Abstract

We present a method to demonstrate Anderson localization in an optically induced randomized potential. By usage of computer controlled spatial light modulators, we are able to implement fully randomized nondiffracting beams of variable structural size in order to control the modulation length (photonic grain size) as well as the depth (disorder strength) of a random potential induced in a photorefractive crystal. In particular, we quantitatively analyze the localization length of light depending on these two parameters and find that they are crucial influencing factors on the propagation behavior leading to variably strong localization. Thus, we corroborate that transverse light localization in a random refractive index landscape strongly depends on the character of the potential, allowing for a flexible regulation of the localization strength by adapting the optical induction configuration.

© 2013 Optical Society of America

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  1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev.109, 1492–1505 (1958).
    [CrossRef]
  2. P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys.57, 287–337 (1985).
    [CrossRef]
  3. S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
    [CrossRef] [PubMed]
  4. F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
    [CrossRef]
  5. H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
    [CrossRef]
  6. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
    [CrossRef]
  7. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett.53, 2169–2172 (1984).
    [CrossRef]
  8. H. De Raedt, A. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett.62, 47–50 (1989).
    [CrossRef] [PubMed]
  9. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
    [CrossRef] [PubMed]
  10. S. Feng, L. Golubović, and Y.-C. Zhang, “Directed wave propagation in random media: superdiffusion and phase transitions,” Phys. Rev. Lett.65, 1028–1031 (1990).
    [CrossRef] [PubMed]
  11. D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E79, 036606 (2009).
    [CrossRef]
  12. D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A84, 043811 (2011).
    [CrossRef]
  13. V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Anderson localization in Bragg-guiding arrays with negative defects,” Opt. Lett.37, 4020–4022 (2012).
    [CrossRef] [PubMed]
  14. A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
    [CrossRef]
  15. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett.100, 013906 (2008).
    [CrossRef] [PubMed]
  16. 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, 193904 (2011).
    [CrossRef] [PubMed]
  17. S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
    [CrossRef]
  18. S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express2, 1496–1503 (2012).
    [CrossRef]
  19. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
    [CrossRef] [PubMed]
  20. L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
    [CrossRef] [PubMed]
  21. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  22. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
    [CrossRef]
  23. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151, 207–211 (1998).
    [CrossRef]
  24. M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
    [CrossRef]
  25. Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
    [CrossRef]
  26. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Cháves-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett.29, 44–46 (2004).
    [CrossRef] [PubMed]
  27. D. M. Cottrell, J. M. Craven, and J. A. Davis, “Nondiffracting random intensity patterns,” Opt. Lett.32, 298–300 (2007).
    [CrossRef] [PubMed]
  28. P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys.14, 033018 (2012).
    [CrossRef]
  29. B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
    [CrossRef]
  30. R. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun.80, 253–258 (1991).
    [CrossRef]
  31. E. S. Maniloff and K. M. Johnson, “Maximized photorefractive holographic storage,”J. Appl Phys.70, 4702–4707 (1991).
    [CrossRef]
  32. B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
    [CrossRef]

2012

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
[CrossRef]

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys.14, 033018 (2012).
[CrossRef]

V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Anderson localization in Bragg-guiding arrays with negative defects,” Opt. Lett.37, 4020–4022 (2012).
[CrossRef] [PubMed]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express2, 1496–1503 (2012).
[CrossRef]

2011

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[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, 193904 (2011).
[CrossRef] [PubMed]

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A84, 043811 (2011).
[CrossRef]

S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
[CrossRef] [PubMed]

2009

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E79, 036606 (2009).
[CrossRef]

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] [PubMed]

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

2007

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

D. M. Cottrell, J. M. Craven, and J. A. Davis, “Nondiffracting random intensity patterns,” Opt. Lett.32, 298–300 (2007).
[CrossRef] [PubMed]

2006

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

2004

2003

Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
[CrossRef]

2000

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

1998

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151, 207–211 (1998).
[CrossRef]

1997

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
[CrossRef]

1991

R. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun.80, 253–258 (1991).
[CrossRef]

E. S. Maniloff and K. M. Johnson, “Maximized photorefractive holographic storage,”J. Appl Phys.70, 4702–4707 (1991).
[CrossRef]

1990

S. Feng, L. Golubović, and Y.-C. Zhang, “Directed wave propagation in random media: superdiffusion and phase transitions,” Phys. Rev. Lett.65, 1028–1031 (1990).
[CrossRef] [PubMed]

1989

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

1987

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

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

1985

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys.57, 287–337 (1985).
[CrossRef]

1984

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

1958

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

Abouraddy, A. F.

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
[CrossRef]

Anderson, P. W.

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

Aspect, A.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[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] [PubMed]

Ballato, J.

Bandres, M. A.

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
[CrossRef]

Belic, M. R.

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A84, 043811 (2011).
[CrossRef]

Bernard, A.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Bersch, C.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

Boguslawski, M.

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys.14, 033018 (2012).
[CrossRef]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

Bouchal, Z.

Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151, 207–211 (1998).
[CrossRef]

Bouyer, P.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

Cháves-Cerda, S.

Cheinet, P.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151, 207–211 (1998).
[CrossRef]

Christodoulides, D. N.

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
[CrossRef]

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

Cottrell, D. M.

Craven, J. M.

Davis, J. A.

De Raedt, H.

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

DeMarco, B.

S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
[CrossRef] [PubMed]

Denz, C.

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys.14, 033018 (2012).
[CrossRef]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A84, 043811 (2011).
[CrossRef]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

Desyatnikov, A. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

Di Giuseppe, G.

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
[CrossRef]

Dimitropoulos, D.

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E79, 036606 (2009).
[CrossRef]

Dreisow, F.

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, 193904 (2011).
[CrossRef] [PubMed]

Durnin, J.

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

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (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] [PubMed]

Ewbank, M. D.

R. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun.80, 253–258 (1991).
[CrossRef]

Feng, S.

S. Feng, L. Golubović, and Y.-C. Zhang, “Directed wave propagation in random media: superdiffusion and phase transitions,” Phys. Rev. Lett.65, 1028–1031 (1990).
[CrossRef] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Freedman, B.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[CrossRef] [PubMed]

Genack, A. Z.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

Ghosh, S.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Golubovic, L.

S. Feng, L. Golubović, and Y.-C. Zhang, “Directed wave propagation in random media: superdiffusion and phase transitions,” Phys. Rev. Lett.65, 1028–1031 (1990).
[CrossRef] [PubMed]

Gutiérrez-Vega, J. C.

Hawkins, T.

Heinrich, M.

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, 193904 (2011).
[CrossRef] [PubMed]

Hu, H.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

Imbrock, J.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

Jalali, B.

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E79, 036606 (2009).
[CrossRef]

Jendrzejewski, F.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

John, S.

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

Johnson, K. M.

E. S. Maniloff and K. M. Johnson, “Maximized photorefractive holographic storage,”J. Appl Phys.70, 4702–4707 (1991).
[CrossRef]

Josse, V.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Jovic, D. M.

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A84, 043811 (2011).
[CrossRef]

Kar, A. K.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Karbasi, S.

Kartashov, Y. V.

Keil, R.

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, 193904 (2011).
[CrossRef] [PubMed]

Kivshar, Y. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

Koch, K. W.

Kondov, S. S.

S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
[CrossRef] [PubMed]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
[CrossRef]

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

Lahini, 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, 013906 (2008).
[CrossRef] [PubMed]

Lee, P. A.

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys.57, 287–337 (1985).
[CrossRef]

Levi, L.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[CrossRef] [PubMed]

Lobanov, V. E.

Mafi, A.

Manela, O.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[CrossRef] [PubMed]

Maniloff, E. S.

E. S. Maniloff and K. M. Johnson, “Maximized photorefractive holographic storage,”J. Appl Phys.70, 4702–4707 (1991).
[CrossRef]

McGehee, W. R.

S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
[CrossRef] [PubMed]

Miceli, J. J.

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

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).
[CrossRef] [PubMed]

Müller, K.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Neurgaonkar, R. R.

R. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun.80, 253–258 (1991).
[CrossRef]

Nolte, S.

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, 193904 (2011).
[CrossRef] [PubMed]

Page, J. H.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

Pal, B. P.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Pezzé, L.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Piraud, M.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Pozzi, F.

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

Psalia, N. D.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Ramakrishnan, T. V.

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys.57, 287–337 (1985).
[CrossRef]

Rechtsman, M.

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, 193904 (2011).
[CrossRef] [PubMed]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[CrossRef] [PubMed]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
[CrossRef]

Rose, P.

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys.14, 033018 (2012).
[CrossRef]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

Saleh, B. E. A.

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
[CrossRef]

Sanches-Palencia, L.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

Schwartz, T.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Segev, M.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[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, 193904 (2011).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

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, 013906 (2008).
[CrossRef] [PubMed]

Skipetrov, S. E.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

Sorel, M.

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

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

Strybulevych, A.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

Szameit, A.

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, 193904 (2011).
[CrossRef] [PubMed]

Tang, L.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

Terhalle, B.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

Thomson, R. R.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Torner, L.

Träger, D.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

van Tiggelen, B. A.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

Varshney, R. K.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Vazquez, R.

R. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun.80, 253–258 (1991).
[CrossRef]

Vysloukh, V. A.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151, 207–211 (1998).
[CrossRef]

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
[CrossRef]

Zhang, Y.-C.

S. Feng, L. Golubović, and Y.-C. Zhang, “Directed wave propagation in random media: superdiffusion and phase transitions,” Phys. Rev. Lett.65, 1028–1031 (1990).
[CrossRef] [PubMed]

Zirbel, J. J.

S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
[CrossRef] [PubMed]

Appl. Phys. B

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B86, 399–405 (2007).
[CrossRef]

Appl. Phys. Lett.

S. Ghosh, N. D. Psalia, R. R. Thomson, B. P. Pal, R. K. Varshney, and A. K. Kar, “Ultrafast laser inscribed waveguide lattice in glass for direct observation of transverse localization of light,” Appl. Phys. Lett.100, 101102 (2012).
[CrossRef]

Czech. J. Phys.

Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
[CrossRef]

J. Appl Phys.

E. S. Maniloff and K. M. Johnson, “Maximized photorefractive holographic storage,”J. Appl Phys.70, 4702–4707 (1991).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Phys.

F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanches-Palencia, A. Aspect, and P. Bouyer, “Three-dimensional localization of ultracold atoms in an optical disordered potential,” Nat. Phys.8, 398–403 (2012).
[CrossRef]

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys.4, 945–948 (2008).
[CrossRef]

Nature

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
[CrossRef]

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

New J. Phys.

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys.14, 033018 (2012).
[CrossRef]

Opt. Commun.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun.151, 207–211 (1998).
[CrossRef]

R. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun.80, 253–258 (1991).
[CrossRef]

Opt. Lett.

Opt. Mater. Express

Phys. Rev.

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

Phys. Rev. A

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A84, 043811 (2011).
[CrossRef]

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A86, 040302 (2012).
[CrossRef]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

Phys. Rev. E

B. Terhalle, D. Träger, L. Tang, J. Imbrock, and C. Denz, “Structure analysis of two-dimensional nonlinear self-trapped photonic lattices in anisotropic photorefractive media,” Phys. Rev. E74, 057601 (2006).
[CrossRef]

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E79, 036606 (2009).
[CrossRef]

Phys. Rev. Lett.

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

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

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, 193904 (2011).
[CrossRef] [PubMed]

S. Feng, L. Golubović, and Y.-C. Zhang, “Directed wave propagation in random media: superdiffusion and phase transitions,” Phys. Rev. Lett.65, 1028–1031 (1990).
[CrossRef] [PubMed]

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

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

Rev. Mod. Phys.

P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys.57, 287–337 (1985).
[CrossRef]

Science

S. S. Kondov, W. R. McGehee, J. J. Zirbel, and B. DeMarco, “Three-dimensional Anderson localization of ultracold matter,” Science334, 66–68 (2011).
[CrossRef] [PubMed]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332, 1541–1544 (2011).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Simulated distributions for a randomized nondiffracting writing beam configuration with a PGS of g = 20 μm. In (a) the intensity and in (b) the phase distributions in real space are depicted. In (c) a comparison between the spatial spectrum of the writing beam (lhs) and the logarithmic spectrum of its intensity (rhs) is drawn, kr is the ring radius of the writing beam’s transverse Fourier spectrum. Distribution in (d) presents the autocorrelation function of the intensity presented in (a). In (e) the mean autocorrelation through the maximum as well as the corresponding correlation length lc and in (f) the mean power spectrum through the spectral center is plotted (both averaged over 100 different distributions).

Fig. 2
Fig. 2

Sketch of the experimental setup to induce random photonic structures. A/PSLM: amplitude/phase spatial light modulator, BS: beam splitter, Cam: camera, L: lens, LED: white light emitting diode, λ/2: half-wave plate, M: mirror, MO: microscope objective, P: polarizer, PH: pin hole, PS: positioning stage, S: shutter, SBN: photorefractive crystal.

Fig. 3
Fig. 3

Experimentally recorded intensity profiles of a nondiffracting writing beam with random transverse intensity distribution. (a) and (b) present nearly identical transverse intensity modulations at the front and the back face of the crystal, (c) and (d) show the intensity development with propagation in z direction in the central vertical and horizontal longitudinal plane, cf. dotted lines in (a).

Fig. 4
Fig. 4

Intensity distribution of probe beam in unmodulated medium at (a) crystal’s front face, (b) back face; in randomly modulated medium at back face: (c) single shot for particular random potential, (d) mean intensity averaging over a set of 100 single probe shots. All intensities are normalized.

Fig. 5
Fig. 5

Logarithmic plot of the central intensity I for blue line: potential without disorder, black solid line: strongly modulated potential in x direction. Red lines mark linear profiles of logarithmic intensity in x direction around the localization center and corresponding mean slope. Black dashed line: strongly modulated potential in y direction.

Fig. 6
Fig. 6

Dependency of localization length ξ against g. Error determined by linear approximation of localization length.

Fig. 7
Fig. 7

Plot of the disorder strength Δ with g = 16.1 μm against the illumination time and exponential fit (blue line).

Fig. 8
Fig. 8

Logarithmic plot of the central intensity I for random potential of different illumination times and g = 16.1 μm, black line: T = 0 s, blue line: T = 25 s, green line: T = 50 s, red line: T = 90 s.

Fig. 9
Fig. 9

Relation of localization length ξ and relative disorder strength Δ for g = 16.1 μm.

Equations (2)

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I ( x ) = exp ( 2 | x x 0 | ξ ) .
Δ ( T ) = 1 exp ( T / τ w ) ,

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