Abstract

We study numerically Anderson localization of light in a disordered photonic lattice containing vacancy defects of different length. The influence of Kerr nonlinearity and disorder level on the transverse localization of light in different triangular lattice geometries is discussed. We demonstrate both suppression and enhancement of light localization in the presence of defects of different size, depending on the disorder level and the strength of the nonlinearity. We find that, in the linear regime, localization is more pronounced in the lattice with the simplest defect type—the single vacancy. In a strongly focusing nonlinear regime, the presence of all defect kinds enhances localization, as compared to the case with no defects. In the defocusing nonlinear regime, a suppression of localization in the presence of all defect types is demonstrated, as compared to the localization in the lattice without defects. In the end, the effect of input beam width on various regimes of Anderson localization is discussed.

© 2013 Optical Society of America

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  1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
    [CrossRef]
  2. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
    [CrossRef]
  3. E. Abrahams, ed. 50 Years of Anderson Localization (World Scientific, 2010).
  4. A. Lagendijk, B. Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
    [CrossRef]
  5. 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]
  6. 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]
  7. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
    [CrossRef]
  8. D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
    [CrossRef]
  9. D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A 85, 031801(R) (2012).
    [CrossRef]
  10. H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
    [CrossRef]
  11. H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
    [CrossRef]
  12. O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
    [CrossRef]
  13. U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
    [CrossRef]
  14. H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11, 3404–3411 (2003).
    [CrossRef]
  15. A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452–459 (2003).
    [CrossRef]
  16. E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
    [CrossRef]
  17. M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
    [CrossRef]
  18. P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
    [CrossRef]
  19. G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
    [CrossRef]
  20. E. C. Nelson and P. V. Braun, “Photons and electrons confined,” Nat. Photonics 2, 650–651 (2008).
    [CrossRef]
  21. M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
    [CrossRef]
  22. M. Belić, M. Petrović, D. Jović, A. Strinić, D. Arsenović, K. Motzek, F. Kaiser, P. Jander, C. Denz, M. Tlidi, and P. Mandel, “Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals,” Opt. Express 12, 708–716 (2004).
    [CrossRef]
  23. D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
    [CrossRef]
  24. D. M. Jović, and M. R. Belić, “Steady-state and dynamical Anderson localization of counterpropagating beams in two-dimensional photonic lattices,” Phys. Rev. A 81, 023813 (2010).
    [CrossRef]

2012 (1)

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A 85, 031801(R) (2012).
[CrossRef]

2011 (4)

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

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

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[CrossRef]

2010 (1)

D. M. Jović, and M. R. Belić, “Steady-state and dynamical Anderson localization of counterpropagating beams in two-dimensional photonic lattices,” Phys. Rev. A 81, 023813 (2010).
[CrossRef]

2009 (1)

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

2008 (2)

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. C. Nelson and P. V. Braun, “Photons and electrons confined,” Nat. Photonics 2, 650–651 (2008).
[CrossRef]

2007 (1)

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

2006 (2)

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
[CrossRef]

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

2004 (2)

2003 (2)

2000 (1)

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

1999 (2)

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

1998 (1)

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

1995 (1)

1984 (1)

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

1958 (1)

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

Ablowitz, M. J.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
[CrossRef]

Aitchison, J. S.

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

Anderson, P. W.

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

Arcizet, O.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Arsenovic, D.

Avidan, A.

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

Bartal, G.

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

Bartelt, H.

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

Belic, M.

Belic, M. R.

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A 85, 031801(R) (2012).
[CrossRef]

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

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[CrossRef]

D. M. Jović, and M. R. Belić, “Steady-state and dynamical Anderson localization of counterpropagating beams in two-dimensional photonic lattices,” Phys. Rev. A 81, 023813 (2010).
[CrossRef]

M. R. Belić, J. Leonardy, D. Timotijević, and F. Kaiser, “Spatiotemporal effects in double phase conjugation,” J. Opt. Soc. Am. B 12, 1602–1616 (1995).
[CrossRef]

Beveratos, A.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Binosi, D.

Braive, R.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Bräuer, A.

Braun, P. V.

E. C. Nelson and P. V. Braun, “Photons and electrons confined,” Nat. Photonics 2, 650–651 (2008).
[CrossRef]

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

Cao, H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Chang, R. P. H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Chang, S.-H.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Christodoulides, D. N.

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

Dai, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

de Córdoba, P. F.

Denz, C.

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A 85, 031801(R) (2012).
[CrossRef]

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

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[CrossRef]

M. Belić, M. Petrović, D. Jović, A. Strinić, D. Arsenović, K. Motzek, F. Kaiser, P. Jander, C. Denz, M. Tlidi, and P. Mandel, “Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals,” Opt. Express 12, 708–716 (2004).
[CrossRef]

Eisenberg, H. S.

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

Ferrando, A.

Fishman, S.

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]

Garcia-Santamaria, F.

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

Gavartin, E.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Harris, J.

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

Ho, S. T.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Ilan, B.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
[CrossRef]

Jander, P.

John, S.

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

Jovic, D.

Jovic, D. M.

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A 85, 031801(R) (2012).
[CrossRef]

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

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[CrossRef]

D. M. Jović, and M. R. Belić, “Steady-state and dynamical Anderson localization of counterpropagating beams in two-dimensional photonic lattices,” Phys. Rev. A 81, 023813 (2010).
[CrossRef]

Kaiser, F.

Kippenberg, T. J.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Kivshar, Yu. S.

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

Kobelke, J.

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

Lagendijk, A.

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

Lahini, Y.

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

Lederer, F.

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

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11, 3404–3411 (2003).
[CrossRef]

Leonardy, J.

Liu, X.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Mandel, P.

Michaelis, D.

Monsoriu, J. A.

Morandotti, R.

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

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

Motzek, K.

Nelson, E. C.

E. C. Nelson and P. V. Braun, “Photons and electrons confined,” Nat. Photonics 2, 650–651 (2008).
[CrossRef]

Nolte, S.

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

Ong, H. C.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Painter, O.

Pertsch, T.

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

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11, 3404–3411 (2003).
[CrossRef]

Peschel, U.

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

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, “Tailoring guided modes in waveguide arrays,” Opt. Express 11, 3404–3411 (2003).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

Petrovic, M.

Piestun, R.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
[CrossRef]

Pozzi, F.

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

Provine, J.

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

Rinne, S. A.

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

Rivoire, K.

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

Robert-Philip, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Sagnes, I.

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

Sarmiento, T.

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

Scherer, A.

Schonbrun, E.

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
[CrossRef]

Schuster, K.

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

Schwartz, T.

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

Seelig, E. W.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Segev, M.

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]

Shambat, G.

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

Silberberg, Y.

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

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

Sorel, M.

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

Streppel, U.

Strinic, A.

Tiggelen, B.

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

Timotijevic, D.

Tlidi, M.

Trompeter, H.

Tünnermann, A.

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

Vuckovic, J.

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

Wiersma, D. S.

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

Wu, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Xu, J. Y.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Zacarés, M.

Zhang, D. Z.

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

Zhao, Y. G.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

Adv. Mater. (1)

P. V. Braun, S. A. Rinne, and F. Garcia-Santamaria, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

G. Shambat, J. Provine, K. Rivoire, T. Sarmiento, J. Harris, and J. Vučković, “Optical fiber tips functionalized with semiconductor photonic crystal cavities,” Appl. Phys. Lett. 99, 191102 (2011).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly induced escape from a defect state in waveguide arrays,” Appl. Phys. Lett. 75, 1348–1350 (1999).
[CrossRef]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycrystalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

E. C. Nelson and P. V. Braun, “Photons and electrons confined,” Nat. Photonics 2, 650–651 (2008).
[CrossRef]

Nature (1)

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

Opt. Express (3)

Phys. Rev. (1)

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

Phys. Rev. A (4)

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

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A 85, 031801(R) (2012).
[CrossRef]

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[CrossRef]

D. M. Jović, and M. R. Belić, “Steady-state and dynamical Anderson localization of counterpropagating beams in two-dimensional photonic lattices,” Phys. Rev. A 81, 023813 (2010).
[CrossRef]

Phys. Rev. E (1)

M. J. Ablowitz, B. Ilan, E. Schonbrun, and R. Piestun, “Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures,” Phys. Rev. E 74, 035601(R) (2006).
[CrossRef]

Phys. Rev. Lett. (5)

H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000).
[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).
[CrossRef]

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

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

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]

Phys. Today (1)

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

Other (1)

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

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Figures (7)

Fig. 1.
Fig. 1.

Top row: sketch of the lattice geometry of the triangular photonic lattice with vacancy defects of different length. The crosses mark the location of input Gaussian beams. Bottom row: intensity distributions of the localized modes in the linear regime for 20% disorder level. A narrow Gaussian beam, with FWHM equal to the lattice spacing, is launched into the medium.

Fig. 2.
Fig. 2.

Transverse localization of light in the linear regime. Effective beam width at the lattice output is shown as a function of the disorder level, for different defect types. Points are ensemble averages and lines are the least-square fits through the points. Error bars depict the spread in values coming from statistics. Physical parameters are crystal length L=50mm, input lattice intensity V0=1, lattice period 11.2 μm, input beam intensity |E0|2=0.5, and input beam FWHM=10μm.

Fig. 3.
Fig. 3.

Averaged effective beam width versus propagation distance, for different disorder levels (0%, 20%, and 90%), and for different defect types. Parameters are as in Fig. 2.

Fig. 4.
Fig. 4.

Comparison between Anderson localization in the linear regime and in different nonlinear regimes. (a) Linear case. (b) Focusing nonlinearity. (c) Defocusing nonlinearity. The normalized effective beam width at the lattice output is depicted as a function of the disorder level. The widths are normalized to their values without disorder. Points are ensemble averages and lines are least-square fits through the points. Parameters are as in Fig. 2.

Fig. 5.
Fig. 5.

Localization length as a function of the strength of nonlinearity for the 30% disorder level and different defect types. Physical parameters are as in Fig. 2.

Fig. 6.
Fig. 6.

Localization of the broad beam in the linear regime. The effective beam width at the lattice output is presented as a function of disorder level, for different defect types. Points are ensemble averages and lines are least-square fits through the points. Physical parameters are input beam FWHM=50μm; other parameters are as in Fig. 2.

Fig. 7.
Fig. 7.

Ensemble-averaged intensity profiles (on the logarithmic scale) at the lattice output in the linear regime for narrow (a) and broad (b) beams for 30% disorder level.

Equations (1)

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iEz=ΔEγ|E|2EVE,

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