Abstract

We demonstrate theoretically and experimentally that induced spatiotemporal modulation instability can exist in a self-defocusing medium if the nonlinearity is noninstantaneous. We predict the growth rate as a function of the spatial and temporal frequencies of the modulation and the response time of the nonlinearity and confirm it by our experiments.

© 2005 Optical Society of America

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References

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  1. See, e.g., E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, 2000).
    [Crossref]
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  3. M. Remoissenet, Waves Called Solitons (Springer-Verlag, 1999).
    [Crossref]
  4. M. Iturbe-Castillo, M. Torres-Cisneros, J. Sanchez-Mondragon, S. Chavez-Cerda, S. Stepanov, V. Vysloukh, and G. Torres-Cisneros, Opt. Lett. 20, 1853 (1995).
    [Crossref] [PubMed]
  5. R. Malendevich, L. Jankovic, G. Stegeman, and J. S. Aitchison, Opt. Lett. 26, 1879 (2001).
    [Crossref]
  6. R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
    [Crossref] [PubMed]
  7. M. Soljacic, M. Segev, T. Coskun, D. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [Crossref] [PubMed]
  8. D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
    [Crossref] [PubMed]
  9. D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
    [Crossref]
  10. W. Firth and C. Pare, Opt. Lett. 13, 1096 (1988).
    [Crossref] [PubMed]
  11. M. Shih and F. Sheu, Phys. Rev. Lett. 86, 2281 (2001).
    [Crossref] [PubMed]
  12. R. Y. Chiao, P. L. Kelley, and E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
    [Crossref]
  13. M. Shih, C. Jeng, F. Sheu, and C. Lin, Phys. Rev. Lett. 88, 133902 (2002).
    [Crossref]
  14. For most nonlinearities other than that from electronic polarization, this criterion is satisfied; see R. W. Boyd, Nonlinear Optics (Academic, 1992).
  15. G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
    [Crossref] [PubMed]
  16. Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. Valley, Opt. Lett. 21, 629 (1996).
    [Crossref] [PubMed]
  17. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [Crossref] [PubMed]
  18. M. Segev, M. Shih, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [Crossref]
  19. Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
    [Crossref]

2002 (1)

M. Shih, C. Jeng, F. Sheu, and C. Lin, Phys. Rev. Lett. 88, 133902 (2002).
[Crossref]

2001 (3)

M. Shih and F. Sheu, Phys. Rev. Lett. 86, 2281 (2001).
[Crossref] [PubMed]

R. Malendevich, L. Jankovic, G. Stegeman, and J. S. Aitchison, Opt. Lett. 26, 1879 (2001).
[Crossref]

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[Crossref] [PubMed]

2000 (2)

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

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

1997 (1)

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[Crossref]

1996 (2)

1995 (2)

1994 (1)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

1988 (1)

1985 (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

1966 (1)

R. Y. Chiao, P. L. Kelley, and E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[Crossref]

Agrawal, G. P.

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

Aitchison, J. S.

Boyd, R. W.

For most nonlinearities other than that from electronic polarization, this criterion is satisfied; see R. W. Boyd, Nonlinear Optics (Academic, 1992).

Chavez-Cerda, S.

Chen, Z.

Chiao, R. Y.

R. Y. Chiao, P. L. Kelley, and E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[Crossref]

Christodoulides, D.

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

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

Coskun, T.

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

Crosignani, B.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

Di Porto, P.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

Duree, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

Eugenieve, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

Fang, H.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[Crossref] [PubMed]

Firth, W.

Garmire, E.

R. Y. Chiao, P. L. Kelley, and E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[Crossref]

Garrett, M.

Huignard, J.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Infeld, E.

See, e.g., E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, 2000).
[Crossref]

Iturbe-Castillo, M.

Jankovic, L.

Jeng, C.

M. Shih, C. Jeng, F. Sheu, and C. Lin, Phys. Rev. Lett. 88, 133902 (2002).
[Crossref]

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, and E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[Crossref]

Kip, D.

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

Lederer, F.

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[Crossref]

Lin, C.

M. Shih, C. Jeng, F. Sheu, and C. Lin, Phys. Rev. Lett. 88, 133902 (2002).
[Crossref]

Malendevich, R.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[Crossref] [PubMed]

R. Malendevich, L. Jankovic, G. Stegeman, and J. S. Aitchison, Opt. Lett. 26, 1879 (2001).
[Crossref]

Michaelis, D.

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[Crossref]

Mitchell, M.

Morin, M.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

Pare, C.

Peschel, U.

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[Crossref]

Rajbenbach, H.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Remoissenet, M.

M. Remoissenet, Waves Called Solitons (Springer-Verlag, 1999).
[Crossref]

Rowlands, G.

See, e.g., E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, 2000).
[Crossref]

Salamo, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

Sanchez-Mondragon, J.

Schiek, R.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[Crossref] [PubMed]

Segev, M.

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

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. Valley, Opt. Lett. 21, 629 (1996).
[Crossref] [PubMed]

M. Segev, M. Shih, and G. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[Crossref]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

Sharp, E.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

Sheu, F.

M. Shih, C. Jeng, F. Sheu, and C. Lin, Phys. Rev. Lett. 88, 133902 (2002).
[Crossref]

M. Shih and F. Sheu, Phys. Rev. Lett. 86, 2281 (2001).
[Crossref] [PubMed]

Shih, M.

Soljacic, M.

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

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

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

Stegeman, G.

Stegeman, G. I.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[Crossref] [PubMed]

Stepanov, S.

Torres-Cisneros, G.

Torres-Cisneros, M.

Valley, G.

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

Vishwanath, A.

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

Vysloukh, V.

Yariv, A.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

J. Appl. Phys. (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. Huignard, J. Appl. Phys. 58, 45 (1985).
[Crossref]

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

Opt. Lett. (4)

Phys. Rev. A (1)

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[Crossref]

Phys. Rev. Lett. (7)

M. Shih and F. Sheu, Phys. Rev. Lett. 86, 2281 (2001).
[Crossref] [PubMed]

R. Y. Chiao, P. L. Kelley, and E. Garmire, Phys. Rev. Lett. 17, 1158 (1966).
[Crossref]

M. Shih, C. Jeng, F. Sheu, and C. Lin, Phys. Rev. Lett. 88, 133902 (2002).
[Crossref]

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[Crossref] [PubMed]

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

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. 74, 1978 (1995).
[Crossref] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[Crossref] [PubMed]

Science (1)

D. Kip, M. Soljacic, M. Segev, E. Eugenieve, and D. Christodoulides, Science 290, 495 (2000).
[Crossref] [PubMed]

Other (4)

See, e.g., E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge U. Press, 2000).
[Crossref]

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

M. Remoissenet, Waves Called Solitons (Springer-Verlag, 1999).
[Crossref]

For most nonlinearities other than that from electronic polarization, this criterion is satisfied; see R. W. Boyd, Nonlinear Optics (Academic, 1992).

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Figures (4)

Fig. 1
Fig. 1

Gain coefficient of the MI in a noninstantaneous self-defocusing medium.

Fig. 2
Fig. 2

Sketch of the experimental setup. BS, beam splitter.

Fig. 3
Fig. 3

Intensity patterns at the (a) input and (b)–(d) output faces of the crystal and their Fourier transform. The component at zero spatial frequency is removed manually since it is too high to be shown.

Fig. 4
Fig. 4

(a) Intensity patterns of the MI. (b),(c) Growth rates as a function of the temporal frequency of the modulation. The solid curves are predicted by the perturbation.

Equations (4)

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2 E = μ 2 ( ε E ) t 2 = μ ε 2 E t 2 + 2 μ ( ε t ) ( E t ) + μ ( 2 ε t 2 ) E .
2 A 2 i k A z + 2 k 2 δ n ( A 2 ) n 0 A = 0 .
2 ( a 1 + i a 2 ) 2 i k ( a 1 + i a 2 ) z 4 k 2 κ Re [ A 0 2 a 1 0 n 0 ( 1 + i Ω τ ) exp ( i Ω t + i k r i h 1 z + h 2 z ) ] = 0 .
h 2 = ± κ k A 0 2 n 0 2 { P 4 2 P 2 1 + ( Ω τ ) 2 + P 2 [ P 4 + 4 + 4 P 2 1 + ( Ω τ ) 2 ] 1 2 } 1 2 ,

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