OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 26 — Dec. 20, 2010
  • pp: 27916–27929

Theory of negative refraction in periodic stratified metamaterials

Ivan D. Rukhlenko, Malin Premaratne, and Govind P. Agrawal  »View Author Affiliations


Optics Express, Vol. 18, Issue 26, pp. 27916-27929 (2010)
http://dx.doi.org/10.1364/OE.18.027916


View Full Text Article

Enhanced HTML    Acrobat PDF (1125 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a general theory of negative refraction in periodic stratified heterostructures with an arbitrary number of homogeneous, isotropic, nonmagnetic layers in a unit cell. With a 4×4-matrix technique, we derive analytic expressions for the normal modes of such a heterostructure slab, introduce the average refraction angles of the energy flow and wavevector for the TE- and TM-polarized plane waves falling obliquely on the slab, and derive expressions for the reflectivity and transmissivity of the whole slab. For a specific case, in which all layers in a unit cell are much thinner than the wavelength of light, we obtain approximate simple formulae for the effective refraction angles. Using the example of a semiconductor heterostructure slab with two layers in a unit cell, we demonstrate that ultrathin layers are preferable for metamaterial applications because they enable higher transmissivity within the frequency band of negative refraction. Our theory can be used to study the optical properties of any stratified metamaterial, irrespective of whether semiconductors or metals are employed for fabricating its various layers, because it includes absorption within each layer.

© 2010 Optical Society of America

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(310.6860) Thin films : Thin films, optical properties
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: November 19, 2010
Revised Manuscript: December 15, 2010
Manuscript Accepted: December 15, 2010
Published: December 17, 2010

Citation
Ivan D. Rukhlenko, Malin Premaratne, and Govind P. Agrawal, "Theory of negative refraction in periodic stratified metamaterials," Opt. Express 18, 27916-27929 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-26-27916


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. V. M. Shalaev, “Optical negative index metamaterials,” Nat. Photonics 1, 41–47 (2007). [CrossRef]
  2. V. A. Podolskiy, and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005). [CrossRef]
  3. J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004). [CrossRef] [PubMed]
  4. N. C. Panoiu, and R. M. Osgood, “Numerical investigation of negative refractive index metamaterials at infrared and optical frequencies,” Opt. Commun. 233, 331–337 (2003). [CrossRef]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]
  6. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef] [PubMed]
  7. A. Boltasseva, and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials (Amst.) 2, 1–17 (2008). [CrossRef]
  8. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224–227 (2007). [CrossRef]
  9. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef] [PubMed]
  10. 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]
  11. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004). [CrossRef] [PubMed]
  12. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53–55 (2007). [CrossRef]
  13. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006). [CrossRef] [PubMed]
  14. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Demonstration of metaldielectric negative-index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B 23, 434–438 (2006). [CrossRef]
  15. V. G. Veselago, L. Braginsky, V. Shklover, and Ch. Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 189–218 (2006).
  16. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2006). [CrossRef] [PubMed]
  17. T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: Going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006). [CrossRef]
  18. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005). [CrossRef] [PubMed]
  19. A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6, 946–950 (2007). [CrossRef]
  20. A. V. Kildishev, and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32, 3432–3434 (2007). [CrossRef] [PubMed]
  21. E. E. Narimanov, and V. M. Shalaev, “Optics: Beyond diffraction,” Nature 447, 266–267 (2007). [CrossRef] [PubMed]
  22. W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72, 193101 (2005). [CrossRef]
  23. J. B. Pendry, “Negative refraction makes a perfect lense,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]
  24. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
  25. U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: Double negative at 813 nm and single negative at 772 nm,” Opt. Lett. 32, 1671–1673 (2007). [CrossRef] [PubMed]
  26. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13, 4922–4930 (2005). [CrossRef] [PubMed]
  27. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, “Terahertz response of a microfabricated rodsplit-ringresonator electromagnetic metamaterial,” Phys. Rev. Lett. 94, 063901 (2005). [CrossRef] [PubMed]
  28. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004). [CrossRef] [PubMed]
  29. V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. Cai, and V. M. Shalaev, “The Ag dielectric function in plasmonic metamaterials,” Opt. Express 16, 1186–1195 (2008). [CrossRef] [PubMed]
  30. H. K. Yuan, U. K. Chettiar, W. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007). [CrossRef] [PubMed]
  31. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. 94, 037402 (2005). [CrossRef] [PubMed]
  32. M. Born, and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  33. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1976). [CrossRef]
  34. D. W. Berreman, “Optics in stratified and anisotropic media: 4×4-matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972). [CrossRef]
  35. V. M. Shalaev, Nonlinear Optics of Random Media: Fractal Composites and Metal-Dielectric Films (Springer, Berlin, 2000).
  36. D. W. Berreman, and T. J. Scheffer, “Order versus temperature in cholesteric liquid crystals from reflectance spectra,” Phys. Rev. A 5, 1397–1403 (1972). [CrossRef]
  37. D. W. Berreman, and T. J. Scheffer, “Bragg reflection of light from single-domain cholesteric liquid-crystal films,” Phys. Rev. Lett. 25, 577–581 (1970). [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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited