Abstract

We investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nanosuspensions. We show that in these systems the process of modulational instability depends on the input beam conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity.

© 2007 Optical Society of America

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  1. A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).
    [CrossRef]
  2. D. V. Grier, Nature 424, 810 (2003).
    [CrossRef] [PubMed]
  3. J. P. Gordon, Phys. Rev. A 8, 14 (1973).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
    [CrossRef] [PubMed]
  5. K. Dholakia, Nat. Mater. 4, 579 (2005).
    [CrossRef] [PubMed]
  6. P. W. Smith, A. Ashkin, and W. J. Tomlinson, Opt. Lett. 6, 284 (1981).
    [CrossRef] [PubMed]
  7. A. Ashkin, J. M. Dziedzic, and P. W. Smith, Opt. Lett. 7, 276 (1982).
    [CrossRef] [PubMed]
  8. V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
    [CrossRef]
  9. P. J. Reece, E. M. Wright, and K. Dholakia, Phys. Rev. Lett. 98, 203902 (2007).
    [CrossRef] [PubMed]
  10. C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).
    [CrossRef] [PubMed]
  11. C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
    [CrossRef] [PubMed]
  12. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.
  13. R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, Opt. Express 15, 10207 (2007).
    [CrossRef] [PubMed]
  14. R. Gordon, J. T. Blakely, and D. Sinton, Phys. Rev. A 75, 055801 (2007).
    [CrossRef]
  15. K. Tai, H. Hasegawa, and A. Tomita, Phys. Rev. Lett. 65, 135 (1986).
    [CrossRef]
  16. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
    [CrossRef] [PubMed]
  17. E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
    [CrossRef]

2007 (3)

P. J. Reece, E. M. Wright, and K. Dholakia, Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, Opt. Express 15, 10207 (2007).
[CrossRef] [PubMed]

R. Gordon, J. T. Blakely, and D. Sinton, Phys. Rev. A 75, 055801 (2007).
[CrossRef]

2006 (1)

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

2005 (3)

C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

K. Dholakia, Nat. Mater. 4, 579 (2005).
[CrossRef] [PubMed]

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

2003 (1)

D. V. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

2000 (2)

A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).
[CrossRef]

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

1986 (3)

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

K. Tai, H. Hasegawa, and A. Tomita, Phys. Rev. Lett. 65, 135 (1986).
[CrossRef]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
[CrossRef] [PubMed]

1982 (1)

1981 (1)

1973 (1)

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

Ashkin, A.

Bjorkholm, J. E.

Blakely, J. T.

R. Gordon, J. T. Blakely, and D. Sinton, Phys. Rev. A 75, 055801 (2007).
[CrossRef]

Chizhov, S. A.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Christodoulides, D. N.

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.

R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, Opt. Express 15, 10207 (2007).
[CrossRef] [PubMed]

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

Chu, S.

Conti, C.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

Dholakia, K.

P. J. Reece, E. M. Wright, and K. Dholakia, Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

K. Dholakia, Nat. Mater. 4, 579 (2005).
[CrossRef] [PubMed]

Dziedzic, J. M.

El-Ganainy, R.

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.

R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, Opt. Express 15, 10207 (2007).
[CrossRef] [PubMed]

Eugenieva, E.

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

Fedorov, S. V.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Ghofraniha, N.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

Gordon, R.

R. Gordon, J. T. Blakely, and D. Sinton, Phys. Rev. A 75, 055801 (2007).
[CrossRef]

Grier, D. V.

D. V. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Hasegawa, H.

K. Tai, H. Hasegawa, and A. Tomita, Phys. Rev. Lett. 65, 135 (1986).
[CrossRef]

Kip, D.

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

Kuznetsov, E. A.

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

Makris, K. G.

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.

Reece, P. J.

P. J. Reece, E. M. Wright, and K. Dholakia, Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

Rothchild, C.

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.

Rotschild, C.

Rozanov, N. N.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Rubenchik, A. M.

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

Ruocco, G.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

Sabirov, R. L.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Segev, M.

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.

R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, Opt. Express 15, 10207 (2007).
[CrossRef] [PubMed]

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

Semenov, V. E.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Sinton, D.

R. Gordon, J. T. Blakely, and D. Sinton, Phys. Rev. A 75, 055801 (2007).
[CrossRef]

Smirnov, V. A.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Smith, P. W.

Soljacic, M.

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

Starchikova, T. V.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Tai, K.

K. Tai, H. Hasegawa, and A. Tomita, Phys. Rev. Lett. 65, 135 (1986).
[CrossRef]

Tomita, A.

K. Tai, H. Hasegawa, and A. Tomita, Phys. Rev. Lett. 65, 135 (1986).
[CrossRef]

Tomlinson, W. J.

Trillo, S.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

Vysotina, N. V.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Wright, E. M.

P. J. Reece, E. M. Wright, and K. Dholakia, Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

Yashin, V. E.

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Zakharov, V. E.

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Ashkin, IEEE J. Sel. Top. Quantum Electron. 6, 841 (2000).
[CrossRef]

Nat. Mater. (1)

K. Dholakia, Nat. Mater. 4, 579 (2005).
[CrossRef] [PubMed]

Nature (1)

D. V. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Opt. Spectrosc. (1)

V. E. Yashin, S. A. Chizhov, R. L. Sabirov, T. V. Starchikova, N. V. Vysotina, N. N. Rozanov, V. E. Semenov, V. A. Smirnov, and S. V. Fedorov, Opt. Spectrosc. 98, 466 (2005).
[CrossRef]

Phys. Rep. (1)

E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 142, 103 (1986).
[CrossRef]

Phys. Rev. A (2)

J. P. Gordon, Phys. Rev. A 8, 14 (1973).
[CrossRef]

R. Gordon, J. T. Blakely, and D. Sinton, Phys. Rev. A 75, 055801 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

K. Tai, H. Hasegawa, and A. Tomita, Phys. Rev. Lett. 65, 135 (1986).
[CrossRef]

P. J. Reece, E. M. Wright, and K. Dholakia, Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

Science (1)

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

Other (1)

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, C. Rothchild, and M. Segev, paper QMB4, presented at the Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 2007, CLEO/QELS 2007, Baltimore, Maryland, May 6-11, 2007.

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Figures (4)

Fig. 1
Fig. 1

MI gain versus perturbation wavenumber for (a) an exponentially nonlinear ( n p n b > 1 ) and (b) an exponentially saturable nonlinear nanosuspension system ( n p n b < 1 ) for the parameters given in the text. The solid/dotted curves depict the MI gain when b = 0 b = 1 for u o = 1 .

Fig. 2
Fig. 2

Transverse MI gain of a stripe soliton versus perturbation wavenumber q for an exponentially nonlinear colloidal system when the 1D soliton solution belongs to (a) the stable ( κ = 1.7 ) and (b) the unstable ( κ = 3 ) branch.

Fig. 3
Fig. 3

(a)–(c) and (d)–(f): Propagation dynamics of the stripe soliton beams associated with Figs. 2a, 2b, respectively. (a), (d) input profiles. Output intensity in (b) a lossless system at z = 1.9 mm , (c) in a lossy system (45% of losses at the output) at 6 mm . (e) Output beam in the absence of losses (after 3 mm ), and (d) effect of losses ( 16 % after 0.8 mm of propagation).

Fig. 4
Fig. 4

(a) Transverse MI gain of a stripe soliton versus perturbation wavenumber for a saturable exponentially nonlinear colloidal dispersion when κ = 0.75 . Corresponding propagation dynamics in this same system after z = 7 mm for (b) an input soliton stripe beam, when (c) losses are neglected and (d) nonlinear Rayleigh losses are included.

Equations (8)

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

i φ z + 1 2 k 0 n b 2 φ + k 0 ( n p n b ) V p ρ 0 exp ( α 4 k B T ( φ 2 φ 0 2 ) ) φ + i 2 σ ρ 0 exp ( α 4 k B T φ 2 ) φ = 0 .
i u ξ + u X X + u Y Y + a exp [ a ( u 2 b u o 2 ) ] u + i δ exp ( a u 2 ) u = 0 ,
i ε ξ + ε X X + u o 2 ( ε + ε * ) exp ( a ( 1 b ) u o 2 ) = 0 .
β 2 = K 2 [ K 2 2 u o 2 exp ( a ( 1 b ) u o 2 ) ] .
i ε ξ κ ε + ε X X + ε Y Y + a exp ( a u s 2 ) ε + u s 2 exp ( a u s 2 ) ( ε + ε * ) = 0 .
ε ( X , Y , ξ ) = ( V ( X ) + W ( X ) ) exp [ i ( β ξ + q Y ) ] + ( V * ( X ) W * ( X ) ) exp [ i ( β * ξ + q Y ) ] ,
V X X + [ a exp ( a u s 2 ) + 2 u s 2 exp ( a u s 2 ) κ q 2 ] V = β W ,
W X X + [ a exp ( a u s 2 ) κ q 2 ] W = β V .

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