OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 4 — Feb. 19, 2007
  • pp: 1639–1646

Group theoretical description of artificial electromagnetic metamaterials

Willie J. Padilla  »View Author Affiliations

Optics Express, Vol. 15, Issue 4, pp. 1639-1646 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (222 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(160.2100) Materials : Electro-optical materials
(160.3820) Materials : Magneto-optical materials
(160.4760) Materials : Optical properties

ToC Category:

Original Manuscript: December 4, 2006
Revised Manuscript: February 1, 2007
Manuscript Accepted: February 6, 2007
Published: February 19, 2007

Willie J. Padilla, "Group theoretical description of artificial electromagnetic metamaterials," Opt. Express 15, 1639-1646 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1. Fig. 2. Fig. 3.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited