Abstract

We report on the observation of Anderson localization of near-visible light in two-dimensional systems. Our structures consist of planar waveguides in which disorder is introduced by randomly placing pores with controlled diameter and density. We show how to design structures in which localization can be observed and describe both the realization of the materials and the actual observation of Anderson localized modes by near-field scanning microscopy.

© 2011 Optical Society of America

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  1. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, 1996).
  2. P. W. Anderson, Phys. Rev. 109, 1452 (1958).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  15. E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
    [CrossRef]

2010

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

A. Z. Genack and J. Wang, Int. J. Mod. Phys. B 24, 1950 (2010).
[CrossRef]

2009

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Phys. Today 62, 24 (2009).
[CrossRef]

A. Aspect and M. Inguscio, Phys. Today 62, 30 (2009).
[CrossRef]

2008

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

2007

T. Schwartz, G. Bartal, S. Fishman, and S. Mordechai, Nature 446, 52 (2007).
[CrossRef] [PubMed]

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

2006

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

1995

Th. M. Nieuwenhuizen and M. C. W. van Rossum, Phys. Rev. Lett. 74, 2674 (1995).
[CrossRef] [PubMed]

1990

R. L. Weaver, Wave Motion 12, 129 (1990).
[CrossRef]

1989

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef] [PubMed]

1979

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

1958

P. W. Anderson, Phys. Rev. 109, 1452 (1958).

Abrahams, E.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

Anderson, P. W.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

P. W. Anderson, Phys. Rev. 109, 1452 (1958).

Aspect, A.

A. Aspect and M. Inguscio, Phys. Today 62, 30 (2009).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and S. Mordechai, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Cassette, S.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Combrie, S.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

De Raedt, H.

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef] [PubMed]

De Rossi, A.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

de Vries, P.

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and S. Mordechai, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Genack, A. Z.

A. Z. Genack and J. Wang, Int. J. Mod. Phys. B 24, 1950 (2010).
[CrossRef]

Hu, H.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Inguscio, M.

A. Aspect and M. Inguscio, Phys. Today 62, 30 (2009).
[CrossRef]

Lagendijk, A.

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Phys. Today 62, 24 (2009).
[CrossRef]

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef] [PubMed]

Laurent, D.

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

Legrand, O.

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

Licciardello, D. C.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

Lodahl, P.

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Mordechai, S.

T. Schwartz, G. Bartal, S. Fishman, and S. Mordechai, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Mortessagne, F.

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

Nagle, J.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Nieuwenhuizen, Th. M.

Th. M. Nieuwenhuizen and M. C. W. van Rossum, Phys. Rev. Lett. 74, 2674 (1995).
[CrossRef] [PubMed]

Page, J. H.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

Ramakrishnan, T. V.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

Sapienza, L.

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and S. Mordechai, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Sebbah, P.

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

Sheng, P.

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, 1996).

Skipetrov, S. E.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

Smolka, S.

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Stobble, S.

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Strybulevych, A.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

Thyrrestrup, H.

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Tran, N.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

van Rossum, M. C. W.

Th. M. Nieuwenhuizen and M. C. W. van Rossum, Phys. Rev. Lett. 74, 2674 (1995).
[CrossRef] [PubMed]

Van Tiggelen, A.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

van Tiggelen, B.

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Phys. Today 62, 24 (2009).
[CrossRef]

Vanneste, C.

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Wang, J.

A. Z. Genack and J. Wang, Int. J. Mod. Phys. B 24, 1950 (2010).
[CrossRef]

Weaver, R. L.

R. L. Weaver, Wave Motion 12, 129 (1990).
[CrossRef]

Weidner, E.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Wiersma, D. S.

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Phys. Today 62, 24 (2009).
[CrossRef]

Appl. Phys. Lett.

E. Weidner, S. Combrie, N. Tran, A. De Rossi, J. Nagle, and S. Cassette, Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Int. J. Mod. Phys. B

A. Z. Genack and J. Wang, Int. J. Mod. Phys. B 24, 1950 (2010).
[CrossRef]

Nature

T. Schwartz, G. Bartal, S. Fishman, and S. Mordechai, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Nature Phys.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and A. Van Tiggelen, Nature Phys. 4, 945 (2008).
[CrossRef]

Phys. Rev.

P. W. Anderson, Phys. Rev. 109, 1452 (1958).

Phys. Rev. Lett.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
[CrossRef]

D. Laurent, O. Legrand, P. Sebbah, C. Vanneste, and F. Mortessagne, Phys. Rev. Lett. 99, 253902 (2007).
[CrossRef]

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

H. De Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef] [PubMed]

Th. M. Nieuwenhuizen and M. C. W. van Rossum, Phys. Rev. Lett. 74, 2674 (1995).
[CrossRef] [PubMed]

Phys. Today

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, Phys. Today 62, 24 (2009).
[CrossRef]

A. Aspect and M. Inguscio, Phys. Today 62, 30 (2009).
[CrossRef]

Science

L. Sapienza, H. Thyrrestrup, S. Stobble, P. D. Garcia, S. Smolka, and P. Lodahl, Science 327, 1352 (2010).
[CrossRef] [PubMed]

Wave Motion

R. L. Weaver, Wave Motion 12, 129 (1990).
[CrossRef]

Other

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, 1996).

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Figures (3)

Fig. 1
Fig. 1

(a) Intensity spectrum inside the structure ( ff = 30 % and hd = 250 nm ) for different waiting times, t, and averaged over position, obtained by Fourier transforming the time evolution of the intensity. (b) Probability distribution of the speckle intensity in transmission ( ff = 30 % and hd = 250 nm ). The two insets show the FDTD layout for the calculation of the intensity spectrum and FWHM (squared layout) and for the calculation of the probability distribution (strip layout).

Fig. 2
Fig. 2

Examples of experimentally observed near-field spectra: (a) ff = 30%, hd = 220 nm ; (b) ff = 30 % , hd = 250 nm . (c) Scanning electron microscope image of one measured sample. (d) Experimental (filled points) and calculated (empty points) spectral width of the localized modes versus the density of holes.

Fig. 3
Fig. 3

(a) Three-dimensional view of one of the many spatially localized modes as observed in Sample 1. Spatial size image, 13.5 μm × 13.5 μm . The spatial extent of this mode is around 1.4 μm . The inset shows the spectrum recorded in the position where the mode has maximum intensity. (Note: the sample is larger than the scanning area. The actual border is far away from the position of the mode). (b) Average spatial extent of the localized modes as a function of the hole diameter for fixed filling fraction ( ff = 0.3 ). The inset shows the experimental map of one localized mode superimposed to the dielectric matrix of the sample.

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