Abstract

We report the observation of modulational instability (MI) of a partially spatially incoherent beam induced by seeding noise through cross-phase modulation. We show experimentally that a threshold exists for such induced incoherent MI to occur that depends on the degree of spatial coherence as well as on the strength of the nonlinearity. Above threshold, the induced MI leads to the formation of ordered and disordered patterns of incoherent light.

© 2001 Optical Society of America

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  1. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995).
  3. Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
    [CrossRef]
  4. P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  5. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
  6. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, Opt. Lett. 14, 1008 (1989).
    [CrossRef] [PubMed]
  7. P. V. Mamyshev, C. Bosshard, and G. I. Stegeman, J. Opt. Soc. Am. B 11, 1254 (1994).
    [CrossRef]
  8. M. Iturbe-Castillo, M. Torres-Cisneros, J. Mondragón, S. Cerda, S. Stepanov, V. Vysloukh, and G. Torres-Cisneros, Opt. Lett. 20, 1853 (1995).
    [CrossRef] [PubMed]
  9. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 126, 167 (1996).
    [CrossRef]
  10. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
    [CrossRef] [PubMed]
  11. D. V. Skryabin and W. J. Firth, Phys. Rev. Lett. 81, 3379 (1998).
    [CrossRef]
  12. R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
    [CrossRef]
  13. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef] [PubMed]
  14. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]
  15. M. Mitchell and M. Segev, Nature 387, 880 (1997).
    [CrossRef]
  16. Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
    [CrossRef] [PubMed]
  17. T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
    [CrossRef] [PubMed]
  18. Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
    [CrossRef] [PubMed]

2000 (4)

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

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

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

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

1999 (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1998 (2)

D. V. Skryabin and W. J. Firth, Phys. Rev. Lett. 81, 3379 (1998).
[CrossRef]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

1997 (2)

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

1996 (2)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 126, 167 (1996).
[CrossRef]

1995 (2)

1994 (1)

1989 (1)

1974 (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

1965 (1)

P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Agrawal, G. P.

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

Babiou, D. M.

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Bosshard, C.

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 126, 167 (1996).
[CrossRef]

Cerda, S.

Chen, Z.

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

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Chernikov, S. V.

Christodoulides, D. N.

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

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

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 126, 167 (1996).
[CrossRef]

Coskun, T.

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

Coskun, T. H.

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

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

Dianov, E. M.

Eugenieva, E.

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Ferro, P.

Firth, W. J.

D. V. Skryabin and W. J. Firth, Phys. Rev. Lett. 81, 3379 (1998).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Iturbe-Castillo, M.

Kelly, P. L.

P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Kim, Y.

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

Kip, D.

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Kivshar, Y. S.

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Lawrence, B.

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Mamyshev, P. V.

Mitchell, M.

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Mondragón, J.

Pelinovsky, D. E.

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Prokhorov, A. M.

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Segev, M.

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

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

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Shih, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 126, 167 (1996).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and W. J. Firth, Phys. Rev. Lett. 81, 3379 (1998).
[CrossRef]

Soljacic, M.

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

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

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

Stegeman, G. I.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

P. V. Mamyshev, C. Bosshard, and G. I. Stegeman, J. Opt. Soc. Am. B 11, 1254 (1994).
[CrossRef]

Stepanov, S.

Torres-Cisneros, G.

Torres-Cisneros, M.

Torruellas, W. E.

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Trillo, S.

Vishwanath, A.

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

Vysloukh, V.

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

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

Nature (1)

M. Mitchell and M. Segev, Nature 387, 880 (1997).
[CrossRef]

Opt. Commun. (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 126, 167 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Rep. (1)

Y. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Phys. Rev. Lett. (6)

P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

D. V. Skryabin and W. J. Firth, Phys. Rev. Lett. 81, 3379 (1998).
[CrossRef]

R. A. Fuerst, D. M. Babiou, B. Lawrence, W. E. Torruellas, and G. I. Stegeman, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

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

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

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

Science (3)

Incoherent MI without seeding noise was reported by D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Speckle pattern taken with the diffuser stationary. (b)–(d), (f) Intensity patterns of a partially incoherent beam at (b) V=0, (c) V=400 without seeding noise, (d) V=400 with seeding noise, and (f) V=500 without seeding noise. (e) Gridlike intensity pattern used for seeding noise (its contrast has been enhanced for clarity).

Fig. 2
Fig. 2

Development of induced incoherent MI as the spatial coherence of the beam is increased gradually: (a) lc=10 μm, (b) lc=20 μm, (c) lc=30 μm, and (d) lc=60 μm. Top, the speckle patterns with the diffuser stationary. Bottom, the corresponding intensity patterns at V=500 with the diffuser rotating.

Fig. 3
Fig. 3

Development of induced incoherent MI as the strength of the nonlinearity is increased gradually. Shown are intensity patterns at lc=20 μm for (a) V=200, (b) V=500, (c) V=800, and (d) V=1400.

Fig. 4
Fig. 4

Measured threshold values of externally applied voltage as a function of coherence length.

Equations (2)

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κI0/n0>θ02,κ=dδn/dI.
δnVlIr1+Ir/Isat,

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