Abstract

We develop an analytical approach to theoretically investigate light speed propagation near the band edge of a coupled cavity waveguide in the presence of residual disorder. This approach that is based on a mean field theory allows us to define the domains of validity of the group velocity and the energy transport velocity concepts as well as a guideline to minimize the role of the residual disorder. Inspired by an analogy with the theory of multiple scattering of classical wave, we derive an analytical formula for the energy transport velocity in periodic photonic structures. Whereas the group velocity diverges near the band edge in the presence of any amount of residual disorder, we show that the energy transport velocity mainly follows the ideal group velocity of the unperturbed structure except for very strong disturbances out of the scope of the presented model.

© 2010 Optical Society of America

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    [Crossref]
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  4. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
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  10. J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  22. J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
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  23. J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications,” Phys. Rep. 195, 127–293 (1990).
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  24. E. N. Economou, Green’s Functions in Quantum Physics, 2nd ed. (Springer-Verlag, 1979).
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    [Crossref]
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    [Crossref]
  29. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, 1995).
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    [Crossref]
  31. K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
    [Crossref] [PubMed]
  32. P. E. Wolf and G. Maret, “Weak localization and coherent backscattering of photons in disordered media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [Crossref] [PubMed]
  33. Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
    [Crossref]
  34. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  35. S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
    [Crossref]
  36. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. 1 and 2.
  37. G. Schwiete and A. M. Finkel’stein, “Non linear wave-packet dynamics in a disordered medium,” Phys. Rev. Lett. 104, 103904 (2010).
    [Crossref] [PubMed]
  38. O. Richoux, C. Depollier, and J. Hardy, “Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice,” Phys. Rev. E 73, 026611 (2006).
    [Crossref]
  39. L. Fontanesi, M. Wouters, and V. Savona, “Superfluid to Bose-glass transition in 1D weakly interacting Bose gas,” Phys. Rev. Lett. 103, 030403 (2009).
    [Crossref] [PubMed]
  40. F. K. Kneubühl, in Theories on Distributed Feedback Laser, Vol. 14 of Laser Science and Technology, V.S.Letokhov, C.V.Shank, Y.R.Shen, and H.Walther, eds. (Hardwood Academic, 1993), p. 18.

2010 (1)

G. Schwiete and A. M. Finkel’stein, “Non linear wave-packet dynamics in a disordered medium,” Phys. Rev. Lett. 104, 103904 (2010).
[Crossref] [PubMed]

2009 (9)

L. Fontanesi, M. Wouters, and V. Savona, “Superfluid to Bose-glass transition in 1D weakly interacting Bose gas,” Phys. Rev. Lett. 103, 030403 (2009).
[Crossref] [PubMed]

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, “Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides,” Opt. Lett. 34, 359–361 (2009).
[Crossref] [PubMed]

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

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

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

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

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

2008 (4)

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

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

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

2007 (2)

2006 (1)

O. Richoux, C. Depollier, and J. Hardy, “Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice,” Phys. Rev. E 73, 026611 (2006).
[Crossref]

2005 (1)

2000 (1)

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[Crossref] [PubMed]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

1996 (1)

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

1992 (1)

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[Crossref]

1991 (1)

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[Crossref]

1990 (2)

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications,” Phys. Rep. 195, 127–293 (1990).
[Crossref]

1987 (1)

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

1985 (1)

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

1982 (1)

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

1970 (1)

C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[Crossref]

Akkermans, E.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge U. Press, 2006).

Alfano, R. R.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Baba, T.

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

Baets, R.

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Bogaerts, W.

Bohm, D.

D. Bohm, Quantum Theory (Prentice-Hall, 1966).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Bouchaud, J. -P.

J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications,” Phys. Rep. 195, 127–293 (1990).
[Crossref]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Chabanov, A. A.

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

Cheung, S. K.

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

Chu, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

Combrié, S.

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

De Rossi, A.

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

Depollier, C.

O. Richoux, C. Depollier, and J. Hardy, “Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice,” Phys. Rev. E 73, 026611 (2006).
[Crossref]

Dumon, P.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Economou, E. N.

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

E. N. Economou, Green’s Functions in Quantum Physics, 2nd ed. (Springer-Verlag, 1979).

Finkel’stein, A. M.

G. Schwiete and A. M. Finkel’stein, “Non linear wave-packet dynamics in a disordered medium,” Phys. Rev. Lett. 104, 103904 (2010).
[Crossref] [PubMed]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Fontanesi, L.

L. Fontanesi, M. Wouters, and V. Savona, “Superfluid to Bose-glass transition in 1D weakly interacting Bose gas,” Phys. Rev. Lett. 103, 030403 (2009).
[Crossref] [PubMed]

Frish, U.

U. Frish, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A.T.Bharucha-Reid, ed. (Academic, 1968), Vol. 1, pp. 75–198.

Gabet, R.

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

Garrett, C. G. B.

C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[Crossref]

Genack, A. Z.

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Georges, A.

J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications,” Phys. Rep. 195, 127–293 (1990).
[Crossref]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Glasgow, S. A.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[Crossref] [PubMed]

Hardy, J.

O. Richoux, C. Depollier, and J. Hardy, “Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice,” Phys. Rev. E 73, 026611 (2006).
[Crossref]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Houdré, R.

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, “Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides,” Opt. Lett. 34, 359–361 (2009).
[Crossref] [PubMed]

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

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

Hughes, S.

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

Hugonin, J. P.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. 1 and 2.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Jágerská, J.

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, “Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides,” Opt. Lett. 34, 359–361 (2009).
[Crossref] [PubMed]

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

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

Jaouën, Y.

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

John, S.

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
[Crossref]

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

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Khurgin, J. B.

Kneubühl, F. K.

F. K. Kneubühl, in Theories on Distributed Feedback Laser, Vol. 14 of Laser Science and Technology, V.S.Letokhov, C.V.Shank, Y.R.Shen, and H.Walther, eds. (Hardwood Academic, 1993), p. 18.

Koschny, Th.

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Kotlyar, M. V.

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

Krauss, T. F.

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[Crossref]

Kuramochi, E.

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

Lagendijk, A.

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

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[Crossref]

Lalanne, P.

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

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Le Thomas, N.

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

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, “Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides,” Opt. Lett. 34, 359–361 (2009).
[Crossref] [PubMed]

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

Liu, F.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Maret, G.

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

Mazoyer, S.

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

McCumber, D. E.

C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[Crossref]

Montambaux, G.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge U. Press, 2006).

Mookherjea, S.

Nieuwenhuizen, T. M.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Notomi, M.

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

Oh, A.

Patterson, M.

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

Peatross, J.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[Crossref] [PubMed]

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Richoux, O.

O. Richoux, C. Depollier, and J. Hardy, “Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice,” Phys. Rev. E 73, 026611 (2006).
[Crossref]

Savona, V.

L. Fontanesi, M. Wouters, and V. Savona, “Superfluid to Bose-glass transition in 1D weakly interacting Bose gas,” Phys. Rev. Lett. 103, 030403 (2009).
[Crossref] [PubMed]

Schwiete, G.

G. Schwiete and A. M. Finkel’stein, “Non linear wave-packet dynamics in a disordered medium,” Phys. Rev. Lett. 104, 103904 (2010).
[Crossref] [PubMed]

Sheng, P.

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

Soukoulis, C. M.

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Tanabe, T.

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

Tassin, P.

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Tip, A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[Crossref]

Tran, N. -V.-Quynh

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

van Albada, M. P.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[Crossref]

van Rossum, M. C. W.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

van Tiggelen, B. A.

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

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[Crossref]

Wang, Y.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Ware, M.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[Crossref] [PubMed]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wolf, P. E.

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

Wong, C. H.

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

Wong, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

Wouters, M.

L. Fontanesi, M. Wouters, and V. Savona, “Superfluid to Bose-glass transition in 1D weakly interacting Bose gas,” Phys. Rev. Lett. 103, 030403 (2009).
[Crossref] [PubMed]

Yoo, K. M.

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

Zabelin, V.

J. Jágerská, N. Le Thomas, V. Zabelin, R. Houdré, W. Bogaerts, P. Dumon, and R. Baets, “Experimental observation of slow mode dispersion in photonic crystal coupled-cavity waveguides,” Opt. Lett. 34, 359–361 (2009).
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N. Le Thomas, H. Zhang, J. Jágerská, V. Zabelin, and R. Houdré, “Light transport regimes in slow light photonic crystal waveguides,” Phys. Rev. B 80, 125332 (2009).
[Crossref]

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

Zhang, H.

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

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

Zhang, L.

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Zhang, Z. Q.

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

Appl. Phys. Lett. (1)

J. Jágerská, H. Zhang, N. Le Thomas, and R. Houdré, “Radiation loss of photonic crystal coupled-cavity waveguides,” Appl. Phys. Lett. 95, 111105 (2009).
[Crossref]

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

J. Phys. D (1)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[Crossref]

Nat. Photonics (2)

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

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

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Nature Mater. (1)

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nature Mater. 8, 758–762 (2009).
[Crossref]

Opt. Lett. (2)

Phys. Rep. (2)

J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications,” Phys. Rep. 195, 127–293 (1990).
[Crossref]

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

Phys. Rev. A (1)

C. G. B. Garrett and D. E. McCumber, “Propagation of a Gaussian light pulse through an anomalous dispersion medium,” Phys. Rev. A 1, 305–313 (1970).
[Crossref]

Phys. Rev. B (4)

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

N. Le Thomas, V. Zabelin, R. Houdré, M. V. Kotlyar, and T. F. Krauss, “Influence of residual disorder on the anticrossing of Bloch modes probed in k space,” Phys. Rev. B 78, 125301 (2008).
[Crossref]

Z. Q. Zhang, A. A. Chabanov, S. K. Cheung, C. H. Wong, and A. Z. Genack, “Dynamics of localized waves: Pulsed microwave transmissions in quasi-one-dimensional media,” Phys. Rev. B 79, 144203 (2009).
[Crossref]

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, and A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[Crossref]

Phys. Rev. E (1)

O. Richoux, C. Depollier, and J. Hardy, “Propagation of mechanical waves in a one-dimensional nonlinear disordered lattice,” Phys. Rev. E 73, 026611 (2006).
[Crossref]

Phys. Rev. Lett. (11)

L. Fontanesi, M. Wouters, and V. Savona, “Superfluid to Bose-glass transition in 1D weakly interacting Bose gas,” Phys. Rev. Lett. 103, 030403 (2009).
[Crossref] [PubMed]

K. M. Yoo, F. Liu, and R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[Crossref] [PubMed]

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

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

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[Crossref]

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370–2373 (2000).
[Crossref] [PubMed]

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

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

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

P. Tassin, L. Zhang, Th. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009).
[Crossref] [PubMed]

G. Schwiete and A. M. Finkel’stein, “Non linear wave-packet dynamics in a disordered medium,” Phys. Rev. Lett. 104, 103904 (2010).
[Crossref] [PubMed]

Phys. Today (1)

S. John, “Localization of light,” Phys. Today 44(5), 32–40 (1991).
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Rev. Mod. Phys. (1)

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

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

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge U. Press, 2006).

E. N. Economou, Green’s Functions in Quantum Physics, 2nd ed. (Springer-Verlag, 1979).

U. Frish, “Wave propagation in random media,” in Probabilistic Methods in Applied Mathematics, A.T.Bharucha-Reid, ed. (Academic, 1968), Vol. 1, pp. 75–198.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vols. 1 and 2.

F. K. Kneubühl, in Theories on Distributed Feedback Laser, Vol. 14 of Laser Science and Technology, V.S.Letokhov, C.V.Shank, Y.R.Shen, and H.Walther, eds. (Hardwood Academic, 1993), p. 18.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

D. Bohm, Quantum Theory (Prentice-Hall, 1966).

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

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Figures (4)

Fig. 1
Fig. 1

Dispersion curves of a coupled cavity structure subject to residual disorder for (a) the real part of the wave vector within the positive part of the first Brillouin zone and (b) the imaginary part of the wave vector. Inset: Dispersion curve over the entire first Brillouin zone. The α parameter quantifies the amount of disorder, and x is the normalized band frequency (see text). Λ is the lattice constant of the coupled cavity structure. u m and Δ u : bandwidth and frequency at the middle of the band, respectively.

Fig. 2
Fig. 2

Variations of the group index n g (top) and of the group velocity v g (bottom) of a wave propagating in a coupled cavity structure according to the normalized band frequency x for different amounts of residual disorder (c: speed of light). The group velocity and the group index are normalized with respect to the bandwidth Δ u . Dashed line: group velocity resulting from a second order approximation of the ideal dispersion curve.

Fig. 3
Fig. 3

Variation of the energy transport velocity v E of a wave propagating in a coupled cavity structure near the band edge for different amounts of residual disorder quantified by the α parameter (see text).

Fig. 4
Fig. 4

Left: Universal dispersion curve of a CCW near the band edge without ( α = 0 , dashed-dotted line) and with ( α = 0.01 , plain line) disorder. Right: Corresponding group velocity v g and energy transport velocity v E (Λ, c, Δ u : lattice constant, speed of light, and bandwidth, respectively). Gray shadow: inhomogeneous linewidth broadening at half-maximum. Inset: Dispersion curve over the entire first Brillouin zone.

Equations (18)

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G 0 ( r , r ; k 0 2 ) = 1 T ρ 1 | l m | ρ 1 ρ 2 = 1 T ( x x 2 1 ) | l m | 2 x 2 1 ,
G ̂ ( k ; k 0 2 ) = 1 [ G ̂ ( k ; k 0 2 ) ] 1 Σ ̂ ( k ; k 0 2 ) ,
G ̂ 0 ( k ; k 0 2 ) = F T { G 0 ( | r r | ; k 0 2 ) } = 1 k 0 2 ω m 2 c 2 + 2 T   cos ( k Λ ) ,
Σ ̂ ( k ; k 0 2 ) = ϵ 2 k 0 4 F T { G ( 0 ) ( | r r | ) Γ μ ( | r r | ) } .
Σ ̂ ( k ; k 0 2 ) = ϵ 2 T k 0 4 ρ 2 ρ 1 1 Λ 2 ( 1 / σ i ( θ 1 / Λ ) ) ( 1 / σ i ( θ 1 / Λ ) ) 2 + k 2     for   | x | < 1 ,
Σ ̂ ( k ; k 0 2 ) = ϵ 2 T k 0 4 ρ 2 ρ 1 1 Λ 2 ( 1 / σ + ln | ρ 1 | / Λ i ( θ 1 / Λ ) ) ( 1 / σ + ln | ρ 1 | / Λ i ( θ 1 / Λ ) ) 2 + k 2     for   | x | > 1 ,
Σ ̂ ( k ; k 0 2 ) = Σ ̂ ( k 0 2 ) = ϵ 2 T σ Λ 2 k 0 4 ρ 2 ρ 1 = ϵ 2 T σ Λ k 0 4 x 2 1     for   all   x .
x cos ( k Λ ) α x 2 1 = 0 ,
y = 1 2 [ x 2 + 1 + α 1 x 2 + ( x 2 + 1 + α 1 x 2 ) 4 x 2 ] .
G ̂ ( ω ; k ) = 1 ( ω / c ) 2 k 2 Σ ̂ ( ω ) ,
G ̂ ( ω ; k ) = 1 ( ω / c ) 2 ( ω m / c ) 2 2 T   cos ( k Λ ) Σ ̂ ( ω ) ,
G ̂ ( ω ; k ) 1 ( ω / c ) 2 k 2 ( T Λ 2 ) ( ω m / c ) 2 + 2 T Σ ̂ ( ω ) .
M ( q , Ω ) = n t ¯ ( ω ) t ( ω + ) G ( p + , ω + ) G ¯ ( p , ω ) d p ( 2 π ) d ,
M ( q , Ω ) = 1 1 d l 2 q 2 i Ω τ ,
τ d w = Im ( 1 t d t d ω ) + 2 π k e t ¯ t Re ( d t d ω ) .
n t ( ω ) = ( ω m / c ) 2 2 T α x 2 1 .
τ d w τ s c = c v g 0 2 x ( 1 x 2 ) α u m Δ u u m 2 ( 1 x 2 ) + α Δ u 2 .
v E = v g 0 1 + v g 0 c τ d w τ s c = v g 0 1 1 + 2 x ( 1 x 2 ) α u m Δ u u m 2 ( 1 x 2 ) + α Δ u 2 .

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