OSA's Digital Library

Optics Express

Optics Express

  • Editor: Micha
  • Vol. 13, Iss. 23 — Nov. 14, 2005
  • pp: 9299–9309

2D metamaterials with hexagonal structure: spatial resonances and near field imaging

O. Zhuromskyy, E. Shamonina, and L. Solymar  »View Author Affiliations


Optics Express, Vol. 13, Issue 23, pp. 9299-9309 (2005)
http://dx.doi.org/10.1364/OPEX.13.009299


View Full Text Article

Enhanced HTML    Acrobat PDF (1751 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The current and field distribution in a 2D metamaterial consisting of resonant elements in a hexagonal arrangement are found assuming magnetic interaction between the elements. The dispersion equation of magnetoinductive (MI) waves is derived with the aid of the direct and reciprocal lattice familiar from solid state theory. A continuous model for the current variation in the elements is introduced leading to the familiar wave equation in the form of a second order differential equation. The current distributions are shown to exhibit a series of spatial resonances for rectangular, circular and hexagonal boundaries. The axial and radial components of the resulting magnetic field are compared with previously obtained experimental results on a Swiss Roll metamaterial with hexagonal boundaries. Experimental and theoretical results are also compared for the near field image of an object in the shape of the letter M followed by a more general discussion of imaging. It is concluded that a theoretical formulation based on the propagation of MI waves can correctly describe the experimental results.

© 2005 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(160.1190) Materials : Anisotropic optical materials
(260.0260) Physical optics : Physical optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Research Papers

History
Original Manuscript: August 25, 2005
Revised Manuscript: November 1, 2005
Published: November 14, 2005

Citation
O. Zhuromskyy, E. Shamonina, and L. Solymar, "2D metamaterials with hexagonal structure: spatial resonances and near field imaging," Opt. Express 13, 9299-9309 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9299


Sort:  Journal  |  Reset  

References

  1. R. E. Collin, Field Theory of Guided Waves (Oxford University Press, Oxford, 1991).
  2. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  3. S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  4. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, �??Magnetism from conductors and enhanced nonlinear phenomena,�?? IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999). [CrossRef]
  5. J. B. Pendry, �??Negative refraction makes a perfect lens,�?? Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  6. D. O. S. Melville and R. J. Blaikie,�?? Super-resolution imaging through a planar silver layer,�?? Opt. Express 13, 2127-2134 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2127.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2127</a> [CrossRef] [PubMed]
  7. N. Fang, H. Lee, C. Sun, and X. Zhang, �??Sub-diffraction-limited optical imaging with a silver superlens,�?? Science 308, 534-537 (2005). [CrossRef] [PubMed]
  8. 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]
  9. M. C. K. Wiltshire, J. V. Hajnal, J. B. Pendry, D. J. Edwards, and C. J. Stevens, �??Metamaterial endoscope for magnetic field transfer: near field imaging with magnetic wires,�?? Opt. Express 11, 709-715 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-709.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-709</a> [CrossRef] [PubMed]
  10. M. J. Freire and R. Marques, �??Planar magnetoinductive lens for three-dimensional subwavelength imaging,�?? Appl. Phys. Lett. 86, 182505-1-3 (2005). [CrossRef]
  11. E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, �??Magneto-inductive waveguide,�?? Electron. Lett. 38, 371-373 (2002). [CrossRef]
  12. E. Shamonina, V.A. Kalinin, K. H. Ringhofer, and L. Solymar, �??Magnetoinductive waves in one, two, and three dimensions,�?? J. Appl. Phys. 92: 6252-6261 (2002). [CrossRef]
  13. M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, �??Dispersion characteristics of magnetoinductive waves: comparison between theory and experiment,�?? Electron. Lett. 39, 215-217 (2003). [CrossRef]
  14. M. C. K. Wiltshire, E. Shamonina, I. R. Young, and L. Solymar, �??Experimental and theoretical study of magneto-inductive waves supported by one-dimensional arrays of �??swiss rolls�??,�?? J. Appl. Phys. 95, 4488-4493 (2004). [CrossRef]
  15. R. Marques, F. Mesa , J. Martel, and F. Medina,�?? Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design - Theory and experiments,�?? IEEE Trans. Antennas Prop. 51, 2572-2581 (2003). [CrossRef]
  16. J. D. Baena, R. Marques, F. Medina, and J. Martel, �??Artificial magnetic metamaterial design by using spiral resonators,�?? Phys. Rev. B 69, 014402-1-5 (2004). [CrossRef]
  17. M. Shamonin, E. Shamonina, V. Kalinin, and L. Solymar, �??Properties of a metamaterial element: analytical solutions and numerical simulations for a singly split double ring,�?? J. Appl. Phys. 95, 3778-3784 (2004). [CrossRef]
  18. F. W. Grover, Inductance Calculations: Working Formulas and Tables (Instrument Society of America, Research Triangle Park, N.C., 1981).
  19. M. C. K. Wiltshire, J. V. Hajnal, J. B. Pendry, and D. J. Edwards, �??RF field transmission through Swiss Rolls �?? an anisotropic magnetic metamaterial,�?? in Proceedings of the 27th ESA Antenna Technology Workshop on Innovative Periodic Antennas: Electromagnetic Bandgap, Left-handed Materials, Fractal and Frequency Selective Surfaces, Santiago de Compostela, Spain, 9-11 March, 2004.
  20. D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, �??Partial focusing of radiation by a slab of indefinite media,�?? Appl. Phys. Lett. 84, 2244-2246 (2004). [CrossRef]
  21. S. Maslovski, S. Tretyakov, and P. Alitalo, �??Near-field enhancement and imaging in double planar polariton-resonant structures,�?? J. Appl. Phys. 96, 1293-1300 (2004). [CrossRef]
  22. I.-H. Lin, C. Caloz, and T. Itoh, �??Near-field focusing by a nonuniform leaky-wave interface,�?? Microw. Opt. Techn. Lett. 44, 416-418 (2005). [CrossRef]
  23. R. Zengerle, �??Light-propagation in singly and doubly periodic planar wave-guides,�?? J. Mod. Opt. 34, 1589-1617 (1987). [CrossRef]
  24. P. A. Belov, C. R. Simovski, and P. Ikonen, �??Canalization of subwavelength images by electromagnetic crystals,�?? Phys. Rev. 71, 193105-1-4 (2005). [CrossRef]
  25. 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]
  26. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, �??Magnetic response of metamaterials at 100 terahertz,�?? Science 306, 1351-1353 (2004). [CrossRef] [PubMed]

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.

Supplementary Material


» Media 1: AVI (2046 KB)     
» Media 2: AVI (2249 KB)     
» Media 3: AVI (2549 KB)     
» Media 4: AVI (2095 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited