Abstract

We report the observation of Lévy-like statistical configuration-to-configuration fluctuations in the intensity of emission from a novel system, the fiber-random amplifying medium, where active fiber segments are embedded randomly in a bulk of pointlike passive scatterers. Some rare configurations of fibers provide long, guided amplifying paths for the photons, leading to high jumps in the intensity, and thus to Lévy statistics. This system provides an optical realization of the Arrhenius cascade.

© 2006 Optical Society of America

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  1. D. Sharma, H. Ramachandran, and N. Kumar, Fluct. Noise Lett. 6, L95 (2006).
    [CrossRef]
  2. V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968).
  3. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
    [CrossRef]
  4. D. S. Wiersma and A. Lagendijk, Phys. Rev. E 54, 4256 (1996).
    [CrossRef]
  5. S. John and G. Pang, Phys. Rev. A 54, 3642 (1996).
    [CrossRef] [PubMed]
  6. B. R. Prasad, H. Ramachandran, A. K. Sood, C. K. Subramanian, and N. Kumar, Appl. Opt. 36, 7718 (1997).
    [CrossRef]
  7. See, e.g., P. A. Mello and N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford U. Press, 2004), for the idea of non-self-averaging.
  8. M.F.Shlesinger, G.M.Zaslavsky, and U.Frisch, eds., Lévy Flights and Related Topics in Physics, Vol. 450 of Lecture Notes in Physics (Springer-Verlag, 1995).
    [CrossRef]
  9. M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
    [CrossRef]
  10. A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
    [CrossRef] [PubMed]
  11. F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
    [CrossRef] [PubMed]
  12. T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
    [CrossRef] [PubMed]
  13. S. Boldyrev and C. R. GwinnPhys. Rev. Lett. 91, 131101 (2003).
    [CrossRef] [PubMed]
  14. F. Bardou, ''Cooling gases with Lévy fights: using the generalized central limit theorem in physics,'' v1, December 20, 2000.
  15. M. I. Tribelsky, ''Tails of probability density for sums of random independent variables,'' v2, June 25, 2001.
  16. C. Kittel, in Introduction to Solid State Physics (Wiley, 1996), pp. 141-172.
  17. Increasing pumping/gain implies reduced lg.
  18. I includes unamplified spontaneous emission Io, which must be subtracted.

2006 (1)

D. Sharma, H. Ramachandran, and N. Kumar, Fluct. Noise Lett. 6, L95 (2006).
[CrossRef]

2004 (1)

See, e.g., P. A. Mello and N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford U. Press, 2004), for the idea of non-self-averaging.

2003 (1)

S. Boldyrev and C. R. GwinnPhys. Rev. Lett. 91, 131101 (2003).
[CrossRef] [PubMed]

2001 (1)

M. I. Tribelsky, ''Tails of probability density for sums of random independent variables,'' v2, June 25, 2001.

2000 (1)

F. Bardou, ''Cooling gases with Lévy fights: using the generalized central limit theorem in physics,'' v1, December 20, 2000.

1997 (1)

1996 (3)

C. Kittel, in Introduction to Solid State Physics (Wiley, 1996), pp. 141-172.

D. S. Wiersma and A. Lagendijk, Phys. Rev. E 54, 4256 (1996).
[CrossRef]

S. John and G. Pang, Phys. Rev. A 54, 3642 (1996).
[CrossRef] [PubMed]

1995 (1)

M.F.Shlesinger, G.M.Zaslavsky, and U.Frisch, eds., Lévy Flights and Related Topics in Physics, Vol. 450 of Lecture Notes in Physics (Springer-Verlag, 1995).
[CrossRef]

1994 (2)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
[CrossRef]

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

1993 (2)

T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
[CrossRef] [PubMed]

M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
[CrossRef]

1990 (1)

A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
[CrossRef] [PubMed]

1968 (1)

V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968).

Aspect, A.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
[CrossRef]

Bardou, F.

F. Bardou, ''Cooling gases with Lévy fights: using the generalized central limit theorem in physics,'' v1, December 20, 2000.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

Boldyrev, S.

S. Boldyrev and C. R. GwinnPhys. Rev. Lett. 91, 131101 (2003).
[CrossRef] [PubMed]

Bouchaud, J. P.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

Emile, O.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
[CrossRef]

Gwinn, C. R.

S. Boldyrev and C. R. GwinnPhys. Rev. Lett. 91, 131101 (2003).
[CrossRef] [PubMed]

John, S.

S. John and G. Pang, Phys. Rev. A 54, 3642 (1996).
[CrossRef] [PubMed]

Kittel, C.

C. Kittel, in Introduction to Solid State Physics (Wiley, 1996), pp. 141-172.

Klafter, J.

M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
[CrossRef]

Kumar, N.

D. Sharma, H. Ramachandran, and N. Kumar, Fluct. Noise Lett. 6, L95 (2006).
[CrossRef]

See, e.g., P. A. Mello and N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford U. Press, 2004), for the idea of non-self-averaging.

B. R. Prasad, H. Ramachandran, A. K. Sood, C. K. Subramanian, and N. Kumar, Appl. Opt. 36, 7718 (1997).
[CrossRef]

Lagendijk, A.

D. S. Wiersma and A. Lagendijk, Phys. Rev. E 54, 4256 (1996).
[CrossRef]

Langevin, D.

A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
[CrossRef] [PubMed]

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
[CrossRef]

Letokhov, V. S.

V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968).

Mello, P. A.

See, e.g., P. A. Mello and N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford U. Press, 2004), for the idea of non-self-averaging.

Ott, A.

A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
[CrossRef] [PubMed]

Pang, G.

S. John and G. Pang, Phys. Rev. A 54, 3642 (1996).
[CrossRef] [PubMed]

Prasad, B. R.

Ramachandran, H.

Sharma, D.

D. Sharma, H. Ramachandran, and N. Kumar, Fluct. Noise Lett. 6, L95 (2006).
[CrossRef]

Shlesinger, M. F.

M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
[CrossRef]

Solomon, T. H.

T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
[CrossRef] [PubMed]

Sood, A. K.

Souvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
[CrossRef]

Subramanian, C. K.

Swinney, H. L.

T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
[CrossRef] [PubMed]

Tribelsky, M. I.

M. I. Tribelsky, ''Tails of probability density for sums of random independent variables,'' v2, June 25, 2001.

Urbach, W.

A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
[CrossRef] [PubMed]

Weeks, E. R.

T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
[CrossRef] [PubMed]

Wiersma, D. S.

D. S. Wiersma and A. Lagendijk, Phys. Rev. E 54, 4256 (1996).
[CrossRef]

Zaslavsky, G. M.

M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
[CrossRef]

Appl. Opt. (1)

Fluct. Noise Lett. (1)

D. Sharma, H. Ramachandran, and N. Kumar, Fluct. Noise Lett. 6, L95 (2006).
[CrossRef]

Nature (2)

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Souvain, Nature 368, 436 (1994).
[CrossRef]

M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature 363, 31 (1993).
[CrossRef]

Phys. Rev. A (1)

S. John and G. Pang, Phys. Rev. A 54, 3642 (1996).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. S. Wiersma and A. Lagendijk, Phys. Rev. E 54, 4256 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

A. Ott, J. P. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 652201 (1990).
[CrossRef] [PubMed]

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, Phys. Rev. Lett. 72, 203 (1994).
[CrossRef] [PubMed]

T. H. Solomon, E. R. Weeks, and H. L. Swinney, Phys. Rev. Lett. 71, 3975 (1993).
[CrossRef] [PubMed]

S. Boldyrev and C. R. GwinnPhys. Rev. Lett. 91, 131101 (2003).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968).

Other (7)

See, e.g., P. A. Mello and N. Kumar, Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations (Oxford U. Press, 2004), for the idea of non-self-averaging.

M.F.Shlesinger, G.M.Zaslavsky, and U.Frisch, eds., Lévy Flights and Related Topics in Physics, Vol. 450 of Lecture Notes in Physics (Springer-Verlag, 1995).
[CrossRef]

F. Bardou, ''Cooling gases with Lévy fights: using the generalized central limit theorem in physics,'' v1, December 20, 2000.

M. I. Tribelsky, ''Tails of probability density for sums of random independent variables,'' v2, June 25, 2001.

C. Kittel, in Introduction to Solid State Physics (Wiley, 1996), pp. 141-172.

Increasing pumping/gain implies reduced lg.

I includes unamplified spontaneous emission Io, which must be subtracted.

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Figures (3)

Fig. 1
Fig. 1

Spectra from an F-RAM at (a) below and (b) above threshold pumping. Inset, schematic of an F-RAM, a typical photon path ( A B ) , with amplifying regions shown by dashed lines.

Fig. 2
Fig. 2

(a)–(c) Intensity versus configuration, (d)–(f) corresponding histograms fitted to the power law ( I I o ) ( 1 + α ) : I o = 619 , 1267, and 1299 for (d), (e), and (f), respectively; (g)–(i) histograms at λ op : I o = 17 , 24, and 12 for (g), (h), and (i), respectively.

Fig. 3
Fig. 3

Histogram at λ p for (a) F-RAM with power-law fit, α = 0.82 and (b) powdered-F-RAM and Gaussian fit.

Equations (2)

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p ( g ) = m = 1 8 ρ o a π l t l g 3 1 g 1 + α m .
p ( g ) = m = 1 8 ρ o a π l eff l g 3 v a 1 g 1 + α m ,

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