Abstract

We study the influence of a constant background noise on the dynamics of spectral incoherent solitons, which are incoherent structures sustained by a noninstantaneous (Raman-like) nonlinearity. As the level of the noise background increases, the incoherent wave enters a novel nonlinear regime characterized by oscillatory dynamics of the incoherent spectrum, which develop within a spectral cone during the propagation. In contrast to the conventional Raman-like spectral red shift, such incoherent spectral dynamics can be characterized by a significant spectral blue shift. On the basis of the kinetic wave theory, we derive explicit analytical expressions of these incoherent oscillatory spectral dynamics.

© 2013 Optical Society of America

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2013 (4)

A. Schwartz and B. Fischer, Opt. Express 21, 6196 (2013).
[CrossRef]

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

2012 (6)

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

S. Derevyanko and E. Small, Phys. Rev. A 85, 053816 (2012).
[CrossRef]

J. Garnier, M. Lisak, and A. Picozzi, J. Opt. Soc. Am. B 29, 2229 (2012).
[CrossRef]

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
[CrossRef]

M. Erkintalo, M. Surakka, J. Turunen, A. T. Friberg, and G. Genty, Opt. Lett. 37, 169 (2012).
[CrossRef]

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

2011 (6)

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
[CrossRef]

P. Suret, A. Picozzi, and S. Randoux, Opt. Express 19, 17852 (2011).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

2010 (7)

C. Conti, M. A. Schmidt, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 105, 263902 (2010).
[CrossRef]

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Opt. Lett. 35, 2367 (2010).
[CrossRef]

D. B. Soh, J. P. Koplow, S. W. Moore, K. L. Schroder, and W. L. Hsu, Opt. Express 18, 22393 (2010).
[CrossRef]

A. Piskarskas, V. Pyragaite, and A. Stabinis, Phys. Rev. A 82, 053817 (2010).
[CrossRef]

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, Nat. Photonics 4, 721 (2010).
[CrossRef]

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

2009 (5)

S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, Opt. Express 17, 20707 (2009).
[CrossRef]

B. Barviau, B. Kibler, A. Kudlinski, A. Mussot, G. Millot, and A. Picozzi, Opt. Express 17, 7392 (2009).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Phys. Rev. A 80, 031804 (2009).
[CrossRef]

Y. Silberberg, Y. Lahini, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

2008 (4)

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef]

2007 (1)

2005 (1)

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

1997 (1)

A. Schwache and F. Mitschke, Phys. Rev. E 55, 7720 (1997).
[CrossRef]

1995 (1)

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

Angelani, L.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Aschieri, P.

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

Babin, S.

Barviau, B.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

B. Barviau, B. Kibler, A. Kudlinski, A. Mussot, G. Millot, and A. Picozzi, Opt. Express 17, 7392 (2009).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

Biancalana, F.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

C. Conti, M. A. Schmidt, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 105, 263902 (2010).
[CrossRef]

Bortolozzo, U.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Bromberg, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, Nat. Photonics 4, 721 (2010).
[CrossRef]

Chang, W.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Churkin, D.

Colman, P.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

Combrie, S.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

Conforti, M.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Conti, C.

C. Conti, M. A. Schmidt, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 105, 263902 (2010).
[CrossRef]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef]

de Rossi, A.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

Della Valle, G.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Derevyanko, S.

S. Derevyanko and E. Small, Phys. Rev. A 85, 053816 (2012).
[CrossRef]

Doya, V.

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

Dylov, D.

D. Dylov and J. Fleischer, in Localized States in Physics: Solitons and Patterns, Part 1 (Springer, 2011), pp. 17–34.

El-Taher, A.

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
[CrossRef]

Erkintalo, M.

Falkovich, G.

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
[CrossRef]

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Phys. Rev. A 80, 031804 (2009).
[CrossRef]

Fanjoux, G.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef]

Fischer, B.

A. Schwartz and B. Fischer, Opt. Express 21, 6196 (2013).
[CrossRef]

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

Fleischer, J.

D. Dylov and J. Fleischer, in Localized States in Physics: Solitons and Patterns, Part 1 (Springer, 2011), pp. 17–34.

Fratalocchi, A.

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Friberg, A. T.

Garnier, J.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

J. Garnier, M. Lisak, and A. Picozzi, J. Opt. Soc. Am. B 29, 2229 (2012).
[CrossRef]

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
[CrossRef]

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

Gat, O.

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

Genty, G.

Harper, P.

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
[CrossRef]

Hölzer, P.

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Hsu, W. L.

Husko, C. A.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

Ismagulov, A.

Jauslin, H. R.

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Opt. Lett. 35, 2367 (2010).
[CrossRef]

Joly, N. Y.

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Kablukov, S.

Kibler, B.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

B. Barviau, B. Kibler, A. Kudlinski, A. Mussot, G. Millot, and A. Picozzi, Opt. Express 17, 7392 (2009).
[CrossRef]

Kobtsev, S.

Koplow, J. P.

Kudlinski, A.

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

B. Barviau, B. Kibler, A. Kudlinski, A. Mussot, G. Millot, and A. Picozzi, Opt. Express 17, 7392 (2009).
[CrossRef]

Kukarin, S.

Lahini, Y.

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, Nat. Photonics 4, 721 (2010).
[CrossRef]

Y. Silberberg, Y. Lahini, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

Latkin, A.

Laurie, J.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Lee, H. W.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Leonetti, M.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Lisak, M.

Longhi, S.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Maillotte, H.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef]

Marini, A.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Mezentsev, V. K.

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Phys. Rev. A 80, 031804 (2009).
[CrossRef]

Michaud, J.

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef]

Michel, C.

B. Kibler, C. Michel, J. Garnier, and A. Picozzi, Opt. Lett. 37, 2472 (2012).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Opt. Lett. 35, 2367 (2010).
[CrossRef]

Millot, G.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

B. Barviau, B. Kibler, A. Kudlinski, A. Mussot, G. Millot, and A. Picozzi, Opt. Express 17, 7392 (2009).
[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

Mitschke, F.

A. Schwache and F. Mitschke, Phys. Rev. E 55, 7720 (1997).
[CrossRef]

Moore, S. W.

Morandotti, R.

Y. Silberberg, Y. Lahini, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

Musher, S. L.

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
[CrossRef]

Mussot, A.

Nazarenko, S.

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

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B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
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B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
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P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
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A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
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A. Piskarskas, V. Pyragaite, and A. Stabinis, Phys. Rev. A 82, 053817 (2010).
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J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
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S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
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A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
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C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
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Russell, P. St. J.

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
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M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
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A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
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A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

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M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
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A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
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Turitsyn, S. K.

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
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E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Phys. Rev. A 80, 031804 (2009).
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Turitsyna, E. G.

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
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E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Phys. Rev. A 80, 031804 (2009).
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Xu, G.

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
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Zakharov, V. E.

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
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C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, Nat. Photonics 4, 721 (2010).
[CrossRef]

Nature Sci. Rep. (1)

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. de Rossi, and C. W. Wong, Nature Sci. Rep. 3, 1100 (2013).

New J. Phys. (1)

A. Marini, M. Conforti, G. Della Valle, H. W. Lee, T. X. Tran, W. Chang, M. A. Schmidt, S. Longhi, P. St. J. Russell, and F. Biancalana, New J. Phys. 15, 013033 (2013).
[CrossRef]

Opt. Express (5)

Opt. Lett. (3)

Phys. Rep. (2)

S. L. Musher, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep. 252, 177 (1995).
[CrossRef]

J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
[CrossRef]

Phys. Rev. A (7)

P. Aschieri, J. Garnier, C. Michel, V. Doya, and A. Picozzi, Phys. Rev. A 83, 033838 (2011).
[CrossRef]

A. Piskarskas, V. Pyragaite, and A. Stabinis, Phys. Rev. A 82, 053817 (2010).
[CrossRef]

B. Barviau, B. Kibler, and A. Picozzi, Phys. Rev. A 79, 063840 (2009).
[CrossRef]

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Phys. Rev. A 80, 031804 (2009).
[CrossRef]

C. Michel, B. Kibler, and A. Picozzi, Phys. Rev. A 83, 023806 (2011).
[CrossRef]

B. Barviau, J. Garnier, G. Xu, B. Kibler, G. Millot, and A. Picozzi, Phys. Rev. A 87, 035803 (2013).
[CrossRef]

S. Derevyanko and E. Small, Phys. Rev. A 85, 053816 (2012).
[CrossRef]

Phys. Rev. E (3)

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, Phys. Rev. E 84, 066605 (2011).
[CrossRef]

A. Schwache and F. Mitschke, Phys. Rev. E 55, 7720 (1997).
[CrossRef]

A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005).
[CrossRef]

Phys. Rev. Lett. (10)

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[CrossRef]

Y. Silberberg, Y. Lahini, E. Small, and R. Morandotti, Phys. Rev. Lett. 102, 233904 (2009).
[CrossRef]

R. Weill, B. Fischer, and O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[CrossRef]

G. Fanjoux, J. Michaud, H. Maillotte, and T. Sylvestre, Phys. Rev. Lett. 100, 013908 (2008).
[CrossRef]

C. Conti, M. A. Schmidt, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 105, 263902 (2010).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St. J. Russell, and F. Biancalana, Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

A. Picozzi and J. Garnier, Phys. Rev. Lett. 107, 233901 (2011).
[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, Phys. Rev. Lett. 101, 093901 (2008).
[CrossRef]

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 104, 054101 (2010).
[CrossRef]

Proc. R. Soc. A (1)

E. G. Turitsyna, G. Falkovich, A. El-Taher, X. Shu, P. Harper, and S. K. Turitsyn, Proc. R. Soc. A 468, 2496 (2012).
[CrossRef]

Other (2)

D. Dylov and J. Fleischer, in Localized States in Physics: Solitons and Patterns, Part 1 (Springer, 2011), pp. 17–34.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

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Figures (4)

Fig. 1.
Fig. 1.

Simulations of (a), (c) NLSE (1) and (b), (d) kinetic equation (2) for the damped harmonic oscillator (Raman-like) response. As the level of the background noise increases [(a), (b) ρ=0.1; (c), (d) ρ=3], the incoherent wave exhibits a transition from the SIS regime (a), (b), to the new regime characterized by oscillations that develop within a spectral cone (c), (d) (τR=2.5τ0).

Fig. 2.
Fig. 2.

(a) Schematic representation of the derivative of the response function for the exponential response, (b) damped harmonic oscillator response for α=0 (dashed green), α=2.6 (solid blue), and the corresponding values of ωmin and ωmax [see Eqs. (5) and (6)]. Note that tj denotes tj/τ0 (j=1, 2, 3).

Fig. 3.
Fig. 3.

Simulations of the NLSE (1) (gray) and KE (2) (green) for the exponential response function (the solid black line denotes the initial condition). The incoherent wave exhibits a spectral blue shift, instead of the expected red shift. Plot of the analytical solution given in Eqs. (7) and (8) (red). Quantitative agreement is obtained between the analytical solution and the simulations of the NLSE and KE [(a) z=1250Lnl; (b) z=2000Lnl]; τR=τ0=32fs, ρ=10. The vertical lines denote the analytical expressions of ωmin,max given in the text.

Fig. 4.
Fig. 4.

Simulations of the NLSE (gray) and KE (green) for the damped harmonic oscillator response: (a), (b) α=0; (c), (d) α=2.6 (the solid black line denotes the initial condition). Quantitative agreement is obtained between the analytical solution [Eq. (7), red] and the simulations of the NLSE and KE [(a) z=400, (b) z=1600, (c) z=300, (d) z=600, in units of Lnl]; τR=τ0=32fs, ρ=10. (e) Typical intensity profiles |A|2(t) corresponding to the spectra (c), (d).

Equations (11)

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

izAβttA+γAR(tt)|A|2(z,t)dt=0,
znω=γπnω+g(ωω)nωdω.
n˜ω(z)=+B˜0(t)exp[2iγn0G(t)ziωt]dt,
n˜ω(z)=20B˜0(t)cos[γn0R(t)z+ωt]dt.
ωmin=γn0zmint>0(R(t)),
ωmax=γn0zmaxt>0(R(t)).
n˜ω(z)22πτRB˜0(t1(ω/z))z|ω/z|cos[K(ω/z)z+π/4],
K(ω/z)=τR[1+log(γn0z/(ωτR2))]ω/z.
ωmax=γn0zτR2(1+α2)exp[α1(atan(2α1α2)+σπ)],
n˜ω(z)j=1m22πB˜0(tj(ω/z))γ|R(tj(ω/z))|n0zcos[Θj(ω,z)],
Kj(ω/z)=γn0R(tj(ω/z))+tj(ω/z)ω/z.

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