Abstract

We demonstrate numerically and experimentally how spatial soliton arrays generated through modulation instability in a planar waveguide with relaxing Kerr nonlinearity can be spatially and temporally destabilized when using a partially spatiotemporally coherent light pulse. However, the amplitude of the shot-to-shot spatial jitter is limited. This jitter depends on the correlation degree of the spatial noise between pulses, and this correlation degree strongly depends on the spatiotemporal coherence of the propagating beam.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
    [CrossRef]
  9. E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
    [CrossRef]
  10. V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).
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    [CrossRef]
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    [CrossRef]
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    [PubMed]
  16. H. Leblond and C. Cambournac, "Spatial modulation instability of coherent light in a weakly-relaxing Kerr medium," J. Opt. A Pure Appl. Opt. 6, 461-468 (2004).
    [CrossRef]
  17. M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of incoherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
    [CrossRef] [PubMed]
  18. G. Fanjoux, F. Devaux, E. Lantz, and H. Maillotte, "The generation of spatial soliton arrays in a planar Kerr waveguide from seeded spontaneous parametric down conversion," J. Opt. A Pure Appl. Opt. 6, S250-S257 (2004).
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    [CrossRef] [PubMed]
  20. H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent 'white' light and modulation instability in non-instantaneous nonlinear media," Phys. Rev. E 66, 035601(R) (2002).
    [CrossRef]
  21. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
    [CrossRef] [PubMed]
  22. J. Klinger, H. Martin, and Z. Chen, "Experiments on induced modulational instability of an incoherent optical beam," Opt. Lett. 26, 271-273 (2001).
    [CrossRef]
  23. T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901 (2004).
    [CrossRef] [PubMed]
  24. A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, "Spectral broadening of a partially CW laser beam in single-mode optical fibers," Opt. Express 12, 2838-2843 (2004).
    [CrossRef] [PubMed]
  25. A. Sauter, S. Pitois, G. Millot, and A. Picozzi, "Incoherent modulation instability in instantaneous nonlinear Kerr media," Opt. Lett. 30, 2143-2145 (2005).
    [CrossRef] [PubMed]
  26. H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, "Spatial modulational instability in one-dimensional lithium niobate slab waveguides," Opt. Lett. 25, 1786-1788 (2000).
    [CrossRef]
  27. L. Jankovic, S. Polyakov, G. Stegeman, S. Carrasco, L. Torner, C. Bosshard, and P. Gunter, "Complex soliton-like pattern generation in Potassium Niobate due to noisy, high intensity, input beams," Opt. Express 11, 2206-2210 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  30. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).
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    [CrossRef]

2005 (1)

2004 (4)

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef] [PubMed]

A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, "Spectral broadening of a partially CW laser beam in single-mode optical fibers," Opt. Express 12, 2838-2843 (2004).
[CrossRef] [PubMed]

H. Leblond and C. Cambournac, "Spatial modulation instability of coherent light in a weakly-relaxing Kerr medium," J. Opt. A Pure Appl. Opt. 6, 461-468 (2004).
[CrossRef]

G. Fanjoux, F. Devaux, E. Lantz, and H. Maillotte, "The generation of spatial soliton arrays in a planar Kerr waveguide from seeded spontaneous parametric down conversion," J. Opt. A Pure Appl. Opt. 6, S250-S257 (2004).

2003 (1)

2002 (5)

2001 (3)

2000 (3)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, "Spatial modulational instability in one-dimensional lithium niobate slab waveguides," Opt. Lett. 25, 1786-1788 (2000).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

1998 (2)

1997 (1)

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

1996 (1)

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, "Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence," Phys. Rev. A 54, 870-879 (1996).
[CrossRef] [PubMed]

1994 (1)

H. Maillotte, J. Monneret, A. Barthélémy, and C. Froehly, "Laser beam self-splitting into solitons by optical Kerr nonlinearity," Opt. Commun. 109, 265-271 (1994).
[CrossRef]

1989 (1)

1986 (1)

1984 (1)

1980 (1)

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. QE-16, 694-697 (1980).
[CrossRef]

1972 (1)

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

1966 (2)

V. I. Bespalov and V. I. Talanov, "Filamentary structure of light beams in nonlinear liquids," JETP Lett. 3, 307-310 (1966).

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Aitchison, J. S.

Akhmediev, N. N.

N. N. Akhmediev, "Spatial solitons in Kerr and Kerr-like media," Opt. Quantum Electron. 30, 535-569 (1998).
[CrossRef]

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, "Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence," Phys. Rev. A 54, 870-879 (1996).
[CrossRef] [PubMed]

Baboiu, D.-M.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Bang, O.

W. Krolikowski, O. Bang, J.-J. Rasmussen, and J. Willer, "Modulational instability in nonlocal Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Barille, R.

Barthélémy, A.

H. Maillotte, J. Monneret, A. Barthélémy, and C. Froehly, "Laser beam self-splitting into solitons by optical Kerr nonlinearity," Opt. Commun. 109, 265-271 (1994).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, "Filamentary structure of light beams in nonlinear liquids," JETP Lett. 3, 307-310 (1966).

Bosshard, C.

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. QE-16, 694-697 (1980).
[CrossRef]

Buljan, H.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef] [PubMed]

H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent 'white' light and modulation instability in non-instantaneous nonlinear media," Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

Cambournac, C.

Carmon, T.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef] [PubMed]

Carrasco, S.

Chauvet, M.

Chen, Z.

Chernikov, S. V.

Chiao, R. Y.

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

Christodoulides, D. N.

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, "(1+1)-Dimensional modulation instability of spatially incoherent light," J. Opt. Soc. Am. B 19, 502-512 (2002).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Devaux, F.

G. Fanjoux, F. Devaux, E. Lantz, and H. Maillotte, "The generation of spatial soliton arrays in a planar Kerr waveguide from seeded spontaneous parametric down conversion," J. Opt. A Pure Appl. Opt. 6, S250-S257 (2004).

Dianov, E. M.

Dudley, J. M.

Eugenieva, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Fang, H.

Fanjoux, G.

G. Fanjoux, F. Devaux, E. Lantz, and H. Maillotte, "The generation of spatial soliton arrays in a planar Kerr waveguide from seeded spontaneous parametric down conversion," J. Opt. A Pure Appl. Opt. 6, S250-S257 (2004).

Froehly, C.

H. Maillotte, J. Monneret, A. Barthélémy, and C. Froehly, "Laser beam self-splitting into solitons by optical Kerr nonlinearity," Opt. Commun. 109, 265-271 (1994).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Garmire, E.

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

Gunter, P.

Hasegawa, A.

A. Hasegawa, "Generation of a train of soliton pulses by induced modulational instability in optical fibers," Opt. Lett. 9, 288-290 (1984).
[CrossRef] [PubMed]

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. QE-16, 694-697 (1980).
[CrossRef]

Jankovic, L.

Jeng, C.-C.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of incoherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Kip, D.

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, "(1+1)-Dimensional modulation instability of spatially incoherent light," J. Opt. Soc. Am. B 19, 502-512 (2002).
[CrossRef]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Klinger, J.

Krolikowski, W.

W. Krolikowski, O. Bang, J.-J. Rasmussen, and J. Willer, "Modulational instability in nonlocal Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Lantz, E.

Lawrence, B.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Leblond, H.

H. Leblond and C. Cambournac, "Spatial modulation instability of coherent light in a weakly-relaxing Kerr medium," J. Opt. A Pure Appl. Opt. 6, 461-468 (2004).
[CrossRef]

Lin, C.-Y.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of incoherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Maillotte, H.

Malendevich, R.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, "Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence," Phys. Rev. A 54, 870-879 (1996).
[CrossRef] [PubMed]

Mamyshev, P. V.

Martin, H.

Millot, G.

Monneret, J.

H. Maillotte, J. Monneret, A. Barthélémy, and C. Froehly, "Laser beam self-splitting into solitons by optical Kerr nonlinearity," Opt. Commun. 109, 265-271 (1994).
[CrossRef]

Mussot, A.

Picozzi, A.

Pitois, S.

Polyakov, S.

Prokhorov, A. M.

Rasmussen, J.-J.

W. Krolikowski, O. Bang, J.-J. Rasmussen, and J. Willer, "Modulational instability in nonlocal Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Rivoire, G.

Saffman, M.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, "Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence," Phys. Rev. A 54, 870-879 (1996).
[CrossRef] [PubMed]

Sauter, A.

Schiek, R.

Schwartz, T.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef] [PubMed]

Sears, S. M.

Segev, M.

T. Schwartz, T. Carmon, H. Buljan, and M. Segev, "Spontaneous pattern formation with incoherent white light," Phys. Rev. Lett. 93, 223901 (2004).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, "(1+1)-Dimensional modulation instability of spatially incoherent light," J. Opt. Soc. Am. B 19, 502-512 (2002).
[CrossRef]

H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent 'white' light and modulation instability in non-instantaneous nonlinear media," Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

Sheu, F.-W.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of incoherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Shih, M.-F.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of incoherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Siber, A.

H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent 'white' light and modulation instability in non-instantaneous nonlinear media," Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

Soljacic, M.

H. Buljan, A. Siber, M. Soljacic, and M. Segev, "Propagation of incoherent 'white' light and modulation instability in non-instantaneous nonlinear media," Phys. Rev. E 66, 035601(R) (2002).
[CrossRef]

D. Kip, M. Soljacic, M. Segev, S. M. Sears, and D. N. Christodoulides, "(1+1)-Dimensional modulation instability of spatially incoherent light," J. Opt. Soc. Am. B 19, 502-512 (2002).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000).
[CrossRef] [PubMed]

Stegeman, G.

Stegeman, G. I.

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, "Spatial modulational instability in one-dimensional lithium niobate slab waveguides," Opt. Lett. 25, 1786-1788 (2000).
[CrossRef]

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Sylvestre, T.

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, "Filamentary structure of light beams in nonlinear liquids," JETP Lett. 3, 307-310 (1966).

Torner, L.

Torruellas, W. E.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Townes, C. H.

E. Garmire, R. Y. Chiao, and C. H. Townes, "Dynamics and characteristics of the self-trapping of intense light beams," Phys. Rev. Lett. 16, 347-349 (1966).
[CrossRef]

Trillo, S.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Vishwanath, A.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in non-instantaneous nonlinear media," Phys. Rev. Lett. 84, 467-470 (2000).
[CrossRef] [PubMed]

Wabnitz, S.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, "Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium," Phys. Rev. Lett. 78, 2756-2759 (1997).
[CrossRef]

Wang, D.

Willer, J.

W. Krolikowski, O. Bang, J.-J. Rasmussen, and J. Willer, "Modulational instability in nonlocal Kerr media," Phys. Rev. E 64, 016612 (2001).
[CrossRef]

Winful, H. G.

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).

Zozulya, A. A.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, "Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence," Phys. Rev. A 54, 870-879 (1996).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

A. Hasegawa and W. F. Brinkman, "Tunable coherent IR and FIR sources utilizing modulational instability," IEEE J. Quantum Electron. QE-16, 694-697 (1980).
[CrossRef]

J. Opt. A Pure Appl. Opt. (2)

H. Leblond and C. Cambournac, "Spatial modulation instability of coherent light in a weakly-relaxing Kerr medium," J. Opt. A Pure Appl. Opt. 6, 461-468 (2004).
[CrossRef]

G. Fanjoux, F. Devaux, E. Lantz, and H. Maillotte, "The generation of spatial soliton arrays in a planar Kerr waveguide from seeded spontaneous parametric down conversion," J. Opt. A Pure Appl. Opt. 6, S250-S257 (2004).

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Figures (14)

Fig. 1
Fig. 1

Experimental setup. CL, cylindrical lenses; SL, spherical lenses; D, diaphragm; SF, spatial filter. Both experimental configurations 1 and 2 are represented.

Fig. 2
Fig. 2

Time-integrated spatial-frequency spectra of both deterministic and random contributions at the waveguide input, coherent beam (black curve) and SPDC (gray curve) with a pulse duration equal to 10 ps for both the SPDC and the coherent beams.

Fig. 3
Fig. 3

Single temporal slice of spatial-frequency spectra of both contributions at the peak of the 10 ps pulse entering the waveguide, coherent beam (black curve) and SPDC (gray curve).

Fig. 4
Fig. 4

Numerical results for five laser shots with the same 10 ps pulse duration for the coherent and SPDC beam and with the input spatial-frequency spectra of Figs. 2, 3: (a) time-integrated waveguide output intensity profiles, (b) corresponding time-integrated spatial spectra.

Fig. 5
Fig. 5

Corresponding spatiotemporal pattern and time-integrated profile for a single shot at the waveguide output.

Fig. 6
Fig. 6

Spatiotemporal and single-shot time-integrated patterns at the waveguide output with a smaller degree of temporal coherence than for Fig. 5.

Fig. 7
Fig. 7

Profiles generated by five successive temporal slices of one pulse after propagation in an instantaneous medium.

Fig. 8
Fig. 8

Experimental measurements of the shot-to-shot jitter of the soliton array in experimental configuration 1.

Fig. 9
Fig. 9

Another experimental observation with the same experimental conditions as for Fig. 8.

Fig. 10
Fig. 10

Temporal adjustment between the coherent ( 38 ps ) and the SPDC ( 10 ps ) pulses with delays equal to + 11 ps (gray curve), 0 ps (solid curve), 11 ps (dotted curve), and 22 ps (dashed curve). All profiles are normalized to 1.

Fig. 11
Fig. 11

Time-integrated waveguide output profiles corresponding to an input beam composed of (a) the coherent pulse without SPDC and the coherent pulse superimposed with SPDC with delays equal to (b) + 11 ps , (c) 0 ps , (d) 11 ps , (e) 22 ps . Five shots are superimposed on each image.

Fig. 12
Fig. 12

Spatiotemporal output pattern for one of the shots of Fig. 11. The vertical white dotted lines indicate the position of the peaks of the coherent spatial soliton array.

Fig. 13
Fig. 13

Experimental time-integrated waveguide output profiles of soliton arrays without SPDC for three consecutive laser shots: (a) output image, (b) the corresponding experimental spatial-frequency spectra.

Fig. 14
Fig. 14

Experimental time-integrated waveguide output beams of soliton arrays with SPDC superimposed on the coherent beam at the waveguide input for three consecutive laser shots: (a) output image, (b) the corresponding experimental spatial spectra.

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