Abstract

When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and analytical modeling, we uncover a set of surprising features that characterize discrete speckle in one- and two-dimensional lattices known to exhibit transverse Anderson localization. First, the fingerprint of localization is embedded in the fluctuations of the discrete speckle and is revealed in the narrowing of the spatial coherence function. Second, the transverse coherence length (or speckle grain size) is frozen during propagation. Third, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. We take these unique features collectively to define a distinct regime that we call discrete Anderson speckle.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Anderson localization in optical waveguide arrays with off-diagonal coupling disorder

Lane Martin, Giovanni Di Giuseppe, Armando Perez-Leija, Robert Keil, Felix Dreisow, Matthias Heinrich, Stefan Nolte, Alexander Szameit, Ayman F. Abouraddy, Demetrios N. Christodoulides, and Bahaa E. A. Saleh
Opt. Express 19(14) 13636-13646 (2011)

Self-trapping threshold in disordered nonlinear photonic lattices

U. Naether, M. Heinrich, Y. Lahini, S. Nolte, R. A. Vicencio, M. I. Molina, and A. Szameit
Opt. Lett. 38(9) 1518-1520 (2013)

Anderson localization in Bragg-guiding arrays with negative defects

Valery E. Lobanov, Yaroslav V. Kartashov, Victor A. Vysloukh, and Lluis Torner
Opt. Lett. 37(19) 4020-4022 (2012)

References

  • View by:
  • |
  • |
  • |

  1. J. D. Rigden, E. I. Gordon, “The granularity of scattered optical maser light,” Proc. IRE 50, 2367 (1962).
  2. B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE 51, 220–221 (1963).
    [Crossref]
  3. J. A. Ratcliffe, J. L. Pawsey, “A study of the intensity variations of downcoming wireless waves,” Math. Proc. Cambridge Philos. Soc. 29, 301–318 (1933).
  4. H. G. Booker, J. A. Ratcliffe, D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Phil. Trans. R. Soc. A 242, 579–607 (1950).
  5. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
    [Crossref]
  6. B. E. A. Saleh, Introduction to Subsurface Imaging (Cambridge University, 2011).
  7. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  8. A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
    [Crossref]
  9. B. Redding, M. A. Choma, H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
    [Crossref]
  10. O. Katz, E. Small, Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
    [Crossref]
  11. O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
    [Crossref]
  12. T. E. Matthews, M. Medina, J. R. Maher, H. Levinson, W. J. Brown, A. Wax, “Deep tissue imaging using spectroscopic analysis of multiply scattered light,” Optica 1, 105–111 (2014).
    [Crossref]
  13. O. Katz, E. Small, Y. Guan, Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
    [Crossref]
  14. E. H. Zhou, H. Ruan, C. Yang, B. Judkewitz, “Focusing on moving targets through scattering samples,” Optica 1, 227–232 (2014).
    [Crossref]
  15. T. Schwartz, G. Bartal, S. Fishman, M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [Crossref]
  16. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
    [Crossref]
  17. L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
    [Crossref]
  18. S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
    [Crossref]
  19. S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
    [Crossref]
  20. J. Topolancik, B. Ilic, F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
    [Crossref]
  21. A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
    [Crossref]
  22. G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
    [Crossref]
  23. A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
    [Crossref]
  24. J. Svozilík, J. Peřina, J. P. Torres, “Measurement-based tailoring of Anderson localization of partially coherent light,” Phys. Rev. A 89, 053808 (2014).
    [Crossref]
  25. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
    [Crossref]
  26. A. Lagendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
    [Crossref]
  27. H. De Raedt, A. Lagendijk, P. de Vries, “Transverse localization of light,” Phys. Rev. Lett. 62, 47–50 (1989).
    [Crossref]
  28. M. Segev, Y. Silberberg, D. N. Christodoulides, “Anderson localization of light,” Nat. Photonics 7, 197–204 (2013).
    [Crossref]
  29. D. N. Christodoulides, F. Lederer, Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
    [Crossref]
  30. D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
    [Crossref]
  31. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).
  32. J. W. Goodman, Statistical Optics (Wiley, 2000).
  33. B. Redding, M. A. Choma, H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
    [Crossref]
  34. Y. Imry, R. Landauer, “Conductance viewed as transmission,” Rev. Mod. Phys. 71, S306–S312 (1999).
    [Crossref]
  35. A. A. Chabanov, M. Stoytchev, A. Z. Genack, “Statistical signatures of photon localization,” Nature 404, 850–853 (2000).
    [Crossref]
  36. J. Wang, A. Z. Genack, “Transport through modes in random media,” Nature 471, 345–348 (2011).
    [Crossref]
  37. C. M. Soukoulis, E. N. Economou, “Off-diagonal disorder in one-dimensional systems,” Phys. Rev. B 24, 5698–5702 (1981).
  38. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [Crossref]
  39. D. N. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Uspekhi 37, 1097–1123 (1994).
  40. S. N. Evangelou, D. E. Katsanos, “Spectral statistics in chiral-orthogonal disordered systems,” J. Phys. A 36, 3237–3254 (2003).
    [Crossref]
  41. Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
    [Crossref]
  42. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
    [Crossref]
  43. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008).
    [Crossref]
  44. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
    [Crossref]
  45. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
    [Crossref]
  46. K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
    [Crossref]
  47. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
    [Crossref]
  48. M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
    [Crossref]
  49. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
    [Crossref]
  50. H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, B. A. van Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nat. Phys. 4, 945–948 (2008).
    [Crossref]

2014 (6)

O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

T. E. Matthews, M. Medina, J. R. Maher, H. Levinson, W. J. Brown, A. Wax, “Deep tissue imaging using spectroscopic analysis of multiply scattered light,” Optica 1, 105–111 (2014).
[Crossref]

O. Katz, E. Small, Y. Guan, Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

E. H. Zhou, H. Ruan, C. Yang, B. Judkewitz, “Focusing on moving targets through scattering samples,” Optica 1, 227–232 (2014).
[Crossref]

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

J. Svozilík, J. Peřina, J. P. Torres, “Measurement-based tailoring of Anderson localization of partially coherent light,” Phys. Rev. A 89, 053808 (2014).
[Crossref]

2013 (5)

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

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

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

2012 (5)

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

B. Redding, M. A. Choma, H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref]

O. Katz, E. Small, Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

2011 (5)

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

B. Redding, M. A. Choma, H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref]

J. Wang, A. Z. Genack, “Transport through modes in random media,” Nature 471, 345–348 (2011).
[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

2010 (1)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

2009 (2)

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

A. Lagendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

2008 (5)

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

S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

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

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

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

2007 (2)

J. Topolancik, B. Ilic, F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

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

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

2003 (2)

S. N. Evangelou, D. E. Katsanos, “Spectral statistics in chiral-orthogonal disordered systems,” J. Phys. A 36, 3237–3254 (2003).
[Crossref]

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

2000 (1)

A. A. Chabanov, M. Stoytchev, A. Z. Genack, “Statistical signatures of photon localization,” Nature 404, 850–853 (2000).
[Crossref]

1999 (2)

Y. Imry, R. Landauer, “Conductance viewed as transmission,” Rev. Mod. Phys. 71, S306–S312 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

1995 (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

1994 (1)

D. N. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Uspekhi 37, 1097–1123 (1994).

1989 (1)

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

1981 (1)

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

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1963 (1)

B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE 51, 220–221 (1963).
[Crossref]

1962 (1)

J. D. Rigden, E. I. Gordon, “The granularity of scattered optical maser light,” Proc. IRE 50, 2367 (1962).

1958 (1)

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

1950 (1)

H. G. Booker, J. A. Ratcliffe, D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Phil. Trans. R. Soc. A 242, 579–607 (1950).

1933 (1)

J. A. Ratcliffe, J. L. Pawsey, “A study of the intensity variations of downcoming wireless waves,” Math. Proc. Cambridge Philos. Soc. 29, 301–318 (1933).

Abouraddy, A. F.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Anderson, P. W.

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

Aspect, A.

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

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, 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, Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[Crossref]

Ballato, J.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Bandaru, P. R.

S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

Bartal, G.

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

Bernard, A.

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

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Billy, J.

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

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Booker, H. G.

H. G. Booker, J. A. Ratcliffe, D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Phil. Trans. R. Soc. A 242, 579–607 (1950).

Bouyer, P.

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

Bromberg, Y.

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Brown, W. J.

Buljan, H.

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

Cao, H.

B. Redding, M. A. Choma, H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref]

B. Redding, M. A. Choma, H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref]

Capeta, D.

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

Chabanov, A. A.

A. A. Chabanov, M. Stoytchev, A. Z. Genack, “Statistical signatures of photon localization,” Nature 404, 850–853 (2000).
[Crossref]

Chen, Z.

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

Choma, M. A.

B. Redding, M. A. Choma, H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref]

B. Redding, M. A. Choma, H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref]

Christodoulides, D. N.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

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

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

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

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

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

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

Clément, D.

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

Crespi, A.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

De Nicola, F.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

De Raedt, H.

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

de Vries, P.

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

Di Giuseppe, G.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Economou, E. N.

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

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Evangelou, S. N.

S. N. Evangelou, D. E. Katsanos, “Spectral statistics in chiral-orthogonal disordered systems,” J. Phys. A 36, 3237–3254 (2003).
[Crossref]

Fazio, R.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Fink, M.

O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

Fishman, S.

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

Frazier, R. J.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Genack, A. Z.

J. Wang, A. Z. Genack, “Transport through modes in random media,” Nature 471, 345–348 (2011).
[Crossref]

A. A. Chabanov, M. Stoytchev, A. Z. Genack, “Statistical signatures of photon localization,” Nature 404, 850–853 (2000).
[Crossref]

Gigan, S.

O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Giovannetti, V.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

J. W. Goodman, Statistical Optics (Wiley, 2000).

Gordon, E. I.

J. D. Rigden, E. I. Gordon, “The granularity of scattered optical maser light,” Proc. IRE 50, 2367 (1962).

Guan, Y.

Hambrecht, B.

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

Hawkins, T.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Heinrich, M.

Hu, H.

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

Ilic, B.

J. Topolancik, B. Ilic, F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Imry, Y.

Y. Imry, R. Landauer, “Conductance viewed as transmission,” Rev. Mod. Phys. 71, S306–S312 (1999).
[Crossref]

Ismail, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Josse, V.

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

Judkewitz, B.

Karbasi, S.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Katsanos, D. E.

S. N. Evangelou, D. E. Katsanos, “Spectral statistics in chiral-orthogonal disordered systems,” J. Phys. A 36, 3237–3254 (2003).
[Crossref]

Katz, O.

O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

O. Katz, E. Small, Y. Guan, Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

O. Katz, E. Small, Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

Keil, R.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Kip, D.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

D. N. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Uspekhi 37, 1097–1123 (1994).

Koch, K. W.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

A. Lagendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

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

Lahini, Y.

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

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

Landauer, R.

Y. Imry, R. Landauer, “Conductance viewed as transmission,” Rev. Mod. Phys. 71, S306–S312 (1999).
[Crossref]

Lederer, F.

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

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

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

Levinson, H.

Lobino, M.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Lugan, P.

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

Lumer, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Mafi, A.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Maher, J. R.

Makris, K. G.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

Martin, L.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Mataloni, P.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Matsuda, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Matthews, J. C. F.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Matthews, T. E.

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Medina, M.

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Mookherjea, S.

S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

Morandotti, R.

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Nolte, S.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

OBrien, J. L.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Oliver, B. M.

B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE 51, 220–221 (1963).
[Crossref]

Osellame, R.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Page, J. H.

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

Park, J. S.

S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

Pawsey, J. L.

J. A. Ratcliffe, J. L. Pawsey, “A study of the intensity variations of downcoming wireless waves,” Math. Proc. Cambridge Philos. Soc. 29, 301–318 (1933).

Peleg, O.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

Perez-Leija, A.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Perina, J.

J. Svozilík, J. Peřina, J. P. Torres, “Measurement-based tailoring of Anderson localization of partially coherent light,” Phys. Rev. A 89, 053808 (2014).
[Crossref]

Peruzzo, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Plotnik, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

Podolsky, D.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Politi, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Poulios, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Pozzi, F.

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

Radic, J.

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

Ramponi, R.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Ratcliffe, J. A.

H. G. Booker, J. A. Ratcliffe, D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Phil. Trans. R. Soc. A 242, 579–607 (1950).

J. A. Ratcliffe, J. L. Pawsey, “A study of the intensity variations of downcoming wireless waves,” Math. Proc. Cambridge Philos. Soc. 29, 301–318 (1933).

Rechtsman, M. C.

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Redding, B.

B. Redding, M. A. Choma, H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref]

B. Redding, M. A. Choma, H. Cao, “Spatial coherence of random laser emission,” Opt. Lett. 36, 3404–3406 (2011).
[Crossref]

Rigden, J. D.

J. D. Rigden, E. I. Gordon, “The granularity of scattered optical maser light,” Proc. IRE 50, 2367 (1962).

Ruan, H.

Rüter, C. E.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

Saleh, B. E. A.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

B. E. A. Saleh, Introduction to Subsurface Imaging (Cambridge University, 2011).

Sanchez-Palencia, L.

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

Sansoni, L.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Schwartz, T.

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

Sciarrino, F.

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

Segev, M.

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

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

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

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

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

Shandarova, K.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

Shechtman, Y.

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

Shinn, D. H.

H. G. Booker, J. A. Ratcliffe, D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Phil. Trans. R. Soc. A 242, 579–607 (1950).

Silberberg, Y.

O. Katz, E. Small, Y. Guan, Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

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

O. Katz, E. Small, Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

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

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

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Skipetrov, S. E.

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

Small, E.

O. Katz, E. Small, Y. Guan, Y. Silberberg, “Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers,” Optica 1, 170–174 (2014).
[Crossref]

O. Katz, E. Small, Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Song, D.

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, 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, E. N. Economou, “Off-diagonal disorder in one-dimensional systems,” Phys. Rev. B 24, 5698–5702 (1981).

Stegeman, G. I.

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

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, A. Z. Genack, “Statistical signatures of photon localization,” Nature 404, 850–853 (2000).
[Crossref]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

Strybulevych, A.

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

Svozilík, J.

J. Svozilík, J. Peřina, J. P. Torres, “Measurement-based tailoring of Anderson localization of partially coherent light,” Phys. Rev. A 89, 053808 (2014).
[Crossref]

Szameit, A.

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).
[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

Thompson, M. G.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Topolancik, J.

J. Topolancik, B. Ilic, F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Torres, J. P.

J. Svozilík, J. Peřina, J. P. Torres, “Measurement-based tailoring of Anderson localization of partially coherent light,” Phys. Rev. A 89, 053808 (2014).
[Crossref]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

van Tiggelen, B.

A. Lagendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

van Tiggelen, B. A.

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

Vollmer, F.

J. Topolancik, B. Ilic, F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Wang, J.

J. Wang, A. Z. Genack, “Transport through modes in random media,” Nature 471, 345–348 (2011).
[Crossref]

Wax, A.

Wiersma, D. S.

A. Lagendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

Wörhoff, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Yang, C.

Yang, S.-H.

S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

Zeuner, J. M.

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

Zhou, E. H.

Zhou, X.-Q.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Zuo, Z.

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

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

J. Phys. A (1)

S. N. Evangelou, D. E. Katsanos, “Spectral statistics in chiral-orthogonal disordered systems,” J. Phys. A 36, 3237–3254 (2003).
[Crossref]

Math. Proc. Cambridge Philos. Soc. (1)

J. A. Ratcliffe, J. L. Pawsey, “A study of the intensity variations of downcoming wireless waves,” Math. Proc. Cambridge Philos. Soc. 29, 301–318 (1933).

Nat. Commun. (1)

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref]

Nat. Photonics (7)

S. Mookherjea, J. S. Park, S.-H. Yang, P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, V. Giovannetti, R. Fazio, L. Sansoni, F. De Nicola, F. Sciarrino, P. Mataloni, “Anderson localization of entangled photons in an integrated quantum walk,” Nat. Photonics 7, 322–328 (2013).
[Crossref]

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

A. P. Mosk, A. Lagendijk, G. Lerosey, M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6, 283–292 (2012).
[Crossref]

B. Redding, M. A. Choma, H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[Crossref]

O. Katz, E. Small, Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photonics 6, 549–553 (2012).
[Crossref]

O. Katz, P. Heidmann, M. Fink, S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Nat. Phys. (1)

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

Nature (7)

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit, “Photonic Floquet topological insulators,” Nature 496, 196–200 (2013).
[Crossref]

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

A. A. Chabanov, M. Stoytchev, A. Z. Genack, “Statistical signatures of photon localization,” Nature 404, 850–853 (2000).
[Crossref]

J. Wang, A. Z. Genack, “Transport through modes in random media,” Nature 471, 345–348 (2011).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

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

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

Opt. Express (1)

Opt. Lett. (1)

Optica (3)

Phil. Trans. R. Soc. A (1)

H. G. Booker, J. A. Ratcliffe, D. H. Shinn, “Diffraction from an irregular screen with applications to ionospheric problems,” Phil. Trans. R. Soc. A 242, 579–607 (1950).

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, 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).
[Crossref]

Phys. Rev. A (4)

J. Svozilík, J. Peřina, J. P. Torres, “Measurement-based tailoring of Anderson localization of partially coherent light,” Phys. Rev. A 89, 053808 (2014).
[Crossref]

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302 (2012).
[Crossref]

D. Čapeta, J. Radić, A. Szameit, M. Segev, H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801 (2011).
[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806 (2011).
[Crossref]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (9)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102, 123905 (2009).
[Crossref]

M. C. Rechtsman, Y. Plotnik, J. M. Zeuner, D. Song, Z. Chen, A. Szameit, M. Segev, “Topological creation and destruction of edge states in photonic graphene,” Phys. Rev. Lett. 111, 103901 (2013).
[Crossref]

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

G. Di Giuseppe, L. Martin, A. Perez-Leija, R. Keil, F. Dreisow, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, B. E. A. Saleh, “Einstein-Podolsky-Rosen spatial entanglement in ordered and Anderson photonic lattices,” Phys. Rev. Lett. 110, 150503 (2013).
[Crossref]

J. Topolancik, B. Ilic, F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[Crossref]

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

Phys. Today (1)

A. Lagendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

Phys. Uspekhi (1)

D. N. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Uspekhi 37, 1097–1123 (1994).

Proc. IEEE (1)

B. M. Oliver, “Sparkling spots and random diffraction,” Proc. IEEE 51, 220–221 (1963).
[Crossref]

Proc. IRE (1)

J. D. Rigden, E. I. Gordon, “The granularity of scattered optical maser light,” Proc. IRE 50, 2367 (1962).

Rev. Mod. Phys. (1)

Y. Imry, R. Landauer, “Conductance viewed as transmission,” Rev. Mod. Phys. 71, S306–S312 (1999).
[Crossref]

Science (1)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

Other (3)

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts & Company, 2007).

J. W. Goodman, Statistical Optics (Wiley, 2000).

B. E. A. Saleh, Introduction to Subsurface Imaging (Cambridge University, 2011).

Supplementary Material (1)

» Supplement 1: PDF (1342 KB)     

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. Conventional speckle and discrete Anderson speckle. (a) A thin random phase screen ( σ ϕ = 4 π ) illuminated with a uniform coherent beam produces conventional speckle. (b) Discrete Anderson speckle is produced from a highly disordered hexagonal (honeycomb) waveguide lattice with maximal off-diagonal disorder when illuminated with a uniform coherent beam. (c) The grain size of conventional speckle increases with propagation distance z , while that of discrete Anderson speckle does not as shown in (d).
Fig. 2.
Fig. 2. Anderson localization and discrete speckle in 1D waveguide lattices. (a) PSF I ( x o ) = | h ( x o , 0 ) | 2 at z = 10 for a 1D periodic array for single-waveguide excitation at x i = 0 . Inset is a schematic of the configuration. (b) Mean PSF I ( x o ) = | h ( x o , 0 ) | 2 for disordered 1D arrays. Insets show the localization length σ s as a function of Δ C (for fixed z = 10 ) and of z (for fixed values of Δ C ). For the values of σ s in the insets, 21 points for Δ C and 200 for z are chosen. (c) Realizations of discrete speckle at various disorder levels ( z = 10 ) for extended uniform coherent input light. The dotted lines are ensemble averages. We use N t = 151 throughout.
Fig. 3.
Fig. 3. Anderson localization and discrete speckle in 2D waveguide lattices. (a) Mean PSF I ( x o , y o ) = | h ( x o , 0 ; y o , 0 ) | 2 for 2D hexagonal (honeycomb) arrays with increasing disorder (from left to right) at z = 10 . For clarity, each panel is normalized separately and convolved with a Gaussian function of width 1.6 for better visualization. (b) Localization radius σ s as a function of disorder level Δ C . For the values of σ s shown, 11 points for Δ C are chosen. (c) Individual realizations of discrete speckle at various disorder levels corresponding to the panels in (a) upon extended uniform coherent illumination. Note that the speckle grain size decreases with increasing disorder. Insets are magnified by a factor of 2. Speckle contrasts are 0, 0.76, 1.22, and 1.24 from left to right. We use N t × N t = 101 × 101 throughout.
Fig. 4.
Fig. 4. Transverse coherence for 1D discrete Anderson speckle. (a) Magnitude of g ( 1 ) ( x ) for 1D arrays for various disorder levels Δ C at propagation distance z = 10 . (b) Long-range-order coherence pedestal | g ( 1 ) ( ) | as a function of Δ C at z = 10 . The circles in (b) correspond to the same values of Δ C in (a). Magnitude of g ( 1 ) ( x ) at various z for (c)  Δ C = 0.2 and (d)  Δ C = 0.4 . The pedestal decreases with z and g ( 1 ) ( x ) becomes stationary with respect to further propagation. (e)  | g ( 1 ) ( ) | as a function of z at various Δ C . (f) Transverse coherence width σ c as a function of Δ C at z = 30 . All areas shaded in gray, and also the dashed arrows, indicate the onset of the discrete Anderson speckle (DAS) regime.
Fig. 5.
Fig. 5. Transverse coherence for 2D discrete Anderson speckle. (a) Magnitude of g ( 1 ) ( r ) for 2D arrays for various disorder levels Δ C at propagation distance z = 10 . (b) Long-range-order coherence pedestal | g ( 1 ) ( ) | as a function of Δ C at z = 10 . The hexagons in (b) correspond to the same values of Δ C in (a). Magnitude of g ( 1 ) ( r ) at various z for (c)  Δ C = 0.2 and (d)  Δ C = 0.4 . The pedestal height decreases with z , and g ( 1 ) ( x ) becomes stationary with respect to further propagation. (e)  | g ( 1 ) ( ) | as a function of z at various Δ C . (f) Transverse coherence width σ c as a function of Δ C at z = 30 . All areas shaded in gray, and also the dashed arrows, indicate the onset of the DAS regime.
Fig. 6.
Fig. 6. Correlation between transverse coherence and localization in the discrete Anderson speckle regime. Correlation between σ s and σ c with varying disorder level at z = 30 . Here, σ s is the FWHM of the mean PSF and σ c is the FWHM of the degree of transverse coherence | g ( 1 ) ( x ) | . The axial distance z = 30 is selected such that the discrete Anderson speckle regime (where | g ( 1 ) ( ) | 0 ) has been reached for all disorder levels from Δ C = 0.5 to 1.
Fig. 7.
Fig. 7. Axial coherence in 1D discrete Anderson speckle. (a) Axial evolution of the intensity in individual realizations of 1D lattices with different Δ C . (b) Amplitude of the axial coherence function | g ( 1 ) ( Δ z ) | . (c) Axial coherence depth σ a for different Δ C .
Fig. 8.
Fig. 8. Heuristic model linking the transverse coherence width to the localization length in an Anderson lattice. (a) Schematic for extended uniform excitation E i ( x i ) = 1 in an array of waveguides resulting in an output field E o ( x o ) having a narrow transverse coherence function with no pedestal. Here, Δ C = 1 and z is taken such that we are in the discrete Anderson speckle regime. Ensemble averaging of the output intensity | I ( x o ) | 2 yields a constant. (b) Representation of Klyshko’s advanced-wave picture in which an unfolded cascade of systems is excited at a single point ( x i = 0 ) and whose output may be put in correspondence with that of the extended illumination configuration in (a). The field propagates backward through the disordered lattice [as a result of the conjugation in Eq. (3)], and a spatial average of the output field η = Σ x h * ( 0 , x ) is evaluated. An extended uniform field with random complex amplitude η propagates forward through the same realization of the lattice to produce an output field E ˜ ( x ) whose ensemble average E ˜ ( x ) corresponds to the coherence function in (a). We also plot the function η h ( x , x ) for reference. Δ C = 1 and ensemble size is 10 4 in (a)–(b).

Equations (10)

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

i d E x ( z ) d z + β x E x + C x , x 1 E x 1 + C x , x + 1 E x + 1 = 0 ,
G ( 1 ) ( x o , x o + x ) = G ( 1 ) ( 0 , x ) = E o * ( 0 ) E o ( x ) = x , x h ( 0 , x ) h ( x , x ) .
G ( 1 ) ( 0 , x ) = x h ( x , x ) forward x averaging h * ( 0 , x ) backward .
i d E ( z ) d z + H ^ E = 0 ,
x h ( x , x ; z ) ϕ n ( x ) = e i b n z ϕ n ( x ) ,
h ( x o , x i ; z ) = n e i b n z ϕ n ( x o ) ϕ n ( x i ) .
G ( 1 ) ( 0 , x ; z , z + Δ z ) = x , x h * ( 0 , x ; z ) h ( x , x ; z + Δ z ) = x , x n , m ϕ n ( 0 ) ϕ n ( x ) ϕ m ( x ) ϕ m ( x ) e i ( b n b m ) z e i b m Δ z .
G ( 1 ) ( 0 , x ; z , z ) = x , x n ϕ n ( 0 ) ϕ n ( x ) ϕ n ( x ) ϕ n ( x ) .
G ( 1 ) ( x , x ; z , z + Δ z ) = x , x n , m ϕ n ( x ) ϕ n ( x ) ϕ m ( x ) ϕ m ( x ) e i ( b n b m ) z e i b m Δ z .
x G ( 1 ) ( x , x ; z , z + Δ z ) = x , x n ϕ n ( x ) ϕ n ( x ) e i b n Δ z ,

Metrics