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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 3 — Mar. 1, 2007
  • pp: 707–715

Existence and control of Shockley surface states of a one-dimensional defect chain in a photonic crystal

N. Malkova and C. Z. Ning  »View Author Affiliations

JOSA B, Vol. 24, Issue 3, pp. 707-715 (2007)

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We present detailed results of analytical and numerical investigation of the Shockley surface states in photonic crystals doped with a chain of alternating s- and p-type defects. Conditions for the existence and control of such surface states are studied using the empirical tight-binding model and verified by the finite-difference time-domain technique. We show for the first time, to our knowledge, that, in contrast to the case of solids, the Shockley states in photonic crystals with complete unit cells of defects do not appear simultaneously with the opening of the inverted bandgap between s and p bands. Rather, the width of the inverted bandgap must reach a critical value equal to the separation between the discrete levels. This results in a system size effect of the Shockley states in photonic crystals. We show how such system size effect can be used to control the surface states. We also demonstrate the control of the Shockley states by controlling the overlap of s and p bands, achieved through change in either the radius of one of the defects or the refractive index via electro-optical effects.

© 2007 Optical Society of America

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.7370) Optical devices : Waveguides
(240.6690) Optics at surfaces : Surface waves

ToC Category:
Photonic Crystals

Original Manuscript: September 6, 2006
Revised Manuscript: November 3, 2006
Manuscript Accepted: November 6, 2006
Published: February 15, 2007

N. Malkova and C. Z. Ning, "Existence and control of Shockley surface states of a one-dimensional defect chain in a photonic crystal," J. Opt. Soc. Am. B 24, 707-715 (2007)

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  1. P. Yeh, A. Yariv, and C.-S. Hong, "Electromagnetic propagation in periodic media. I. General theory," J. Opt. Soc. Am. 67, 423-438 (1977). [CrossRef]
  2. P. Yeh and A. Yariv, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104-105 (1978). [CrossRef]
  3. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961-10964 (1991). [CrossRef]
  4. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 18, 528-530 (1993). [CrossRef] [PubMed]
  5. J. M. Elson and P. Tran, "Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal," Phys. Rev. B 54, 1711-1715 (1996). [CrossRef]
  6. F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112-15120 (1999). [CrossRef]
  7. Y. A. Vlasov, N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett. 29, 2175-2177 (2004). [CrossRef] [PubMed]
  8. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004). [CrossRef] [PubMed]
  9. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402(R) (2004). [CrossRef]
  10. A. Many, Y. Goldstein, and N. B. Grover, Semiconductor Surfaces (North-Holland, 1965).
  11. S. G. Davison and M. Stesliska, Basic Theory of Surface States (Oxford U. Press, 1992).
  12. I. E. Tamm, "On the possible bound states of electrons on a crystal surface," Phys. Z. Sowjetunion 1, 733-735 (1932).
  13. W. Shockley, "On surface states associated with a periodic potential," Phys. Rev. 56, 317-323 (1939). [CrossRef]
  14. N. Malkova and C. Z. Ning, "Shockley and Tamm surface states in photonic crystals," Phys. Rev. B 73, 113113 (2006). [CrossRef]
  15. N. Malkova and C. Z. Ning, "Tamm surface states in a finite chain of defects in a photonic crystal," J. Phys. Condens. Matter (to be published).
  16. E. Lidorokis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998). [CrossRef]
  17. A. L. Reynolds, U. Peschel, F. Lederer, P. J. Robertson, T. F. Krauss, and P. J. I. de Maagt, "Coupled defects in photonic crystals," IEEE Trans. Microwave Theory Tech. 49, 1860-1866 (2001). [CrossRef]
  18. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  19. N. Malkova, S. Kim, and V. Gopalan, "Jahn-Teller effect in two-dimensional photonic crystals," Phys. Rev. B 68, 045105 (2003). [CrossRef]

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