Abstract

By employing Random Matrix Theory (RMT) and first-principle calculations, we investigated the behavior of Anderson localization in 1D, 2D and 3D systems characterized by a varying disorder. In particular, we considered random binary layer sequences in 1D and structurally disordered photonic crystals in two and three dimensions. We demonstrated the existence of a unique optimal degree of disorder that yields the strongest localization possible. In this regime, localized modes are constituted by defect states, which can show subwavelength confinement properties. These results suggest that disorder offers a new avenue for subwavelength light localization in purely dielectric media.

© 2012 OSA

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  1. P. 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. C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nature Phys.4, 794–798 (2008).
    [CrossRef]
  4. M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett.55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  5. S. Gentilini, A. Fratalocchi, L. Angelani, G. Ruocco, and C. Conti, “Ultrashort pulse propagation and the Anderson localization,” Opt. Lett.34, 130–132 (2009).
    [CrossRef] [PubMed]
  6. P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett.55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  7. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature390, 671–673 (1997).
    [CrossRef]
  8. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
    [CrossRef] [PubMed]
  9. S. Gentilini, A. Fratalocchi, and C. Conti, “Signatures of Anderson localization excited by an optical frequency comb,” Phys. Rev. B81, 014209 (2010).
    [CrossRef]
  10. 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]
  11. M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett.96, 063904 (2006).
    [CrossRef] [PubMed]
  12. R. Frank, A. Lubatsch, and J. Kroha, “Theory of strong localization effects of light in disordered loss or gain media,” Phys. Rev. B73, 245107 (2006).
    [CrossRef]
  13. F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature398, 206–209 (1999).
    [CrossRef]
  14. S. E. Skipetrov and B. A. van Tiggelen, “Dynamics of Anderson localization in open 3D media,” Phys. Rev. Lett.96, 043902 (2006).
    [CrossRef] [PubMed]
  15. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett.53, 2169–2174 (1984).
    [CrossRef]
  16. A. R. McGurn, K. T. Christensen, F. M. Mueller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B47, 13120–13125 (1993).
    [CrossRef]
  17. V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. McGurn, “Enhanced transmission due to disorder,” Phys. Rev. E51, 6301–6304 (1995).
    [CrossRef]
  18. Y. A. Vlasov, M. I. Kaliteevski, and V. V. Nikolaev, Phys. Rev. B, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B60, 1555–1562 (1999).
    [CrossRef]
  19. M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
    [CrossRef]
  20. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic Press, San Diego, 1995).
  21. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett.56, 1471–1474 (1986).
    [CrossRef] [PubMed]
  22. A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices in Statistical Physics (Springer, Berlin, 1993).
    [CrossRef]
  23. P. Markos and C. M. Soukoulis, Wave Propagation: from Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, New Jersey, 2008).
  24. S. Zhang, J. Park, V. Milner, and A. Z. Genack, “Photon delocalization transition in dimensional crossover in layered media,” Phys. Rev. Lett.101, 183901 (2008).
    [CrossRef] [PubMed]
  25. M. Ghulinyan, “Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems,” Phys. Rev. Lett.99, 063905 (2007).
    [CrossRef] [PubMed]
  26. 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]
  27. J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett.62, 695–698 (1989).
    [CrossRef] [PubMed]
  28. F. Haake, Quantum Signatures of Chaos (Springer, New York, 2001).

2012

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]

2010

S. Gentilini, A. Fratalocchi, and C. Conti, “Signatures of Anderson localization excited by an optical frequency comb,” Phys. Rev. B81, 014209 (2010).
[CrossRef]

2009

2008

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nature Phys.4, 794–798 (2008).
[CrossRef]

S. Zhang, J. Park, V. Milner, and A. Z. Genack, “Photon delocalization transition in dimensional crossover in layered media,” Phys. Rev. Lett.101, 183901 (2008).
[CrossRef] [PubMed]

2007

M. Ghulinyan, “Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems,” Phys. Rev. Lett.99, 063905 (2007).
[CrossRef] [PubMed]

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]

2006

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett.96, 063904 (2006).
[CrossRef] [PubMed]

R. Frank, A. Lubatsch, and J. Kroha, “Theory of strong localization effects of light in disordered loss or gain media,” Phys. Rev. B73, 245107 (2006).
[CrossRef]

S. E. Skipetrov and B. A. van Tiggelen, “Dynamics of Anderson localization in open 3D media,” Phys. Rev. Lett.96, 043902 (2006).
[CrossRef] [PubMed]

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
[CrossRef]

2000

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

1999

Y. A. Vlasov, M. I. Kaliteevski, and V. V. Nikolaev, Phys. Rev. B, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B60, 1555–1562 (1999).
[CrossRef]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature398, 206–209 (1999).
[CrossRef]

1997

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

1995

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. McGurn, “Enhanced transmission due to disorder,” Phys. Rev. E51, 6301–6304 (1995).
[CrossRef]

1993

A. R. McGurn, K. T. Christensen, F. M. Mueller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B47, 13120–13125 (1993).
[CrossRef]

1989

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett.62, 695–698 (1989).
[CrossRef] [PubMed]

1987

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

1986

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett.56, 1471–1474 (1986).
[CrossRef] [PubMed]

1985

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett.55, 2696–2699 (1985).
[CrossRef] [PubMed]

M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett.55, 2692–2695 (1985).
[CrossRef] [PubMed]

1984

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett.53, 2169–2174 (1984).
[CrossRef]

1958

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

Abram, R. A.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
[CrossRef]

Aegerter, C. M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett.96, 063904 (2006).
[CrossRef] [PubMed]

Akkermans, E.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett.56, 1471–1474 (1986).
[CrossRef] [PubMed]

Albada, M. P. V.

M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett.55, 2692–2695 (1985).
[CrossRef] [PubMed]

Anderson, P.

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

Angelani, L.

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]

Beggs, D. M.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
[CrossRef]

Brand, S.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

Christensen, K. T.

A. R. McGurn, K. T. Christensen, F. M. Mueller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B47, 13120–13125 (1993).
[CrossRef]

Conti, C.

S. Gentilini, A. Fratalocchi, and C. Conti, “Signatures of Anderson localization excited by an optical frequency comb,” Phys. Rev. B81, 014209 (2010).
[CrossRef]

S. Gentilini, A. Fratalocchi, L. Angelani, G. Ruocco, and C. Conti, “Ultrashort pulse propagation and the Anderson localization,” Opt. Lett.34, 130–132 (2009).
[CrossRef] [PubMed]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nature Phys.4, 794–798 (2008).
[CrossRef]

Crisanti, A.

A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices in Statistical Physics (Springer, Berlin, 1993).
[CrossRef]

Deutsch, J. M.

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett.62, 695–698 (1989).
[CrossRef] [PubMed]

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]

Frank, R.

R. Frank, A. Lubatsch, and J. Kroha, “Theory of strong localization effects of light in disordered loss or gain media,” Phys. Rev. B73, 245107 (2006).
[CrossRef]

Fratalocchi, A.

S. Gentilini, A. Fratalocchi, and C. Conti, “Signatures of Anderson localization excited by an optical frequency comb,” Phys. Rev. B81, 014209 (2010).
[CrossRef]

S. Gentilini, A. Fratalocchi, L. Angelani, G. Ruocco, and C. Conti, “Ultrashort pulse propagation and the Anderson localization,” Opt. Lett.34, 130–132 (2009).
[CrossRef] [PubMed]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nature Phys.4, 794–798 (2008).
[CrossRef]

Freilikher, V. D.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. McGurn, “Enhanced transmission due to disorder,” Phys. Rev. E51, 6301–6304 (1995).
[CrossRef]

Genack, A. Z.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, “Photon delocalization transition in dimensional crossover in layered media,” Phys. Rev. Lett.101, 183901 (2008).
[CrossRef] [PubMed]

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

Gentilini, S.

S. Gentilini, A. Fratalocchi, and C. Conti, “Signatures of Anderson localization excited by an optical frequency comb,” Phys. Rev. B81, 014209 (2010).
[CrossRef]

S. Gentilini, A. Fratalocchi, L. Angelani, G. Ruocco, and C. Conti, “Ultrashort pulse propagation and the Anderson localization,” Opt. Lett.34, 130–132 (2009).
[CrossRef] [PubMed]

Ghosh, S.

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]

Ghulinyan, M.

M. Ghulinyan, “Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems,” Phys. Rev. Lett.99, 063905 (2007).
[CrossRef] [PubMed]

Gross, P.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett.96, 063904 (2006).
[CrossRef] [PubMed]

Haake, F.

F. Haake, Quantum Signatures of Chaos (Springer, New York, 2001).

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, 2169–2174 (1984).
[CrossRef]

Kaliteevski, M. A.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
[CrossRef]

Kaliteevski, M. I.

Y. A. Vlasov, M. I. Kaliteevski, and V. V. Nikolaev, Phys. Rev. B, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B60, 1555–1562 (1999).
[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 (2012).
[CrossRef]

Kroha, J.

R. Frank, A. Lubatsch, and J. Kroha, “Theory of strong localization effects of light in disordered loss or gain media,” Phys. Rev. B73, 245107 (2006).
[CrossRef]

Lagendijk, A.

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

M. P. V. Albada and A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett.55, 2692–2695 (1985).
[CrossRef] [PubMed]

Lenke, R.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature398, 206–209 (1999).
[CrossRef]

Liansky, B. A.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. McGurn, “Enhanced transmission due to disorder,” Phys. Rev. E51, 6301–6304 (1995).
[CrossRef]

Lubatsch, A.

R. Frank, A. Lubatsch, and J. Kroha, “Theory of strong localization effects of light in disordered loss or gain media,” Phys. Rev. B73, 245107 (2006).
[CrossRef]

Maradudin, A. A.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. McGurn, “Enhanced transmission due to disorder,” Phys. Rev. E51, 6301–6304 (1995).
[CrossRef]

A. R. McGurn, K. T. Christensen, F. M. Mueller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B47, 13120–13125 (1993).
[CrossRef]

Maret, G.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett.96, 063904 (2006).
[CrossRef] [PubMed]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature398, 206–209 (1999).
[CrossRef]

P.-E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett.55, 2696–2699 (1985).
[CrossRef] [PubMed]

Markos, P.

P. Markos and C. M. Soukoulis, Wave Propagation: from Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, New Jersey, 2008).

Maynard, R.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett.56, 1471–1474 (1986).
[CrossRef] [PubMed]

McGurn, A. R.

V. D. Freilikher, B. A. Liansky, I. V. Yurkevich, A. A. Maradudin, and A. R. McGurn, “Enhanced transmission due to disorder,” Phys. Rev. E51, 6301–6304 (1995).
[CrossRef]

A. R. McGurn, K. T. Christensen, F. M. Mueller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B47, 13120–13125 (1993).
[CrossRef]

Milner, V.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, “Photon delocalization transition in dimensional crossover in layered media,” Phys. Rev. Lett.101, 183901 (2008).
[CrossRef] [PubMed]

Mueller, F. M.

A. R. McGurn, K. T. Christensen, F. M. Mueller, and A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B47, 13120–13125 (1993).
[CrossRef]

Nikolaev, V. V.

M. A. Kaliteevski, D. M. Beggs, S. Brand, R. A. Abram, and V. V. Nikolaev, “Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals,” Phys. Rev. E73, 056616–(10) (2006).
[CrossRef]

Y. A. Vlasov, M. I. Kaliteevski, and V. V. Nikolaev, Phys. Rev. B, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B60, 1555–1562 (1999).
[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 (2012).
[CrossRef]

Paladin, G.

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett.62, 695–698 (1989).
[CrossRef] [PubMed]

A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices in Statistical Physics (Springer, Berlin, 1993).
[CrossRef]

Park, J.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, “Photon delocalization transition in dimensional crossover in layered media,” Phys. Rev. Lett.101, 183901 (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 (2012).
[CrossRef]

Righini, R.

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

Ruocco, G.

Scheffold, F.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature398, 206–209 (1999).
[CrossRef]

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]

Sheng, P.

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

Skipetrov, S. E.

S. E. Skipetrov and B. A. van Tiggelen, “Dynamics of Anderson localization in open 3D media,” Phys. Rev. Lett.96, 043902 (2006).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Markos and C. M. Soukoulis, Wave Propagation: from Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, New Jersey, 2008).

Störzer, M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett.96, 063904 (2006).
[CrossRef] [PubMed]

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, “Statistical signatures of photon localization,” Nature404, 850–853 (2000).
[CrossRef] [PubMed]

Thomson, R. R.

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]

Tweer, R.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature398, 206–209 (1999).
[CrossRef]

van Tiggelen, B. A.

S. E. Skipetrov and B. A. van Tiggelen, “Dynamics of Anderson localization in open 3D media,” Phys. Rev. Lett.96, 043902 (2006).
[CrossRef] [PubMed]

Varshney, R. 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 (2012).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. I. Kaliteevski, and V. V. Nikolaev, Phys. Rev. B, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B60, 1555–1562 (1999).
[CrossRef]

Vulpiani, A.

A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices in Statistical Physics (Springer, Berlin, 1993).
[CrossRef]

Wiersma, D. S.

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

Wolf, P. E.

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Figures (4)

Fig. 1
Fig. 1

(a) Graphical analysis of Eq. (6); (b) Localization length lc vs p for γa = π/4, ha = hb = 1 and γb = π/4+0.2: numerical evaluation based on the product of 106 matrices (solid line), analytical estimates (circle markers) from Eq. (5) and localization minimum (diamond marker) from Eq. (6).

Fig. 2
Fig. 2

Summary of two dimensional FDTD simulations. (a) Refractive index distribution for χ = 0.15; (b) local density of states LDOS (solid line) for the ordered crystal at χ = 0 and spectrum of the input source used in FDTD simulations (dashed line); (c) single localization length l̂c for a sample with χ = 0.15; (d) normalized averaged localization length lc versus disorder strength χ: (e)–(f) strongest localization regime for χ = 0.15: (e) LDOS and (f) energy section along y (solid line) compared to a gaussian spot (dashed line) whose size s = 2ωy (being ωy the waist) corresponds to one internal wavelength λ in Silicon. The inset of (f) reports the spatial energy distribution (x, y) in the strongest localized case.

Fig. 3
Fig. 3

(a) LDOS for the ordered crystal (solid line) and input source spectrum (dashed line) used in 3D FDTD experiments; (b) normalized localization length lc versus χ; (c)–(d) strongest localization regime for χ = 0.05: (c) LDOS and (d) refractive index (semitransparent volume density plot) with electromagnetic energy (isosurface plot) distribution.

Fig. 4
Fig. 4

3D subwavelength localization for χ = 0.05: (a) spatial (x, y) distribution of the electromagnetic energy (x, y, z) calculated at z = −2μm; (b) Energy profile along x for z = −2μm, y = −1.5μm (solid line) compared to an equivalent gaussian spot of size equal to one internal wavelength λ = λ0/n (dashed line).

Equations (7)

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M j = [ cos γ j h j sin γ j h j γ j γ j sin γ j h j cos γ j h j ] ,
M = M 0 + Δ M ,
Tr ( M ) = Tr ( M 0 ) + Tr ( Δ M ) ,
Tr ( Δ M ) = ( N N ) 1 1 2 π i 𝒞 Q ( z ) e N ln γ z ( 1 p ) d z
δ ( p ) = ln [ ( 1 p h ) 1 p p p γ ] , ln γ ln z | z = h = 1 p ,
2 tan 1 ( 1 2 p * ) = ln h ( p * ) ,
l c = l ^ c = ( V d x ) 2 V V d x 2 ,

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