Abstract

Slow light devices such as photonic crystal waveguides (PhCW) and coupled resonator optical waveguides (CROW) have much promise for optical signal processing applications and a number of successful demonstrations underpinning this promise have already been made. Most of these applications are limited by propagation losses, especially for higher group indices. These losses are caused by technological imperfections (“extrinsic loss”) that cause scattering of light from the waveguide mode. The relationship between this loss and the group velocity is complex and until now has not been fully understood. Here, we present a comprehensive explanation of the extrinsic loss mechanisms in PhC waveguides and address some misconceptions surrounding loss and slow light that have arisen in recent years. We develop a theoretical model that accurately describes the loss spectra of PhC waveguides. One of the key insights of the model is that the entire hole contributes coherently to the scattering process, in contrast to previous models that added up the scattering from short sections incoherently. As a result, we have already realised waveguides with significantly lower losses than comparable photonic crystal waveguides as well as achieving propagation losses, in units of loss per unit time (dB/ns) that are even lower than those of state-of-the-art coupled resonator optical waveguides based on silicon photonic wires. The model will enable more advanced designs with further loss reduction within existing technological constraints.

© 2010 OSA

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    [CrossRef] [PubMed]
  5. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
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  6. D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Ultracompact and low power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
    [CrossRef] [PubMed]
  7. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
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  8. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  16. J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
    [CrossRef] [PubMed]
  17. M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15(26), 17458 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
  20. 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]
  21. Here α is defined as <lnT> = -αL, with <lnT> the ensemble-averaged logarithm of the transmission, which is valid both in the ballistic and the multiple scattering regime [24].
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    [CrossRef]
  23. A. Petrov, M. Krause, and M. Eich, “Backscattering and disorder limits in slow light photonic crystal waveguides,” Opt. Express 17(10), 8676–8684 (2009).
    [CrossRef] [PubMed]
  24. 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]
  25. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
    [CrossRef] [PubMed]
  26. B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78(24), 245108 (2008).
    [CrossRef]
  27. 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]
  28. The code written by D. M. Beggs and S. A. Schulz is available for free at: www.st-andrews.ac.uk/microphotonics
  29. D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).
  30. L. O'Faolain, T. P. White, D. O'Brien, X. D. 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]
  31. L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
    [CrossRef]
  32. S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
    [CrossRef]
  33. 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]
  34. 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]
  35. 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]
  36. S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18(14), 14654–14663 (2010).
    [CrossRef] [PubMed]
  37. M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
    [CrossRef] [PubMed]
  38. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15(1), 219–226 (2007).
    [CrossRef] [PubMed]
  39. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
    [CrossRef]

2010 (5)

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18(14), 14654–14663 (2010).
[CrossRef] [PubMed]

2009 (6)

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[CrossRef] [PubMed]

A. Petrov, M. Krause, and M. Eich, “Backscattering and disorder limits in slow light photonic crystal waveguides,” Opt. Express 17(10), 8676–8684 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

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]

2008 (8)

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

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
[CrossRef]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Ultracompact and low power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
[CrossRef] [PubMed]

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008).
[CrossRef] [PubMed]

A. Melloni, F. Morichetti, and M. Martinelli, “Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides,” J. Opt. Soc. Am. B 25(12), C87–C97 (2008).
[CrossRef]

T. P. White, L. O'Faolain, J. T. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
[CrossRef] [PubMed]

2007 (8)

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15(1), 219–226 (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]

L. O'Faolain, T. P. White, D. O'Brien, X. D. 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]

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15(26), 17458 (2007).
[CrossRef] [PubMed]

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]

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. 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]

2006 (1)

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

2005 (3)

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).
[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]

2004 (2)

2001 (3)

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

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]

1969 (1)

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).

Adachi, J.

Andreani, L. C.

T. P. White, L. O'Faolain, J. T. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
[CrossRef] [PubMed]

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]

Baba, T.

Balistreri, M. L. M.

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
[CrossRef] [PubMed]

Beggs, D. M.

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18(14), 14654–14663 (2010).
[CrossRef] [PubMed]

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Ultracompact and low power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
[CrossRef] [PubMed]

Canciamilla, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

Chai, Y. J.

Chong, H.

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

De La Rue, R.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

De La Rue, R. M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
[CrossRef]

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Ebnali-Heidari, M.

Eggleton, B. J.

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Eich, M.

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]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15(1), 219–226 (2007).
[CrossRef] [PubMed]

Fan, S.

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92(8), 083901 (2004).
[CrossRef] [PubMed]

Ferrari, C.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[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]

Gersen, H.

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
[CrossRef] [PubMed]

Gnan, M.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
[CrossRef]

Gomez-Iglesias, A.

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[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).
[CrossRef]

Grillet, C.

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Hamachi, Y.

Hughes, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[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]

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.

Ilic, B.

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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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]

Joannopoulos, J. D.

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]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

Johnson, S. G.

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]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

Karalis, A.

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]

Karle, T.

Kawaaski, T.

Korterik, J. P.

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
[CrossRef] [PubMed]

Krause, M.

Krauss, T. F.

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18(14), 14654–14663 (2010).
[CrossRef] [PubMed]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Ultracompact and low power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
[CrossRef] [PubMed]

T. P. White, L. O'Faolain, J. T. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
[CrossRef] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15(1), 219–226 (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).
[CrossRef]

L. O'Faolain, T. P. White, D. O'Brien, X. D. 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]

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

T. Karle, Y. J. Chai, C. N. Morgan, I. H. White, and T. F. Krauss, “Observation of pulse compression in photonic crystal coupled cavity waveguides,” J. Lightwave Technol. 22(2), 514–519 (2004).
[CrossRef]

Kubo, S.

Kuipers, L.

Kuramochi, E.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15(26), 17458 (2007).
[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]

Lalanne, P.

Lecamp, G.

Li, J.

Li, J. T.

Macintyre, D. S.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
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D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).

Martinelli, M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[CrossRef] [PubMed]

A. Melloni, F. Morichetti, and M. Martinelli, “Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides,” J. Opt. Soc. Am. B 25(12), C87–C97 (2008).
[CrossRef]

Mazoyer, S.

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18(14), 14654–14663 (2010).
[CrossRef] [PubMed]

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]

Mcintyre, D.

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

A. Melloni, F. Morichetti, and M. Martinelli, “Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides,” J. Opt. Soc. Am. B 25(12), C87–C97 (2008).
[CrossRef]

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]

Mitsugi, S.

Monat, C.

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Morgan, C. N.

Mori, D.

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, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008).
[CrossRef] [PubMed]

Morichetti, F.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

A. Melloni, F. Morichetti, and M. Martinelli, “Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides,” J. Opt. Soc. Am. B 25(12), C87–C97 (2008).
[CrossRef]

Morita, M.

Moss, D. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

Notomi, M.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15(26), 17458 (2007).
[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]

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]

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.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[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]

O'Brien, D.

O'Faolain, L.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Ultracompact and low power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
[CrossRef] [PubMed]

T. P. White, L. O'Faolain, J. T. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
[CrossRef] [PubMed]

L. O'Faolain, T. P. White, D. O'Brien, X. D. 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]

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Patterson, M.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

Petrov, A.

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]

Ramunno, L.

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]

Rodier, J. C.

Salib, M.

Samarelli, A.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

Samatelli, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

Sasaki, H.

Schulz, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

Schulz, S. A.

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Settle, M. D.

Shinya, A.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15(26), 17458 (2007).
[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]

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]

Sipe, J. E.

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]

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).
[CrossRef]

Sorel, M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[CrossRef]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
[CrossRef]

Spasenovic, M.

Takahashi, C.

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]

Takahashi, J.

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]

Tanabe, T.

Taniyama, H.

Thoms, S.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
[CrossRef]

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Topolancik, J.

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]

Torregiani, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[CrossRef] [PubMed]

van Hulst, N. F.

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
[CrossRef] [PubMed]

Vlasov, Y.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Vollmer, F.

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).
[CrossRef]

Watanabe, T.

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, I. H.

White, T. P.

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (2009).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

T. P. White, L. O'Faolain, J. T. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
[CrossRef] [PubMed]

D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Ultracompact and low power optical switch based on silicon photonic crystals,” Opt. Lett. 33(2), 147–149 (2008).
[CrossRef] [PubMed]

L. O'Faolain, T. P. White, D. O'Brien, X. D. 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]

Xia, F.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

Yanik, M. F.

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92(8), 083901 (2004).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Yuan, X.

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

Yuan, X. D.

Appl. Phys. B (1)

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. (2)

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96(8), 081112 (2010).
[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]

Bell Syst. Tech. J. (1)

D. Marcuse, “Mode conversion caused by surface imperfections of a dielectric slab waveguide,” Bell Syst. Tech. J. 48, 3187–3215 (1969).

Electron. Lett. (2)

L. O'Faolain, X. Yuan, D. Mcintyre, S. Thoms, H. Chong, R. M. De La Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
[CrossRef]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samatelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics Technol. Lett. 2, 181–194 (2010).

J. Lightwave Technol. (1)

J. Opt. (1)

S. A. Schulz, L. O'Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12(10), 104004 (2010).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Photonics (2)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
[CrossRef]

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Opt. Express (11)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

T. P. White, L. O'Faolain, J. T. Li, L. C. Andreani, and T. F. Krauss, “Silica-embedded silicon photonic crystal waveguides,” Opt. Express 16(21), 17076–17081 (2008).
[CrossRef] [PubMed]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O'Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009).
[CrossRef] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15(1), 219–226 (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]

L. O'Faolain, T. P. White, D. O'Brien, X. D. 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]

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15(26), 17458 (2007).
[CrossRef] [PubMed]

J. Li, T. P. White, L. O'Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[CrossRef] [PubMed]

T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008).
[CrossRef] [PubMed]

A. Petrov, M. Krause, and M. Eich, “Backscattering and disorder limits in slow light photonic crystal waveguides,” Opt. Express 17(10), 8676–8684 (2009).
[CrossRef] [PubMed]

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18(14), 14654–14663 (2010).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (3)

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O'Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80(19), 195305 (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]

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]

Phys. Rev. Lett. (7)

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]

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92(8), 083901 (2004).
[CrossRef] [PubMed]

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]

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]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness Induced Backscattering in Optical Silicon Waveguides,” Phys. Rev. Lett. 104(3), 033902 (2010).
[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]

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]

Phys. Status Solidi, B Basic Res. (1)

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]

Science (1)

M. L. M. Balistreri, H. Gersen, J. P. Korterik, L. Kuipers, and N. F. van Hulst, “Tracking Femtosecond Laser Pulses in Space and Time,” Science 294(5544), 1080–1082 (2001).
[CrossRef] [PubMed]

Other (2)

Here α is defined as <lnT> = -αL, with <lnT> the ensemble-averaged logarithm of the transmission, which is valid both in the ballistic and the multiple scattering regime [24].

The code written by D. M. Beggs and S. A. Schulz is available for free at: www.st-andrews.ac.uk/microphotonics

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Figures (7)

Fig. 1
Fig. 1

a) SEM Micrograph of a photonic crystal waveguide. The waveguide is formed by a missing line of holes in a photonic crystal lattice and referred to as a W1 waveguide. The specific waveguide shown here is designed to operate in the mode anticrossing regime [15] and has been dispersion-engineered by symmetrically shifting the two rows of holes nearest to the line defect [16]. b) Corresponding dispersion curve and c) group index vs. wavelength curve. The frequency range of 0.256c/a < ν < 0.258c/a (where a is the lattice period) of nearly constant slope in b) corresponds to the “plateau” of nearly constant group index between 1587nm < λ < 1595nm in c).

Fig. 2
Fig. 2

Modal field intensity as a function of group index for the waveguide with dispersion shown in Fig. 1b. The fields were calculated as a function of wavevector modulus |k| using 3D MPB [25] and mapped onto group indices via the dispersion curve.

Fig. 3
Fig. 3

Backscattering coefficient ρ vs. group index. The solid red curve represents ρ given by Eq. (3) with the integration performed over an entire hole boundary, while the green dashed curve corresponds to point-by point addition, which assumes scatterers to be independent. The black dot-dashed curve corresponds to a correlation length of 40 nm, which is also not able to represent the observed strong increase of backscattering for higher group indices shown in Fig. 4.

Fig. 4
Fig. 4

Loss vs. group index for different waveguide designs. The losses were extracted from transmission measurements of waveguides ranging between 180 um and 2000 um in length. a) Waveguide designed to exhibit a constant group index of ng≈38 over a Δλ≈8nm wavelength range (s 1 = −48nm, s 2 = 16nm) [16]. The green dashed curve is the best fit according to Eq. (2) with losses assessed point by point, while the red solid curve assumes a coherence length equal to the entire hole.b) Waveguide designed to have a constant group index of ng≈27 over a Δλ≈10nm wavelength range (s 1 = 52nm, s 2 = 0nm). c) Standard W1 waveguide (s 1 = s 2 = 0nm). Identical values of c 1 and c 2 (2cm−1 and 110cm−1 respectively) were used for all three waveguides.

Fig. 5
Fig. 5

a) Transmitted and reflected power directly measured through a dispersion engineered waveguide of 180µm length. The transmission signal is normalised to a PhC waveguide in the fast light regime, thus accounting for the insertion loss. b) The loss-measurement from Fig. 4 (a), plotted against wavelength is included for comparison. The black dotted line corresponds to ng≈38

Fig. 6
Fig. 6

a) Scanning near field optical micrograph of the amplitude of the electric field. The figure is a montage of scans along the same waveguide taken at different wavelengths. No measurements were taken in the black region between 1555nm and 1557.5nm b) Corresponding experimentally-measured group index curve c) Calculated loss curve clearly highlighting the difference between anticrossing and bandedge slow light. Significantly, anticrossing slow light at point B achieves significantly higher group indices with lower losses than bandedge slow light at point D.

Fig. 7
Fig. 7

a) Calculated loss curve for s 1 = −0.10a, s 2 = 0.05a and r = 0.286a. The curve shows that the propagation loss can be kept linear with respect to ng for group indices in excess of 50. b) Calculated loss per unit time for a structure with s 1 = −0.10a, s 2 = 0.08a, r = 0.286a and r 2 = 0.240a highlighting that the loss per unit time can be reduced further (20dB/ns). Where s 1 and s 2 are the lateral shifts of the 1st and 2nd row respectively and r 2 is the radius of the second row, following [32].

Equations (5)

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α = c 1 ' n g + c 2 ' n g 2 .
α = c 1 γ n g + c 2 ρ n g 2 .
ρ = n | L c E T . E T +   ( ε 1 ε 2 ) -1 D N . D N d r | 2 ,
γ = n | L c E T + ( ε 1 ) 1 D N d r | 2 ,
ρ = | H b E T . E T * + ( ε 1 ε 2 ) 1 D N . D N * d r | 2 = | H b | E T | 2 + ( ε 1 ε 2 ) 1 | D N | 2 d r | 2 ,

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