Abstract

We recently reported the observation of transverse Anderson localization as the waveguiding mechanism in optical fibers with random transverse refractive index profiles [1]. Here, we explore the impact of the design parameters of the disordered fiber on the beam radius of the propagating transverse localized beam. We show that the optimum value of the fill-fraction of the disorder is 50% and a lower value results in a larger beam radius. We also explore the impact of the average size of the individual random features on the value of the localized beam radius and show how the boundary of the fiber can impact the observed localization radius. A larger refractive index contrast between the host medium and the disorder sites results in smaller value of the beam radius.

© 2012 Optical Society of America

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  1. 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]
  2. T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
    [Crossref] [PubMed]
  3. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 211547–1549 (1996).
    [Crossref] [PubMed]
  4. T. A. Birks, J. C. Knight, and P. S. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [Crossref] [PubMed]
  5. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
    [Crossref]
  6. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [Crossref]
  7. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 20, 1476–1478 (1998).
    [Crossref]
  8. S. Coleman, Aspects of Symmetry: Selected Erice Lectures (Cambridge University Press, 1985).
    [Crossref]
  9. F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Physik 52, 555–600 (1928).
    [Crossref]
  10. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492–1505 (1958).
    [Crossref]
  11. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
    [Crossref]
  12. P. W. Anderson, “The question of classical localization: a theory of white paint?” Phil. Mag. B 52, 505–509 (1985).
    [Crossref]
  13. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  14. A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 6224–29 (2009).
    [Crossref]
  15. A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4237–291 (1960).
  16. H. De Raedt, A. D. Lagendijk, and P. de Vries, “Transverse localization of light,” Phys. Rev. Lett. 62, 47–50 (1989).
    [Crossref] [PubMed]
  17. P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57, 287–337 (1985).
    [Crossref]
  18. 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] [PubMed]
  19. 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, 075701–075705 (2012).
    [Crossref]
  20. 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, 013906–013909 (2008).
    [Crossref] [PubMed]
  21. L. Martin, G. D. 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, 13636–3646 (2011).
    [Crossref] [PubMed]
  22. 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, 101102–101105 (2012).
    [Crossref]
  23. O. Abdi, K. C. Wong, T. Hassan, K. J. Peters, and M. J. Kowalsky, “Cleaving of solid single mode polymer optical fiber for strain sensor applications,” Opt. Commun. 282, 856–861 (2009).
    [Crossref]
  24. W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 292639–2649 (1993).
  25. J. C. Butcher, Numerical Methods for Ordinary Differential Equations (Wiely, 2008).
    [Crossref]
  26. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992).
    [Crossref]
  27. 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]
  28. D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813–033817 (2011).
    [Crossref]
  29. J. M. Ziman, Models of Disorder (Cambridge University Press, 1979).
  30. M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18, 222–228 (1997).
    [Crossref]

2012 (3)

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]

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, 101102–101105 (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, 075701–075705 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (2)

O. Abdi, K. C. Wong, T. Hassan, K. J. Peters, and M. J. Kowalsky, “Cleaving of solid single mode polymer optical fiber for strain sensor applications,” Opt. Commun. 282, 856–861 (2009).
[Crossref]

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 6224–29 (2009).
[Crossref]

2008 (2)

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906–013909 (2008).
[Crossref] [PubMed]

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] [PubMed]

2000 (2)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
[Crossref]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
[Crossref]

1998 (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 20, 1476–1478 (1998).
[Crossref]

1997 (2)

T. A. Birks, J. C. Knight, and P. S. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[Crossref] [PubMed]

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

1996 (1)

1993 (1)

W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 292639–2649 (1993).

1992 (1)

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

1985 (2)

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

P. W. Anderson, “The question of classical localization: a theory of white paint?” Phil. Mag. B 52, 505–509 (1985).
[Crossref]

1984 (1)

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

1960 (1)

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4237–291 (1960).

1958 (1)

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

1928 (1)

F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Physik 52, 555–600 (1928).
[Crossref]

Abdi, O.

O. Abdi, K. C. Wong, T. Hassan, K. J. Peters, and M. J. Kowalsky, “Cleaving of solid single mode polymer optical fiber for strain sensor applications,” Opt. Commun. 282, 856–861 (2009).
[Crossref]

Abouraddy, A. F.

Agrawal, G. P.

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, 075701–075705 (2012).
[Crossref]

Anderson, P. W.

P. W. Anderson, “The question of classical localization: a theory of white paint?” Phil. Mag. B 52, 505–509 (1985).
[Crossref]

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

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
[Crossref]

Atkin, D. M.

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, 013906–013909 (2008).
[Crossref] [PubMed]

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] [PubMed]

Belic, M. R.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813–033817 (2011).
[Crossref]

Berry, M. V.

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

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 20, 1476–1478 (1998).
[Crossref]

T. A. Birks, J. C. Knight, and P. S. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 211547–1549 (1996).
[Crossref] [PubMed]

Bloch, F.

F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Physik 52, 555–600 (1928).
[Crossref]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 20, 1476–1478 (1998).
[Crossref]

Butcher, J. C.

J. C. Butcher, Numerical Methods for Ordinary Differential Equations (Wiely, 2008).
[Crossref]

Christodoulides, D. N.

L. Martin, G. D. 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, 13636–3646 (2011).
[Crossref] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906–013909 (2008).
[Crossref] [PubMed]

Coleman, S.

S. Coleman, Aspects of Symmetry: Selected Erice Lectures (Cambridge University Press, 1985).
[Crossref]

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. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813–033817 (2011).
[Crossref]

Dreisow, F.

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] [PubMed]

Frazier, R. J.

Ghosh, S.

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, 075701–075705 (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, 101102–101105 (2012).
[Crossref]

Giuseppe, G. D.

Hadley, G. R.

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

Hassan, T.

O. Abdi, K. C. Wong, T. Hassan, K. J. Peters, and M. J. Kowalsky, “Cleaving of solid single mode polymer optical fiber for strain sensor applications,” Opt. Commun. 282, 856–861 (2009).
[Crossref]

Heinrich, M.

Hill, S.

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

Huang, W. P.

W. P. Huang and C. L. Xu, “Simulation of three-dimesional optical waveguides by full-vector beam propagation method,” J. Lightwave Technol. 292639–2649 (1993).

Ioffe, A. F.

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4237–291 (1960).

John, S.

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

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

Jovic, D. M.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813–033817 (2011).
[Crossref]

Kar, A. K.

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, 101102–101105 (2012).
[Crossref]

Karbasi, S.

Kartashov, Y. V.

Keil, R.

Kivshar, Y. S.

D. M. Jović, Y. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813–033817 (2011).
[Crossref]

Klein, S.

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

Knight, J. C.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 20, 1476–1478 (1998).
[Crossref]

T. A. Birks, J. C. Knight, and P. S. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 211547–1549 (1996).
[Crossref] [PubMed]

Koch, K. W.

Konig, F.

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

Kowalsky, M. J.

O. Abdi, K. C. Wong, T. Hassan, K. J. Peters, and M. J. Kowalsky, “Cleaving of solid single mode polymer optical fiber for strain sensor applications,” Opt. Commun. 282, 856–861 (2009).
[Crossref]

Kuklewicz, C.

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

Lagendijk, A. D.

A. D. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 6224–29 (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. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906–013909 (2008).
[Crossref] [PubMed]

Lee, P. A.

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

Leonhardt, U.

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

Mafi, A.

Martin, L.

Mirr, C. R.

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, 013906–013909 (2008).
[Crossref] [PubMed]

Nolte, S.

Ortigosa-Blanch, A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
[Crossref]

Pal, B. P.

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, 101102–101105 (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, 075701–075705 (2012).
[Crossref]

Perez-Leija, A.

Peters, K. J.

O. Abdi, K. C. Wong, T. Hassan, K. J. Peters, and M. J. Kowalsky, “Cleaving of solid single mode polymer optical fiber for strain sensor applications,” Opt. Commun. 282, 856–861 (2009).
[Crossref]

Philbin, T.

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

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, 013906–013909 (2008).
[Crossref] [PubMed]

Psaila, N. D.

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, 101102–101105 (2012).
[Crossref]

Ramakrishnan, T. V.

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

Ranka, J. K.

Regel, A. R.

A. F. Ioffe and A. R. Regel, “Non-crystalline, amorphous and liquid electronic semiconductors,” Prog. Semicond. 4237–291 (1960).

Robertson, S.

T. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, and U. Leonhardt, “Fiber optical analog of the event horizon,” Science,  3191367–1370 (2008).
[Crossref] [PubMed]

Russell, P. S. J.

Russell, P. St. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Tech. Lett. 12, 807–809 (2000).
[Crossref]

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Supplementary Material (1)

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Figures (9)

Fig. 1
Fig. 1 (a) An example cross section of a fiber with site size of 0.9μm used for our simulations, corresponding to a fiber of side width equal to 250μm. (b) and (c) SEM images of the fibers with the side width of 150μm and 250μm, respectively. All three figures (a), (b), and (c) only feature a 24μm × 24μm region of the total fiber cross section for a more clear view. The captions on the SEM images show 15KV at 5000x magnification, with a marker to show the physical scale of the images. The darker regions in the SEM images indicate the PMMA material.

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Fig. 2
Fig. 2 Effective beam radius versus propagation distance for different values of the site size: d = 0.9μm corresponding to a fiber side width of 250μm, and d = 0.6μm corresponding to a fiber side width of 150μm. The mean beam radius in the case of the fibers with side width of 150μm is greatly affected by the large refractive index step at the boundary of the fiber, otherwise it would have been even larger than that of the fibers with side width of 150μm. We note that the one standard-deviation regions for experimental measurments marked with green and red color are from the measurments at the end of the fiber samples at the 5.5cm length.

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Fig. 3
Fig. 3 (a) and (b) show the refractive index profile of a sample optical fiber with 1mm side width taken at different locations along the fiber (5cm apart). The images are taken with an optical microscope and are zoomed in at a small region on the cross section of the fiber and clearly show that the refractive index profile remains invariant along the fiber over the 5cm long samples. Similarly, the (c) – (d) pair, (e) – (f) pair, and (g) – (h) pair are taken each at 5cm apart locations along the fibers where the optical microscope is zoomed in over the same regions for each pair but different regions for different pairs across the fiber tip.

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Fig. 4
Fig. 4 The effect of reducing the incident wavelength (λ) on the localization radius(ξ) versus propagation distance.

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Fig. 5
Fig. 5 Cross section of the intensity profile of the localized beam averaged over 100 samples of raw data in dB units. (a) shows a comparison between the experimental results for fibers with side width of 150μm and 250μm. (b) shows a comparison between the experimental and numerical results for fibers with side width of 150μm, where the difference between simulation and experiment is caused by the larger variation in the experimental results (see Fig. 2), and also the noise in the CCD beam profiler at low intensities.

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Fig. 6
Fig. 6 Effective beam radius versus propagation distance for different values of the fill-fraction of p = 40%, and p = 50%. The optimal fill-fraction of p = 50% results in the lowest effective beam radius and localization length.

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Fig. 7
Fig. 7 Effective beam radius vs propagation distance for different values of refractive index contrast Δn. Larger index contrast results in smaller localization radius.

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Fig. 8
Fig. 8 Effective beam radius vs propagation distance for different values of fill-fraction, p, in glass disordered optical fibers with random air holes.

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Fig. 9
Fig. 9 Exponential decay of the average intensity for different values of fill-fractions, p, in glass disordered optical fibers with random air holes.

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Equations (2)

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i ∂ A ∂ z + 1 2 n 0 k 0 [ ∇ T 2 A + k 0 2 ( n 2 − n 0 2 ) A ] = 0 .
ξ ( z ) = 〈 A ( r ) | ( R − R ¯ ) 2 | A ( r ) 〉

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