Abstract

We demonstrate theoretically and experimentally in an optical fiber system that partially temporally incoherent light exhibits modulational instability during its propagation in an instantaneous response nonlinear medium. We show that the modulation frequency and gain are substantially increased with respect to the corresponding values of coherent modulational instability.

© 2005 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  2. M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef]
  3. J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
    [CrossRef]
  4. H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
    [CrossRef]
  5. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
    [CrossRef]
  6. D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
    [CrossRef]
  7. D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
    [CrossRef] [PubMed]
  8. T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
    [CrossRef] [PubMed]
  9. J. Klinger, H. Martin, and Z. Chen, Opt. Lett. 26, 271 (2001).
    [CrossRef]
  10. D. Kip, M. Solja?i?, M. Segev, S. M. Sears, and D. N. Christodoulides, J. Opt. Soc. Am. B 19, 502 (2002).
    [CrossRef]
  11. T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
    [CrossRef]
  12. M. Segev and D. N. Christodoulides, in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, 2001), pp. 87–125.
  13. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
    [CrossRef]
  14. V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, 1992).
    [CrossRef]
  15. S. B. Cavalcanti, G. P. Agrawal, and M. Yu, Phys. Rev. A 51, 4086 (1995).
    [CrossRef] [PubMed]
  16. A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, Opt. Express 12, 2838 (2004).
    [CrossRef] [PubMed]

2004 (4)

D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef]

A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, Opt. Express 12, 2838 (2004).
[CrossRef] [PubMed]

2002 (3)

D. Kip, M. Solja?i?, M. Segev, S. M. Sears, and D. N. Christodoulides, J. Opt. Soc. Am. B 19, 502 (2002).
[CrossRef]

H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

2001 (2)

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

J. Klinger, H. Martin, and Z. Chen, Opt. Lett. 26, 271 (2001).
[CrossRef]

2000 (3)

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

1995 (1)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, Phys. Rev. A 51, 4086 (1995).
[CrossRef] [PubMed]

Agrawal, G. P.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, Phys. Rev. A 51, 4086 (1995).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Anastassiou, C.

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

Anderson, D.

D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

Buljan, H.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef]

H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

Carmon, T.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef]

Cavalcanti, S. B.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, Phys. Rev. A 51, 4086 (1995).
[CrossRef] [PubMed]

Chen, Z.

J. Klinger, H. Martin, and Z. Chen, Opt. Lett. 26, 271 (2001).
[CrossRef]

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. Kip, M. Solja?i?, M. Segev, S. M. Sears, and D. N. Christodoulides, J. Opt. Soc. Am. B 19, 502 (2002).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

M. Segev and D. N. Christodoulides, in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, 2001), pp. 87–125.

Coskun, T.

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Eugenieva, E.

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Falkovich, G.

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, 1992).
[CrossRef]

Fedele, R.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

Finot, C.

Haelterman, M.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef]

Hall, B.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

Helczynski, L.

D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

Kim, Y.

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

Kip, D.

D. Kip, M. Solja?i?, M. Segev, S. M. Sears, and D. N. Christodoulides, J. Opt. Soc. Am. B 19, 502 (2002).
[CrossRef]

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Klinger, J.

L’vov, V. S.

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, 1992).
[CrossRef]

Lantz, E.

Lisak, M.

D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

Maillotte, H.

Martin, H.

Millot, G.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef]

Mussot, A.

Picozzi, A.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef]

Pitois, S.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef]

A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, Opt. Express 12, 2838 (2004).
[CrossRef] [PubMed]

Schwartz, T.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef]

Sears, S. M.

Segev, M.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef]

D. Kip, M. Solja?i?, M. Segev, S. M. Sears, and D. N. Christodoulides, J. Opt. Soc. Am. B 19, 502 (2002).
[CrossRef]

H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

M. Segev and D. N. Christodoulides, in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, 2001), pp. 87–125.

Semenov, V.

D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

Semenov, V. E.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

Šiber, A.

H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

Soljacic, M.

H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

D. Kip, M. Solja?i?, M. Segev, S. M. Sears, and D. N. Christodoulides, J. Opt. Soc. Am. B 19, 502 (2002).
[CrossRef]

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

Sylvestre, T.

Torres, J. P.

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

Vishwanath, A.

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

Yu, M.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, Phys. Rev. A 51, 4086 (1995).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, 1992).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, Phys. Rev. A 51, 4086 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (4)

J. P. Torres, C. Anastassiou, M. Segev, M. Solja?i?, and D. N. Christodoulides, Phys. Rev. E 65, 015601(R) (2001).
[CrossRef]

H. Buljan, A. Šiber, M. Solja?i?, and M. Segev, Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602(R) (2002).
[CrossRef]

D. Anderson, L. Helczynski, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

T. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Solja?i?, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

M. Solja?i?, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef]

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef]

Science (1)

D. Kip, M. Solja?i?, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, 1992).
[CrossRef]

M. Segev and D. N. Christodoulides, in Spatial Solitons, S. Trillo and W. Torruellas, eds. (Springer, 2001), pp. 87–125.

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Figures (3)

Fig. 1
Fig. 1

(a) Solid curve, simulated MI spectrum in the case of a Gaussian-shaped spectrum (an average over 50 realizations was taken). The average peak power was fixed to 40 W and the pump wavelength was λ = 1320 nm . (b) Corresponding simulated coherent MI spectrum with the same power.

Fig. 2
Fig. 2

(a) Schematic of the experimental setup: P, polarizer; SMF, single-mode fiber; MO, microscope objective. (b) Experimental incoherent MI spectrum recorded at λ = 1326.34 nm with a pump average peak power of 40 W .

Fig. 3
Fig. 3

Modulation frequency versus pump wavelength at a power of 40 W . Solid curve, numerical simulations for an incoherent Gaussian-shaped spectrum (an average over 50 realizations was taken). Circles, experimental measurements with an incoherent wave. Dashed curve, numerical simulation for a coherent monochromatic pump. Dotted curve, optimal modulation frequencies obtained from Eq. (3) for a Lorentzian-shaped spectrum.

Equations (3)

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i z B = β 2 2 ( t 1 2 t 2 2 ) B γ ( E 1 2 E 1 * E 2 * E 2 * 2 E 1 E 2 ) ,
i z B = β 2 η τ 2 B + 2 γ ( E 2 2 E 1 2 ) B ,
g ( ω ) = 2 β 2 ω σ + β 2 ω 8 γ P o β 2 ω 2 .

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