. Rev. B 65, 144440-(1-6) (2002).
    [CrossRef]
  16. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
    [CrossRef]
  17. J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelinek, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103-1-9 (2005).
    [CrossRef]
  18. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective Medium Theory of Left-handed Materials," Phys. Rev. Lett. 93, 107402-1-4 (2004).
    [CrossRef]
  19. M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
    [CrossRef]
  20. .K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Experimental Observation of True Left-Handed Transmission Peaks in Metamaterials," Opt. Lett. 29, 2623-2625 (2004).
    [CrossRef] [PubMed]
  21. F. Bilotti, A. Toscano, and L. Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples," IEEE Trans. Antennas Propag. 55, 2258-2267 (2007).
    [CrossRef]
  22. R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
    [CrossRef]
  23. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168-1-15 (2005).
    [CrossRef]
  24. M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
    [CrossRef] [PubMed]
  25. V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
    [CrossRef]
  26. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative index metamaterials at optical wavelengths," Science 315, 47-49 (2007).
    [CrossRef] [PubMed]
  27. S. Linden et al., "Photonic metamaterials: Magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006).
    [CrossRef]
  28. J. Zhou, Th. 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, 223902-1-4 (2005).
    [CrossRef]
  29. Th. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic 3d left-handed and related metamaterials," Phys. Rev. B 71, 121103(R)-1-4 (2005).
  30. J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
    [CrossRef]
  31. P. Gay-Balmaz and O.J.F. Martin, "Electromagnetic Resonances in Individual and Coupled Split-ring Resonators," J. Appl. Phys. 92, 2929-2936 (2002).
    [CrossRef]
  32. J. Garcia-Garcia et al., "Miniaturized microstrip and CPW filters using coupled metamaterials resonators," IEEE Trans. Microwave Theory Tech. 54, 2628-2635 (2006).
    [CrossRef]
  33. E. N. Economou, Th. Koschny, and C. M. Soukoulis, "Strong diamagnetic response of in split-ring-resonator metamaterials: Numerical study and two-loop model," Phys. Rev. B 77, 092401-1-4 (2008).
    [CrossRef]
  34. S. E. Harris, J. E. Field, and A. Imamoglou, "Nonlinear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107-1110 (1990).
    [CrossRef] [PubMed]
  35. C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussensveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2002).
    [CrossRef]

2007 (8)

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative index metamaterials at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

F. Bilotti, A. Toscano, and L. Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples," IEEE Trans. Antennas Propag. 55, 2258-2267 (2007).
[CrossRef]

2006 (6)

J. Garcia-Garcia et al., "Miniaturized microstrip and CPW filters using coupled metamaterials resonators," IEEE Trans. Microwave Theory Tech. 54, 2628-2635 (2006).
[CrossRef]

S. Linden et al., "Photonic metamaterials: Magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006).
[CrossRef]

J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
[CrossRef]

H. Danithe, S. Foteinopoulou, and C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photon. Nanostruct. 4, 123-131 (2006).
[CrossRef]

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

C. M.  Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

2005 (1)

A. J. Holden, "Towards some real applications for negative materials," Photon. Nanostruct. 3, 96-99 (2005).
[CrossRef]

2004 (3)

.K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Experimental Observation of True Left-Handed Transmission Peaks in Metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (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]

2003 (2)

"Focus Issue: Negative Refraction and Metamaterials," Opt. Express 11, 639−755 (2003).
[PubMed]

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

2002 (2)

P. Gay-Balmaz and O.J.F. Martin, "Electromagnetic Resonances in Individual and Coupled Split-ring Resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussensveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2002).
[CrossRef]

2001 (2)

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

R. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
[CrossRef]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglou, "Nonlinear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ," Sov. Phys. Usp. 10, 509-514 (1968)
[CrossRef]

Alu, A.

A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).

Aydin, K.

Baena, J. D.

J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
[CrossRef]

Bilotti, F.

F. Bilotti, A. Toscano, and L. Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples," IEEE Trans. Antennas Propag. 55, 2258-2267 (2007).
[CrossRef]

Chakrabartib, S.

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Danithe, H.

H. Danithe, S. Foteinopoulou, and C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photon. Nanostruct. 4, 123-131 (2006).
[CrossRef]

Economou, E. N.

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

C. M.  Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Engheta, N.

A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).

Enocha, S.

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Erentok, A.

A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglou, "Nonlinear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Foteinopoulou, S.

H. Danithe, S. Foteinopoulou, and C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photon. Nanostruct. 4, 123-131 (2006).
[CrossRef]

Garcia-Garcia, J.

J. Garcia-Garcia et al., "Miniaturized microstrip and CPW filters using coupled metamaterials resonators," IEEE Trans. Microwave Theory Tech. 54, 2628-2635 (2006).
[CrossRef]

Garrido Alzar, C. L.

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussensveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2002).
[CrossRef]

Gay-Balmaz, P.

P. Gay-Balmaz and O.J.F. Martin, "Electromagnetic Resonances in Individual and Coupled Split-ring Resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Gilderdale, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

Gokkavas, M.

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

Gralaka, B.

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Guenneaua, S.

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Gundogdu, T. F.

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

Guven, K.

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

.K. Aydin, K. Guven, Lei Zhang, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Experimental Observation of True Left-Handed Transmission Peaks in Metamaterials," Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

Hajnal, J. V.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoglou, "Nonlinear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Holden, A.

J. B.  Pendry, A.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
[CrossRef]

Holden, A. J.

A. J. Holden, "Towards some real applications for negative materials," Photon. Nanostruct. 3, 96-99 (2005).
[CrossRef]

Imamoglou, A.

S. E. Harris, J. E. Field, and A. Imamoglou, "Nonlinear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Jelinek, L.

J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
[CrossRef]

Kafesaki, M.

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

C. M.  Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Katsarakis, N.

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Koschny, T.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Koschny, Th.

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

Larkman, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

Lei Zhang, K.

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative index metamaterials at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

S. Linden et al., "Photonic metamaterials: Magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006).
[CrossRef]

Marqués, R.

J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
[CrossRef]

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Martel, J.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Martin, O.J.F.

P. Gay-Balmaz and O.J.F. Martin, "Electromagnetic Resonances in Individual and Coupled Split-ring Resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Martinez, M. A. G.

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussensveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2002).
[CrossRef]

Medina, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Mesa, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

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]

Nussensveig, P.

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussensveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2002).
[CrossRef]

Ozbay, E.

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[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] [PubMed]

Penciu, R.

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

Pendry, J. B.

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

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

Pendry, J. B.

J. B.  Pendry, A.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
[CrossRef]

Ramakrishnab, S. A.

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Robbins, D.

J. B.  Pendry, A.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
[CrossRef]

Schultz, S.

R. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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]

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
[CrossRef]

Shelby, R.

R. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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]

R. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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]

Soukoulis, C. M.

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative index metamaterials at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

H. Danithe, S. Foteinopoulou, and C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photon. Nanostruct. 4, 123-131 (2006).
[CrossRef]

Soukoulis, C. M.

C. M.  Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Soukoulis, C. M.

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Stewart, W.

J. B.  Pendry, A.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
[CrossRef]

Tayeba, G.

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Toscano, A.

F. Bilotti, A. Toscano, and L. Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples," IEEE Trans. Antennas Propag. 55, 2258-2267 (2007).
[CrossRef]

Tsiapa, I.

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

Vegni, L.

F. Bilotti, A. Toscano, and L. Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples," IEEE Trans. Antennas Propag. 55, 2258-2267 (2007).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ," Sov. Phys. Usp. 10, 509-514 (1968)
[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]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative index metamaterials at optical wavelengths," Science 315, 47-49 (2007).
[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]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

Young, I. R.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

Zehentner, J.

J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
[CrossRef]

Zhou, J.

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

Ziolkowski, R. W.

A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).

Adv. Mater. (1)

C. M.  Soukoulis, M. Kafesaki, and E. N. Economou, "Negative index materials: New frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Am. J. Phys. (1)

C. L. Garrido Alzar, M. A. G. Martinez, and P. Nussensveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2002).
[CrossRef]

Appl. Phys. Lett. (2)

J. D. Baena, L. Jelinek, R. Marqués, and J. Zehentner, "Electrically small isotropic three-dimensional magnetic resonators for metamaterial design," Appl. Phys. Lett. 88, 134108-134110 (2006).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split-ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Linden et al., "Photonic metamaterials: Magnetism at optical frequencies," IEEE J. Sel. Top. Quantum Electron. 12, 1097-1105 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

F. Bilotti, A. Toscano, and L. Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples," IEEE Trans. Antennas Propag. 55, 2258-2267 (2007).
[CrossRef]

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design—Theory and experiment," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

A. Alu, N. Engheta, A. Erentok, and R. W. Ziolkowski, "Single-negative, double-negative and low index metamaterials and their electromagnetic applications," IEEE Trans. Antennas Propag. 49, 23-36 (2007).

IEEE Trans. Microwave Theory Tech. (1)

J. Garcia-Garcia et al., "Miniaturized microstrip and CPW filters using coupled metamaterials resonators," IEEE Trans. Microwave Theory Tech. 54, 2628-2635 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B.  Pendry, A.  Holden, D.  Robbins, and W.  Stewart, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech.  47, 2075-2084 (1999).
[CrossRef]

J. Appl. Phys. (1)

P. Gay-Balmaz and O.J.F. Martin, "Electromagnetic Resonances in Individual and Coupled Split-ring Resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Nature Photon. (1)

V. M. Shalaev, "Optical negative-index materials," Nature Photon. 1, 41-48 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Photon. Nanostruct. (6)

R. Penciu, M. Kafesaki, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, "Theoretical study of left-handed behavior of composite metamaterials," Photon. Nanostruct. 4, 12-16 (2006).
[CrossRef]

T. F. Gundogdu, M. Gokkavas, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Simulations and micro-fabrication of optically switchable split ring resonators," Photon. Nanostruct. 5, 106-112 (2007).
[CrossRef]

H. Danithe, S. Foteinopoulou, and C. M. Soukoulis, "Omni-reflectance and enhanced resonant tunneling from multilayers containing left-handed materials," Photon. Nanostruct. 4, 123-131 (2006).
[CrossRef]

N. Katsarakis, M. Kafesaki, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, "High transmittance left-handed materials involving symmetric split-ring resonators," Photon. Nanostruct. 5, 149-155 (2007).
[CrossRef]

A. J. Holden, "Towards some real applications for negative materials," Photon. Nanostruct. 3, 96-99 (2005).
[CrossRef]

S. Guenneaua, S. A. Ramakrishnab, S. Enocha, S. Chakrabartib, G. Tayeba, and B. Gralaka, "Cloaking and imaging effects in plasmonic checkerboards of negative ε and μ and dielectric photonic crystal checkerboards," Photon. Nanostruct. 5, 63-72 (2007).
[CrossRef]

Phys. Rev. Lett. (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]

S. E. Harris, J. E. Field, and A. Imamoglou, "Nonlinear optical processes using electromagnetically induced transparency," Phys. Rev. Lett. 64, 1107-1110 (1990).
[CrossRef] [PubMed]

Physica B (1)

M. Kafesaki, Th. Koschny, J. Zhou, N. Katsarakis, I. Tsiapa, E. N. Economou, and C. M. Soukoulis, ``Electromagnetic behavior of left-handed materials,' Physica B 394, 148-154 (2007).
[CrossRef]

Science (4)

R. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849 - 851 (2001)
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative index metamaterials at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ," Sov. Phys. Usp. 10, 509-514 (1968)
[CrossRef]

Other (7)

J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelinek, "On the resonances and polarizabilities of split-ring resonators," J. Appl. Phys. 98, 033103-1-9 (2005).
[CrossRef]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective Medium Theory of Left-handed Materials," Phys. Rev. Lett. 93, 107402-1-4 (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-(1-6) (2002).
[CrossRef]

J. Zhou, Th. 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, 223902-1-4 (2005).
[CrossRef]

Th. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic 3d left-handed and related metamaterials," Phys. Rev. B 71, 121103(R)-1-4 (2005).

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonances for different split-ring resonator parameters and designs," New J. Phys. 7, 168-1-15 (2005).
[CrossRef]

E. N. Economou, Th. Koschny, and C. M. Soukoulis, "Strong diamagnetic response of in split-ring-resonator metamaterials: Numerical study and two-loop model," Phys. Rev. B 77, 092401-1-4 (2008).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1.

The SRRs studied. Panel (a) shows the single gap SRR, where the SRR parameters are marked, panel (b) shows the two-gap SRR and panel (c) the four-gap SRR. The SRR parameters are as follows: Side length l=7 mm, width of the gap/gaps g=0.2 mm, metal width w=0.9 mm, metal thickness tm=0.03 mm (along z-direction).

Fig. 2a.
Fig. 2a.

(a). Transmission vs frequency for a single-gap ring. The incident electromagnetic (EM) field is as shown in Fig. 2(b). The dip around 3.8 GHz shows the magnetic resonance frequency.

Fig. 2b.
Fig. 2b.

(b). Current and field components at the magnetic resonance frequency for a single gap SRR. Panel (A) shows the surface current (larger arrows indicate larger current values), panel (B) shows the electric field amplitude and panel (C) the magnetic field component H z (perpendicular to the SRR). Red color indicates large positive values (relative to the axes system shown), blue large negative values, and green small values. The propagation direction of the incident electromagnetic field is also shown in panel (A), along with the direction of the incident E at the specific time point that the fields are plotted.

Fig. 3a.
Fig. 3a.

(a). Transmission vs frequency for a two-gap ring. The incident EM field is as shown in Fig. 3(b). The dip around 6.6 GHz shows the magnetic resonance frequency.

Fig. 3b.
Fig. 3b.

(b). Current and field components at the magnetic resonance frequency for a two-gap SRR. Panel (A) shows the surface current (larger arrows indicate larger current values), panel (B) shows the electric field amplitude and panel (C) the magnetic field component H z (perpendicular to the SRR). Red color indicates large positive values (relative to the axes system shown), blue large negative values, and green small values. The propagation direction of the incident electromagnetic field is also shown in panel (A), along with the direction of the incident E at the specific time point that the fields are plotted.

Fig. 4a.
Fig. 4a.

(a). Transmission vs frequency for a four-gap ring. The incident EM field is as shown in Fig. 4(b). The dip around 11.1 GHz shows the magnetic resonance frequency.

Fig. 4b.
Fig. 4b.

(b). Current and field components at the magnetic resonance frequency for a four-gap SRR. Panel (A) shows the surface current (larger and red color arrows indicate larger current values), panel (B) shows the electric field amplitude and panel (C) the magnetic field component H z (perpendicular to the SRR). Red color indicates large positive values (relative to the axes system shown), blue large negative values, and green small values. The propagation direction of the incident electromagnetic field is also shown in panel (A), along with the direction of the incident E at the specific time point that the fields are plotted.

Fig. 5.
Fig. 5.

Transmission vs frequency for pairs of strongly interacting SRRs, paired along the external electric field (E) direction. The transmission for different relative orientations of the two SRRs in the pair is shown, marked as orientation 1 (panel (a)), 2 (panel (b)), and 3 (panel (c)). For comparison, the transmission (simulated) for a single SRR is also shown (blue, dotted-dashed line). Panels (a) and (c) show both simulation and experimental data for the pair transmission. The SRR parameters are those mentioned in Fig. 1; the SRRs distance in the pair is 0.2 mm (from metal edge to neighboring metal edge).

Fig. 6.
Fig. 6.

The electric field amplitude |E| (left) and the magnetic field component H z (right), at the magnetic resonance frequency, for a pair of single-gap SRRs in orientation 1. Red color indicates large positive values and blue color large negative values (i.e. of field direction opposite to the axes shown). The polarization and the propagation direction of the incident field are also shown. Left panel shows that the electric field intensity is higher is the regime close to the SRR gaps; right panel indicates the excitation of circular currents of the same direction in both rings and the presence of high magnetic field in the regime between the SRRs.

Fig. 7.
Fig. 7.

The electric field amplitude |E| (left) and the magnetic field component H z (right), at the magnetic resonance frequency, for a pair of single-gap SRRs in orientation 2. Red color indicates large positive values and blue color large negative values for the magnetic field. The polarization and the propagation direction of the incident field are also shown. Left panel shows that higher electric field intensity occurs in the SRR gaps and in the regime between the two SRRs; right panel indicates the excitation of circular currents of the same direction in both rings and the presence of negligible magnetic field in the regime between the rings.

Fig. 8.
Fig. 8.

Electromagnetic wave transmission vs frequency for a pair of strongly interacting twogap SRRs in two relative orientations. For comparison, the transmission (simulated) for a single SRR is also shown (blue-dotted line).

Fig. 9.
Fig. 9.

Electromagnetic wave transmission vs frequency for a pair of strongly interacting 4-gap SRRs. Solid-black line shows the simulations data and dashed-red the corresponding experimental ones. For comparison the transmission (simulated) for a single SRR is also shown (dotted-blue line).

Fig. 10.
Fig. 10.

Transmission vs. frequency if two pairs of single-gap SRRs, like those of Fig. 5, are placed next to each other along propagation direction (distance between pairs is 0.2 mm – from metal edge to metal edge). Solid-black lines show simulation results and dashed-red lines experimental data (where available). For comparison, the simulated transmission for a single pair is shown (blue-dotted-dashed lines).

Fig. 11.
Fig. 11.

The magnetic field component H z at the different magnetic resonance frequencies appearing in Fig. 10. (a): Orientation 1, shown in Fig. 10(a). Panel (A) shows the first resonance, at 3.8 GHz, panel (B) the second resonance, at 4.2 GHz. (b): Orientation 2, shown in Fig. 10(b). Panel (A) shows the first resonance, at 2.71 GHz, panel (B) the second resonance, at 3 GHz. (c): Orientation 3a, shown in Fig. 10(c). Panel (A) shows the first resonance, at 3.65 GHz, panel (B) the second resonance, at 4.2 GHz. (d): Orientation 3b, shown in Fig. 10(d). Panel (A) shows the first resonance, at 2.5 GHz, panel (B) the second resonance, at 4.5 GHz. Red color indicates large positive values, blue color large negative values, green color small values. The external wave incidents always from left-side of the system.

Fig. 12.
Fig. 12.

Panels (a) and (b): Transmission vs. frequency if two pairs of two-gap SRRs, like those discussed in Fig. 8, are place next to each other along propagation direction (distance between pairs is 0.2 mm – from metal edge to metal edge). Solid-black lines show simulation results and dashed-red lines experimental data. For comparison, the simulated transmission for a single pair is shown (blue-dotted-dashed lines). Panel (c) shows the same data as panels (a) and (b) for 4-gap SRRs.

Metrics