Abstract

We demonstrate specular photonic “lattices” with random index variations at disordered positions of lattice sites. These amorphous lattice structures, optically induced in a bulk nonlinear crystal, remain invariant during propagation since they are constructed from random components residing on a fixed ring in momentum space. We observe linear spatial localization of a light beam when probing through different “defect” points in such specular lattices, as well as the nonlinear destruction of localized modes. In addition, we illustrate the possibility of image transmission through the disordered lattices, when a self-defocusing nonlinearity is employed.

© 2016 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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  6. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106(19), 193904 (2011).
    [Crossref] [PubMed]
  16. 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(9), 1518–1520 (2013).
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  18. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
    [Crossref] [PubMed]
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  20. M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21(26), 31713–31724 (2013).
    [Crossref] [PubMed]
  21. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005).
    [Crossref] [PubMed]
  22. S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
    [Crossref] [PubMed]
  23. S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
    [Crossref]
  24. 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(6928), 147–150 (2003).
    [Crossref] [PubMed]
  25. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
    [Crossref] [PubMed]
  26. A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
    [Crossref] [PubMed]
  27. P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
    [Crossref] [PubMed]
  28. J. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36(5), 772–774 (2011).
    [Crossref] [PubMed]
  29. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
    [Crossref]
  30. C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
    [Crossref]
  31. R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Opt. Lett. 37(5), 809–811 (2012).
    [Crossref] [PubMed]

2013 (4)

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7(3), 188–196 (2013).
[Crossref]

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110(40), 15886–15891 (2013).
[Crossref] [PubMed]

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(9), 1518–1520 (2013).
[Crossref] [PubMed]

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21(26), 31713–31724 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (3)

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106(19), 193904 (2011).
[Crossref] [PubMed]

J. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36(5), 772–774 (2011).
[Crossref] [PubMed]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332(6037), 1541–1544 (2011).
[Crossref] [PubMed]

2010 (4)

P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
[Crossref] [PubMed]

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

2009 (3)

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A. 106(49), 20658–20663 (2009).
[Crossref] [PubMed]

2008 (3)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (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(1), 013906 (2008).
[Crossref] [PubMed]

N. K. Efremidis and K. Hizanidis, “Disordered lattice solitons,” Phys. Rev. Lett. 101(14), 143903 (2008).
[Crossref] [PubMed]

2007 (1)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

2005 (1)

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005).
[Crossref] [PubMed]

2004 (1)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[Crossref] [PubMed]

2003 (2)

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(6928), 147–150 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

1999 (1)

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

1989 (1)

H. De Raedt, A. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett. 62(1), 47–50 (1989).
[Crossref] [PubMed]

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

1985 (1)

A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55(24), 2692–2695 (1985).
[Crossref] [PubMed]

Armijo, J.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 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(1), 013906 (2008).
[Crossref] [PubMed]

Barsi, C.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005).
[Crossref] [PubMed]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[Crossref]

Boguslawski, M.

Brake, S.

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005).
[Crossref] [PubMed]

Cao, H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Chaikin, P. M.

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110(40), 15886–15891 (2013).
[Crossref] [PubMed]

Chang, R. P. H.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

J. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36(5), 772–774 (2011).
[Crossref] [PubMed]

P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[Crossref] [PubMed]

P. Zhang, P. Ni, X. Qi, W. Man, Z. Chen, J. Yang, M. Rechtsman, and M. Segev, “Specular amorphous photonic bandgap lattices,” in Quantum Electronics and Laser Science Conference (OSA, 2012), pp. QF3H–1.

Christodoulides, D. N.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (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(1), 013906 (2008).
[Crossref] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[Crossref] [PubMed]

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(6928), 147–150 (2003).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Cižmár, T.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005).
[Crossref] [PubMed]

De Raedt, H.

H. De Raedt, A. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett. 62(1), 47–50 (1989).
[Crossref] [PubMed]

de Vries, P.

H. De Raedt, A. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett. 62(1), 47–50 (1989).
[Crossref] [PubMed]

Denz, C.

Dholakia, K.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Diebel, F.

Dreisow, F.

R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Opt. Lett. 37(5), 809–811 (2012).
[Crossref] [PubMed]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106(19), 193904 (2011).
[Crossref] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
[Crossref] [PubMed]

Efremidis, N. K.

P. Zhang, N. K. Efremidis, A. Miller, Y. Hu, and Z. Chen, “Observation of coherent destruction of tunneling and unusual beam dynamics due to negative coupling in three-dimensional photonic lattices,” Opt. Lett. 35(19), 3252–3254 (2010).
[Crossref] [PubMed]

N. K. Efremidis and K. Hizanidis, “Disordered lattice solitons,” Phys. Rev. Lett. 101(14), 143903 (2008).
[Crossref] [PubMed]

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(6928), 147–150 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,” Phys. Rev. Lett. 92(12), 123902 (2004).
[Crossref] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[Crossref] [PubMed]

Fleischer, J. W.

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” Phys. Rev. Lett. 94(16), 163902 (2005).
[Crossref] [PubMed]

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(6928), 147–150 (2003).
[Crossref] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4), 046602 (2002).
[Crossref] [PubMed]

Florescu, M.

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110(40), 15886–15891 (2013).
[Crossref] [PubMed]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A. 106(49), 20658–20663 (2009).
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L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332(6037), 1541–1544 (2011).
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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(9), 1518–1520 (2013).
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Qi, X.

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Rechtsman, M.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332(6037), 1541–1544 (2011).
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P. Zhang, P. Ni, X. Qi, W. Man, Z. Chen, J. Yang, M. Rechtsman, and M. Segev, “Specular amorphous photonic bandgap lattices,” in Quantum Electronics and Laser Science Conference (OSA, 2012), pp. QF3H–1.

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H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
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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(7131), 52–55 (2007).
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Shechtman, Y.

Silberberg, Y.

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(1), 013906 (2008).
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F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463(1–3), 1–126 (2008).
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D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
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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(1), 013906 (2008).
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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110(40), 15886–15891 (2013).
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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(9), 1518–1520 (2013).
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A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V. A. Vysloukh, F. Lederer, and L. Torner, “Inhibition of light tunneling in waveguide arrays,” Phys. Rev. Lett. 102(15), 153901 (2009).
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S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110(40), 15886–15891 (2013).
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R. Keil, Y. Lahini, Y. Shechtman, M. Heinrich, R. Pugatch, F. Dreisow, A. Tünnermann, S. Nolte, and A. Szameit, “Perfect imaging through a disordered waveguide lattice,” Opt. Lett. 37(5), 809–811 (2012).
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Vysloukh, V. A.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to generate complex quasinondiffracting optical lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
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H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
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D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7(3), 188–196 (2013).
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W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. C. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,” Proc. Natl. Acad. Sci. U.S.A. 110(40), 15886–15891 (2013).
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S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
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P. Zhang, P. Ni, X. Qi, W. Man, Z. Chen, J. Yang, M. Rechtsman, and M. Segev, “Specular amorphous photonic bandgap lattices,” in Quantum Electronics and Laser Science Conference (OSA, 2012), pp. QF3H–1.

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S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
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H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
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Appl. Phys. B (1)

S. Liu, P. Zhang, X. Gan, F. Xiao, and J. Zhao, “Visualization of the Bragg reflection in complex photonic lattices by employing Brillouin zone spectroscopy,” Appl. Phys. B 99(4), 727–731 (2010).
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Nat. Photonics (3)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

C. Barsi, W. Wan, and J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3(4), 211–215 (2009).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 A Sketch of the experimental setup. The red (left-side) route is for generating the non-diffracting disordered photonic lattice. The green (middle) route is for Brillouin zone spectroscopy, which can be added or blocked. The navy-blue (right-side) route is the probe beam. RT: reversed telescope; BS: beam splitter; RD: rotating diffuser; SBN: strontium barium niobate crystal.
Fig. 2
Fig. 2 Simulation (a, top) and experimental results (b, bottom) of a non-diffracting amorphous lattice and its Brillouin zone spectroscopy. (a1, b1) Spectrum of a diffused light beam after a ring-shaped spatial filter, (a2, b2) lattice input, (a3, b3) lattice output after 1cm of propagation, and (a4, b4) corresponding Brillouin zone spectrum.
Fig. 3
Fig. 3 (a) Calculated eigenvalue spectrum of the amouphous specular lattice and (b) observation of localized modes by launching the probe beam at different locations of the lattice with random spacing and amplitude modulation. (c) Output of the probe beam launched at a weak spot (solid circle) shows a long tail for Anderson-type localization. (d) Output of the probe beam launched at a strong positive defect point (dotted circle) shows a well-confined and much tighter localization. (c1 and d1 are from experiment while c2 and d2 are from simulation.)
Fig. 4
Fig. 4 Experimental results of the probe beam’s output intensity pattern showing a linear localized mode (a) and its nonlinear evolution (b, c, d) in the presence of a gradually increasing nonlinearity. The disordered lattice is optically induced with a self-focusing nonlinearity, which increases in a photorefractive crystal under a positive bias electric field. The probe beam itself is initially localized as a linear defect mode. With the increasing nonlinearity, the localized defect mode is gradually destroyed from (a) to (d), and the bright spot at the center of the dashed circle disappears.
Fig. 5
Fig. 5 Experimental demonstration of image transmission through an amorphous lattice under the action of a self-defocusing nonlinearity. (a) Input images (intensity pattern of a cross or H shape as created from an amplitude mask). (b) Output patterns after 1 cm of propagation through free space. (c, d) Output patterns after 1 cm of propagation through the disordered lattice at a (c) low and (d) high self-defocusing nonlinearity controlled by the negative bias field.

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