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Transmission delay times of localized waves

H. Schomerus

  • Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
  • Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany

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Phys. Rev. E 64, 026606 – Published 18 July, 2001

DOI: https://doi.org/10.1103/PhysRevE.64.026606

Abstract

We investigate the effects of wave localization on the delay time τ (frequency sensitivity of the scattering phase shift) of a wave transmitted through a disordered waveguide. Localization results in a separation τ=χ+χ′ of the delay time into two independent but equivalent contributions, associated to the left and right end of the waveguide. For N=1 propagating modes, χ and χ′ are identical to half the reflection delay time of each end of the waveguide. In this case the distribution function P(τ) in an ensemble of random disorder can be obtained analytically. For N>1 propagating modes the distribution function can be approximated by a simple heuristic modification of the single-channel problem. We find a strong correlation between channels with long reflection delay times and the dominant transmission channel.

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References (36)

  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  2. P. Sheng, Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).
  3. R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994).
  4. S. John, Phys. Today 44(5), 32 (1991).
  5. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  6. B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993).
  7. C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
  8. N. Garcia and A. Z. Genack, Phys. Rev. Lett. 66, 1850 (1991).
  9. A. Z. Genack and N. Garcia, Phys. Rev. Lett. 66, 2064 (1991).
  10. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature (London) 390, 671 (1997).
  11. F. Scheffold, R. Lenke, R. Tweer, and G. Maret, Nature (London) 398, 206 (1999).
  12. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature (London) 404, 850 (2000).
  13. E. P. Wigner, Phys. Rev. 98, 145 (1955).
  14. F. T. Smith, Phys. Rev. 118, 349 (1960).
  15. Y. V. Fyodorov and H.-J. Sommers, J. Math. Phys. 38, 1918 (1997).
  16. A. Z. Genack, P. Sebbah, M. Stoytchev, and B. A. van Tiggelen, Phys. Rev. Lett. 82, 715 (1999).
  17. A. Lagendijk, J. Gómez Rivas, A. Imhof, F. J. P. Schuurmans, and R. Sprik, in Photonic Crystals and Light Localization in the 21st Century, Vol. 563 of NATO Science Series, edited by C. M. Soukoulis (Kluwer, Dordrecht, 2001).
  18. B. A. van Tiggelen, P. Sebbah, M. Stoytchev, and A. Z. Genack, Phys. Rev. E 59, 7166 (1999).
  19. A. M. Jayannavar, G. V. Vijayagovindan, and N. Kumar, Z. Phys. B: Condens. Matter 75, 77 (1989).
  20. J. Heinrichs, J. Phys.: Condens. Matter 2, 1559 (1990).
  21. A. Comtet and C. Texier, J. Phys. A 30, 8017 (1997).
  22. C. Texier and A. Comtet, Phys. Rev. Lett. 82, 4220 (1999).
  23. C. W. J. Beenakker and P. W. Brouwer, Physica E (Amsterdam) 9, 463 (2001).
  24. H. Schomerus, K. J. H. van Bemmel, and C. W. J. Beenakker, Europhys. Lett. 52, 518 (2000).
  25. H. Schomerus, K. J. H. van Bemmel, and C. W. J. Beenakker, Phys. Rev. E 63, 026605 (2001).
  26. C. W. J. Beenakker, e-print cond-mat/0009061v2.
  27. C. J. Bolton-Heaton, C. J. Lambert, V. I. Fal’ko, V. Progodin, and A. J. Epstein, Phys. Rev. B 60, 10 569 (1999).
  28. A. D. Mirlin, Phys. Rep. 326, 259 (2000).
  29. P. A. Mello and A. D. Stone, Phys. Rev. B 44, 3559 (1991).
  30. A. Edelman, Linear Algebr. Appl. 159, 55 (1991).
  31. B. White, P. Sheng, Z. Q. Zhang, and G. Papanicolaou, Phys. Rev. Lett. 59, 1918 (1987).
  32. M. Titov and C. W. J. Beenakker, Phys. Rev. Lett. 85, 3388 (2000).
  33. O. N. Dorokhov, Pis’ma Zh. Éksp. Teor. Fiz. 36, 259 (1982) [JETP Lett. 36, 318 (1982)].
  34. P. A. Mello, P. Pereyra, and N. Kumar, Ann. Phys. (N.Y.) 181, 290 (1988).
  35. C. W. J. Beenakker, J. C. J. Paasschens, and P. W. Brouwer, Phys. Rev. Lett. 76, 1368 (1996).
  36. P. W. Brouwer, Phys. Rev. B 57, 10 526 (1998).

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Phys. Rev. E 64, 026606– Published 18 July, 2001
  • Received 5 March 2001

© 2001 American Physical Society

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