Abstract

We study managing of light beam propagation by competing disorder and nonlinearity in one-dimensional disordered, nonlinear photonic lattices (PLs). The system is modeled by a paraxial time-independent Helmholtz equation, which includes the nonlinear saturable self-interacting term and the quenched or nonquenched disordered PL potential. Diverse PL structures with alternating length of the regular and disordered parts are investigated showing the possibility to change the light propagation from ballistic to the propagation of the transversely localized structures originating from the Anderson-like localization or self-trapping mechanism. Dynamical calculations indicate the possibility of guiding light through the lattice by proper lattice management.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, “Localization of light in evanescently coupled disordered waveguide lattices: dependence on the input beam profile,” Opt. Commun. 284, 201–206 (2011).
    [CrossRef]
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    [CrossRef]
  31. 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]
  32. Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Superdiffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
    [CrossRef]
  33. G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillations,” Sov. Phys. Usp. 14, 549–566 (1972).
    [CrossRef]
  34. M. N. Rosenbluth, “Comment on classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 69, 1831 (1992).
    [CrossRef]
  35. I. R. Gabitov and P. M. Lushnikov, “Nonlinearity management in a dispersion-managed system,” Opt. Lett. 27, 113–115 (2002).
    [CrossRef]
  36. B. G. Bale, S. Boscolo, O. Y. Schwartz, and S. K. Turitsyn, “Localized waves in optical systems with periodic dispersion and nonlinearity management,” Int. J. Opt. 2009, 181467 (2009).
  37. R. Driben, B. A. Malomed, and U. Mahlab, “Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links,” Opt. Commun. 232, 129–138 (2004).
    [CrossRef]
  38. A. Kanshu, C. E. Rüter, D. Kip, and V. M. Shandarov, “Optically-induced defect states in photonic lattices: formation of defect channels, directional couplers, and disordered lattices leading to Anderson-like light localization,” Appl. Phys. B 95, 537–543 (2009).
    [CrossRef]
  39. G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, “Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole–dipole interactions,” J. Phys. B 42, 145302 (2009).
    [CrossRef]
  40. Ch. Skokos, D. O. Krimer, S. Komineas, and S. Flach, “Delocalization of wave packets in disordered nonlinear chains,” Phys. Rev. E 79, 056211 (2009).
    [CrossRef]
  41. 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]
  42. S. Flach, “Spreading of waves in nonlinear disordered media,” Chem. Phys. 375, 548–556 (2010).
    [CrossRef]
  43. G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
    [CrossRef]

2013

2012

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]

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Superdiffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

2011

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, “Localization of light in evanescently coupled disordered waveguide lattices: dependence on the input beam profile,” Opt. Commun. 284, 201–206 (2011).
[CrossRef]

2010

S. Flach, “Spreading of waves in nonlinear disordered media,” Chem. Phys. 375, 548–556 (2010).
[CrossRef]

2009

A. Kanshu, C. E. Rüter, D. Kip, and V. M. Shandarov, “Optically-induced defect states in photonic lattices: formation of defect channels, directional couplers, and disordered lattices leading to Anderson-like light localization,” Appl. Phys. B 95, 537–543 (2009).
[CrossRef]

G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, “Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole–dipole interactions,” J. Phys. B 42, 145302 (2009).
[CrossRef]

Ch. Skokos, D. O. Krimer, S. Komineas, and S. Flach, “Delocalization of wave packets in disordered nonlinear chains,” Phys. Rev. E 79, 056211 (2009).
[CrossRef]

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

B. G. Bale, S. Boscolo, O. Y. Schwartz, and S. K. Turitsyn, “Localized waves in optical systems with periodic dispersion and nonlinearity management,” Int. J. Opt. 2009, 181467 (2009).

2008

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]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
[CrossRef]

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

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

2007

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]

D. N. Neshev, A. A. Sukhorukov, W. Królikowski, and Yu. S. Kivshar, “Nonlinear optics and light localization in periodic photonic lattices,” J. Nonlinear Opt. Phys. Mater. 16, 1–25 (2007).
[CrossRef]

S. A. Rinne, F. Garcia-Santamaria, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

2006

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

C. E. Rüter, J. Wisniewski, and D. Kip, “Prism coupling method to excite and analyze Floquet–Bloch modes in linear and nonlinear waveguide arrays,” Opt. Lett. 31, 2768–2770 (2006).
[CrossRef]

2005

2004

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Królikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef]

R. Driben, B. A. Malomed, and U. Mahlab, “Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links,” Opt. Commun. 232, 129–138 (2004).
[CrossRef]

2003

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet–Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

2002

2000

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

1999

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[CrossRef]

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

1994

D. Belitz and T. R. Kirkpatrick, “The Anderson–Mott transition,” Rev. Mod. Phys. 66, 261–380 (1994).
[CrossRef]

1993

A. R. McGurn, K. T. Christensen, F. M. Müller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

1992

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

1988

1986

J. Fröhlich, T. Spencer, and C. E. Wayne, “Localization in disordered, nonlinear dynamical systems,” J. Stat. Phys. 42, 247–274 (1986).
[CrossRef]

1980

S. S. Abdullaev and F. Kh. Abdullaev, “On the light propagation in the system of tunnel-coupled waveguides,” Radiofizika 23, 766–767 (1980).

1972

G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillations,” Sov. Phys. Usp. 14, 549–566 (1972).
[CrossRef]

1958

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

Abdullaev, F. Kh.

S. S. Abdullaev and F. Kh. Abdullaev, “On the light propagation in the system of tunnel-coupled waveguides,” Radiofizika 23, 766–767 (1980).

Abdullaev, S. S.

S. S. Abdullaev and F. Kh. Abdullaev, “On the light propagation in the system of tunnel-coupled waveguides,” Radiofizika 23, 766–767 (1980).

Agrawal, G. P.

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, “Localization of light in evanescently coupled disordered waveguide lattices: dependence on the input beam profile,” Opt. Commun. 284, 201–206 (2011).
[CrossRef]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet–Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Anderson, P. W.

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

Aspect, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[CrossRef]

Aubry, S.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

Avidan, A.

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]

Bale, B. G.

B. G. Bale, S. Boscolo, O. Y. Schwartz, and S. K. Turitsyn, “Localized waves in optical systems with periodic dispersion and nonlinearity management,” Int. J. Opt. 2009, 181467 (2009).

Bartal, G.

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]

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780–1795 (2005).
[CrossRef]

Bartelt, H.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Belitz, D.

D. Belitz and T. R. Kirkpatrick, “The Anderson–Mott transition,” Rev. Mod. Phys. 66, 261–380 (1994).
[CrossRef]

Bernard, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[CrossRef]

Billy, J.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[CrossRef]

Boscolo, S.

B. G. Bale, S. Boscolo, O. Y. Schwartz, and S. K. Turitsyn, “Localized waves in optical systems with periodic dispersion and nonlinearity management,” Int. J. Opt. 2009, 181467 (2009).

Bouyer, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Brauer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[CrossRef]

Braun, P. V.

S. A. Rinne, F. Garcia-Santamaria, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
[CrossRef]

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

Buljan, H.

Chen, F.

Chirikov, B. V.

G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillations,” Sov. Phys. Usp. 14, 549–566 (1972).
[CrossRef]

Christensen, K. T.

A. R. McGurn, K. T. Christensen, F. M. Müller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

Christodoulides, D. N.

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
[CrossRef]

Clément, D.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[CrossRef]

Cohen, O.

Cugliandolo, L. F.

L. F. Cugliandolo, “Dynamics of glassy systems,” in Les Houuches 2002 (Springer, 2003).

D’Errico, C.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
[CrossRef]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
[CrossRef]

Donth, E. J.

E. J. Donth, The Glass Transition: Relaxation Dynamics in Liquids and Disordered Materials (Springer, 2001).

Driben, R.

R. Driben, B. A. Malomed, and U. Mahlab, “Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links,” Opt. Commun. 232, 129–138 (2004).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780–1795 (2005).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet–Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Elflein, W.

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G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
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S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, “Localization of light in evanescently coupled disordered waveguide lattices: dependence on the input beam profile,” Opt. Commun. 284, 201–206 (2011).
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G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
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T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
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Ch. Skokos, D. O. Krimer, S. Komineas, and S. Flach, “Delocalization of wave packets in disordered nonlinear chains,” Phys. Rev. E 79, 056211 (2009).
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G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
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G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
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Ch. Skokos, D. O. Krimer, S. Komineas, and S. Flach, “Delocalization of wave packets in disordered nonlinear chains,” Phys. Rev. E 79, 056211 (2009).
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S. Flach, D. O. Krimer, and Ch. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
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Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Superdiffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
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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).
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D. N. Neshev, A. A. Sukhorukov, W. Królikowski, and Yu. S. Kivshar, “Nonlinear optics and light localization in periodic photonic lattices,” J. Nonlinear Opt. Phys. Mater. 16, 1–25 (2007).
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D. Neshev, A. A. Sukhorukov, B. Hanna, W. Królikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).
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T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
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T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752–4755 (1999).
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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).
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Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Superdiffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
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J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
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G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, “Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole–dipole interactions,” J. Phys. B 42, 145302 (2009).
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R. Driben, B. A. Malomed, and U. Mahlab, “Integration of nonlinearity-management and dispersion-management for pulses in fiber-optic links,” Opt. Commun. 232, 129–138 (2004).
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G. Gligorić, A. Maluckov, Lj. Hadžievski, and B. A. Malomed, “Collapse instability of solitons in the nonpolynomial Schrodinger equation with dipole–dipole interactions,” J. Phys. B 42, 145302 (2009).
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G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
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G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
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Morandotti, R.

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).
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D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
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D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet–Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
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A. R. McGurn, K. T. Christensen, F. M. Müller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
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D. Neshev, A. A. Sukhorukov, B. Hanna, W. Królikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).
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D. N. Neshev, A. A. Sukhorukov, W. Królikowski, and Yu. S. Kivshar, “Nonlinear optics and light localization in periodic photonic lattices,” J. Nonlinear Opt. Phys. Mater. 16, 1–25 (2007).
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U. Naether, S. Rojas-Rojas, A. J. Martinez, S. Sützer, A. Tünnermann, S. Nolte, M. I. Molina, R. A. Vicencio, and A. Szameit, “Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity,” Opt. Express 21, 927–957 (2013).
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T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
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S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, “Localization of light in evanescently coupled disordered waveguide lattices: dependence on the input beam profile,” Opt. Commun. 284, 201–206 (2011).
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T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
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T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
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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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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).
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S. A. Rinne, F. Garcia-Santamaria, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).
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P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
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G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
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T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
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B. G. Bale, S. Boscolo, O. Y. Schwartz, and S. K. Turitsyn, “Localized waves in optical systems with periodic dispersion and nonlinearity management,” Int. J. Opt. 2009, 181467 (2009).

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
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J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780–1795 (2005).
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M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics 7, 197–204 (2013).
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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).
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Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Superdiffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
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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).
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J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780–1795 (2005).
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Shandarov, V. M.

A. Kanshu, C. E. Rüter, D. Kip, and V. M. Shandarov, “Optically-induced defect states in photonic lattices: formation of defect channels, directional couplers, and disordered lattices leading to Anderson-like light localization,” Appl. Phys. B 95, 537–543 (2009).
[CrossRef]

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

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M. Segev, Y. Silberberg, and D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics 7, 197–204 (2013).
[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).
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D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet–Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003).
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[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
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S. Flach, D. O. Krimer, and Ch. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
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Ch. Skokos, D. O. Krimer, S. Komineas, and S. Flach, “Delocalization of wave packets in disordered nonlinear chains,” Phys. Rev. E 79, 056211 (2009).
[CrossRef]

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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).
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Sukhorukov, A. A.

D. N. Neshev, A. A. Sukhorukov, W. Królikowski, and Yu. S. Kivshar, “Nonlinear optics and light localization in periodic photonic lattices,” J. Nonlinear Opt. Phys. Mater. 16, 1–25 (2007).
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[CrossRef]

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Szameit, A.

Tünnermann, A.

U. Naether, S. Rojas-Rojas, A. J. Martinez, S. Sützer, A. Tünnermann, S. Nolte, M. I. Molina, R. A. Vicencio, and A. Szameit, “Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity,” Opt. Express 21, 927–957 (2013).
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[CrossRef]

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B. G. Bale, S. Boscolo, O. Y. Schwartz, and S. K. Turitsyn, “Localized waves in optical systems with periodic dispersion and nonlinearity management,” Int. J. Opt. 2009, 181467 (2009).

Varshney, R. K.

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, “Localization of light in evanescently coupled disordered waveguide lattices: dependence on the input beam profile,” Opt. Commun. 284, 201–206 (2011).
[CrossRef]

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Wayne, C. E.

J. Fröhlich, T. Spencer, and C. E. Wayne, “Localization in disordered, nonlinear dynamical systems,” J. Stat. Phys. 42, 247–274 (1986).
[CrossRef]

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Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Superdiffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
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Wisniewski, J.

Zaccanti, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a noninteracting Bose–Einstein condensate,” Nature 453, 895–898 (2008).
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Figures (9)

Fig. 1.
Fig. 1.

Schematic of the regular (red-dotted curve) and disordered lattice potential (black solid line). The blue (thick solid) line shows the input Gaussian beam shape.

Fig. 2.
Fig. 2.

2D plot of the averaged beam amplitude profile in (a) regular, (b) quenched disordered, and (c) nonquenched disordered lattice for parameter |γ|0.001. (d) averaged participation number P(z) for regular (black solid line), nonquenched disordered (green-dotted line), and quenched disordered lattice (red-dashed line). The disordered strength was fixed at d=0.5, and in the case of nonquenched lattice, the disordered realizations with fixed strength were changed every half-millimeter in the z direction.

Fig. 3.
Fig. 3.

Averaged participation number P(z) for regular lattice (black solid line) and nonquenched disordered lattice realized with different intervals between two successive realizations of the disorder: Δz=0.5mm (red-dashed line), Δz=0.2mm (green short-dashed line), Δz=0.125mm (blue-dotted line), and Δz=0.2μm (orange-dashed–dotted line).

Fig. 4.
Fig. 4.

2D plot of the averaged beam amplitude profile in (a) regular, (b) quenched disordered, and (c) nonquenched disordered lattice for parameter |γ|0.01. (d) Averaged participation number P(z) for regular (black solid line), nonquenched disordered (green-dotted line), and quenched disordered lattice (red-dashed line). The disordered strength was fixed at d=0.5, and in the case of nonquenched lattice, the disordered realizations with fixed strength were changed every half-millimeter in the z direction.

Fig. 5.
Fig. 5.

(a) P(z) curves for |γ|0.01 and quenched disorder lattices with disorder strengths d=0.25 (black solid lines), d=0.5 (red-dashed lines), and d=0.75 (green-dotted lines). Lines with symbols correspond to |γ|0.001: circles d=0.25, triangles d=0.5, and squares d=0.75. (b) mean values around which the participation numbers saturate P(z) for different disorder strengths d and |γ|0.001.

Fig. 6.
Fig. 6.

2D plot of the averaged beam amplitude profile in (a) regular and (b) quenched disordered lattice. (c) Averaged participation number P(z) for regular (black solid line) and quenched disordered (red-dashed line) lattice. The disordered strength was fixed at d=0.5 and |γ|0.005.

Fig. 7.
Fig. 7.

2D plot of the averaged beam amplitude profiles in the lattices composed of regular lattice until (a) z=3mm, (b) z=5mm, and (c) z=10mm and quenched disorder lattice of disorder strength d=0.5 after that. (d) The averaged participation number P(z) for the defined lattices (a) (green-dotted line), (b) (black solid line), and (c) (red-dashed line).

Fig. 8.
Fig. 8.

(a) 2D plot of the averaged beam amplitude profile in lattice combined of the quenched disordered lattice until z=5mm, the nonquenched disordered lattice from z=5mm until z=10mm, and quenched disordered lattice again from z=10mm to z=30mm. (b) averaged participation number P(z) for the given lattice. The disordered strength was fixed at d=0.5, and in the case of nonquenched lattice, the disordered realizations with fixed strength were changed every half-millimeter in the z direction.

Fig. 9.
Fig. 9.

(a) 2D plot of the averaged beam amplitude profile in lattice combined of the regular lattice until z=10mm, the nonquenched disordered lattice from z=10mm to z=15mm, and regular lattice again from z=15mm to z=25mm. (b) averaged participation number P(z) for the given lattice. The disordered strength was fixed at d=0.5 and |γ|=0.01. In the case of nonquenched lattice, the disordered realizations with fixed strength were changed every half-millimeter in the z direction.

Equations (6)

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

iEz+12k0n02Ex2+k0n0n(x)E=0,
n(x)=nl(x)+nnl(x)=ΔnG(x)12n02rEpv|E|2Id+|E|2.
iψη+12n02ψξ2+n0ΔnG(ξ)ψ+γ|ψ|21+|ψ|2ψ=0,
ψη=i(R^+L^+N^)ψ,
ψ(η+dη,ξ)=eidηN^eidηR^eidηL^ψ(η,ξ).
P(z)=1k0(dξ|ψ(ξ,η)|2)2dξ|ψ(ξ,η)|4,η=k0z,

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