OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 14, Iss. 5 — May. 1, 1997
  • pp: 1066–1073

Transmission-line matrix modeling of superluminal electromagnetic-pulse tunneling through the forbidden gap in two-dimensional photonic band structures

W. M. Robertson  »View Author Affiliations

JOSA B, Vol. 14, Issue 5, pp. 1066-1073 (1997)

View Full Text Article

Acrobat PDF (284 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The transmission-line matrix (TLM) method is shown to be an effective technique for calculating the propagation of electromagnetic waves in dielectric arrays exhibiting photonic band gaps. The simulator is particularly valuable for modeling processes whose parameters of interest are intrinsically in the time domain. To illustrate the capabilities of the technique for such temporal problems, the tunneling of electromagnetic pulses through the forbidden gap of a two-dimensional dielectric array is simulated. As researchers have recently measured in one-dimensional systems, pulses tunnel with a group velocity that exceeds the speed of light in vacuum. The TLM simulations show directly that for this superluminal tunneling process the group velocity continues to be a valid descriptor of the peak of the pulse. Furthermore, the results show that once sufficient periodicity exists to create a forbidden gap the tunneling time is constant independent of the thickness of the photonic crystal through which tunneling occurs.

© 1997 Optical Society of America

W. M. Robertson, "Transmission-line matrix modeling of superluminal electromagnetic-pulse tunneling through the forbidden gap in two-dimensional photonic band structures," J. Opt. Soc. Am. B 14, 1066-1073 (1997)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2063 (1987).
  2. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonics bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
  3. S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
  4. G. Kurizki and A. Z. Genack, “Suppression of molecular interactions in periodic dielectric structures,” Phys. Rev. Lett. 61, 2269–2271 (1988).
  5. K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
  6. Ze Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
  7. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
  8. J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
  9. A. M. Steinberg, P. G. Kwait, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
  10. Ch. Spielmann, R. Szipocs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
  11. A. Sommerfeld, “Uber die Fortpflanzung des Lichtes in Dispergierenden Medien,” Ann. Physik 44, 177–201 (1914).
  12. A. Sommerfeld, “Ein einwand gegen die Relativtheorie der Elektrodynamik und seine Beseitigung,” Physik Z. 8, 841–860 (1907).
  13. L. Brillouin, “Uber die Fortpflanzung des Lichtes in Dispergierenden Medien,” Ann. Physik 44, 203–240 (1914).
  14. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960), pp. 17–42.
  15. C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
  16. M. D. Crisp, “Concept of group velocity in resonant pulse propagation,” Phys. Rev. A 4, 2104–2108 (1971).
  17. S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982). See also A. Katz and R. R. Alfano, “Comment, pulse propagation in an absorbing medium,” Phys. Rev. Lett. 49, 1292 (1982); and “Reply,” S. Chu and S. Wong, Phys. Rev. Lett. PRLTAO 49, 1293 (1982).
  18. E. L. Bolda, R. Y. Chiao, and J. C. Garrison, “Two theorems for the group velocity in dispersive media,” Phys. Rev. A 48, 3890–3894 (1993).
  19. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 302.
  20. J. Brown, “Faster than the speed of light,” New Scientist, April 1995, pp. 26–30.
  21. W. J. R. Hoefer and P. P. M. So, The Electromagnetic Wave Simulator (Wiley, New York, 1991). This book comes with a PC version of the TLM simulator suitable for exploring many of the features detailed in this paper.
  22. W. J. R. Hoefer, “The Transmission Line Matrix (TLM) Method,” in Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, T. Itoh, ed. (Wiley, New York, 1989), pp. 496–591.
  23. S. M. Moniri-Ardakani and E. N. Glytsis, “Application of the transmission line matrix method to the analysis of slab and channel optical waveguides,” Appl. Opt. 34, 2704–2711 (1995).
  24. S. A. Boothroyd, L. Chan, and W. M. Robertson, “Visualizing coherent light with an electromagnetic wave simulator,” IEEE Trans. Educ. 39, 29–39 (1996).
  25. W. M. Robertson, S. A. Boothroyd, and L. Chan, “Photonic band structure calculations using a two-dimensional electromagnetic simulator,” J. Mod. Opt. 41, 285–293 (1994).
  26. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in two-dimensional dielectric arrays,” Phys. Rev. Lett. 68, 2023–2026 (1992).
  27. M. Scalora, J. P. Dowling, A. S. Manka, C. M. Bowden, and J. W. Haus, “Pulse propagation near highly reflective surfaces: application to photonic band-gap structures and the question of superluminal tunneling times,” Phys. Rev. A 52, 726–734 (1995).
  28. G. Arjavalingam, Y. Pastol, J.-M. Halbout, and G. V. Kopcsay, “Broad-band microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans. Microwave Theory Tech. 38, 615–621 (1990).
  29. E. R. Brown and O. B. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystals,” Appl. Phys. Lett. 67, 2138–2140 (1995).

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