Abstract

We report the first observation of transverse Anderson localization in a glass optical fiber. The strong localization happens near the outer boundary of the fiber and no trace of localization is observed in the central regions. However, these observations complement previous reports that the boundary of a disordered medium has a de-localizing effect. Our observations can be explained by considering the non-uniform distribution of disorder in the fiber, where the substantially larger disorder near the outer boundary of the fiber offsets the de-localizing effect of the boundary.

© 2012 OSA

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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, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett.58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  3. A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today62, 24–29 (2009).
    [CrossRef]
  4. A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond.4, 237–291 (1960).
  5. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
    [CrossRef]
  6. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic Press, 1995).
  7. H. De Raedt, A. D. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett.62, 47–50 (1989).
    [CrossRef] [PubMed]
  8. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
    [CrossRef] [PubMed]
  9. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett.100, 013906 (2008).
    [CrossRef] [PubMed]
  10. 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. Express19, 13636–13646 (2011).
    [CrossRef] [PubMed]
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  12. 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] [PubMed]
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    [CrossRef]
  14. A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Wave localization at the boundary of disordered photonic lattices,” Opt. Lett.35, 1172–1174 (2010).
    [CrossRef] [PubMed]
  15. D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A83, 033813 (2011).
    [CrossRef]
  16. Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Light localization in nonuniformly randomized lattices,” Opt. Lett.37, 286–288 (2012).
    [CrossRef] [PubMed]
  17. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern.SMC-9, 62–66 (1979).

2012 (3)

2011 (2)

2010 (1)

2009 (1)

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today62, 24–29 (2009).
[CrossRef]

2008 (1)

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

2007 (1)

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

1997 (1)

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

1989 (1)

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

1987 (1)

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

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern.SMC-9, 62–66 (1979).

1960 (1)

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

1958 (1)

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

1939 (1)

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

Abouraddy, A. F.

Anderson, P. W.

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

Avidan, A.

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

Bartal, G.

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

Bartolini, P.

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

Belic, M. R.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A83, 033813 (2011).
[CrossRef]

Christodoulides, D.

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

Christodoulides, D. N.

De Raedt, H.

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

de Vries, P.

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

Denz, C.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A83, 033813 (2011).
[CrossRef]

Di Giuseppe, G.

Dreisow, F.

Fishman, S.

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

Fraizer, Ry. J.

Frazier, R. J.

Heinrich, M.

Ioffe, A. F.

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

John, S.

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

Jovic, D. M.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A83, 033813 (2011).
[CrossRef]

Karbasi, S.

Kartashov, Y. V.

Keil, R.

Kivshar, Y. S.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A83, 033813 (2011).
[CrossRef]

Koch, K. W.

Konotop, V. V.

Lagendijk, A.

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

Lagendijk, A. D.

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today62, 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] [PubMed]

Lahini, Y.

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

Mafi, A.

Martin, L.

Mirr, C. R.

Morandotti, R.

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

Nolte, S.

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern.SMC-9, 62–66 (1979).

Perez-Leija, A.

Pozzi, F.

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

Rechtsman, M.

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

Regel, A. R.

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

Righini, R.

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

Saleh, B. E. A.

Schwartz, T.

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

Segev, M.

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

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

Sheng, P.

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

Silberberg, Y.

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

Sorel, M.

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

Szameit, A.

Torner, L.

Tünnermann, A.

van Tiggelen, B.

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today62, 24–29 (2009).
[CrossRef]

Vysloukh, V. A.

Wiersma, D. S.

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today62, 24–29 (2009).
[CrossRef]

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

Yarandi, P. G.

Zeil, P.

IEEE Trans. Syst. Man. Cybern. (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern.SMC-9, 62–66 (1979).

Nature (2)

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

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

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. (1)

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

Phys. Rev. A (1)

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belic, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A83, 033813 (2011).
[CrossRef]

Phys. Rev. Lett. (4)

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

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

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

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

Phys. Today (1)

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today62, 24–29 (2009).
[CrossRef]

Prog. Semicond. (1)

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

Other (1)

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

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Figures (7)

Fig. 1
Fig. 1

(a) SEM image of the glass optical fiber with random air-holes. For ease of viewing, the polymer coating has been removed. (b) Refractive index profile used in our simulations.

Fig. 2
Fig. 2

The experimental measurement of the near-field intensity when the beam is launched near the center of the fiber, where no localization is observed.

Fig. 3
Fig. 3

Near-field intensity measurements at the output facet of the disordered fiber samples for 4 different launch positions.

Fig. 4
Fig. 4

Near-field intensity simulations at the output facet of the disordered fiber for 4 different launch positions.

Fig. 5
Fig. 5

(a) The region highlighted in red corresponds to one standard deviation in each direction around the average experimental measurement of the localization length parameter represented by ξavg ± σξ. The region highlighted in black corresponds to theoretical simulation of the effective beam radius ξavg ± σξ as a function of propagation distance. (b) Cross section of the intensity profile of the highest peak in the localized beam averaged over 100 samples of raw data from simulations and 100 samples from experiments in dB units.

Fig. 6
Fig. 6

(a) Density plot shows the air fill-fraction over the tip of the fiber, where the disorder level is generally higher near the outer boundary than the central regions. (b) Segmentation of fiber to different regions for averaging over the angular coordinate, where red and blue colors are used in order to make it easier for the reader to distinguish the regions closer to the center versus regions closer to the outer boundary of the fiber. (c) Air fill-fraction averaged over the angular coordinate as a function of the radial coordinate over the tip of the fiber. The error bars signify the change in the value of the air fill-fraction, if the global image threshold varies by 0.07 around an Otsu’s threshold of 0.37.

Fig. 7
Fig. 7

Simulation of the near-field intensity profile when the beam is launched near the center of the fiber, for uniform disorder distribution with (a) 3% air fill-fraction, (b) 6% air fill-fraction, and (c) 10% air fill-fraction. (d) Cross section of the intensity profile for uniformly disordered fibers with 3%, 6%, and 10% air fill-fraction, where the beam is launched near the center of the fiber. All figures are plotted for the intensity profile after propagating 5 cm along the fiber.

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