Abstract

We study nonlinear light propagation in colloidal nanosuspensions. We introduce a novel model for the nonlinear response of colloids which describes consistently the system in the regimes of low and high light intensities and low/large concentrations of colloidal particles. We employ this model to study the light-induced instabilities and demonstrate the formation of stable spatial solitons as well as the existence of a bistability regime.

© 2008 Optical Society of America

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    [CrossRef]
  6. P. J. Reece, E. M. Wright, and K. Dholakia, "Experimental Observation of Modulation instability and optical spatial soliton arrays in soft condensed matter," Phys. Rev. Lett. 98, 203902 (2007).
    [CrossRef] [PubMed]
  7. C. Lopez-Mariscal, J. C. Gutierrez-Vega, D. McGloin, and K. Dholakia, "Direct detection of optical phase conjugation in a colloidal medium," Opt. Express 15, 6330-6335 (2007).
    [CrossRef] [PubMed]
  8. C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
    [CrossRef] [PubMed]
  9. C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
    [CrossRef] [PubMed]
  10. R. Gordon, J. T. Blakely, and D. Sinton, "Particle-optical self-trapping," Phys. Rev. A 75, 055801 (2007).
    [CrossRef]
  11. R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, "Soliton dynamics and self-induced transparency in nonlinear nanosuspensions," Opt. Express 15, 10207-10218 (2007).
    [CrossRef] [PubMed]
  12. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, (Elsevier, 3rd ed., 2006).
  13. J. C. M. Garnett, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
    [CrossRef]
  14. R. El-Ganainy and D. N. Christodoulides, Z. H. Musslimani, C. Rotschild, and M. Segev, "Optical beam instabilities in nonlinear nanosuspensions," Opt. Lett. 32, 3185-3187 (2007).
    [CrossRef] [PubMed]
  15. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals, (Academic Press, San Diego, 2003), See, e.g., details and references in Chap. 2, pp. 540.
  16. A. E. Kaplan, "Bistable solitons," Phys. Rev. Lett. 55, 1291 (1985).
    [CrossRef] [PubMed]

2007 (5)

2006 (1)

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

2005 (2)

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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

1985 (1)

A. E. Kaplan, "Bistable solitons," Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

1982 (2)

1981 (1)

1980 (1)

1904 (1)

J. C. M. Garnett, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
[CrossRef]

Ashkin, A.

Blakely, J. T.

R. Gordon, J. T. Blakely, and D. Sinton, "Particle-optical self-trapping," 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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Christodoulides, D. N.

Conti, C.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

Dholakia, K.

P. J. Reece, E. M. Wright, and K. Dholakia, "Experimental Observation of Modulation instability and optical spatial soliton arrays in soft condensed matter," Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

C. Lopez-Mariscal, J. C. Gutierrez-Vega, D. McGloin, and K. Dholakia, "Direct detection of optical phase conjugation in a colloidal medium," Opt. Express 15, 6330-6335 (2007).
[CrossRef] [PubMed]

Dziedzic, J. M.

El-Ganainy, R.

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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Garnett, J. C. M.

J. C. M. Garnett, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
[CrossRef]

Ghofraniha, N.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

Gordon, R.

R. Gordon, J. T. Blakely, and D. Sinton, "Particle-optical self-trapping," Phys. Rev. A 75, 055801 (2007).
[CrossRef]

Gutierrez-Vega, J. C.

Kaplan, A. E.

A. E. Kaplan, "Bistable solitons," Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

Lopez-Mariscal, C.

Maloney, P. J.

McGloin, D.

Musslimani, Z. H.

Palmer, A. J.

Reece, P. J.

P. J. Reece, E. M. Wright, and K. Dholakia, "Experimental Observation of Modulation instability and optical spatial soliton arrays in soft condensed matter," Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Ruocco, G.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," 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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Segev, M.

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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Sinton, D.

R. Gordon, J. T. Blakely, and D. Sinton, "Particle-optical self-trapping," 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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Smith, P. W.

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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Tomlison, W. J.

Trillo, S.

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," 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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Wright, E. M.

P. J. Reece, E. M. Wright, and K. Dholakia, "Experimental Observation of Modulation instability and optical spatial soliton arrays in soft condensed matter," 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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

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, "Formation of soliton-like light beams in an aqueous suspension of polystyrene particles," Opt. Spectrosc. 98, 511-514 (2005).
[CrossRef]

Philos. Trans. R. Soc. London (1)

J. C. M. Garnett, "Colors in metal glasses and in metallic films," Philos. Trans. R. Soc. London 203, 385-420 (1904).
[CrossRef]

Phys. Rev. A (1)

R. Gordon, J. T. Blakely, and D. Sinton, "Particle-optical self-trapping," Phys. Rev. A 75, 055801 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

A. E. Kaplan, "Bistable solitons," Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

P. J. Reece, E. M. Wright, and K. Dholakia, "Experimental Observation of Modulation instability and optical spatial soliton arrays in soft condensed matter," Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

C. Conti, G. Ruocco, and S. Trillo, "Optical spatial solitons in soft matter," Phys. Rev. Lett. 95, 183902 (2005).
[CrossRef] [PubMed]

C. Conti, N. Ghofraniha, G. Ruocco, and S. Trillo, "Laser beam filamentation in fractal aggregates," Phys. Rev. Lett. 97, 123903 (2006).
[CrossRef] [PubMed]

Other (2)

J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, (Elsevier, 3rd ed., 2006).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals, (Academic Press, San Diego, 2003), See, e.g., details and references in Chap. 2, pp. 540.

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Figures (4)

Fig. 1.
Fig. 1.

Packing fraction η of colloidal particles vs. the light intensity (solid line). The dashed line shows the dependence of the exponential model, see Eq. (6).

Fig. 2.
Fig. 2.

Profile of colloidal particle packing fraction (solid) and light intensity (dashed) of a soliton solution for parameters η 0=10-3, κ=0.1, P=35, m>1.

Fig. 3.
Fig. 3.

Soliton power against the propagation constant for η 0=10-3 in (a) logarithmic scale (b) square root scale up to κ 1/2=0.06. Solid line shows the value of the integral (15) and circles correspond to stable numerical solutions of the Eq. (9). The dashed line in (b) is a linear fit to the Kerr-like dependence for low κ.

Fig. 4.
Fig. 4.

Propagation of a perturbed unstable soliton for η0=10-3, κ=9×10-3, P=41, m>1: (a) increasing the soliton power by 1% results in switching to a stable soliton after losing about 10% of the beam power to radiation; (b) decreasing the soliton power by 1% leads to diffraction rather than switching to the first stable branch.

Equations (15)

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β P ρ = Z ( η ) ,
j = ρ μ ( f ex + f int ) = ρ μ f ex D ( ρ Z ) ,
α = 3 V p ε 0 n b 2 ( m 2 1 m 2 + 2 ) ,
ρ α β 4 d I d x = d ( ρ Z ) d x ,
α β 4 I ( η ) = g ( η ) g ( η 0 ) ,
η = η 0 exp ( α β 4 I ) .
ε eff = ε b + 3 η ε b ( ε p ε b ) [ ε p + 2 ε b η ( ε p ε b ) ] .
ε eff ε b + 3 ε b ( ε p ε b ) ( ε p + 2 ε b ) η = ε b + δ η .
i u z + 1 2 2 u ± ( η η 0 ) u = 0 ,
u 2 = ± [ g ( η ) g ( η 0 ) ] .
u = { u s + a ( t ) e ikx + b ( t ) e ikx } e i η s t ,
ω 2 = k 2 ( k 2 4 η ( u S 2 ) u S 2 ) .
± d η d u 2 = ± ( d u 2 d η ) 1 = [ 1 η + 2 4 η ( 1 η ) 4 ] 1 .
κ A + 1 2 d 2 A d x 2 + ( η η 0 ) A = 0 .
P = + A 2 d x = 2 η 0 η max A 2 ( η ) ( d η d x ) 1 d η ,

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