Abstract

Quantum photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers are studied on the basis of the complex Ginzburg–Landau equation model. We find that, depending on their phase difference, the total photon-number noise of the bound soliton pair can be larger or smaller than that of a single soliton, and the two solitons in the soliton pair have a corresponding positive or negative photon-number correlation. It is predicted for the first time to our knowledge that out-of-phase soliton pairs can exhibit less noise as a result of negative correlation.

© 2005 Optical Society of America

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  1. S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
    [CrossRef] [PubMed]
  2. P. D. Drummond and S. J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987).
    [CrossRef]
  3. Y. Lai and H. A. Haus, Phys. Rev. A 40, 844 (1989).
    [CrossRef] [PubMed]
  4. Y. Lai and H. A. Haus, Phys. Rev. A 40, 854 (1989).
    [CrossRef] [PubMed]
  5. Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
    [CrossRef] [PubMed]
  6. Ch. Silberhorn, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 88, 167902 (2002).
    [CrossRef]
  7. F. König, M. A. Zielonka, and A. Sizmann, Phys. Rev. A 66, 013812 (2002).
    [CrossRef]
  8. H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990).
    [CrossRef]
  9. Y. Lai, J. Opt. Soc. Am. B 10, 475 (1993).
    [CrossRef]
  10. M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991).
    [CrossRef] [PubMed]
  11. K. Bergman and H. A. Haus, Opt. Lett. 16, 663 (1991).
    [CrossRef] [PubMed]
  12. S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
    [CrossRef] [PubMed]
  13. D. Krylov, K. Bergman, and Y. Lai, Opt. Lett. 24, 774 (1999).
    [CrossRef]
  14. S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
    [CrossRef]
  15. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
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    [CrossRef] [PubMed]
  17. N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
    [CrossRef]
  18. J. M. Soto-Crespo, N. N. Akhmediev, P. Grelu, and F. Belhache, Opt. Lett. 28, 1757 (2003).
    [CrossRef] [PubMed]
  19. D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
    [CrossRef]
  20. N. H. Seong and Dug Y. Kim, Opt. Lett. 27, 1321 (2002).
    [CrossRef]
  21. P. Grelu, F. Belhache, F. Gutty, and J. M. Soto-Crespo, J. Opt. Soc. Am. B 20, 863 (2003).
    [CrossRef]
  22. B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  24. R.-K. Lee, Y. Lai, and B. A. Malomed, Phys. Rev. A 70, 063817 (2004).
    [CrossRef]

2004 (2)

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

R.-K. Lee, Y. Lai, and B. A. Malomed, Phys. Rev. A 70, 063817 (2004).
[CrossRef]

2003 (2)

2002 (3)

N. H. Seong and Dug Y. Kim, Opt. Lett. 27, 1321 (2002).
[CrossRef]

Ch. Silberhorn, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

F. König, M. A. Zielonka, and A. Sizmann, Phys. Rev. A 66, 013812 (2002).
[CrossRef]

2001 (2)

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

1999 (1)

1998 (1)

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

1996 (2)

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

1995 (1)

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

1993 (1)

1991 (3)

K. Bergman and H. A. Haus, Opt. Lett. 16, 663 (1991).
[CrossRef] [PubMed]

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef] [PubMed]

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (2)

Y. Lai and H. A. Haus, Phys. Rev. A 40, 844 (1989).
[CrossRef] [PubMed]

Y. Lai and H. A. Haus, Phys. Rev. A 40, 854 (1989).
[CrossRef] [PubMed]

1987 (2)

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987).
[CrossRef]

Afanasjev, V. V.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Akhmediev, N. N.

J. M. Soto-Crespo, N. N. Akhmediev, P. Grelu, and F. Belhache, Opt. Lett. 28, 1757 (2003).
[CrossRef] [PubMed]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Belhache, F.

Bergman, K.

Brunel, M.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

Carter, S. J.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987).
[CrossRef]

Chartier, T.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

Drummond, P. D.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987).
[CrossRef]

Friberg, S. R.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Grelu, P.

Gutty, F.

Haus, H. A.

Hideur, A.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

Kim, Dug Y.

König, F.

F. König, M. A. Zielonka, and A. Sizmann, Phys. Rev. A 66, 013812 (2002).
[CrossRef]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Korolkova, N.

Ch. Silberhorn, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Krylov, D.

Lai, Y.

R.-K. Lee, Y. Lai, and B. A. Malomed, Phys. Rev. A 70, 063817 (2004).
[CrossRef]

D. Krylov, K. Bergman, and Y. Lai, Opt. Lett. 24, 774 (1999).
[CrossRef]

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Y. Lai, J. Opt. Soc. Am. B 10, 475 (1993).
[CrossRef]

H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990).
[CrossRef]

Y. Lai and H. A. Haus, Phys. Rev. A 40, 854 (1989).
[CrossRef] [PubMed]

Y. Lai and H. A. Haus, Phys. Rev. A 40, 844 (1989).
[CrossRef] [PubMed]

Lam, P. K.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Leblond, H.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

Lee, R.-K.

R.-K. Lee, Y. Lai, and B. A. Malomed, Phys. Rev. A 70, 063817 (2004).
[CrossRef]

Leuchs, G.

Ch. Silberhorn, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Levanon, A.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Machida, S.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Malomed, B. A.

R.-K. Lee, Y. Lai, and B. A. Malomed, Phys. Rev. A 70, 063817 (2004).
[CrossRef]

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef] [PubMed]

Man, W. S.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

Mukai, T.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Ortac, B.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

Reid, M. D.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Rosenbluh, M.

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

Sanchez, F.

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

Seong, N. H.

Shelby, R. M.

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Silberhorn, Ch.

Ch. Silberhorn, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Sizmann, A.

F. König, M. A. Zielonka, and A. Sizmann, Phys. Rev. A 66, 013812 (2002).
[CrossRef]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Soto-Crespo, J. M.

Spälter, S.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Tam, H. Y.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

Tang, D. Y.

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

Weiss, O.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Werner, M. J.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

Yu, S.-S.

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Zielonka, M. A.

F. König, M. A. Zielonka, and A. Sizmann, Phys. Rev. A 66, 013812 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. Ortac, A. Hideur, T. Chartier, M. Brunel, P. Grelu, H. Leblond, and F. Sanchez, IEEE Photon. Technol. Lett. 16, 1274 (2004).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Lett. (4)

Phys. Rev. A (7)

Y. Lai and S.-S. Yu, Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

R.-K. Lee, Y. Lai, and B. A. Malomed, Phys. Rev. A 70, 063817 (2004).
[CrossRef]

B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
[CrossRef] [PubMed]

Y. Lai and H. A. Haus, Phys. Rev. A 40, 844 (1989).
[CrossRef] [PubMed]

Y. Lai and H. A. Haus, Phys. Rev. A 40, 854 (1989).
[CrossRef] [PubMed]

F. König, M. A. Zielonka, and A. Sizmann, Phys. Rev. A 66, 013812 (2002).
[CrossRef]

D. Y. Tang, W. S. Man, H. Y. Tam, and P. D. Drummond, Phys. Rev. A 64, 033814 (2001).
[CrossRef]

Phys. Rev. E (1)

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, Phys. Rev. E 53, 1190 (1996).
[CrossRef]

Phys. Rev. Lett. (6)

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996).
[CrossRef] [PubMed]

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991).
[CrossRef] [PubMed]

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Ch. Silberhorn, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

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Figures (3)

Fig. 1
Fig. 1

(A) Photon-number correlation parameter, C 12 , for bound-state soliton pairs with different relative phases. (B) Contour plot of the classical solution for the bound state. All the results are presented for D = 1 , δ = 0.01 , ϵ = 1.8 , β = 0.5 , μ = 0.05 , and ν = 0 in the CGLE, Eq. (1).

Fig. 2
Fig. 2

Time-domain photon-number correlation patterns, η i j , for bound soliton pairs with different relative phases, after the normalized propagation distance z = 0.4 . (A) θ = 0 , (B) θ = π 2 , and (C) θ = π . Time-division length Δ t = 0.3 .

Fig. 3
Fig. 3

Comparison of the total photon-number fluctuations in the bound soliton pairs with different relative phases (three solid curves), and around the single soliton (dashed curve).

Equations (4)

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

i U z + ( D 2 ) U t t + U 2 U = i δ U + i ϵ U 2 U + i β U t t + i μ U 4 U ν U 4 U ,
C 12 = : Δ N ̂ 1 Δ N ̂ 2 : Δ N ̂ 1 2 Δ N ̂ 2 2 .
η i j : Δ n ̂ i Δ n ̂ j : Δ n ̂ i 2 Δ n ̂ j 2 ,
Δ n ̂ j = Δ t j d t [ U 0 ( z , t ) u ̂ ( z , t ) + U 0 * ( z , t ) u ̂ ( z , t ) ] .

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