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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 28, Iss. 10 — Oct. 1, 2011
  • pp: 2537–2542

Tunneling time of an optical pulse in a photonic bandgap

Rihei Endo and Riichiro Saito  »View Author Affiliations


JOSA B, Vol. 28, Issue 10, pp. 2537-2542 (2011)
http://dx.doi.org/10.1364/JOSAB.28.002537


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Abstract

Tunneling time (or group delay) for an optical pulse to transmit the energy through a photonic bandgap is calculated analytically for a one-dimensional multilayered optical superlattice. The analytical solution shows that the calculated tunneling time converges to a finite value with increasing numbers of layers, and we have derived the formula for the converged value of the tunneling time. This effect is similar to the so-called Hartman effect in a quantum system. Because of the destructive interference of multireflected light in the superlattice, the tunneling time is determined by an exponentially decaying evanescent wave, which is the reason for this effect.

© 2011 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

ToC Category:
Thin Films

History
Original Manuscript: May 31, 2011
Revised Manuscript: July 5, 2011
Manuscript Accepted: July 14, 2011
Published: September 29, 2011

Citation
Rihei Endo and Riichiro Saito, "Tunneling time of an optical pulse in a photonic bandgap," J. Opt. Soc. Am. B 28, 2537-2542 (2011)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-10-2537


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References

  1. L. A. MacColl, “Note on the transmission and reflection of wave packets by potential barriers,” Phys. Rev. 40, 621–626 (1932). [CrossRef]
  2. T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33, 3427–3433 (1962). [CrossRef]
  3. E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955). [CrossRef]
  4. V. S. Olkhovsky and E. Recami, “Recent developments in the time analysis of tunneling processes,” Phys. Rep. 214, 339–356 (1992). [CrossRef]
  5. H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: a proposed resolution of an old paradox,” Phys. Rep. 436, 1–69 (2006). [CrossRef]
  6. A. Ranfagni, D. Mugnai, P. Fabeni, and G. P. Pazzi, “Delay-time measurements in narrowed waveguides as a test of tunneling,” Appl. Phys. Lett. 58, 774–776 (1991). [CrossRef]
  7. L. Ragni, “Group delay of evanescent signals in a waveguide with barrier,” Phys. Rev. E 79, 046609 (2009). [CrossRef]
  8. Ph. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997). [CrossRef]
  9. D. Mugnai, A. Ranfagni, and L. Ronchi, “The question of tunneling time duration: a new experimental test at microwave scale,” Phys. Lett. A 247, 281–286 (1998). [CrossRef]
  10. J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett. 84, 1431–1434 (2000). [CrossRef] [PubMed]
  11. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711(1993). [CrossRef] [PubMed]
  12. Ch. Spielmann, R. Szipoc¨s, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994). [CrossRef] [PubMed]
  13. M. Mojahedi, E. Schamiloglu, F. Hegeler, and K. J. Malloy, “Time-domain detection of superluminal group velocity for single microwave pulses,” Phys. Rev. E 62, 5758–5766(2000). [CrossRef]
  14. S. Longhi, M. Marano, and P. Laporta, “Superluminal optical pulse propagation at 1.5 μm in periodic fiber Bragg gratings,” Phys. Rev. E 64, 055602 (2001). [CrossRef]
  15. A. Hache and L. Poirier, “Long-range superluminal pulse propagation in a coaxial photonic crystal,” Appl. Phys. Lett. 80, 518–520 (2002). [CrossRef]
  16. R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling: a proposed experiment to measure photon tunneling times,” Physica B 175, 257–262(1991). [CrossRef]
  17. Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992). [CrossRef] [PubMed]
  18. E. H. Hauge and J. A. Støvneng, “Tunneling times: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989). [CrossRef]
  19. V. Laude and P. 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). [CrossRef]
  20. P. Pereyra, “Closed formulas for tunneling time in superlattices,” Phys. Rev. Lett. 84, 1772–1775 (2000). [CrossRef] [PubMed]
  21. S. Esposito, “Universal photonic tunneling time,” Phys. Rev. E 64, 026609 (2001). [CrossRef]
  22. H. G. Winful, “The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities,” New J. Phys. 8, 101 (2006). [CrossRef]
  23. H. G. Winful, “Energy storage in superluminal barrier tunneling: origin of the Hartman effect,” Opt. Express 10, 1491–1496(2002). [PubMed]
  24. H. G. Winful, “Nature of ‘superluminal’ barrier tunneling,” Phys. Rev. Lett. 90, 023901 (2003). [CrossRef] [PubMed]
  25. P. Pereyra and H. P. Simanjuntak, “Time evolution of electromagnetic wave packets through superlattices: evidence for superluminal velocities,” Phys. Rev. E 75, 056604 (2007). [CrossRef]
  26. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics(Wiley, 1991). [CrossRef]
  27. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996). [CrossRef]

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