Abstract

We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.

© 2013 Optical Society of America

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    [CrossRef]
  2. Z. Chen, M. Segev, and D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. R. El-Ganainy, D. N. Christodoulides, C. Rotschild, and M. Segev, Opt. Express 15, 10207 (2007).
    [CrossRef]
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    [CrossRef]
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2012 (2)

2010 (1)

Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Phys. Rev. Lett. 105, 163906 (2010).
[CrossRef]

2009 (3)

R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, Phys. Rev. A 80, 053805 (2009).
[CrossRef]

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. A 79, 023814 (2009).
[CrossRef]

W. M. Lee, R. El-Ganainy, D. N. Christodoulides, K. Dholakia, and E. M. Wright, Opt. Express 17, 10277 (2009).
[CrossRef]

2008 (2)

2007 (2)

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

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

2006 (1)

S. Duhr and D. Braun, Phys. Rev. Lett. 96, 168301 (2006).
[CrossRef]

2005 (1)

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

1999 (1)

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

1995 (1)

1994 (1)

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

1991 (1)

1982 (1)

1981 (1)

1974 (1)

J. E. Bjorkholm and A. A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

1965 (1)

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

Agrawal, G.

Y. Kivshar and G. Agrawal, Optical Solitons, Fibers to Photonic Crystals (Elsevier, 2003).

Aitchison, J. S.

Anyfantakis, M.

Ashkin, A.

Ashkin, A. A.

J. E. Bjorkholm and A. A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

Barak, A.

Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Phys. Rev. Lett. 105, 163906 (2010).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm and A. A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

Braun, D.

S. Duhr and D. Braun, Phys. Rev. Lett. 96, 168301 (2006).
[CrossRef]

Cannan, D.

Carvalho, M. I.

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Chizhov, S.

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

Christodoulides, D. N.

Z. Chen, M. Segev, and D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

W. M. Lee, R. El-Ganainy, D. N. Christodoulides, K. Dholakia, and E. M. Wright, Opt. Express 17, 10277 (2009).
[CrossRef]

R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, Phys. Rev. A 80, 053805 (2009).
[CrossRef]

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

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Crosignani, B.

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

Dholakia, K.

W. M. Lee, R. El-Ganainy, D. N. Christodoulides, K. Dholakia, and E. M. Wright, Opt. Express 17, 10277 (2009).
[CrossRef]

R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, Phys. Rev. A 80, 053805 (2009).
[CrossRef]

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

DiPorto, P.

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

Duhr, S.

S. Duhr and D. Braun, Phys. Rev. Lett. 96, 168301 (2006).
[CrossRef]

Dziedzic, J. M.

El-Ganainy, R.

Fardad, S.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Fedorov, S.

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

Fytas, G.

Heinrich, M.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Hu, Y.

Hulst, H.

H. Hulst and H. Van De Hulst, Light Scattering by Small Particles (Dover, 1957).

Jackel, J. L.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Kelley, P. L.

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

Kivshar, Y.

Y. Kivshar and G. Agrawal, Optical Solitons, Fibers to Photonic Crystals (Elsevier, 2003).

Kivshar, Y. S.

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. A 79, 023814 (2009).
[CrossRef]

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 1371 (2008).
[CrossRef]

Krolikowski, W.

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. A 79, 023814 (2009).
[CrossRef]

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 1371 (2008).
[CrossRef]

Lamhot, Y.

Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Phys. Rev. Lett. 105, 163906 (2010).
[CrossRef]

Lau, M.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Leaird, D. E.

Lee, W. M.

R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, Phys. Rev. A 80, 053805 (2009).
[CrossRef]

W. M. Lee, R. El-Ganainy, D. N. Christodoulides, K. Dholakia, and E. M. Wright, Opt. Express 17, 10277 (2009).
[CrossRef]

Li, T.

Loppinet, B.

Man, W.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Matuszewski, M.

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. A 79, 023814 (2009).
[CrossRef]

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 1371 (2008).
[CrossRef]

Morandotti, R.

Oliver, M. K.

Peleg, O.

Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Phys. Rev. Lett. 105, 163906 (2010).
[CrossRef]

Pispas, S.

Prakash, J.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Reece, P. J.

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

Rotschild, C.

Rozanov, N.

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

Sabirov, R.

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

Salandrino, A.

Segev, M.

Z. Chen, M. Segev, and D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Phys. Rev. Lett. 105, 163906 (2010).
[CrossRef]

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

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

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

Semenov, V.

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

Silberberg, Y.

Smirnov, V.

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

Smith, P. W.

Smith, P. W. E.

Starchikova, T.

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

Stegeman, G. I.

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

Tomlinson, W. J.

Valley, G. C.

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

Van De Hulst, H.

H. Hulst and H. Van De Hulst, Light Scattering by Small Particles (Dover, 1957).

Vysotina, N.

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

Weiner, A. M.

Wright, E. M.

W. M. Lee, R. El-Ganainy, D. N. Christodoulides, K. Dholakia, and E. M. Wright, Opt. Express 17, 10277 (2009).
[CrossRef]

R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, Phys. Rev. A 80, 053805 (2009).
[CrossRef]

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

Yariv, A.

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

Yashin, V.

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

Zhang, P.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

Zhang, X.

Zhang, Z.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

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

Opt. Express (3)

Opt. Lett. (5)

Opt. Spectrosc. (1)

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

Phys. Rev. A (2)

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. A 79, 023814 (2009).
[CrossRef]

R. El-Ganainy, D. N. Christodoulides, E. M. Wright, W. M. Lee, and K. Dholakia, Phys. Rev. A 80, 053805 (2009).
[CrossRef]

Phys. Rev. Lett. (6)

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

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

J. E. Bjorkholm and A. A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).
[CrossRef]

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

S. Duhr and D. Braun, Phys. Rev. Lett. 96, 168301 (2006).
[CrossRef]

Y. Lamhot, A. Barak, O. Peleg, and M. Segev, Phys. Rev. Lett. 105, 163906 (2010).
[CrossRef]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D. N. Christodoulides, Rep. Prog. Phys. 75, 086401 (2012).
[CrossRef]

Science (1)

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

Other (4)

Y. Kivshar and G. Agrawal, Optical Solitons, Fibers to Photonic Crystals (Elsevier, 2003).

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Engineered optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” arXiv:1308.3039 (2013).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

H. Hulst and H. Van De Hulst, Light Scattering by Small Particles (Dover, 1957).

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Figures (4)

Fig. 1.
Fig. 1.

Self-trapped beam propagation through a PTFE nano-suspension: (a) experimental results, (b) theoretical model, and (c) experimental setup used.

Fig. 2.
Fig. 2.

Repulsion of two π out of phase, 13 μm apart, self-trapped beams in a PTFE nano-suspension. (a)–(c) Numerical simulations of repelling beam interaction, (b) beam profile at the input, and (c) output. (d) Beam diffraction at low powers (linear regime). (e), (f) Corresponding experimental snapshots. In (g), one beam is blocked before the cuvette. In this case, the beam remains at the same distance from the dashed line.

Fig. 3.
Fig. 3.

Interaction of two in-phase self-trapped beams with an initial 26 μm separation after 3 mm of propagation. (a)–(c) Numerical simulations indicate attraction. (b) Combined beam profile at the input and (c) output. (d), (e) Shows corresponding experimental results at the input and output, respectively.

Fig. 4.
Fig. 4.

Interaction of between two π/2 out-of-phase, self-trapped beams after 3 mm. (a)–(c) Numerical simulations show power exchange between the two beams. (d), (e) Corresponding experimental results display similar behavior for the same initial conditions.

Equations (1)

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iϕz+12k0nb2ϕ+k0(npnb)fϕ+iσf2Vpϕ=0,

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