Abstract

Mode-locked lasers with intracavity dispersion are experimentally shown to exhibit localization behavior in their frequency domain. The localization, with its typical exponential spectrum structure, is analogous to that which occurs for the quantum kicked rotor. The experimental demonstration of our optical kicked rotor is done with a long mode-locked dispersive fiber laser. The localization effect sets a basic limit on the spectrum bandwidth and the minimum pulse width in such lasers. It also provides a special experimental test bed for the study of optical kicked rotors and localization effects.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Fischer, A. Rosen, and S. Fishman, Opt. Lett. 24, 1463 (1999).
    [CrossRef]
  2. S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
    [CrossRef]
  3. D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
    [CrossRef]
  4. F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
  5. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
    [CrossRef]
  6. For reviews, see D. J. Thouless, in Critical Phenomena, Random Systems, Gauge Theories, Proceedings of the Les-Houches Summer School, K. Osterwalder and R. Stora, eds. (North-Holland, Amsterdam, 1986), p. 681.
  7. I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
  8. F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
    [CrossRef] [PubMed]
  9. B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
    [CrossRef]
  10. H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
    [CrossRef]
  11. B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
    [CrossRef]
  12. A. Rosen, B. Fischer, A. Bekker, and S. Fishman, J. Opt. Soc. Am. B 17, 1579 (2000).
    [CrossRef]
  13. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  14. B. Fischer, B. Vodonos, S. Atkins, and A. Bekker, Opt. Lett. 25, 728 (2000).
    [CrossRef]

2000 (3)

1999 (1)

1998 (2)

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
[CrossRef]

H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

1995 (1)

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

1984 (1)

D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

1982 (1)

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
[CrossRef]

1958 (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Ammann, H.

H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Anderson, P. W.

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Atkins, S.

Barucha, C. F.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Bekker, A.

Christensen, N.

H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Fischer, B.

Fishman, S.

A. Rosen, B. Fischer, A. Bekker, and S. Fishman, J. Opt. Soc. Am. B 17, 1579 (2000).
[CrossRef]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
[CrossRef]

B. Fischer, A. Rosen, and S. Fishman, Opt. Lett. 24, 1463 (1999).
[CrossRef]

D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
[CrossRef]

Gray, R.

H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Gredeskul, S. A.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Grempel, D. R.

D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
[CrossRef]

Haake, F.

F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).

Klappauf, B. G.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
[CrossRef]

Lifshits, I. M.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Moore, F. L.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Oskay, W. H.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
[CrossRef]

Pastur, L. A.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Prange, R. E.

D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
[CrossRef]

Raizen, M. G.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
[CrossRef]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Robinson, J. C.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Rosen, A.

Shvarchuck, I.

H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Steck, D. A.

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
[CrossRef]

Sundaram, B.

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

Thouless, D. J.

For reviews, see D. J. Thouless, in Critical Phenomena, Random Systems, Gauge Theories, Proceedings of the Les-Houches Summer School, K. Osterwalder and R. Stora, eds. (North-Holland, Amsterdam, 1986), p. 681.

Vodonos, B.

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Phys. Rev. A (1)

D. R. Grempel, R. E. Prange, and S. Fishman, Phys. Rev. A 29, 1639 (1984).
[CrossRef]

Phys. Rev. E (1)

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

S. Fishman, D. R. Grempel, and R. E. Prange, Phys. Rev. Lett. 49, 509 (1982).
[CrossRef]

F. L. Moore, J. C. Robinson, C. F. Barucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
[CrossRef] [PubMed]

B. G. Klappauf, W. H. Oskay, D. A. Steck, and M. G. Raizen, Phys. Rev. Lett. 81, 1203 (1998).
[CrossRef]

H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, Phys. Rev. Lett. 80, 4111 (1998).
[CrossRef]

Other (4)

For reviews, see D. J. Thouless, in Critical Phenomena, Random Systems, Gauge Theories, Proceedings of the Les-Houches Summer School, K. Osterwalder and R. Stora, eds. (North-Holland, Amsterdam, 1986), p. 681.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Experimental configuration of the mode-locked laser, consisting of a fiber ring cavity with an erbium-doped fiber amplifier and a LiNbO3 modulator. PC, polarization controller; EDFA, erbium-doped fiber amplifier.

Fig. 2
Fig. 2

Output spectra for l=50 km and β2-20 ps2/km: (a) Corresponding to the localization case. Here Ω/2π=13.8 GHz. The exponential envelope fit is centered around 1530.47 nm, and its width is 0.0535 nm, giving approximately ξ0.485 sidebands. (b) At resonance with the extended spectrum. Here Ω/2π=12.8 GHz. The Gaussian fit is centered around 1531.04 nm, and its width is 0.37 nm, or approximately 3.61 sidebands.

Fig. 3
Fig. 3

Output spectra showing localization for l=1 km and β2+142 ps2/km (at λ=1550 nm) and (a) Ω/2π=2 GHz, (b) Ω/2π=4 GHz, (c) Ω/2π=6 GHz, and (d) Ω/2π=10.1 GHz. Note the difference in the wavelength scale, presented to show the dependence of the spectra on the number of the sidebands.

Fig. 4
Fig. 4

Output spectra for l=1 km and β2+142 ps2/km (at λ=1550 nm) and Ω/2π=4 GHz for (a) strong and (b) a weak (approximately 15 times weaker) modulation amplitudes. Note that for weak modulation the spectrum no longer has an exponential shape.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

iψz=β222ψT2+κ cosΩTNδz-Nz0ψ,

Metrics