Abstract

We report statistical fluctuations for the transmissions of a series of photonic-crystal waveguides (PhCWs) that are supposedly identical and that only differ because of statistical structural fabrication-induced imperfections. For practical PhCW lengths offering tolerable −3dB attenuation with moderate group indices (ng≈60), the transmission spectra contains very narrow peaks (Q≈20,000) that vary from one waveguide to another. The physical origin of the peaks is explained by calculating the actual electromagnetic-field pattern inside the waveguide. The peaks that are observed in an intermediate regime between the ballistic and localization transports are responsible for a smearing of the local density of states, for a rapid broadening of the probability density function of the transmission, and bring a severe constraint on the effective use of slow light for on-chip optical information processing. The experimental results are quantitatively supported by theoretical results obtained with a coupled-Bloch-mode approach that takes into account multiple scattering and localization effects.

© 2010 OSA

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  1. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
    [CrossRef] [PubMed]
  2. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
    [CrossRef] [PubMed]
  3. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
    [CrossRef] [PubMed]
  4. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31(4), 456–458 (2006).
    [CrossRef] [PubMed]
  5. D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15(3), 1228–1233 (2007).
    [CrossRef] [PubMed]
  6. F. Morichetti, A. Melloni, A. Breda, A. Canciamilla, C. Ferrari, and M. Martinelli, “A reconfigurable architecture for continuously variable optical slow-wave delay lines,” Opt. Express 15(25), 17273–17282 (2007).
    [CrossRef] [PubMed]
  7. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
    [CrossRef]
  8. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
    [CrossRef]
  9. S. John, “Electromagnetic Absorption in a Disordered Medium near a Photon Mobility Edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
    [CrossRef]
  10. S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
    [CrossRef]
  11. J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
    [CrossRef]
  12. P. Erdös and R. C. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31(2), 65–163 (1982).
    [CrossRef]
  13. C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69(3), 731–808 (1997).
    [CrossRef]
  14. S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
    [CrossRef] [PubMed]
  15. Strictly speaking, lc is defined for lossless transport systems, only. As shown by recent theoretical results [14], backscattering is largely dominant for ng>20 in the present PhCW. The out-of-plane losses being negligible, the transmitted photons may undergo many multiple-reflections without any significant damping and the expression <ln(T)> = -L/lc may be used safely to evaluate the localization length.
  16. E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
    [CrossRef]
  17. L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007).
    [CrossRef] [PubMed]
  18. R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
    [CrossRef] [PubMed]
  19. N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
    [CrossRef]
  20. M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
    [CrossRef] [PubMed]
  21. J. Topolancik, F. Vollmer, R. Ilic, and M. Crescimanno, “Out-of-plane scattering from vertically asymmetric photonic crystal slab waveguides with in-plane disorder,” Opt. Express 17(15), 12470–12480 (2009).
    [CrossRef] [PubMed]
  22. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270(3), 143–215 (1996).
    [CrossRef]
  23. G. Lecamp, J. P. Hugonin, and P. Lalanne, “Theoretical and computational concepts for periodic optical waveguides,” Opt. Express 15(18), 11042–11060 (2007).
    [CrossRef] [PubMed]
  24. D. M. Beggs, L. O'Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slabs using optical methods,” Photonics Nanostruct. Fundam. Appl. 6(3-4), 213–218 (2008).
    [CrossRef]
  25. M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express 13(7), 2487–2502 (2005).
    [CrossRef] [PubMed]
  26. J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007).
    [CrossRef] [PubMed]
  27. P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
    [CrossRef]
  28. A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
    [CrossRef]
  29. D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
    [CrossRef]
  30. D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004).
    [CrossRef] [PubMed]
  31. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
    [CrossRef] [PubMed]
  32. S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
    [CrossRef]
  33. L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi, B Basic Res. 244(10), 3528–3539 (2007).
    [CrossRef]
  34. B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
    [CrossRef]
  35. J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
    [CrossRef] [PubMed]
  36. P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
    [CrossRef] [PubMed]
  37. J. B. Pendry, “Symmetry and transport of waves in one-dimensional disordered systems,” Adv. Phys. 43(4), 461–542 (1994).
    [CrossRef]
  38. Since I(z) = |c+(z)|2–|c–(z)|2 represents the net flow of energy in the positive-z direction, I(z)–I(z + a)≈a ∂I(z)/∂z represents the out-of-plane loss of the unit cell located between z and z + a.
  39. Chaotic transmission spectra that strongly depart from theory predictions are also observed with slow light in coupled-cavity systems, see Ref. 8 for instance.

2009

S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
[CrossRef] [PubMed]

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
[CrossRef]

M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

J. Topolancik, F. Vollmer, R. Ilic, and M. Crescimanno, “Out-of-plane scattering from vertically asymmetric photonic crystal slab waveguides with in-plane disorder,” Opt. Express 17(15), 12470–12480 (2009).
[CrossRef] [PubMed]

2008

D. M. Beggs, L. O'Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slabs using optical methods,” Photonics Nanostruct. Fundam. Appl. 6(3-4), 213–218 (2008).
[CrossRef]

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
[CrossRef] [PubMed]

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
[CrossRef]

2007

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi, B Basic Res. 244(10), 3528–3539 (2007).
[CrossRef]

D. O’Brien, M. D. Settle, T. Karle, A. Michaeli, M. Salib, and T. F. Krauss, “Coupled photonic crystal heterostructure nanocavities,” Opt. Express 15(3), 1228–1233 (2007).
[CrossRef] [PubMed]

G. Lecamp, J. P. Hugonin, and P. Lalanne, “Theoretical and computational concepts for periodic optical waveguides,” Opt. Express 15(18), 11042–11060 (2007).
[CrossRef] [PubMed]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007).
[CrossRef] [PubMed]

L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, A. Breda, A. Canciamilla, C. Ferrari, and M. Martinelli, “A reconfigurable architecture for continuously variable optical slow-wave delay lines,” Opt. Express 15(25), 17273–17282 (2007).
[CrossRef] [PubMed]

2006

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31(4), 456–458 (2006).
[CrossRef] [PubMed]

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
[CrossRef] [PubMed]

2005

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

M. Skorobogatiy, G. Bégin, and A. Talneau, “Statistical analysis of geometrical imperfections from the images of 2D photonic crystals,” Opt. Express 13(7), 2487–2502 (2005).
[CrossRef] [PubMed]

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
[CrossRef] [PubMed]

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
[CrossRef]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[CrossRef]

2004

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004).
[CrossRef] [PubMed]

2001

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

1997

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69(3), 731–808 (1997).
[CrossRef]

1996

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270(3), 143–215 (1996).
[CrossRef]

1994

J. B. Pendry, “Symmetry and transport of waves in one-dimensional disordered systems,” Adv. Phys. 43(4), 461–542 (1994).
[CrossRef]

1984

S. John, “Electromagnetic Absorption in a Disordered Medium near a Photon Mobility Edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[CrossRef]

1982

P. Erdös and R. C. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31(2), 65–163 (1982).
[CrossRef]

Abram, R. A.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

Albert, J. P.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

Andreani, L. C.

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi, B Basic Res. 244(10), 3528–3539 (2007).
[CrossRef]

D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004).
[CrossRef] [PubMed]

Baba, T.

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
[CrossRef] [PubMed]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Bandaru, P. R.

S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
[CrossRef]

Beenakker, C. W. J.

C. W. J. Beenakker, “Random-matrix theory of quantum transport,” Rev. Mod. Phys. 69(3), 731–808 (1997).
[CrossRef]

Beggs, D. M.

D. M. Beggs, L. O'Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slabs using optical methods,” Photonics Nanostruct. Fundam. Appl. 6(3-4), 213–218 (2008).
[CrossRef]

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

Bégin, G.

Bertolotti, J.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Brand, S.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

Breda, A.

Canciamilla, A.

Cassagne, D.

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

Charvolin, T.

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

Combrié, S.

M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

Crescimanno, M.

De Rossi, A.

M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

DeRose, G. A.

Engelen, R. J. P.

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
[CrossRef] [PubMed]

Erdös, P.

P. Erdös and R. C. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31(2), 65–163 (1982).
[CrossRef]

Ferrari, C.

Gabet, R.

M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

Genack, A. Z.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
[CrossRef] [PubMed]

Gerace, D.

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi, B Basic Res. 244(10), 3528–3539 (2007).
[CrossRef]

D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004).
[CrossRef] [PubMed]

Ghulinyan, M.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Gomez-Iglesias, A.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

Gottardo, S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Hadji, E.

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Herndon, R. C.

P. Erdös and R. C. Herndon, “Theories of electrons in one-dimensional disordered systems,” Adv. Phys. 31(2), 65–163 (1982).
[CrossRef]

Houdré, R.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
[CrossRef]

Hu, B.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
[CrossRef] [PubMed]

Hughes, S.

M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[CrossRef]

Hugonin, J. P.

S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
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J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007).
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J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
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Jacobs, S.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
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N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
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M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
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S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
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D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
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S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
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Klosner, J. M.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
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D. M. Beggs, L. O'Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slabs using optical methods,” Photonics Nanostruct. Fundam. Appl. 6(3-4), 213–218 (2008).
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J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007).
[CrossRef] [PubMed]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
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R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
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M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270(3), 143–215 (1996).
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S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
[CrossRef] [PubMed]

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
[CrossRef]

G. Lecamp, J. P. Hugonin, and P. Lalanne, “Theoretical and computational concepts for periodic optical waveguides,” Opt. Express 15(18), 11042–11060 (2007).
[CrossRef] [PubMed]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, “Coupling into slow-mode photonic crystal waveguides,” Opt. Lett. 32(18), 2638–2640 (2007).
[CrossRef] [PubMed]

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

Le Thomas, N.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
[CrossRef]

Lecamp, G.

Martinelli, M.

Mazoyer, S.

S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
[CrossRef] [PubMed]

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
[CrossRef]

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Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
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Michaeli, A.

Miller, A.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

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S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
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R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
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M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

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Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

O’Brien, D.

O’Faolain, L.

O'Brien, D.

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

O'Faolain, L.

D. M. Beggs, L. O'Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slabs using optical methods,” Photonics Nanostruct. Fundam. Appl. 6(3-4), 213–218 (2008).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

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S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
[CrossRef]

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M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

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J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
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J. B. Pendry, “Symmetry and transport of waves in one-dimensional disordered systems,” Adv. Phys. 43(4), 461–542 (1994).
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P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

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P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
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Povinelli, M. L.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
[CrossRef]

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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
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P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

Sagnes, I.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
[CrossRef]

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Sebbah, P.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
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Shinya, A.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
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S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
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Soljacic, M.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
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M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
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M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
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M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Talneau, A.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
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M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
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J. Topolancik, F. Vollmer, R. Ilic, and M. Crescimanno, “Out-of-plane scattering from vertically asymmetric photonic crystal slab waveguides with in-plane disorder,” Opt. Express 17(15), 12470–12480 (2009).
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J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef]

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M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[CrossRef] [PubMed]

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A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270(3), 143–215 (1996).
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P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Vollmer, F.

J. Topolancik, F. Vollmer, R. Ilic, and M. Crescimanno, “Out-of-plane scattering from vertically asymmetric photonic crystal slab waveguides with in-plane disorder,” Opt. Express 17(15), 12470–12480 (2009).
[CrossRef] [PubMed]

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observation of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[CrossRef]

Wang, B.

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[CrossRef]

White, T. P.

Wiersma, D. S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
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S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
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Yariv, A.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001).
[CrossRef] [PubMed]

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
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Yuan, X.

Zabelin, V.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
[CrossRef]

Zhang, H.

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
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Adv. Phys.

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Appl. Phys. B

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B 81(2-3), 283–293 (2005).
[CrossRef]

Appl. Phys. Lett.

P. Velha, J. C. Rodier, P. Lalanne, J. P. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, “Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance,” Appl. Phys. Lett. 89(17), 171121 (2006).
[CrossRef]

A. Gomez-Iglesias, D. O'Brien, L. O'Faolain, A. Miller, and T. F. Krauss, “Direct measurement of the group index of photonic crystal waveguides via Fourier transform spectral interferometry,” Appl. Phys. Lett. 90(26), 261107 (2007).
[CrossRef]

J. Phys. Condens. Matter

D. M. Beggs, M. A. Kaliteevski, S. Brand, R. A. Abram, D. Cassagne, and J. P. Albert, “Disorder induced modification of reflection and transmission spectra of a two-dimensional photonic crystal with an incomplete band-gap,” J. Phys. Condens. Matter 17(26), 4049–4055 (2005).
[CrossRef]

Nat. Mater.

M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

Nat. Photonics

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2(2), 90–93 (2008).
[CrossRef]

Nature

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Photonics Nanostruct. Fundam. Appl.

D. M. Beggs, L. O'Faolain, and T. F. Krauss, “Accurate determination of the functional hole size in photonic crystal slabs using optical methods,” Photonics Nanostruct. Fundam. Appl. 6(3-4), 213–218 (2008).
[CrossRef]

Phys. Rep.

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270(3), 143–215 (1996).
[CrossRef]

Phys. Rev. B

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[CrossRef]

N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, R. Houdré, I. Sagnes, and A. Talneau, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80(12), 125332 (2009).
[CrossRef]

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
[CrossRef]

Phys. Rev. Lett.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, “Extended quasimodes within nominally localized random waveguides,” Phys. Rev. Lett. 96(18), 183902 (2006).
[CrossRef] [PubMed]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94(3), 033903 (2005).
[CrossRef] [PubMed]

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Other

Strictly speaking, lc is defined for lossless transport systems, only. As shown by recent theoretical results [14], backscattering is largely dominant for ng>20 in the present PhCW. The out-of-plane losses being negligible, the transmitted photons may undergo many multiple-reflections without any significant damping and the expression <ln(T)> = -L/lc may be used safely to evaluate the localization length.

Since I(z) = |c+(z)|2–|c–(z)|2 represents the net flow of energy in the positive-z direction, I(z)–I(z + a)≈a ∂I(z)/∂z represents the out-of-plane loss of the unit cell located between z and z + a.

Chaotic transmission spectra that strongly depart from theory predictions are also observed with slow light in coupled-cavity systems, see Ref. 8 for instance.

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Figures (7)

Fig. 1
Fig. 1

Scanning Electron Microscope image of a single-row-missing PhCW. The wafer is composed of a series of twenty supposedly identical parallel waveguides etched into a Si-membrane. The top inset shows the dispersion diagram of the ideal waveguide, calculated for the geometric parameters actually measured on the device and for a 3.48 Si refractive index. The bottom inset represents an enlarged view of the injector [26] used for efficient coupling between the ridge-access waveguide and the PhCW.

Fig. 2
Fig. 2

Experimental data collected for the twenty PhCWs. (a) Spectra of two different waveguide instances (black and red curves). ng dependence (top axis) is deduced from interferometric measurements (b) ng(λ) curves recorded for every waveguide. The large spreading at large ng’s (inset) results from disorder−induced fluctuations that smear the sharp cutoff at vg = 0. The thick-black curve represents the ensemble-averaged curve used to relate the actual wavelength to an averaged group index.

Fig. 3
Fig. 3

Test of the median-filter method with purely-calculated transmission spectra. (a) Typical transmission spectrum calculated by including light injection from the ridge to the PhCW and multiple-reflection on the ridge cleaved facets. (b) Termination-less transmission spectrum obtained by directly calculating the transmission of the disordered PhCW used for the calculation in (a). (c) Transmission spectrum obtained by filtering the curve in (a). Although the filtering process is imperfect, it provides reliable estimates for the termination-less transmission.

Fig. 4
Fig. 4

Examples of experimental filtered spectra (b) and (d) used in the following statistical analysis. The corresponding measured spectra are shown in (a) and (c). The red arrows point at the spectral locations of the insets. Note the important similarities between the filtered spectra and the theoretical spectra of Figs. 3(b) and 3(c).

Fig. 5
Fig. 5

Comparison between the experimental results (black) and the model predictions (red) for the averaged transmission <T>. The experimental ensemble−averages are collected over N = 18 independent realizations. Those of the theoretical data are collected over 1000 independent realizations with σ = 1.7 nm. The vertical bars represent the statistical error σT/N1/2. The inset is a log-log representation for different values of the standard deviation of the hole diameter, σ = 1 nm (green), σ = 1.7 nm (red), σ = 2 nm (blue).

Fig. 6
Fig. 6

Histograms (black bars) of the 18 values of the transmission for <T> = 0.9 (a), <T> = 0.5 (b) and <T> = 0.1 (c). The red curves are the corresponding calculated probability density function obtained by collecting 5.105 independent disorder realizations at the corresponding n g’s, n g = 25 (a), 55 (b) and 90 (c). The bar width of the experimental data is ΔT = 0.05 and the bar heights are normalized such that ΣpPp(T)ΔT = 1, to allows us for a direct comparison with the theoretical data.

Fig. 7
Fig. 7

Field pattern inside a 185-a-long PhCW for the ballistic (left, ng ≈40, L≈0.25l c), intermediate (middle, ng ≈65, L≈1.3l c) and localization (right, ng ≈105, L≈6l c) regimes. Top: Calculated data for termination-less PhCW showing the forward- and backward-propagating Bloch mode intensities, |c+(z)|2 (red) and |c(z)|2 (blue). Note the changes of the vertical axes. Middle: The calculated out-of-plane losses, ∂(|c+|2−|c(z)|2)/∂z (black). Bottom: Far-field patterns obtained by imaging the sample surface onto an IR-camera. Note that since the experimental and theoretical data do not correspond to the same disorder instance, the spike locations in the black curves and in the images are not expected to be identical. In all graphs, light is incoming from the left side. Note that the color scale is logarithmic.

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