Abstract

We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed the formation of solitary waves that will appear during the modulation instability process at those preferred intervals. Afterwards, optical-event horizon effects between dispersive waves and solitons produce an artificial collective acceleration that favours the collision of solitons, which could eventually lead to a rogue-soliton generation.

© 2017 Optical Society of America

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References

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2016 (3)

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Integrable turbulence and rogue waves: Breathers or solitons?” Phys. Rev. Lett. 116, 103901 (2016).
[Crossref] [PubMed]

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94, 033811 (2016).
[Crossref]

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Efficient all-optical control of solitons,” Opt. Quantum Electron. 48, 503 (2016).
[Crossref]

2015 (3)

2014 (5)

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photon. 8, 755–764 (2014).
[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).
[Crossref] [PubMed]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the anderson regime,” Nat. Commun. 5, 4534 (2014).
[Crossref] [PubMed]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref] [PubMed]

2013 (5)

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref] [PubMed]

M. F. Saleh and F. Biancalana, “Soliton-radiation trapping in gas-filled photonic crystal fibers,” Phys. Rev. A 87, 043807 (2013).
[Crossref]

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

P. T. S. DeVore, D. R. Solli, D. Borlaug, C. Ropers, and B. Jalali, “Rogue events and noise shaping in nonlinear silicon photonics,” J. Opt. 15, 064001 (2013).
[Crossref]

2012 (6)

R. Driben and I. Babushkin, “Accelerated rogue waves generated by soliton fusion at the advanced stage of super-continuum formation in photonic-crystal fibers,” Opt. Lett. 37, 5157–5159 (2012).
[Crossref] [PubMed]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).
[Crossref]

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear schrÃűdinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53 (2012).
[Crossref]

C. Conti, “Solitonization of the anderson localization,” Phys. Rev. A 86, 061801 (2012).
[Crossref]

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[Crossref] [PubMed]

2011 (2)

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref] [PubMed]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref] [PubMed]

2010 (2)

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, V. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).
[Crossref] [PubMed]

G. Genty, C. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989 – 996 (2010).
[Crossref]

2009 (2)

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref] [PubMed]

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[Crossref] [PubMed]

2008 (5)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[Crossref] [PubMed]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
[Crossref]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
[Crossref] [PubMed]

2007 (3)

D. Tuürke, S. Pricking, A. Husakou, J. Teipel, J. Herrmann, and H. Giessen, “Coherence of subsequent supercontinuum pulses generated in tapered fibers in the femtosecond regime,” Opt. Express 15, 2732–2741 (2007).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

2006 (5)

S. M. Kobtsev and S. V. Smirnov, “Coherent properties of super-continuum containing clearly defined solitons,” Opt. Express 14, 3968–3980 (2006).
[Crossref] [PubMed]

A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2006).
[Crossref]

M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2003 (4)

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944–946 (2003).
[Crossref] [PubMed]

A. V. Avdokhin, S. V. Popov, and J. R. Taylor, “Continuous-wave, high-power, raman continuum generation in holey fibers,” Opt. Lett. 28, 1353–1355 (2003).
[Crossref] [PubMed]

T. Schreiber, J. Limpert, H. Zellmer, A. TÃijnnermann, and K. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71 – 78 (2003).
[Crossref]

C. Kharif and E. Pelinovsky, “Physical mechanisms of the rogue wave phenomenon,” Europ. J. Mechan. B Fluids 22, 603 – 634 (2003).
[Crossref]

2001 (2)

S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001).
[Crossref]

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, “Compact broadband continuum source based on microchip laser pumped microstructured fibre,” Electron. Lett. 37, 558–560 (2001).
[Crossref]

2000 (2)

G. Kopidakis and S. Aubry, “Discrete breathers and delocalization in nonlinear disordered systems,” Phys. Rev. Lett. 84, 3236–3239 (2000).
[Crossref] [PubMed]

L. I. Deych, A. A. Lisyansky, and B. L. Altshuler, “Single parameter scaling in one-dimensional localization revisited,” Phys. Rev. Lett. 84, 2678–2681 (2000).
[Crossref] [PubMed]

1992 (1)

M. N. Rosenbluth, “Comment on “classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 69, 1831 (1992).
[Crossref]

1991 (1)

L. Golubović, S. Feng, and F.-A. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).
[Crossref]

1989 (1)

H. De Raedt, A. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett. 62, 47–50 (1989).
[Crossref] [PubMed]

1986 (1)

1985 (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

1982 (1)

A. M. Jayannavar and N. Kumar, “Nondiffusive quantum transport in a dynamically disordered medium,” Phys. Rev. Lett. 48, 553–556 (1982).
[Crossref]

1980 (1)

P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, “New method for a scaling theory of localization,” Phys. Rev. B 22, 3519–3526 (1980).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
[Crossref]

Abrahams, E.

P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, “New method for a scaling theory of localization,” Phys. Rev. B 22, 3519–3526 (1980).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

Akhmediev, N.

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Integrable turbulence and rogue waves: Breathers or solitons?” Phys. Rev. Lett. 116, 103901 (2016).
[Crossref] [PubMed]

G. Genty, C. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989 – 996 (2010).
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M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).
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E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).
[Crossref] [PubMed]

Mitschke, F.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[Crossref] [PubMed]

Mitschke, F. M.

Mollenauer, L. F.

Morandotti, R.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref] [PubMed]

Morgner, U.

Mussot, A.

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92, 023837 (2015).
[Crossref]

Nakamura, K.

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).
[Crossref] [PubMed]

Newbury, N. R.

Nolte, S.

Oreshnikov, I.

Osborne, A. R.

A. R. Osborne, Nonlinear Ocean Waves and the Inverse Scattering Transform (Academic Press, 2010).

Pastur, L. A.

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

Pelinovsky, E.

C. Kharif and E. Pelinovsky, “Physical mechanisms of the rogue wave phenomenon,” Europ. J. Mechan. B Fluids 22, 603 – 634 (2003).
[Crossref]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Pickartz, S.

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Efficient all-optical control of solitons,” Opt. Quantum Electron. 48, 503 (2016).
[Crossref]

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94, 033811 (2016).
[Crossref]

Pikovsky, A. S.

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[Crossref] [PubMed]

Popov, S. V.

Pozzi, F.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref] [PubMed]

Pricking, S.

Prokhorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Provino, L.

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, “Compact broadband continuum source based on microchip laser pumped microstructured fibre,” Electron. Lett. 37, 558–560 (2001).
[Crossref]

Pugatch, R.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref] [PubMed]

Rechtsman, M.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref] [PubMed]

Robertson, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

Ropers, C.

P. T. S. DeVore, D. R. Solli, D. Borlaug, C. Ropers, and B. Jalali, “Rogue events and noise shaping in nonlinear silicon photonics,” J. Opt. 15, 064001 (2013).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Rosenbluth, M. N.

M. N. Rosenbluth, “Comment on “classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 69, 1831 (1992).
[Crossref]

Russell, P. S. J.

Saleh, M. F.

M. F. Saleh and F. Biancalana, “Soliton-radiation trapping in gas-filled photonic crystal fibers,” Phys. Rev. A 87, 043807 (2013).
[Crossref]

Schreiber, T.

T. Schreiber, J. Limpert, H. Zellmer, A. TÃijnnermann, and K. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71 – 78 (2003).
[Crossref]

Schwartz, T.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
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T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Segev, M.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).
[Crossref]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Shepelyansky, D. L.

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[Crossref] [PubMed]

Silberberg, Y.

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref] [PubMed]

Skokos, C.

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[Crossref] [PubMed]

Skryabin, D. V.

Smirnov, S. V.

Soffer, A.

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear schrÃűdinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53 (2012).
[Crossref]

Solli, D. R.

P. T. S. DeVore, D. R. Solli, D. Borlaug, C. Ropers, and B. Jalali, “Rogue events and noise shaping in nonlinear silicon photonics,” J. Opt. 15, 064001 (2013).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

Sorel, M.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref] [PubMed]

Soto-Crespo, J. M.

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Integrable turbulence and rogue waves: Breathers or solitons?” Phys. Rev. Lett. 116, 103901 (2016).
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Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
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A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
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A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
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Stel’makh, M. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Szameit, A.

TÃijnnermann, A.

T. Schreiber, J. Limpert, H. Zellmer, A. TÃijnnermann, and K. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71 – 78 (2003).
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Taylor, J. R.

Teipel, J.

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P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, “New method for a scaling theory of localization,” Phys. Rev. B 22, 3519–3526 (1980).
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Tünnermann, A.

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Vanholsbeeck, F.

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Wadsworth, W. J.

Wang, S. F.

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92, 023837 (2015).
[Crossref]

Washburn, B. R.

Wilkinson, M.

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).
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Windeler, R. S.

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber,” Opt. Lett. 28, 944–946 (2003).
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L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, “Compact broadband continuum source based on microchip laser pumped microstructured fibre,” Electron. Lett. 37, 558–560 (2001).
[Crossref]

Yulin, A. V.

Zeil, P.

Zellmer, H.

T. Schreiber, J. Limpert, H. Zellmer, A. TÃijnnermann, and K. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71 – 78 (2003).
[Crossref]

Zeng, F.-A.

L. Golubović, S. Feng, and F.-A. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).
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Zeng, X. L.

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92, 023837 (2015).
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Appl. Phys. B (1)

A. Demircan and U. Bandelow, “Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation,” Appl. Phys. B 86, 31–39 (2006).
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Appl. Phys. Lett. (1)

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).
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Electron. Lett. (1)

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, “Compact broadband continuum source based on microchip laser pumped microstructured fibre,” Electron. Lett. 37, 558–560 (2001).
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Europ. J. Mechan. B Fluids (1)

C. Kharif and E. Pelinovsky, “Physical mechanisms of the rogue wave phenomenon,” Europ. J. Mechan. B Fluids 22, 603 – 634 (2003).
[Crossref]

J. Opt. (1)

P. T. S. DeVore, D. R. Solli, D. Borlaug, C. Ropers, and B. Jalali, “Rogue events and noise shaping in nonlinear silicon photonics,” J. Opt. 15, 064001 (2013).
[Crossref]

JETP Lett. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

Nat. Commun. (1)

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the anderson regime,” Nat. Commun. 5, 4534 (2014).
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Nat. Photon. (2)

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photon. 8, 755–764 (2014).
[Crossref]

M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photon. 7, 197–204 (2013).
[Crossref]

Nat. Phys. (2)

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).
[Crossref]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
[Crossref]

Nature (2)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Nonlinearity (1)

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear schrÃűdinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53 (2012).
[Crossref]

Opt. Commun. (1)

T. Schreiber, J. Limpert, H. Zellmer, A. TÃijnnermann, and K. Hansen, “High average power supercontinuum generation in photonic crystal fibers,” Opt. Commun. 228, 71 – 78 (2003).
[Crossref]

Opt. Express (8)

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. S. J. Russell, “Supercontinuum and four-wave mixing with q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004).
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F. Vanholsbeeck, S. Martin-Lopez, M. González-Herráez, and S. Coen, “The role of pump incoherence in continuous-wave supercontinuum generation,” Opt. Express 13, 6615–6625 (2005).
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M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
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J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
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D. Tuürke, S. Pricking, A. Husakou, J. Teipel, J. Herrmann, and H. Giessen, “Coherence of subsequent supercontinuum pulses generated in tapered fibers in the femtosecond regime,” Opt. Express 15, 2732–2741 (2007).
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S. M. Kobtsev and S. V. Smirnov, “Coherent properties of super-continuum containing clearly defined solitons,” Opt. Express 14, 3968–3980 (2006).
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A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref] [PubMed]

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[Crossref]

Opt. Lett. (7)

Opt. Quantum Electron. (1)

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Efficient all-optical control of solitons,” Opt. Quantum Electron. 48, 503 (2016).
[Crossref]

Optica (1)

Phys. Lett. A (1)

G. Genty, C. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989 – 996 (2010).
[Crossref]

Phys. Rev. (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
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Phys. Rev. A (4)

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94, 033811 (2016).
[Crossref]

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92, 023837 (2015).
[Crossref]

C. Conti, “Solitonization of the anderson localization,” Phys. Rev. A 86, 061801 (2012).
[Crossref]

M. F. Saleh and F. Biancalana, “Soliton-radiation trapping in gas-filled photonic crystal fibers,” Phys. Rev. A 87, 043807 (2013).
[Crossref]

Phys. Rev. B (2)

P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, “New method for a scaling theory of localization,” Phys. Rev. B 22, 3519–3526 (1980).
[Crossref]

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).
[Crossref]

Phys. Rev. Lett. (15)

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[Crossref] [PubMed]

G. Kopidakis and S. Aubry, “Discrete breathers and delocalization in nonlinear disordered systems,” Phys. Rev. Lett. 84, 3236–3239 (2000).
[Crossref] [PubMed]

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
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M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).
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L. I. Deych, A. A. Lisyansky, and B. L. Altshuler, “Single parameter scaling in one-dimensional localization revisited,” Phys. Rev. Lett. 84, 2678–2681 (2000).
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A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
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Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref] [PubMed]

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
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A. M. Jayannavar and N. Kumar, “Nondiffusive quantum transport in a dynamically disordered medium,” Phys. Rev. Lett. 48, 553–556 (1982).
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L. Golubović, S. Feng, and F.-A. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).
[Crossref]

M. N. Rosenbluth, “Comment on “classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 69, 1831 (1992).
[Crossref]

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).
[Crossref] [PubMed]

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Integrable turbulence and rogue waves: Breathers or solitons?” Phys. Rev. Lett. 116, 103901 (2016).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Sci. Rep. (1)

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[Crossref] [PubMed]

Science (2)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref] [PubMed]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref] [PubMed]

Other (4)

A. R. Osborne, Nonlinear Ocean Waves and the Inverse Scattering Transform (Academic Press, 2010).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

M. F. Limonov and R. M. De La Rue, Optical Properties of Photonic Structures: Interplay of Order and Disorder,(CRC, 2012).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

(a) Temporal evolution of a superGaussian pulse A = exp [−1/2(t/T0)10] at wavelength 1060 nm, with T0 = 3.63 ps (FWHM = 7 ps) and input power 100 W inside the solid silica-core photonic crystal fibre of Ref. [14] in the absence of higher-order dispersion, Raman effect and self-steepening. (b) Temporal evolution of the ground Anderson state of the induced temporal-waveguide. (c) Spatial dependence of the quantity L NL z σ ˜ 2. (d) Spatial evolution of the localisation times and eigenvalues of four Anderson modes with k = 0, 5, 10, 15. (e) Temporal evolution of the amplitude of the first 20 linear modes on the top of each other. Each mode is normalised such that its energy is unity. (f) Spatial dependency of the Lyapunov exponent Γ, its mean (dashed blue), and variance (solid black) of an ensemble of 50 different input shot noise.

Fig. 2
Fig. 2

(a) Wavelength-dependence of first-order β1 and second-order β2 dispersion coefficients. The dotted rectangle shows a group of a soliton and a dispersive-wave with nearly group velocities. (b) XFROG representation of the superGaussian pulse at z = 8.2 m. The inset is XFROG at z = 0. (c) Temporal evolution of the superGaussian pulse. (d) XFROG representation of the superGaussian pulse at z = 20 m. Simulations in this figure are performed using Eqs. (1) and (3) in the absence of βm≥4, τsh, and Raman nonlinearity.

Fig. 3
Fig. 3

(a,b) Spectral and temporal evolution of the superGaussian pulse. The temporal contour plot is normalised to its peak. (c) Temporal evolution of the first 20 Anderson eigenmodes. (d) Spatial dependency of the Lyapunov exponent Γ, its mean (dashed blue), and variance (solid black) of an ensemble of 50 different input shot noise. (e,f) XFROG representation of the superGaussian pulse inside the fibre at z =13.3 m and 14.73 m. The inset in (e) is XFROG at z = 0. Simulations in this figure are performed using the full Eqs. (1) and (3).

Equations (4)

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[ i z + m 2 β m ( i t ) m m ! + γ ( 1 + i τ s h t ) ( R ( t ) | A | 2 ) ] A = 0 ,
i z A β 2 2 t 2 A + ω 0 c Δ n ( z , t ) A = 0 ,
i z u k β 2 2 t 2 u k + U ( z , t ) u k = 0 ,
T loc ( k ) ( z ) = ( | f k ( z , t ) | 2 d t ) 2 | f k ( z , t ) | 4 d t .

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