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

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the Anderson regime,” Nat. Commun. 5, 4534 (2014).

[Crossref]

M. Chen and M.-J. Li, “Observing transverse Anderson localization in random air line based fiber,” Proc. SPIE 8994, 89941S (2014).

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse-Anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).

[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Modal perspective on the transverse Anderson localization of light in disordered optical lattices,” J. Opt. Soc. Am. B 30, 1452–1461 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Image transport quality can be improved in disordered waveguides,” Opt. Commun. 311, 72–76 (2013).

[Crossref]

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

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Multiple-beam propagation in an Anderson localized optical fiber,” Opt. Express 21, 305–313 (2013).

[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. A 86, 040302(R) (2012).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52 (2012).

[Crossref]

S. Ghosh, N. D. Psaila, 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]

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of Anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase-front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt. 14, 075701 (2012).

[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express 2, 1496–1503 (2012).

[Crossref]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).

[Crossref]

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

[Crossref]

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear Schrödinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53–R72 (2012).

[Crossref]

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

[Crossref]

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

[Crossref]

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

[Crossref]

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).

[Crossref]

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

[Crossref]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett. 105, 163905 (2010).

[Crossref]

C. Thompson, G. Vemuri, and G. S. Agarwal, “Anderson localization with second quantized fields in a coupled array of waveguides,” Phys. Rev. A 82, 053805 (2010).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

S. Ghosh, R. K. Varshney, B. P. Pal, and G. Monnom, “A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping,” Opt. Quantum Electron. 42, 1–14 (2010).

[Crossref]

J.-H. Han, J. Lee, and J. U. Kang, “Pixelation effect removal from fiber bundle probe based optical coherence tomography imaging,” Opt. Express 18, 7427–7439 (2010).

[Crossref]

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

[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]

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

[Crossref]

X. Chen, K. L. Reichenbach, and C. Xu, “Experimental and theoretical analysis of core-to-core coupling on fiber bundle imaging,” Opt. Express 16, 21598–21607 (2008).

[Crossref]

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

[Crossref]

E. N. Tsoy, C. M. de Sterke, and F. K. Abdullaev, “Gap-soliton trapping in random one-dimensional gratings,” Phys. Rev. A 78, 031803(R) (2008).

[Crossref]

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

[Crossref]

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (2006).

[Crossref]

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).

[Crossref]

A. Mafi and J. V. Moloney, “Shaping modes in multicore photonic crystal fibers,” IEEE Photon. Technol. Lett. 17, 348–350 (2005).

K. Y. Bliokh and V. D. Freilikher, “Localization of transverse waves in randomly layered media at oblique incidence,” Phys. Rev. B 70, 245121 (2004).

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

[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

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

[Crossref]

G. Kopidakis and S. Aubry, “Discrete breathers and delocalization in nonlinear disordered systems,” Phys. Rev. Lett. 84, 3236 (2000).

[Crossref]

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. II. Localization,” Physica D 139, 247–275 (2000).

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. I. Delocalization,” Physica D 130, 155–186 (1999).

J. Garnier and F. Abdullaev, “Solitons in media with random dispersive perturbations,” Physica D 134, 303–315 (1999).

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light?” Nature 398, 206–207 (1999).

[Crossref]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).

[Crossref]

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).

[Crossref]

F. M. Izrailev, T. Kottos, A. Politi, and G. P. Tsironis, “Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: diffusion versus localization,” Phys. Rev. E 55, 4951–4963 (1997).

[Crossref]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18, 222–228 (1997).

[Crossref]

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

[Crossref]

B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56, 1469–1564 (1993).

[Crossref]

W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 29, 2639–2649 (1993).

D. L. Shepelyansky, “Delocalization of quantum chaos by weak nonlinearity,” Phys. Rev. Lett. 70, 1787–1790 (1993).

[Crossref]

M. N. Rosenbluth, “Comment on ‘Classical and quantum superdiffusion in a time-dependent random potential’,” Phys. Rev. Lett. 69, 1831–1831 (1992).

[Crossref]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).

[Crossref]

L. Golubovic, S. Feng, and F. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).

[Crossref]

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).

[Crossref]

C. Albanese and J. Frohlich, “Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems,” Commun. Math. Phys. 138, 193–205 (1991).

[Crossref]

I. S. Graham, L. Piche, and M. Grant, “Experimental evidence for localization of acoustic waves in three dimensions,” Phys. Rev. Lett. 64, 3135–3138 (1990).

[Crossref]

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

[Crossref]

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

[Crossref]

E. P. Nakhmedov, V. N. Prigodin, and Y. A. Firsov, “Localization dynamics in weakly disordered systems,” Sov. Phys. J. Exp. Theor. Phys. 65, 1202–1209 (1987).

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

[Crossref]

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

[Crossref]

C. M. Soukoulis, I. Webman, G. S. Grest, and E. N. Economou, “Study of electronic states with off-diagonal disorder in two dimensions,” Phys. Rev. B 26, 1838–1841 (1982).

A. M. Jayannavar and N. K. Kumar, “Nondiffusive quantum transport in a dynamically disordered medium,” Phys. Rev. Lett. 48, 553–556 (1982).

[Crossref]

A. Douglas Stone and J. D. Joannopoulos, “Probability distribution and new scaling law for the resistance of a one-dimensional Anderson model,” Phys. Rev. B 24, 3592–3595 (1981).

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

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Israel Phys. Soc. 3, 133–140 (1980).

S. S. Abdullaev and F. K. Abdullaev, “On propagation of light in fiber bundles with random parameters,” Radiofizika 23, 766–767 (1980).

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–675 (1979).

[Crossref]

G. Theodorou and M. H. Cohen, “Extended states in a one-demensional system with off-diagonal disorder,” Phys. Rev. B 13, 4597–4601 (1976).

G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillation,” Sov. Phys. Usp. 14, 549–568 (1972).

[Crossref]

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237–291 (1960).

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

[Crossref]

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).

[Crossref]

H. H. Hopkins and N. S. Kapany, “A flexible fiberscope, using static scanning,” Nature 173, 39–41 (1954).

[Crossref]

J. Garnier and F. Abdullaev, “Solitons in media with random dispersive perturbations,” Physica D 134, 303–315 (1999).

E. N. Tsoy, C. M. de Sterke, and F. K. Abdullaev, “Gap-soliton trapping in random one-dimensional gratings,” Phys. Rev. A 78, 031803(R) (2008).

[Crossref]

S. S. Abdullaev and F. K. Abdullaev, “On propagation of light in fiber bundles with random parameters,” Radiofizika 23, 766–767 (1980).

S. S. Abdullaev and F. K. Abdullaev, “On propagation of light in fiber bundles with random parameters,” Radiofizika 23, 766–767 (1980).

A. F. Abouraddy, G. Di Giuseppe, D. N. Christodoulides, and B. E. A. Saleh, “Anderson localization and colocalization of spatially entangled photons,” Phys. Rev. A 86, 040302(R) (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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–675 (1979).

[Crossref]

E. Abrahams, 50 Years of Anderson Localization (World Scientific, 2010).

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52 (2012).

[Crossref]

C. Thompson, G. Vemuri, and G. S. Agarwal, “Anderson localization with second quantized fields in a coupled array of waveguides,” Phys. Rev. A 82, 053805 (2010).

[Crossref]

S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase-front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt. 14, 075701 (2012).

[Crossref]

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

[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

C. Albanese and J. Frohlich, “Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems,” Commun. Math. Phys. 138, 193–205 (1991).

[Crossref]

G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices (Cambridge University, 2009).

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (2006).

[Crossref]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–675 (1979).

[Crossref]

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

[Crossref]

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Israel Phys. Soc. 3, 133–140 (1980).

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).

[Crossref]

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

[Crossref]

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. II. Localization,” Physica D 139, 247–275 (2000).

G. Kopidakis and S. Aubry, “Discrete breathers and delocalization in nonlinear disordered systems,” Phys. Rev. Lett. 84, 3236 (2000).

[Crossref]

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. I. Delocalization,” Physica D 130, 155–186 (1999).

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Israel Phys. Soc. 3, 133–140 (1980).

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]

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

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express 2, 1496–1503 (2012).

[Crossref]

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

[Crossref]

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

[Crossref]

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

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

[Crossref]

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).

[Crossref]

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).

[Crossref]

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

[Crossref]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18, 222–228 (1997).

[Crossref]

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

[Crossref]

K. Y. Bliokh and V. D. Freilikher, “Localization of transverse waves in randomly layered media at oblique incidence,” Phys. Rev. B 70, 245121 (2004).

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

[Crossref]

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

[Crossref]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett. 105, 163905 (2010).

[Crossref]

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52 (2012).

[Crossref]

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

[Crossref]

J. C. Butcher, Numerical Methods for Ordinary Differential Equations (Wiley, 2008).

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

[Crossref]

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

[Crossref]

M. Chen and M.-J. Li, “Observing transverse Anderson localization in random air line based fiber,” Proc. SPIE 8994, 89941S (2014).

G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillation,” Sov. Phys. Usp. 14, 549–568 (1972).

[Crossref]

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

[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. A 86, 040302(R) (2012).

[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, and Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806(R) (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, and 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, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett. 105, 163905 (2010).

[Crossref]

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

[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

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

[Crossref]

G. Theodorou and M. H. Cohen, “Extended states in a one-demensional system with off-diagonal disorder,” Phys. Rev. B 13, 4597–4601 (1976).

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the Anderson regime,” Nat. Commun. 5, 4534 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse-Anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).

[Crossref]

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

[Crossref]

E. N. Tsoy, C. M. de Sterke, and F. K. Abdullaev, “Gap-soliton trapping in random one-dimensional gratings,” Phys. Rev. A 78, 031803(R) (2008).

[Crossref]

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

[Crossref]

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (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. A 86, 040302(R) (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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

A. Douglas Stone and J. D. Joannopoulos, “Probability distribution and new scaling law for the resistance of a one-dimensional Anderson model,” Phys. Rev. B 24, 3592–3595 (1981).

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

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

C. M. Soukoulis, I. Webman, G. S. Grest, and E. N. Economou, “Study of electronic states with off-diagonal disorder in two dimensions,” Phys. Rev. B 26, 1838–1841 (1982).

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

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of Anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of Anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).

L. Golubovic, S. Feng, and F. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).

[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

[Crossref]

E. P. Nakhmedov, V. N. Prigodin, and Y. A. Firsov, “Localization dynamics in weakly disordered systems,” Sov. Phys. J. Exp. Theor. Phys. 65, 1202–1209 (1987).

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).

[Crossref]

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

[Crossref]

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear Schrödinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53–R72 (2012).

[Crossref]

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

[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

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

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Karbasi, R. J. Frazier, C. R. Mirr, K. W. Koch, and A. Mafi, “Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light,” J. Vis. Exp., doi: 10.3791/50679 (2013).

[Crossref]

K. Y. Bliokh and V. D. Freilikher, “Localization of transverse waves in randomly layered media at oblique incidence,” Phys. Rev. B 70, 245121 (2004).

C. Albanese and J. Frohlich, “Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems,” Commun. Math. Phys. 138, 193–205 (1991).

[Crossref]

J. Garnier and F. Abdullaev, “Solitons in media with random dispersive perturbations,” Physica D 134, 303–315 (1999).

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

[Crossref]

S. Ghosh, N. D. Psaila, 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]

S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase-front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt. 14, 075701 (2012).

[Crossref]

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

[Crossref]

S. Ghosh, R. K. Varshney, B. P. Pal, and G. Monnom, “A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping,” Opt. Quantum Electron. 42, 1–14 (2010).

[Crossref]

L. Golubovic, S. Feng, and F. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).

[Crossref]

I. S. Graham, L. Piche, and M. Grant, “Experimental evidence for localization of acoustic waves in three dimensions,” Phys. Rev. Lett. 64, 3135–3138 (1990).

[Crossref]

I. S. Graham, L. Piche, and M. Grant, “Experimental evidence for localization of acoustic waves in three dimensions,” Phys. Rev. Lett. 64, 3135–3138 (1990).

[Crossref]

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

C. M. Soukoulis, I. Webman, G. S. Grest, and E. N. Economou, “Study of electronic states with off-diagonal disorder in two dimensions,” Phys. Rev. B 26, 1838–1841 (1982).

G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices (Cambridge University, 2009).

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).

[Crossref]

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

[Crossref]

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).

[Crossref]

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

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express 2, 1496–1503 (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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

H. H. Hopkins and N. S. Kapany, “A flexible fiberscope, using static scanning,” Nature 173, 39–41 (1954).

[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]

W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 29, 2639–2649 (1993).

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237–291 (1960).

F. M. Izrailev, T. Kottos, A. Politi, and G. P. Tsironis, “Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: diffusion versus localization,” Phys. Rev. E 55, 4951–4963 (1997).

[Crossref]

A. M. Jayannavar and N. K. Kumar, “Nondiffusive quantum transport in a dynamically disordered medium,” Phys. Rev. Lett. 48, 553–556 (1982).

[Crossref]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).

[Crossref]

A. Douglas Stone and J. D. Joannopoulos, “Probability distribution and new scaling law for the resistance of a one-dimensional Anderson model,” Phys. Rev. B 24, 3592–3595 (1981).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).

[Crossref]

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

[Crossref]

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

[Crossref]

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

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

[Crossref]

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).

[Crossref]

H. H. Hopkins and N. S. Kapany, “A flexible fiberscope, using static scanning,” Nature 173, 39–41 (1954).

[Crossref]

S. Ghosh, N. D. Psaila, 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]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the Anderson regime,” Nat. Commun. 5, 4534 (2014).

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

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

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse-Anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Multiple-beam propagation in an Anderson localized optical fiber,” Opt. Express 21, 305–313 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Modal perspective on the transverse Anderson localization of light in disordered optical lattices,” J. Opt. Soc. Am. B 30, 1452–1461 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Image transport quality can be improved in disordered waveguides,” Opt. Commun. 311, 72–76 (2013).

[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express 2, 1496–1503 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

S. Karbasi, R. J. Frazier, C. R. Mirr, K. W. Koch, and A. Mafi, “Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light,” J. Vis. Exp., doi: 10.3791/50679 (2013).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).

[Crossref]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18, 222–228 (1997).

[Crossref]

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

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

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

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Multiple-beam propagation in an Anderson localized optical fiber,” Opt. Express 21, 305–313 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Image transport quality can be improved in disordered waveguides,” Opt. Commun. 311, 72–76 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Modal perspective on the transverse Anderson localization of light in disordered optical lattices,” J. Opt. Soc. Am. B 30, 1452–1461 (2013).

[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express 2, 1496–1503 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

S. Karbasi, R. J. Frazier, C. R. Mirr, K. W. Koch, and A. Mafi, “Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light,” J. Vis. Exp., doi: 10.3791/50679 (2013).

[Crossref]

G. Kopidakis and S. Aubry, “Discrete breathers and delocalization in nonlinear disordered systems,” Phys. Rev. Lett. 84, 3236 (2000).

[Crossref]

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. II. Localization,” Physica D 139, 247–275 (2000).

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. I. Delocalization,” Physica D 130, 155–186 (1999).

F. M. Izrailev, T. Kottos, A. Politi, and G. P. Tsironis, “Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: diffusion versus localization,” Phys. Rev. E 55, 4951–4963 (1997).

[Crossref]

B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56, 1469–1564 (1993).

[Crossref]

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

[Crossref]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).

[Crossref]

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear Schrödinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53–R72 (2012).

[Crossref]

A. M. Jayannavar and N. K. Kumar, “Nondiffusive quantum transport in a dynamically disordered medium,” Phys. Rev. Lett. 48, 553–556 (1982).

[Crossref]

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of Anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

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

[Crossref]

A. Lagendijk, “Can light be localised?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, 1994), Chap. 4.

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

[Crossref]

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

[Crossref]

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

[Crossref]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett. 105, 163905 (2010).

[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]

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

[Crossref]

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

[Crossref]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light?” Nature 398, 206–207 (1999).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the Anderson regime,” Nat. Commun. 5, 4534 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse-Anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).

[Crossref]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).

[Crossref]

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

[Crossref]

M. Chen and M.-J. Li, “Observing transverse Anderson localization in random air line based fiber,” Proc. SPIE 8994, 89941S (2014).

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–675 (1979).

[Crossref]

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

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

[Crossref]

B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56, 1469–1564 (1993).

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

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

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the Anderson regime,” Nat. Commun. 5, 4534 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse-Anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Modal perspective on the transverse Anderson localization of light in disordered optical lattices,” J. Opt. Soc. Am. B 30, 1452–1461 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Image transport quality can be improved in disordered waveguides,” Opt. Commun. 311, 72–76 (2013).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Multiple-beam propagation in an Anderson localized optical fiber,” Opt. Express 21, 305–313 (2013).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Karbasi, T. Hawkins, J. Ballato, K. W. Koch, and A. Mafi, “Transverse Anderson localization in a disordered glass optical fiber,” Opt. Mater. Express 2, 1496–1503 (2012).

[Crossref]

A. Mafi and J. V. Moloney, “Shaping modes in multicore photonic crystal fibers,” IEEE Photon. Technol. Lett. 17, 348–350 (2005).

S. Karbasi, R. J. Frazier, C. R. Mirr, K. W. Koch, and A. Mafi, “Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light,” J. Vis. Exp., doi: 10.3791/50679 (2013).

[Crossref]

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52 (2012).

[Crossref]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light?” Nature 398, 206–207 (1999).

[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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).

[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

S. Karbasi, R. J. Frazier, C. R. Mirr, K. W. Koch, and A. Mafi, “Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light,” J. Vis. Exp., doi: 10.3791/50679 (2013).

[Crossref]

A. Mafi and J. V. Moloney, “Shaping modes in multicore photonic crystal fibers,” IEEE Photon. Technol. Lett. 17, 348–350 (2005).

S. Ghosh, R. K. Varshney, B. P. Pal, and G. Monnom, “A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping,” Opt. Quantum Electron. 42, 1–14 (2010).

[Crossref]

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

[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]

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).

[Crossref]

E. P. Nakhmedov, V. N. Prigodin, and Y. A. Firsov, “Localization dynamics in weakly disordered systems,” Sov. Phys. J. Exp. Theor. Phys. 65, 1202–1209 (1987).

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

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

[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]

S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase-front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt. 14, 075701 (2012).

[Crossref]

S. Ghosh, N. D. Psaila, 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]

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

[Crossref]

S. Ghosh, R. K. Varshney, B. P. Pal, and G. Monnom, “A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping,” Opt. Quantum Electron. 42, 1–14 (2010).

[Crossref]

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

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

[Crossref]

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

[Crossref]

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

[Crossref]

I. S. Graham, L. Piche, and M. Grant, “Experimental evidence for localization of acoustic waves in three dimensions,” Phys. Rev. Lett. 64, 3135–3138 (1990).

[Crossref]

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

[Crossref]

F. M. Izrailev, T. Kottos, A. Politi, and G. P. Tsironis, “Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: diffusion versus localization,” Phys. Rev. E 55, 4951–4963 (1997).

[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]

E. P. Nakhmedov, V. N. Prigodin, and Y. A. Firsov, “Localization dynamics in weakly disordered systems,” Sov. Phys. J. Exp. Theor. Phys. 65, 1202–1209 (1987).

S. Ghosh, N. D. Psaila, 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]

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

[Crossref]

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

[Crossref]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–675 (1979).

[Crossref]

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237–291 (1960).

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

[Crossref]

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

[Crossref]

M. N. Rosenbluth, “Comment on ‘Classical and quantum superdiffusion in a time-dependent random potential’,” Phys. Rev. Lett. 69, 1831–1831 (1992).

[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. A 86, 040302(R) (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, and 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 and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

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

[Crossref]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light?” Nature 398, 206–207 (1999).

[Crossref]

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

[Crossref]

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

[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

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

[Crossref]

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

[Crossref]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).

[Crossref]

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

[Crossref]

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

[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

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

[Crossref]

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, 1995).

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

[Crossref]

D. L. Shepelyansky, “Delocalization of quantum chaos by weak nonlinearity,” Phys. Rev. Lett. 70, 1787–1790 (1993).

[Crossref]

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

[Crossref]

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

[Crossref]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett. 105, 163905 (2010).

[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]

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]

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear Schrödinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53–R72 (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]

C. M. Soukoulis, I. Webman, G. S. Grest, and E. N. Economou, “Study of electronic states with off-diagonal disorder in two dimensions,” Phys. Rev. B 26, 1838–1841 (1982).

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

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52 (2012).

[Crossref]

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

[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]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, and Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806(R) (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, and 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, and H. Buljan, “Anderson localization of partially incoherent light,” Phys. Rev. A 84, 011801(R) (2011).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

G. Theodorou and M. H. Cohen, “Extended states in a one-demensional system with off-diagonal disorder,” Phys. Rev. B 13, 4597–4601 (1976).

C. Thompson, G. Vemuri, and G. S. Agarwal, “Anderson localization with second quantized fields in a coupled array of waveguides,” Phys. Rev. A 82, 053805 (2010).

[Crossref]

S. Ghosh, N. D. Psaila, 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]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

F. M. Izrailev, T. Kottos, A. Politi, and G. P. Tsironis, “Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: diffusion versus localization,” Phys. Rev. E 55, 4951–4963 (1997).

[Crossref]

E. N. Tsoy, C. M. de Sterke, and F. K. Abdullaev, “Gap-soliton trapping in random one-dimensional gratings,” Phys. Rev. A 78, 031803(R) (2008).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

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

[Crossref]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light?” Nature 398, 206–207 (1999).

[Crossref]

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).

[Crossref]

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

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

[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]

S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase-front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt. 14, 075701 (2012).

[Crossref]

S. Ghosh, N. D. Psaila, 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]

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

[Crossref]

S. Ghosh, R. K. Varshney, B. P. Pal, and G. Monnom, “A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping,” Opt. Quantum Electron. 42, 1–14 (2010).

[Crossref]

C. Thompson, G. Vemuri, and G. S. Agarwal, “Anderson localization with second quantized fields in a coupled array of waveguides,” Phys. Rev. A 82, 053805 (2010).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

C. M. Soukoulis, I. Webman, G. S. Grest, and E. N. Economou, “Study of electronic states with off-diagonal disorder in two dimensions,” Phys. Rev. B 26, 1838–1841 (1982).

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

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

[Crossref]

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

[Crossref]

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

[Crossref]

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 29, 2639–2649 (1993).

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillation,” Sov. Phys. Usp. 14, 549–568 (1972).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices (Cambridge University, 2009).

L. Golubovic, S. Feng, and F. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).

[Crossref]

J. M. Ziman, Models of Disorder (Cambridge University, 1979).

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

[Crossref]

S. Aubry and G. Andre, “Analyticity breaking and Anderson localization in incommensurate lattices,” Ann. Israel Phys. Soc. 3, 133–140 (1980).

S. Ghosh, N. D. Psaila, 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]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Experimental observation of disorder induced self-focusing in optical fibers,” Appl. Phys. Lett. 105, 171102 (2014).

[Crossref]

C. Albanese and J. Frohlich, “Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems,” Commun. Math. Phys. 138, 193–205 (1991).

[Crossref]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18, 222–228 (1997).

[Crossref]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).

[Crossref]

A. Mafi and J. V. Moloney, “Shaping modes in multicore photonic crystal fibers,” IEEE Photon. Technol. Lett. 17, 348–350 (2005).

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).

[Crossref]

W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 29, 2639–2649 (1993).

S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase-front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt. 14, 075701 (2012).

[Crossref]

A. Mafi, S. Karbasi, K. W. Koch, T. Hawkins, and J. Ballato, “Transverse Anderson localization in disordered glass optical fibers: a review,” Materials 7, 5520–5527 (2014).

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

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Light focusing in the Anderson regime,” Nat. Commun. 5, 4534 (2014).

[Crossref]

D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7, 354–362 (2013).

[Crossref]

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

[Crossref]

T. Sperling, W. Bührer, C. M. Aegerter, and G. Maret, “Direct determination of the transition to localization of light in three dimensions,” Nat. Photonics 7, 48–52 (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]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys. 8, 912–917 (2012).

[Crossref]

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).

[Crossref]

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

[Crossref]

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

[Crossref]

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

[Crossref]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light?” Nature 398, 206–207 (1999).

[Crossref]

H. H. Hopkins and N. S. Kapany, “A flexible fiberscope, using static scanning,” Nature 173, 39–41 (1954).

[Crossref]

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

[Crossref]

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

[Crossref]

S. Fishman, Y. Krivolapov, and A. Soffer, “The nonlinear Schrödinger equation with a random potential: results and puzzles,” Nonlinearity 25, R53–R72 (2012).

[Crossref]

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

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Image transport quality can be improved in disordered waveguides,” Opt. Commun. 311, 72–76 (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, and B. E. A. Saleh, “Anderson localization in optical waveguide arrays with off-diagonal coupling disorder,” Opt. Express 19, 13636–13646 (2011).

[Crossref]

S. Karbasi, C. R. Mirr, R. J. Frazier, P. G. Yarandi, K. W. Koch, and A. Mafi, “Detailed investigation of the impact of the fiber design parameters on the transverse Anderson localization of light in disordered optical fibers,” Opt. Express 20, 18692–18706 (2012).

[Crossref]

J.-H. Han, J. Lee, and J. U. Kang, “Pixelation effect removal from fiber bundle probe based optical coherence tomography imaging,” Opt. Express 18, 7427–7439 (2010).

[Crossref]

X. Chen, K. L. Reichenbach, and C. Xu, “Experimental and theoretical analysis of core-to-core coupling on fiber bundle imaging,” Opt. Express 16, 21598–21607 (2008).

[Crossref]

K. L. Reichenbach and C. Xu, “Numerical analysis of light propagation in image fibers or coherent fiber bundles,” Opt. Express 15, 2151–2165 (2007).

[Crossref]

S. Karbasi, K. W. Koch, and A. Mafi, “Multiple-beam propagation in an Anderson localized optical fiber,” Opt. Express 21, 305–313 (2013).

[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).

[Crossref]

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett. 35, 1172–1174 (2010).

[Crossref]

S. Ghosh, R. K. Varshney, B. P. Pal, and G. Monnom, “A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping,” Opt. Quantum Electron. 42, 1–14 (2010).

[Crossref]

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (2006).

[Crossref]

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

[Crossref]

C. Thompson, G. Vemuri, and G. S. Agarwal, “Anderson localization with second quantized fields in a coupled array of waveguides,” Phys. Rev. A 82, 053805 (2010).

[Crossref]

Y. Lahini, Y. Bromberg, Y. Shechtman, A. Szameit, D. N. Christodoulides, R. Morandotti, and Y. Silberberg, “Hanbury Brown and Twiss correlations of Anderson localized waves,” Phys. Rev. A 84, 041806(R) (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. A 86, 040302(R) (2012).

[Crossref]

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).

[Crossref]

E. N. Tsoy, C. M. de Sterke, and F. K. Abdullaev, “Gap-soliton trapping in random one-dimensional gratings,” Phys. Rev. A 78, 031803(R) (2008).

[Crossref]

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

[Crossref]

T. van der Beek, P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A. Lagendijk, “Light transport through disordered layers of dense gallium arsenide submicron particles,” Phys. Rev. B 85, 115401 (2012).

K. Y. Bliokh and V. D. Freilikher, “Localization of transverse waves in randomly layered media at oblique incidence,” Phys. Rev. B 70, 245121 (2004).

C. M. Soukoulis, I. Webman, G. S. Grest, and E. N. Economou, “Study of electronic states with off-diagonal disorder in two dimensions,” Phys. Rev. B 26, 1838–1841 (1982).

G. Theodorou and M. H. Cohen, “Extended states in a one-demensional system with off-diagonal disorder,” Phys. Rev. B 13, 4597–4601 (1976).

A. Douglas Stone and J. D. Joannopoulos, “Probability distribution and new scaling law for the resistance of a one-dimensional Anderson model,” Phys. Rev. B 24, 3592–3595 (1981).

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

R. G. S. El-Dardiry, S. Faez, and A. Lagendijk, “Snapshots of Anderson localization beyond the ensemble average,” Phys. Rev. B 86, 125132 (2012).

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E 66, 046602 (2002).

[Crossref]

F. M. Izrailev, T. Kottos, A. Politi, and G. P. Tsironis, “Evolution of wave packets in quasi-one-dimensional and one-dimensional random media: diffusion versus localization,” Phys. Rev. E 55, 4951–4963 (1997).

[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]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42, 673–675 (1979).

[Crossref]

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

[Crossref]

Y. Lahini, Y. Bromberg, D. N. Christodoulides, and Y. Silberberg, “Quantum correlations in two-particle Anderson localization,” Phys. Rev. Lett. 105, 163905 (2010).

[Crossref]

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

[Crossref]

I. S. Graham, L. Piche, and M. Grant, “Experimental evidence for localization of acoustic waves in three dimensions,” Phys. Rev. Lett. 64, 3135–3138 (1990).

[Crossref]

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

[Crossref]

D. L. Shepelyansky, “Delocalization of quantum chaos by weak nonlinearity,” Phys. Rev. Lett. 70, 1787–1790 (1993).

[Crossref]

M. Leonetti, S. Karbasi, A. Mafi, and C. Conti, “Observation of migrating transverse-Anderson localizations of light in nonlocal media,” Phys. Rev. Lett. 112, 193902 (2014).

[Crossref]

A. M. Jayannavar and N. K. Kumar, “Nondiffusive quantum transport in a dynamically disordered medium,” Phys. Rev. Lett. 48, 553–556 (1982).

[Crossref]

L. Golubovic, S. Feng, and F. Zeng, “Classical and quantum superdiffusion in a time-dependent random potential,” Phys. Rev. Lett. 67, 2115–2118 (1991).

[Crossref]

M. N. Rosenbluth, “Comment on ‘Classical and quantum superdiffusion in a time-dependent random potential’,” Phys. Rev. Lett. 69, 1831–1831 (1992).

[Crossref]

E. Arvedson, M. Wilkinson, B. Mehlig, and K. Nakamura, “Staggered ladder spectra,” Phys. Rev. Lett. 96, 030601 (2006).

[Crossref]

G. Kopidakis and S. Aubry, “Discrete breathers and delocalization in nonlinear disordered systems,” Phys. Rev. Lett. 84, 3236 (2000).

[Crossref]

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

[Crossref]

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

[Crossref]

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).

[Crossref]

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

[Crossref]

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. I. Delocalization,” Physica D 130, 155–186 (1999).

G. Kopidakis and S. Aubry, “Intraband discrete breathers in disordered nonlinear systems. II. Localization,” Physica D 139, 247–275 (2000).

J. Garnier and F. Abdullaev, “Solitons in media with random dispersive perturbations,” Physica D 134, 303–315 (1999).

M. Chen and M.-J. Li, “Observing transverse Anderson localization in random air line based fiber,” Proc. SPIE 8994, 89941S (2014).

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4, 237–291 (1960).

S. S. Abdullaev and F. K. Abdullaev, “On propagation of light in fiber bundles with random parameters,” Radiofizika 23, 766–767 (1980).

B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56, 1469–1564 (1993).

[Crossref]

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

[Crossref]

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69, 731–808 (1997).

[Crossref]

E. P. Nakhmedov, V. N. Prigodin, and Y. A. Firsov, “Localization dynamics in weakly disordered systems,” Sov. Phys. J. Exp. Theor. Phys. 65, 1202–1209 (1987).

G. M. Zaslavskii and B. V. Chirikov, “Stochastic instability of nonlinear oscillation,” Sov. Phys. Usp. 14, 549–568 (1972).

[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices (Cambridge University, 2009).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

S. Karbasi, R. J. Frazier, C. R. Mirr, K. W. Koch, and A. Mafi, “Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light,” J. Vis. Exp., doi: 10.3791/50679 (2013).

[Crossref]

J. C. Butcher, Numerical Methods for Ordinary Differential Equations (Wiley, 2008).

http://www.fujikura.co.uk/products/medical-industrial-optical-fibre/image-fibre/ .

http://www.us.schott.com

A. Lagendijk, “Can light be localised?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, 1994), Chap. 4.

J. M. Ziman, Models of Disorder (Cambridge University, 1979).

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

E. Abrahams, 50 Years of Anderson Localization (World Scientific, 2010).

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, 1995).