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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 16, Iss. 1 — Jan. 1, 1999
  • pp: 194–198

Superluminal asymptotic tunneling times through one-dimensional photonic bandgaps in quarter-wave-stack dielectric mirrors

Vincent Laude and Pierre Tournois  »View Author Affiliations

JOSA B, Vol. 16, Issue 1, pp. 194-198 (1999)

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It is shown that the time needed for light to pass through the optical barrier associated with an antiresonant quarter-wave-stack dielectric mirror, as measured by the group-delay, or phase time, asymptotically reaches a limit that is independent of the barrier thickness and hence of the number of layers. This limit, which scales as the inverse of the refractive-index difference between successive layers, is equal to the mean value of the asymptotic group delays needed for light to reflect off each side of the barrier. This superluminal transmission does not violate causality, as the transmitted intensity is always lower than the intensity that would have been transmitted in vacuum in the absence of the barrier.

© 1999 Optical Society of America

OCIS Codes
(310.0310) Thin films : Thin films
(310.6870) Thin films : Thin films, other properties
(320.2250) Ultrafast optics : Femtosecond phenomena

Vincent Laude and Pierre Tournois, "Superluminal asymptotic tunneling times through one-dimensional photonic bandgaps in quarter-wave-stack dielectric mirrors," J. Opt. Soc. Am. B 16, 194-198 (1999)

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  1. L. A. Mac Coll, Phys. Rev. 40, 621 (1932). [CrossRef]
  2. T. E. Hartman, J. Appl. Phys. 33, 3427 (1962). [CrossRef]
  3. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, Phys. Rev. Lett. 71, 708 (1993). [CrossRef] [PubMed]
  4. Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, Phys. Rev. Lett. 73, 2308 (1994). [CrossRef] [PubMed]
  5. M. Büttiker and R. Landauer, Phys. Rev. Lett. 49, 1739 (1982). [CrossRef]
  6. M. Büttiker, Phys. Rev. B 27, 6178 (1983). [CrossRef]
  7. R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, Physica B 175, 257 (1991). [CrossRef]
  8. B. Lee and W. Lee, J. Opt. Soc. Am. B 14, 777 (1997). [CrossRef]
  9. A. Enders and G. Nimtz, J. Phys. I (France) 3, 1089 (1993). [CrossRef]
  10. P. Tournois, IEEE J. Quantum Electron. 33, 519 (1997). [CrossRef]
  11. Wang Yun-ping and Zhang Dian-lin, Phys. Rev. A 52, 2597 (1995). [CrossRef] [PubMed]
  12. F. Abelès, Ann. Phys. (Paris) 5, 596 and 706 (1950).
  13. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  14. A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994). [CrossRef] [PubMed]
  15. A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 51, 3525 (1995). [CrossRef] [PubMed]
  16. E. H. Hauge and J. A. Støvneng, Rev. Mod. Phys. 61, 917 (1989). [CrossRef]
  17. R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994). [CrossRef]
  18. R. Y. Chiao and A. M. Steinberg, in Progress in Optics, E. Wolf, ed. (North Holland, Amsterdam, 1997), Vol. XXXVII, p. 347.
  19. G. Nimtz and W. Heitmann, Prog. Quantum Electron. 21, 81 (1997). [CrossRef]

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