Abstract

Point group theoretical methods are used to determine the electromagnetic properties of metamaterials, based solely upon the symmetries of the underlying constituent particles. From the transformation properties of an electromagnetic (EM) basis under symmetries of the particles, it is possible to determine, (i) the EM modes of the particles, (ii) the form of constitutive relations (iii) magneto-optical response of a metamaterial or lack thereof. Based upon these methods, we predict an ideal planar artificial magnetic metamaterial, and determine the subset of point groups of which particles must belong to in order to yield an isotropic 3D magnetic response, and we show an example.

© 2007 Optical Society of America

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  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  2. V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,"Soviet Physics USPEKI 10, 509-514 (1968).
    [CrossRef]
  3. W. E. Kock, Metallic delay lenses, Bell System Technical J. 27, 58 (1948).
  4. R. N. Bracewell, "Analogues of An Ionized Medium: Applications to the Ionosphere," Wireless Engineer (Iliff & Sons Ltd., London, 1954), p. 320-326.
  5. W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
    [CrossRef]
  6. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  7. J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  8. R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  9. D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).
    [CrossRef]
  10. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
    [CrossRef]
  11. 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 314977-980 (2006).
    [CrossRef] [PubMed]
  12. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
    [CrossRef] [PubMed]
  13. 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]
  14. 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]
  15. W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
    [CrossRef] [PubMed]
  16. W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
    [CrossRef]
  17. Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
    [CrossRef]
  18. W. J. Padilla, "Group theoretical description of artificial magnetic metamaterials utilized for negative index of refraction," http://xxx.lanl.gov/abs/cond-mat/0508307
  19. Here we only consider point groups and do not consider other symmetries, i.e. translations (lattice groups), screw axis and glide planes (space groups).
  20. For a review of the conditions of effective media applicable to metamaterials see ref. [17] and the references therein.
  21. R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
    [CrossRef]
  22. J. A. Kong, Electromagnetic Wave Theory (John Wiley & Sons, Inc., New York, 1990).
  23. S. F. A. Kettle, Symmetry and Structure (John Wiley & Sons, West Sussex, England, 1995).
  24. Daniel C.  Harris and Michael D. Bertolucci, Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy (Dover Publications Inc., Mineola, NY, 1989).
  25. Melvin Lax, Symmetry Principles in Solid State and Molecular Physics (Dover Publications Inc., Mineola, NY, 2001).
  26. N. Engheta, M. M. I. Saadun, "Novel pseudochiral or Ω medium and its application", Proc. Progr. Electromag. Res. Syms., PIERS 1991, Cambridge, MA, July 1991.
  27. Enantiomer in this sense is defined as "the exact opposite" meaning that the polarization mixing which results from one orientation of the split gap can be corrected by another SRR with the split gap oriented oppositely.
  28. 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]

2006

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[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 314977-980 (2006).
[CrossRef] [PubMed]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef] [PubMed]

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

2005

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

2004

D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).
[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]

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]

2002

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[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]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999

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

1968

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

1962

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
[CrossRef]

1948

W. E. Kock, Metallic delay lenses, Bell System Technical J. 27, 58 (1948).

Averitt, R. D.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

Basov, D. N.

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[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]

Chen, H.-T.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

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 314977-980 (2006).
[CrossRef] [PubMed]

Economou, E. N.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[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]

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]

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]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[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]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[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 314977-980 (2006).
[CrossRef] [PubMed]

Kafesaki, M.

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.

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]

Kock, W. E.

W. E. Kock, Metallic delay lenses, Bell System Technical J. 27, 58 (1948).

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.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[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]

Markos, P.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Marqués, R.

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Medina, F.

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[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 314977-980 (2006).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "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. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[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 314977-980 (2006).
[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]

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]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Robbins, D. J.

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

Rotman, W.

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, 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, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[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 314977-980 (2006).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[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 314977-980 (2006).
[CrossRef] [PubMed]

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (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. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).
[CrossRef]

R. A. Shelby, D. R. Smith, 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, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[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]

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 314977-980 (2006).
[CrossRef] [PubMed]

Taylor, A. J.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

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

Vier, D. C.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (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, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

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]

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]

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]

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]

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett.

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]

Bell System Technical J.

W. E. Kock, Metallic delay lenses, Bell System Technical J. 27, 58 (1948).

IEEE Trans. Microwave Theory Tech.

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

IRE Trans. Antennas Propag.

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
[CrossRef]

J. Opt. Soc. Am. B

Nature

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef] [PubMed]

Phys. Rev. B

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Phys. Rev. E

D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef] [PubMed]

Science

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]

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. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
[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 314977-980 (2006).
[CrossRef] [PubMed]

Soviet Physics USPEKI

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

Other

R. N. Bracewell, "Analogues of An Ionized Medium: Applications to the Ionosphere," Wireless Engineer (Iliff & Sons Ltd., London, 1954), p. 320-326.

W. J. Padilla, "Group theoretical description of artificial magnetic metamaterials utilized for negative index of refraction," http://xxx.lanl.gov/abs/cond-mat/0508307

Here we only consider point groups and do not consider other symmetries, i.e. translations (lattice groups), screw axis and glide planes (space groups).

For a review of the conditions of effective media applicable to metamaterials see ref. [17] and the references therein.

J. A. Kong, Electromagnetic Wave Theory (John Wiley & Sons, Inc., New York, 1990).

S. F. A. Kettle, Symmetry and Structure (John Wiley & Sons, West Sussex, England, 1995).

Daniel C.  Harris and Michael D. Bertolucci, Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy (Dover Publications Inc., Mineola, NY, 1989).

Melvin Lax, Symmetry Principles in Solid State and Molecular Physics (Dover Publications Inc., Mineola, NY, 2001).

N. Engheta, M. M. I. Saadun, "Novel pseudochiral or Ω medium and its application", Proc. Progr. Electromag. Res. Syms., PIERS 1991, Cambridge, MA, July 1991.

Enantiomer in this sense is defined as "the exact opposite" meaning that the polarization mixing which results from one orientation of the split gap can be corrected by another SRR with the split gap oriented oppositely.

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Figures (3)

Fig. 1.
Fig. 1.

Point group symmetries of the SRR particle. Panel (a) shows the coordinate system convention. Panel (b) shows the symmetry axis of the SRR and the C2 symmetry (rotation about the axis by 2π/n, n=2), and the electromagnetic basis (red arrows). Panels (c) and (d) demonstrate the mirror plane symmetries.

Fig. 2.
Fig. 2.

Basis utilized (red arrows in left column) for magnetic metamaterials used to calculate the EM modes (red arrows in the remaining columns). The remaining columns for each row show the SALCs and modes of the SRR particle, as determined by point group symmetries. For each column, the irrep is shown above and the corresponding component of the an external electromagnetic wave, or function is shown.

Fig. 3.
Fig. 3.

Predicted ideal planar and ideal 3D magnetic particles. In panel (a) we show a planar magnetic particle with D4h symmetry. The currents under the A2g magnetic mode are shown. Panel (b) shows a 3D isotropic magnetic particle with O h symmetry. The electric response of this particles is also isotropic, but importantly does not occur at the same frequency as the magnetic resonance.

Tables (3)

Tables Icon

Table 1. Character table for the C2v point group

Tables Icon

Table 2. Results summarizing the effect of each symmetry operation on the basis vectors

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Table 3. Character table for the D4h point group.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

[ D ¯ B ¯ ] = [ ε ̿ ξ ̿ ζ ̿ μ ̿ ] [ E ¯ H ¯ ]
a m = 1 h c n c χ ( g ) χ m ( g )
ϕ i = χ k g ( g ) i
ϕ ( A 1 ) ϕ ( A 2 ) ϕ ( B 1 ) ϕ ( B 2 ) = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . e 1 e 2 e 3 e 4 e 5 e 2 e 1 e 4 e 3 e 5 e 2 e 1 e 4 e 3 e 5 e 1 e 2 e 3 e 4 e 5
ϕ ( A 1 ) ϕ ( A 2 ) ϕ ( B 1 ) ϕ ( B 2 ) = 2 · e 1 + e 2 e 1 + e 2 e 3 e 4 e 3 e 4 0 0 0 0 0 0 0 0 0 0 0 e 1 e 2 e 2 e 1 e 3 + e 4 e 3 + e 4 2 e 5
ε = [ ε xx 0 ε xz 0 1 0 ε zx 0 ε zz ] ; μ = [ 1 0 0 0 μ yy 0 0 0 1 ]

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