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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 3 — Mar. 1, 2000
  • pp: 401–406

Complex traversal time for optical pulse transmission in a Fabry–Perot cavity

Jae Yong Lee, Hai-Woong Lee, and Jae Won Hahn  »View Author Affiliations

JOSA B, Vol. 17, Issue 3, pp. 401-406 (2000)

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We show that the physical clock approach can be applied to the problem of optical pulse transmission in the Fabry–Perot cavity. Our theoretical analysis leads directly to a complex-valued traversal time for the pulse. Real and imaginary parts of the traversal time, referred to as the phase time and the loss time, are associated, respectively, with the rotation angle of polarization and the change in the polarization ellipticity of the outgoing pulse in the presence of a magnetic clock. The physical significance of the phase time and the loss time is discussed in relation to the superluminal group velocity and the spectral shift of the pulse.

© 2000 Optical Society of America

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.7000) Instrumentation, measurement, and metrology : Transmission

Jae Yong Lee, Hai-Woong Lee, and Jae Won Hahn, "Complex traversal time for optical pulse transmission in a Fabry–Perot cavity," J. Opt. Soc. Am. B 17, 401-406 (2000)

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  1. E. H. Hauge and J. A. Støvneng, “Tunneling times: a critical review,” Rev. Mod. Phys. 61, 917–936 (1989).
  2. R. Landauer and Th. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–228 (1994).
  3. M. Büttiker and R. Landauer, “Traversal time for tunneling,” Phys. Rev. Lett. 49, 1739–1742 (1982).
  4. A. I. Baz’, “Life-time of intermediate states,” Yad. Fiz. 4, 252–260 (1966).
  5. M. Büttiker, “Larmor precession and the traversal time for tunneling,” Phys. Rev. B 27, 6178–6188 (1983).
  6. V. Gasparian, M. Ortuño, J. Ruiz, and E. Cuevas, “Faraday rotation and complex-valued traversal time for classical light waves,” Phys. Rev. Lett. 75, 2312–2315 (1995).
  7. M. Deutsch and J. E. Golub, “Optical Larmor clock: measurement of the photonic tunneling time,” Phys. Rev. A 53, 434–439 (1996).
  8. Ph. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
  9. E. Pollak and W. H. Miller, “New physical interpretation for time in scattering theory,” Phys. Rev. Lett. 53, 115–118 (1984).
  10. D. Sokolovski and L. M. Baskin, “Traversal time in quantum scattering,” Phys. Rev. A 36, 4604–4611 (1987).
  11. K. L. Jensen and F. A. Buot, “Numerical calculation of particle trajectories and tunneling times for resonant tunneling barrier structures,” Appl. Phys. Lett. 55, 669–671 (1989).
  12. J. G. Muga, S. Brouard, and R. Sala, “Transmission and reflection tunneling times,” Phys. Lett. A 167, 24–28 (1992).
  13. K. L. Jensen and F. A. Buot, “The methodology of simulating particle trajectories through tunneling structures using a Wigner distribution approach,” IEEE Trans. Electron Devices 38, 2337–2347 (1991).
  14. A. Enders and G. Nimtz, “Photonic-tunneling experiments,” Phys. Rev. B 47, 9605–9609 (1993).
  15. R. Pelster, V. Gasparian, and G. Nimtz, “Propagation of plane waves and of waveguide modes in quasiperiodic dielectric heterostructures,” Phys. Rev. E 55, 7645–7655 (1997).
  16. Ch. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
  17. A. M. Steinberg and R. Y. Chiao, “Subfemtosecond determination of transmission delay times for a dielectric mirror (photonic band gap) as a function of the angle of incidence,” Phys. Rev. A 51, 3525–3528 (1995).
  18. 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).
  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).
  20. Th. Martin and R. Landauer, “Time delay of evanescent electromagnetic waves and the analogy to particle tunneling,” Phys. Rev. A 45, 2611–2617 (1992).
  21. A. M. Steinberg and R. Y. Chiao, “Tunneling delay times in one and two dimensions,” Phys. Rev. A 49, 3283–3295 (1994).
  22. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1986).
  23. E. P. Wigner, “Lower limit for the energy derivative of the scattering phase shift,” Phys. Rev. 98, 145–147 (1955).
  24. T. E. Hartman, “Tunneling of a wave packet,” J. Appl. Phys. 33, 3427–3433 (1962).
  25. G. Diener, “Superluminal group velocities and information transfer,” Phys. Lett. A 223, 327–331 (1996).
  26. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
  27. 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).
  28. S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
  29. R. Y. Chiao and J. Boyce, “Superluminality, paraelectricity, and Earnshaw’s theorem in media with inverted populations,” Phys. Rev. Lett. 73, 3383–3386 (1994).
  30. E. L. Bolda, “Theory and simulation of superluminal optical pulses in gain media,” Phys. Rev. A 54, 3514–3518 (1996).
  31. D. Mugnai, A. Ranfagni, and L. S. Schuman, “Delay time measurements in a diffraction experiment: a case of optical tunneling,” Phys. Rev. E 55, 3593–3597 (1977).
  32. R. Y. Chiao, “Atomic coherence effects which produce superluminal (but causal) propagation of wavepackets,” Quantum Opt. 6, 359–369 (1994).

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