OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 21 — Oct. 16, 2006
  • pp: 9805–9814

Positive phase evolution of waves propagating along a photonic crystal with negative index of refraction

Alejandro Martínez and Javier Martí  »View Author Affiliations


Optics Express, Vol. 14, Issue 21, pp. 9805-9814 (2006)
http://dx.doi.org/10.1364/OE.14.009805


View Full Text Article

Enhanced HTML    Acrobat PDF (624 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We analyze propagation of electromagnetic waves in a photonic crystal at frequencies at which it behaves as an effective medium with a negative index in terms of refraction at its interface with free space. We show that the phase evolution along the propagation direction is positive, despite the fact that the photonic crystal displays negative refraction following Snell’s law, and explain it in terms of the Fourier components of the Bloch wave. Two distinct behaviors are found at frequencies far and close to the band edge of the negative-index photonic band. These findings contrast with the negative phase evolution that occurs in left-handed materials, so care has to be taken when applying the term left-handed to photonic crystals.

© 2006 Optical Society of America

OCIS Codes
(160.4760) Materials : Optical properties
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Metamaterials

History
Original Manuscript: June 15, 2006
Manuscript Accepted: July 18, 2006
Published: October 16, 2006

Citation
Alejandro Martínez and Javier Martí, "Positive phase evolution of waves propagating along a photonic crystal with negative index of refraction," Opt. Express 14, 9805-9814 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-21-9805


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
  3. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003);A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003). [CrossRef] [PubMed]
  4. A. Grbic and G. V. Eleftheriades, "Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens," Phys. Rev. Lett. 92, 117403 (2004). [CrossRef] [PubMed]
  5. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000). [CrossRef]
  6. S. Foteinopoulou and C. M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003). [CrossRef]
  7. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127401 (2004). [CrossRef] [PubMed]
  8. A. Martínez and J. Martí, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005). [CrossRef]
  9. A. Martínez, H. Míguez, J. Sánchez-Dehesa, and J. Martí, "Analysis of wave propagation in a two-dimensional photonic crystal with negative index of refraction: plane wave decomposition of the Bloch modes," Opt. Express 13, 4160-4174, (2005). [CrossRef] [PubMed]
  10. B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, "Fourier analysis of Bloch wave propagation in photonic crystals," J. Opt. Soc. Am. B 22, 1179-1190 (2005). [CrossRef]
  11. I. De Leon and F. S. Roux, "Fourier analysis of reflection and refraction in two-dimensional photonic crystals," Phys. Rev. B 71, 235105 (2005). [CrossRef]
  12. R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005). [CrossRef] [PubMed]
  13. S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165112 (2005). [CrossRef]
  14. In this article, calculations of photonic bands have been done with BandSolveTM, which implements the plane wave expansion method, and FDTD simulations with FullwaveTM, both by RSoft Design Group.
  15. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944-947 (2003). [CrossRef]
  16. P. F. Loschialpo, D. L. Smith, D. W. Forester, F. J. Rachford, and J. Schelleng, "Electromagnetic waves focused by a negative-index planar lens," Phys. Rev. E 67, 025602 (2003). [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