Abstract

We study the light refraction behavior at the entrance surface of the width-disordered one-dimensional waveguide array. As compared to the case in a uniform periodic waveguide array, anomalous refraction behavior is observed for the eigenmodes in the first band of the disordered waveguide array. The transverse propagation velocities of the eigenmodes in the first band are dramatically suppressed and the light is tightly confined around and propagates along the initially exciting waveguides. This may provide an effective method for beam coupling and collimation in the disordered photonic lattices.

© 2013 Optical Society of America

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2013 (2)

L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[CrossRef]

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit, “Self-trapping threshold in disordered nonlinear photonic lattices,” Opt. Lett. 38, 1518–1520 (2013).
[CrossRef]

2012 (3)

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

S. Ghosh, B. P. Pal, and R. Varshney, “Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice,” Opt. Commun. 285, 2785–2789 (2012).
[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

2011 (1)

D. Jović, Y. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

2010 (2)

2009 (4)

N. Efremidis, “Bifurcations of nonlinear localized modes in disordered lattices,” Phys. Rev. A 79, 063831 (2009).
[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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

2008 (5)

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

T. Schwartz, S. Fishman, and M. Segev, “Localisation of light in disordered lattices,” Electron. Lett. 44, 165–168 (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]

N. Efremidis and K. Hizanidis, “Disordered lattice solitons,” Phys. Rev. Lett. 101, 2–5 (2008).
[CrossRef]

J. J. Miret and C. J. Zapata-Rodrguez, “Diffraction-free beams with elliptic Bessel envelope in periodic media,” J. Opt. Soc. Am. B 25, 1–6 (2008).
[CrossRef]

2007 (1)

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]

2005 (1)

2004 (2)

H. Martin, E. D. Eugenieva, and Z. Chen, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 10–13 (2004).
[CrossRef]

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]

2003 (4)

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, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (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]

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

2000 (1)

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

1998 (1)

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]

1989 (1)

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

1988 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1985 (1)

P. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (1985).
[CrossRef]

1984 (1)

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[CrossRef]

1982 (1)

P. Erdös and R. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31, 65–163 (1982).
[CrossRef]

1981 (1)

C. M. Soukoulis and E. N. Economou, “Off-diagonal disorder in one-dimensional systems,” Phys. Rev. B 24, 5698–5702 (1981).
[CrossRef]

1973 (1)

S. Somekh, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–47 (1973).
[CrossRef]

1965 (1)

1958 (1)

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

Aitchison, J.

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

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

Anderson, P.

P. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (1985).
[CrossRef]

Anderson, P. W.

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

Assanto, G.

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (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]

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]

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

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]

Belic, M. R.

D. Jović, Y. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Bo, F.

L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[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]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Buljan, H.

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

Chen, Z.

H. Martin, E. D. Eugenieva, and Z. Chen, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 10–13 (2004).
[CrossRef]

Christodoulides, D.

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Christodoulides, D. N.

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]

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30, 2611–2613 (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]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (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]

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

Cohen, O.

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

Davidson, N.

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]

de Vries, P.

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

Denz, C.

D. Jović, Y. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Dreisow, F.

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Economou, E. N.

C. M. Soukoulis and E. N. Economou, “Off-diagonal disorder in one-dimensional systems,” Phys. Rev. B 24, 5698–5702 (1981).
[CrossRef]

Efremidis, N.

N. Efremidis, “Bifurcations of nonlinear localized modes in disordered lattices,” Phys. Rev. A 79, 063831 (2009).
[CrossRef]

N. Efremidis and K. Hizanidis, “Disordered lattice solitons,” Phys. Rev. Lett. 101, 2–5 (2008).
[CrossRef]

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Efremidis, N. K.

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]

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

Eisenberg, H.

H. Eisenberg, Y. Silberberg, R. Morandotti, and J. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[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, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Erdös, P.

P. Erdös and R. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31, 65–163 (1982).
[CrossRef]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, and Z. Chen, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 10–13 (2004).
[CrossRef]

Fishman, S.

T. Schwartz, S. Fishman, and M. Segev, “Localisation of light in disordered lattices,” Electron. Lett. 44, 165–168 (2008).
[CrossRef]

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]

Fleischer, J.

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

Fleischer, J. W.

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]

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Ghosh, S.

S. Ghosh, B. P. Pal, and R. Varshney, “Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice,” Opt. Commun. 285, 2785–2789 (2012).
[CrossRef]

Guryev, I. V.

I. A. Sukhoivanov and I. V. Guryev, Photonic Crystals: Physics and Practical Modeling (Springer, 2009).

Heinrich, M.

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit, “Self-trapping threshold in disordered nonlinear photonic lattices,” Opt. Lett. 38, 1518–1520 (2013).
[CrossRef]

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

Herndon, R.

P. Erdös and R. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31, 65–163 (1982).
[CrossRef]

Hizanidis, K.

N. Efremidis and K. Hizanidis, “Disordered lattice solitons,” Phys. Rev. Lett. 101, 2–5 (2008).
[CrossRef]

Hudock, J.

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

John, S.

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[CrossRef]

Jones, A. L.

Joseph, R. I.

Jovic, D.

D. Jović, Y. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

Keil, R.

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

Kivshar, Y.

D. Jović, Y. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Kobelke, J.

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]

Lagendijk, A.

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

Lahini, Y.

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit, “Self-trapping threshold in disordered nonlinear photonic lattices,” Opt. Lett. 38, 1518–1520 (2013).
[CrossRef]

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[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]

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]

Lederer, F.

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

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. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

Mandelik, D.

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]

Manela, O.

Martin, H.

H. Martin, E. D. Eugenieva, and Z. Chen, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 10–13 (2004).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Miret, J. J.

Molina, M. I.

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]

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]

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. Eisenberg, Y. Silberberg, R. Morandotti, and J. 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]

Naether, U.

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit, “Self-trapping threshold in disordered nonlinear photonic lattices,” Opt. Lett. 38, 1518–1520 (2013).
[CrossRef]

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

Nolte, S.

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit, “Self-trapping threshold in disordered nonlinear photonic lattices,” Opt. Lett. 38, 1518–1520 (2013).
[CrossRef]

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

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]

Pal, B. P.

S. Ghosh, B. P. Pal, and R. Varshney, “Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice,” Opt. Commun. 285, 2785–2789 (2012).
[CrossRef]

Pertsch, T.

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]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Peschel, U.

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]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

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]

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]

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]

Qi, Y.

Raedt, H. D.

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

Schuster, K.

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]

Schwartz, T.

T. Schwartz, S. Fishman, and M. Segev, “Localisation of light in disordered lattices,” Electron. Lett. 44, 165–168 (2008).
[CrossRef]

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]

Segev, M.

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

T. Schwartz, S. Fishman, and M. Segev, “Localisation of light in disordered lattices,” Electron. Lett. 44, 165–168 (2008).
[CrossRef]

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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O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett. 30, 2611–2613 (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]

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef]

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

Silberberg, Y.

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]

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]

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (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]

H. Eisenberg, Y. Silberberg, R. Morandotti, and J. 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]

Somekh, S.

S. Somekh, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–47 (1973).
[CrossRef]

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]

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]

Soukoulis, C. M.

C. M. Soukoulis and E. N. Economou, “Off-diagonal disorder in one-dimensional systems,” Phys. Rev. B 24, 5698–5702 (1981).
[CrossRef]

Stegemanb, G. I.

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[CrossRef]

Sukhoivanov, I. A.

I. A. Sukhoivanov and I. V. Guryev, Photonic Crystals: Physics and Practical Modeling (Springer, 2009).

Sukhorukova, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

Szameit, A.

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit, “Self-trapping threshold in disordered nonlinear photonic lattices,” Opt. Lett. 38, 1518–1520 (2013).
[CrossRef]

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

Tünnermann, A.

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

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]

Varshney, R.

S. Ghosh, B. P. Pal, and R. Varshney, “Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice,” Opt. Commun. 285, 2785–2789 (2012).
[CrossRef]

Vicencio, R. A.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

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L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[CrossRef]

Xu, L.

L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[CrossRef]

Yin, Y.

L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[CrossRef]

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Zapata-Rodríguez, C. J.

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Zhang, G.

L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[CrossRef]

Y. Qi and G. Zhang, “Linear discrete diffraction and transverse localization of light in two-dimensional backbone lattices,” Opt. Express 18, 20170–20182 (2010).
[CrossRef]

Adv. Phys. (1)

P. Erdös and R. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31, 65–163 (1982).
[CrossRef]

Appl. Phys. Lett. (1)

S. Somekh, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–47 (1973).
[CrossRef]

Electron. Lett. (1)

T. Schwartz, S. Fishman, and M. Segev, “Localisation of light in disordered lattices,” Electron. Lett. 44, 165–168 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Laser Photon. Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

Nature (3)

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, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[CrossRef]

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]

New J. Phys. (1)

M. Heinrich, R. Keil, Y. Lahini, U. Naether, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Disorder-enhanced nonlinear delocalization in segmented waveguide arrays,” New J. Phys. 14, 073026 (2012).
[CrossRef]

Opt. Commun. (2)

S. Ghosh, B. P. Pal, and R. Varshney, “Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice,” Opt. Commun. 285, 2785–2789 (2012).
[CrossRef]

L. Xu, Y. Yin, F. Bo, J. Xu, and G. Zhang, “Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes,” Opt. Commun. 296, 65–71 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

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P. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (1985).
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Phys. Rep. (2)

I. L. Garanovich, S. Longhi, A. A. Sukhorukova, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518, 1–79 (2012).
[CrossRef]

F. Lederer, G. I. Stegemanb, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
[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 (2)

N. Efremidis, “Bifurcations of nonlinear localized modes in disordered lattices,” Phys. Rev. A 79, 063831 (2009).
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D. Jović, Y. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Phys. Rev. B (1)

C. M. Soukoulis and E. N. Economou, “Off-diagonal disorder in one-dimensional systems,” Phys. Rev. B 24, 5698–5702 (1981).
[CrossRef]

Phys. Rev. Lett. (13)

N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[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]

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]

N. Efremidis and K. Hizanidis, “Disordered lattice solitons,” Phys. Rev. Lett. 101, 2–5 (2008).
[CrossRef]

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

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]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[CrossRef]

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

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[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]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[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]

H. Martin, E. D. Eugenieva, and Z. Chen, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92, 10–13 (2004).
[CrossRef]

Prog. Opt. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009).
[CrossRef]

Other (2)

N. K. Efremidis, J. W. Fleischer, G. Bartal, O. Cohen, H. Buljan, D. N. Christodoulides, and M. Segev, Introduction to solitons in photonic lattices, in Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. S. Kivshar, eds. (Springer, 2010), Vol. 150, Chap. 5, pp. 73–99.

I. A. Sukhoivanov and I. V. Guryev, Photonic Crystals: Physics and Practical Modeling (Springer, 2009).

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Figures (4)

Fig. 1.
Fig. 1.

Light propagation dynamics (lower) and the intensity distribution at the output port (upper) with different input tilts in waveguide arrays. Here (a), (b), (c), and (d) give the results for the uniform periodic waveguide array with kx=0, 0.5π/D, 1.0π/D, and 1.2π/D, respectively. (e), (f), (g), and (h) give the results for the width-disordered waveguide array (ΔW=2.0μm) with kx=0, 0.5π/D, 1.0π/D, and 1.2π/D, respectively.

Fig. 2.
Fig. 2.

Bands of eigenvalues and the transverse propagation velocities of eigenmodes for the uniform periodic and width-disordered waveguide arrays. (a) Band gap structure diagram (left) for the uniform periodic waveguide array. The right column gives the transverse propagation velocities vx for the corresponding eigenmodes within the bands. (b) Band gap structure diagram (left) for the width-disordered waveguide array with ΔW=2.0μm. The inset shows a magnified mini-band gap structure. The right column gives the corresponding vx for the eigenmodes within the bands. Note that here the band diagram is first calculated using a supercell with 41 waveguides and then folded into the first Brillouin zone based on the initial one-waveguide unit cell with a periodicity D in both cases.

Fig. 3.
Fig. 3.

Bands of eigenvalues; the qvx curves and the corresponding light propagation dynamics at an oblique incidence kx=0.5π/D in waveguide arrays with different width-disorder levels. Here (a) and (d) are the cases with ΔW=0.5μm, (b) and (e) are for ΔW=1.5μm, and (c) and (f) are the results with ΔW=2.5μm, respectively. The input beam is identical to the one used in Fig. 1.

Fig. 4.
Fig. 4.

Transverse space locations of the output beam at different input tilts. (a) is the case for a uniform periodic waveguide array, and (b) is the case for a width-disordered waveguide array with ΔW=2.0μm, respectively.

Equations (2)

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2ik0n0ψZ+2ψX2+2V(X)ψ=0,
iφz+122φx2+V(x)φ=0,

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