Abstract

We experimentally demonstrate and model dark spatial solitons in azo-doped liquid crystals, in the presence of saturation and nonlocality of the effective nonlinearity due to changes in molecular order. The guiding properties of dark solitons are probed with a weak input of different wavelength.

© 2011 Optical Society of America

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  2. C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, pp. 43–55.
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  31. U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
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2010 (3)

2009 (1)

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

2008 (3)

G. Assanto, T. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

G. Assanto and M. Peccianti, Mol. Cryst. Liq. Cryst. 488, 163 (2008).
[CrossRef]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

2007 (1)

2006 (5)

C. Conti, M. Peccianti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, IEEE Photon. Technol. Lett. 18, 1287 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nature Phys. 2, 769 (2006).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

W. Wan, S. Jia, and J. W. Fleischer, Nature Phys. 3, 46 (2006).
[CrossRef]

2004 (3)

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, W. Królikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286(2004).
[CrossRef] [PubMed]

N. Tabiryan, U. Hrozhyk, and S. Serak, Phys. Rev. Lett. 93, 113901 (2004).
[CrossRef] [PubMed]

2003 (2)

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. A 68, 025602 (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

2002 (2)

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

2000 (2)

G. Stegeman, D. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

M. Peccianti, G. Assanto, A. D. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

1998 (2)

1995 (1)

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]

1992 (1)

1991 (2)

G. R. Allan, S. R. Skinner, D. R. Andersen, and A. L. Smirl, Opt. Lett. 16, 156 (1991).
[PubMed]

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

1990 (1)

1973 (1)

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171(1973).
[CrossRef]

Abbate, G.

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

Alberucci, A.

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nature Phys. 2, 769 (2006).
[CrossRef]

Allan, G. R.

Andersen, D. R.

Assanto, G.

A. Piccardi, A. Alberucci, and G. Assanto, Phys. Rev. Lett. 104, 213904 (2010).
[CrossRef] [PubMed]

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, Opt. Lett. 35, 390 (2010).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, Mol. Cryst. Liq. Cryst. 488, 163 (2008).
[CrossRef]

G. Assanto, T. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, IEEE Photon. Technol. Lett. 18, 1287 (2006).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. A 68, 025602 (2003).
[CrossRef]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

M. Peccianti, G. Assanto, A. D. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, pp. 43–55.

Bang, O.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, W. Królikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286(2004).
[CrossRef] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Bortolozzo, U.

Brzadkiewicz, K.

Christiansen, P. L.

Christodoulides, D.

G. Stegeman, D. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

Cohen, O.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nature Phys. 2, 769 (2006).
[CrossRef]

Conti, C.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. A 68, 025602 (2003).
[CrossRef]

C. Conti and G. Assanto, in Encyclopedia of Modern Optics (Elsevier, 2004), Vol.  5, pp. 43–55.

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]

DeGennes, P. G.

P. G. DeGennes and J. Prost, The Physics of Liquid Crystals (Oxford Science, 1993).

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]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[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]

Fleischer, J. W.

W. Wan, S. Jia, and J. W. Fleischer, Nature Phys. 3, 46 (2006).
[CrossRef]

Fratalocchi, A.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

Grover, J.

Hasegawa, A.

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171(1973).
[CrossRef]

Henninot, J. F.

Hoke, L.

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Opt. Express 18, 8697(2010).
[CrossRef] [PubMed]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

Hooton, D. E.

Hrozhyk, U.

N. Tabiryan, U. Hrozhyk, and S. Serak, Phys. Rev. Lett. 93, 113901 (2004).
[CrossRef] [PubMed]

Hrozhyk, U. A.

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Opt. Express 18, 8697(2010).
[CrossRef] [PubMed]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

Jia, S.

W. Wan, S. Jia, and J. W. Fleischer, Nature Phys. 3, 46 (2006).
[CrossRef]

Kaplan, A. E.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

D. R. Andersen, D. E. Hooton, J. Grover, A. Swartzlander, and A. E. Kaplan, Opt. Lett. 15, 783 (1990).
[CrossRef] [PubMed]

Kartashov, Y. V.

Khoo, I. C.

M. Peccianti, G. Assanto, A. D. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Kimball, B. R.

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Opt. Express 18, 8697(2010).
[CrossRef] [PubMed]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons(Academic, 2003).

Krolikowski, W.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Królikowski, W.

Luca, A. D.

M. Peccianti, G. Assanto, A. D. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

B. Luther-Davies and Y. Xiaoping, Opt. Lett. 17, 496(1992).
[CrossRef] [PubMed]

Marchant, T.

G. Assanto, T. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

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]

Neshev, D.

Neshev, D. N.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Nikolov, N. I.

Peccianti, M.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

G. Assanto and M. Peccianti, Mol. Cryst. Liq. Cryst. 488, 163 (2008).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, IEEE Photon. Technol. Lett. 18, 1287 (2006).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, Phys. Rev. A 68, 025602 (2003).
[CrossRef]

M. Peccianti, K. Brzadkiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

M. Peccianti, G. Assanto, A. D. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Petersen, D. E.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Piccardi, A.

Prost, J.

P. G. DeGennes and J. Prost, The Physics of Liquid Crystals (Oxford Science, 1993).

Rasmussen, J. J.

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Residori, S.

Rotschild, C.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nature Phys. 2, 769 (2006).
[CrossRef]

Ruocco, G.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

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]

Segev, M.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nature Phys. 2, 769 (2006).
[CrossRef]

G. Stegeman, D. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[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]

Serak, S.

N. Tabiryan, U. Hrozhyk, and S. Serak, Phys. Rev. Lett. 93, 113901 (2004).
[CrossRef] [PubMed]

Serak, S. V.

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Opt. Express 18, 8697(2010).
[CrossRef] [PubMed]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, IEEE Photon. Technol. Lett. 18, 1287 (2006).
[CrossRef]

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]

Simoni, F.

F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, 1997).

Skinner, S. R.

Smirl, A. L.

Smyth, N. F.

G. Assanto, T. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

Steeves, D. M.

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Opt. Express 18, 8697(2010).
[CrossRef] [PubMed]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

Stegeman, G.

G. Stegeman, D. Christodoulides, and M. Segev, IEEE J. Sel. Top. Quantum Electron. 6, 1419 (2000).
[CrossRef]

Swartzlander, A.

Swartzlander, G. A.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Tabiryan, N.

N. Tabiryan, U. Hrozhyk, and S. Serak, Phys. Rev. Lett. 93, 113901 (2004).
[CrossRef] [PubMed]

Tabiryan, N. V.

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Opt. Express 18, 8697(2010).
[CrossRef] [PubMed]

U. A. Hrozhyk, S. V. Serak, N. V. Tabiryan, L. Hoke, D. M. Steeves, and B. R. Kimball, Mol. Cryst. Liq. Cryst. 489, 257 (2008).
[CrossRef]

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, IEEE Photon. Technol. Lett. 18, 1287 (2006).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 171(1973).
[CrossRef]

Torner, L.

Trillo, S.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

Umeton, C.

M. Peccianti, G. Assanto, A. D. Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Wan, W.

W. Wan, S. Jia, and J. W. Fleischer, Nature Phys. 3, 46 (2006).
[CrossRef]

Warenghem, M.

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Xiaoping, Y.

Yariv, A.

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Figures (5)

Fig. 1
Fig. 1

(a) Sketch of the NLC sample. (b) Measured beam waist scaled to the input value w 0 , evaluated in z = 500 μm for ordinary (circles) and extraordinary (squares) polarization. (c)–(e) Evolution of an extraordinary beam for (c)  P = 0.02 , (d) 1.00, and (e)  2.50 m W , respectively. (f)–(h) Evolution of an ordinary beam for the same input powers.

Fig. 2
Fig. 2

Acquired propagation of an input e-beam with a π-phase jump across its profile: acquired images and transverse distribution in (top) z = 50 , (middle) z = 300 , and (bottom) z = 600 μm from the input, respectively. For P = 1.2 mW [column (a)] no appreciable self-confinement is observed, whereas for P = 4 mW [column (b)] the dark notch propagates with a nearly constant profile.

Fig. 3
Fig. 3

(a) Measured notch-FWHM for P = 1.2 (square), P = 2.5 (circle), P = 3.5 (triangle), and P = 4 mW (black dot). (b) Measured notch-FWHM versus power in z = 600 μm .

Fig. 4
Fig. 4

Simulated beam propagation for a TM 1 -like excitation in plane y z for power densities (a)  P 1 D = 1 × 10 6 , (b)  5 × 10 3 , (c)  1 × 10 5 , and (d) 5 × 10 5 Wm 1 , respectively. Insets, normalized intensity profile at z = 600 μm ; the lower inset in (a) shows the input profile. (e) Magnified profiles in z = 600 μm . (f) As in (e) but with the output profile convolved with the NLC blurring function exp ( y 2 / σ 2 ) , with σ = 4 μm [27]. Dashed curves in (e)–(f) correspond to the input beam.

Fig. 5
Fig. 5

Acquired evolution of (a) an e- or (b) an o-probe beam colaunched with the soliton beam. The input (e-soliton) powers are (a), (d)  P = 1 and (b), (e)  P = 4 mW . (c), (f) Normalized probe waist versus soliton power in z = 500 μm , for (c) extraordinary and (f) ordinary polarizations.

Equations (1)

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2 i k 0 n 0 A z + D 2 A y 2 + i α A + 2 n 0 k 0 2 Δ n ( | A | 2 ) A = 0 ,

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