OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 16514–16527

Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials

Ruey-Lin Chern  »View Author Affiliations

Optics Express, Vol. 21, Issue 14, pp. 16514-16527 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (11228 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The feature of spatial dispersion in periodic layered metamaterials is theoretically investigated. An effective medium model is proposed to derive the nonlocal effective permittivity tensor, which exhibits drastic variations in the wave vector domain. Strong spatial dispersion is found in the frequency range where surface plasmon polaritons are excited. In particular, the nonlocal effect gives rise to additional waves that are identified as the bonding or antibonding modes with symmetric or antisymmetric surface charge alignments. Spatial dispersion is also manifest on the parabolic-like dispersion, a non-standard type of dispersion in the medium. The associated negative refraction and backward wave occur even when the effective permittivity components are all positive, which is considered a property not available in the local medium.

© 2013 OSA

OCIS Codes
(230.4170) Optical devices : Multilayers
(240.6680) Optics at surfaces : Surface plasmons
(260.2065) Physical optics : Effective medium theory

ToC Category:

Original Manuscript: April 30, 2013
Revised Manuscript: June 26, 2013
Manuscript Accepted: June 26, 2013
Published: July 2, 2013

Ruey-Lin Chern, "Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials," Opt. Express 21, 16514-16527 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. J. Hopfield and D. G. Thomas, “Theoretical and experimental effects of spatial dispersion on the optical properties of crystals,” Phys. Rev.132, 563–572 (1963). [CrossRef]
  2. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevski, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenan, 1984).
  3. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons (Springer-Verlag, 1984). [CrossRef]
  4. J. J. Hopfield, “Theory of the contribution of excitons to the complex dielectric constant of crystals,” Phys. Rev.112, 1555–1567 (1958). [CrossRef]
  5. S. I. Pekar, “Theory of electromagnetic waves in a crystal with excitons,” J. Phys. Chem. Solids5, 11–22 (1958). [CrossRef]
  6. R. Ruppin, “Reflectivity of a nonlocal dielectric with an excitonic surface potential,” Phys. Rev. B29, 2232–2237 (1984). [CrossRef]
  7. B. Chen and D. F. Nelson, “Wave propagation of exciton polaritons by a wave-vector-space method,” Phys. Rev. B48, 15372–15389 (1993). [CrossRef]
  8. G. E. H. Reuter and E. H. Sondheimer, “The theory of the anomalous skin effect in metals,” Proc. R. Soc. A-Math. Phys. Eng. Sci.195, 336–364 (1948). [CrossRef]
  9. K. L. Kliewer and R. Fuchs, “Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence,” Phys. Rev.172, 607–624 (1968). [CrossRef]
  10. R. Ruppin, “Optical properties of a spatially dispersive cylinder,” J. Opt. Soc. Am. B6, 1559–1563 (1989). [CrossRef]
  11. R. Ruppin, “Extinction properties of thin metallic nanowires,” Opt. Comm.190, 205–209 (2001). [CrossRef]
  12. A. A. Maradudin and D. L. Mills, “Effect of spatial dispersion on the properties of a semi-infinite dielectric,” Phys. Rev. B7, 2787–2810 (1973). [CrossRef]
  13. A. R. Melnyk and M. J. Harrison, “Resonant excitation of plasmons in thin films by elecromagnetic waves,” Phys. Rev. Lett.21, 85–88 (1968). [CrossRef]
  14. W. E. Jones, K. L. Kliewer, and R. Fuchs, “Nonlocal theory of the optical properties of thin metallic films,” Phys. Rev.178, 1201–1203 (1969). [CrossRef]
  15. A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B2, 835–850 (1970). [CrossRef]
  16. R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B11, 2871–2876 (1975). [CrossRef]
  17. V. Yannopapas, “Non-local optical response of two-dimensional arrays of metallic nanoparticles,” J. Phys.-Condes. Matter20, 325211 (2008). [CrossRef]
  18. R. J. Pollard, A. Murphy, W. R. Hendren, P. R. Evans, R. Atkinson, G. A. Wurtz, A. V. Zayats, and V. A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett.102, 127405 (2009). [CrossRef] [PubMed]
  19. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett.103, 097403 (2009). [CrossRef] [PubMed]
  20. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Optical properties of nanowire dimers with a spatially nonlocal dielectric function,” Nano Lett.10, 3473–3481 (2010). [CrossRef] [PubMed]
  21. S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412 (2011). [CrossRef]
  22. B. Gompf, J. Braun, T. Weiss, H. Giessen, M. Dressel, and U. Hubner, “Periodic nanostructures: spatial dispersion mimics chirality,” Phys. Rev. Lett.106, 185501 (2011). [CrossRef] [PubMed]
  23. S. I. Pekar and O. D. Kocherga, Crystal Optics and Additional Light Waves (Benjamin/Cummings, 1983).
  24. A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B84, 045424 (2011). [CrossRef]
  25. M. F. Bishop and A. A. Maradudin, “Energy flow in a semi-infinite spatially dispersive absorbing dielectric,” Phys. Rev. B14, 3384–3393 (1976). [CrossRef]
  26. D. F. Nelson, “Generalizing the Poynting vector,” Phys. Rev. Lett.76, 4713–4716 (1996). [CrossRef] [PubMed]
  27. M. A. Vladimir and N. G. Yu, “Spatial dispersion and negative refraction of light,” Phys. Usp.49, 1029 (2006). [CrossRef]
  28. P. A. Belov, R. Marques, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B67, 113103 (2003). [CrossRef]
  29. C. R. Simovski and P. A. Belov, “Low-frequency spatial dispersion in wire media,” Phys. Rev. E70, 046616 (2004). [CrossRef]
  30. F. J. Garcia de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C112, 17983–17987 (2008). [CrossRef]
  31. L. Brillouin, Wave Propagation in Periodic Structures (Dover, 1953).
  32. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett.90, 191109 (2007). [CrossRef]
  33. A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B84, 115438 (2011). [CrossRef]
  34. A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B86, 115420 (2012). [CrossRef]
  35. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B74, 115116 (2006). [CrossRef]
  36. A. Fang, T. Koschny, and C. M. Soukoulis, “Optical anisotropic metamaterials: Negative refraction and focusing,” Phys. Rev. B79, 245127 (2009). [CrossRef]
  37. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett.97, 073901 (2006). [CrossRef] [PubMed]
  38. E. Verhagen, R. de Waele, L. Kuipers, and A. Polman, “Three-dimensional negative index of refraction at optical frequencies by coupling plasmonic waveguides,” Phys. Rev. Lett.105, 223901 (2010). [CrossRef]
  39. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev.182, 539–554 (1969). [CrossRef]
  40. P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microw. Opt. Technol. Lett.37, 259–263 (2003). [CrossRef]
  41. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London203, 385 (1904). [CrossRef]
  42. R. M. Hornreich and S. Shtrikman, “Theory of gyrotropic birefringence,” Phys. Rev.171, 1065–1074 (1968). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited