Abstract

We present a general recipe for tailoring flat dispersion curves in photonic crystal waveguides. Our approach is based on the critical coupling criterion that equates the coupling strength of guided modes with their frequency spacing and results in a significant number of the modes lying collectively in the slow-light regime. We first describe the critical coupling scheme in photonic crystal waveguides using a simple coupled mode theory model. We also determine that canonical photonic crystal waveguides natively correspond to strongly coupled modes. Based on these analyses, our design recipe is as follows: Tune the profile of the first Fourier component of the waveguide periodic dielectric boundary to lower the coupling strength of the guided modes down to its critical value. We check that this generalized tuning may be accomplished by adjusting any desired optogeometric parameter such as hole size, position, index etc. We explore the validity of this general approach down to the narrow two-missing rows waveguides. The interest of this method is to circumvent most of the common trial-and-error procedures for flatband engineering.

© 2009 Optical Society of America

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  1. H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef] [PubMed]
  7. Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  23. H. Benisty, "Modal analysis of optical guides with two-dimensional photonic band-gap boundaries," J. Appl. Phys. 79, 7483-7492 (1996).
    [CrossRef]
  24. M. L. Cohen and T. K. Bergstresser, "Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures," Phys. Rev. 141, 556 (1966).
  25. O. Khayam, H. Benisty, and C. Cambournac, "Experimental observation of minigap stripes in periodically corrugated broad photonic wires," Phys. Rev. B 78, 153107 (2008).
    [CrossRef]
  26. W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 (2002).
    [CrossRef]
  27. Y. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 (2004).
    [CrossRef]
  28. S. G. Johnson, M. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. Joannopoulos, "Roughness losses and volume-current methods in photonic-crystal waveguides," Appl. Phys. B 81, 283-293 (2005).
    [CrossRef]
  29. C. Vassallo, "About coupled-mode theories for dielectric waveguides," IEEE J. Lightwave Technol. 6, 294-303 (1988).
    [CrossRef]
  30. D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85, 1101-1103 (2004).
    [CrossRef]
  31. B. M. Möller, U. Woggon, and M. V. Artemyev, "Band Formation in Coupled-Resonator Slow-Wave Structures," Opt. Express 15, 17362-17370 (2007).
    [CrossRef] [PubMed]
  32. M. Notomi, E. Kuramochi, and T. Takasumi, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
    [CrossRef]
  33. 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]
  34. D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5976 (2005).
    [CrossRef] [PubMed]
  35. H. Benisty, "Graphene nanoribbons: Photonic crystal waveguide analogy and minigap stripes," Phys. Rev. B 79, 155409 (2009).
    [CrossRef]

2009 (4)

2008 (6)

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, 6227-6232 (2008).
[CrossRef] [PubMed]

J. Ma and C. Jiang, "Demonstration of Ultraslow Modes in Asymmetric Line-Defect Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 20, 1237-1239 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Takasumi, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465 (2008).
[CrossRef]

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

O. Khayam, H. Benisty, and C. Cambournac, "Experimental observation of minigap stripes in periodically corrugated broad photonic wires," Phys. Rev. B 78, 153107 (2008).
[CrossRef]

2007 (5)

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

S. Kubo, D. Mori, and T. Baba, "Low-group-velocity and low-dispersion slow light in photonic crystal waveguides," Opt. Lett. 32, 2981-2983 (2007).
[CrossRef] [PubMed]

B. M. Möller, U. Woggon, and M. V. Artemyev, "Band Formation in Coupled-Resonator Slow-Wave Structures," Opt. Express 15, 17362-17370 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (6)

D. Englund, I. Fushman, and J. Vuckovic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5976 (2005).
[CrossRef] [PubMed]

M. Povinelli, S. Johnson, and J. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145 (2005).
[CrossRef] [PubMed]

D. Mori and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Express 13, 9398-9408 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

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

2004 (4)

Y. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 (2004).
[CrossRef]

D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85, 1101-1103 (2004).
[CrossRef]

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, "Light Localizations in Photonic Crystal Line Defect Waveguides," IEEE J. Sel. Top. Quantum. Electron. 10, 484-491 (2004).
[CrossRef]

2002 (1)

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

2001 (1)

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

1997 (1)

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

1996 (1)

H. Benisty, "Modal analysis of optical guides with two-dimensional photonic band-gap boundaries," J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

1988 (1)

C. Vassallo, "About coupled-mode theories for dielectric waveguides," IEEE J. Lightwave Technol. 6, 294-303 (1988).
[CrossRef]

1973 (1)

A. Yariv, "Coupled mode theory for guided wave optics," J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

1966 (1)

M. L. Cohen and T. K. Bergstresser, "Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures," Phys. Rev. 141, 556 (1966).

Ahopelto, J.

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

Arpiainen, S.

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

Artemyev, M. V.

Ayre, M.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Baba, T.

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, 1072-1074 (2009).
[CrossRef] [PubMed]

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465 (2008).
[CrossRef]

S. Kubo, D. Mori, and T. Baba, "Low-group-velocity and low-dispersion slow light in photonic crystal waveguides," Opt. Lett. 32, 2981-2983 (2007).
[CrossRef] [PubMed]

D. Mori and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Express 13, 9398-9408 (2005).
[CrossRef] [PubMed]

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, "Light Localizations in Photonic Crystal Line Defect Waveguides," IEEE J. Sel. Top. Quantum. Electron. 10, 484-491 (2004).
[CrossRef]

D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85, 1101-1103 (2004).
[CrossRef]

Baets, R.

Benisty, H.

H. Benisty, "Graphene nanoribbons: Photonic crystal waveguide analogy and minigap stripes," Phys. Rev. B 79, 155409 (2009).
[CrossRef]

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

O. Khayam, H. Benisty, and C. Cambournac, "Experimental observation of minigap stripes in periodically corrugated broad photonic wires," Phys. Rev. B 78, 153107 (2008).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

H. Benisty, "Modal analysis of optical guides with two-dimensional photonic band-gap boundaries," J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

Bergstresser, T. K.

M. L. Cohen and T. K. Bergstresser, "Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures," Phys. Rev. 141, 556 (1966).

Bogaerts, W.

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]

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Borel, P. I.

Brenot, R.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Cambournac, C.

O. Khayam, H. Benisty, and C. Cambournac, "Experimental observation of minigap stripes in periodically corrugated broad photonic wires," Phys. Rev. B 78, 153107 (2008).
[CrossRef]

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Cohen, M. L.

M. L. Cohen and T. K. Bergstresser, "Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures," Phys. Rev. 141, 556 (1966).

Duan, G. H.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Dumon, P.

Ebnali-Heidari, M.

Eggleton, B. J.

Eich, M.

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Engelen, J. P.

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Englund, D.

Fage-Pedersen, J.

Fan, S.

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

Frandsen, L. H.

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

Fushman, I.

Gersen, H.

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Gomez-Iglesias, A.

Grillet, C.

Hamachi, Y.

Hamman, H. F.

Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Houdré, R.

Inoshita, K.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, "Light Localizations in Photonic Crystal Line Defect Waveguides," IEEE J. Sel. Top. Quantum. Electron. 10, 484-491 (2004).
[CrossRef]

Jacobs, S.

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

Jágerská, J.

Jiang, C.

J. Ma and C. Jiang, "Demonstration of Ultraslow Modes in Asymmetric Line-Defect Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 20, 1237-1239 (2008).
[CrossRef]

Joannopoulos, J.

M. Povinelli, S. Johnson, and J. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145 (2005).
[CrossRef] [PubMed]

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

Johnson, S.

Johnson, S. G.

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

Karalis, A.

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

Karle, T. J.

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Khayam, O.

O. Khayam, H. Benisty, and C. Cambournac, "Experimental observation of minigap stripes in periodically corrugated broad photonic wires," Phys. Rev. B 78, 153107 (2008).
[CrossRef]

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Korterik, J. P.

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

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, 6227-6232 (2008).
[CrossRef] [PubMed]

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kubo, S.

Kuipers, L.

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kuramochi, E.

M. Notomi, E. Kuramochi, and T. Takasumi, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

Kuroki, Y.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, "Light Localizations in Photonic Crystal Line Defect Waveguides," IEEE J. Sel. Top. Quantum. Electron. 10, 484-491 (2004).
[CrossRef]

Kurt, H.

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

Lau, W. T.

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

Lavrinenko, A. V.

Le Thomas, N.

Li, J.

Lipsanen, H.

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

Ma, J.

J. Ma and C. Jiang, "Demonstration of Ultraslow Modes in Asymmetric Line-Defect Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 20, 1237-1239 (2008).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Y. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 (2004).
[CrossRef]

Melo, T.

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

Moll, N.

Y. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 (2004).
[CrossRef]

Möller, B. M.

Monat, C.

Mori, D.

S. Kubo, D. Mori, and T. Baba, "Low-group-velocity and low-dispersion slow light in photonic crystal waveguides," Opt. Lett. 32, 2981-2983 (2007).
[CrossRef] [PubMed]

D. Mori and T. Baba, "Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide," Opt. Express 13, 9398-9408 (2005).
[CrossRef] [PubMed]

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, "Light Localizations in Photonic Crystal Line Defect Waveguides," IEEE J. Sel. Top. Quantum. Electron. 10, 484-491 (2004).
[CrossRef]

D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85, 1101-1103 (2004).
[CrossRef]

Mulot, M.

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

Notomi, M.

M. Notomi, E. Kuramochi, and T. Takasumi, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

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

O'Boyle, M.

Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

O'Faolain, L.

Pernice, W.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Petrov, A. Y.

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Povinelli, M.

M. Povinelli, S. Johnson, and J. Joannopoulos, "Slow-light, band-edge waveguides for tunable time delays," Opt. Express 13, 7145 (2005).
[CrossRef] [PubMed]

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

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

Säynätjoki, A.

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

Shinya, A.

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

Soljacic, M.

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

Takahashi, J.

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

Takasumi, T.

M. Notomi, E. Kuramochi, and T. Takasumi, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

van Hulst, N. F.

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Vassallo, C.

C. Vassallo, "About coupled-mode theories for dielectric waveguides," IEEE J. Lightwave Technol. 6, 294-303 (1988).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Y. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 (2004).
[CrossRef]

Vuckovic, J.

White, T. P.

Woggon, U.

Yamada, K.

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

Yariv, A.

A. Yariv, "Coupled mode theory for guided wave optics," J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

Yokoyama, I.

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

Zabelin, V.

App. Phys. Lett. (1)

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, R. Brenot, G. H. Duan, and W. Pernice, "In-plane Littrow lasing of broad photonic crystal waveguides," App. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Appl. Phys. B (1)

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

Appl. Phys. Lett. (3)

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 (2002).
[CrossRef]

D. Mori and T. Baba, "Dispersion-controlled optical group delay device by chirped photonic crystal waveguides," Appl. Phys. Lett. 85, 1101-1103 (2004).
[CrossRef]

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

IEEE J. Lightwave Technol. (1)

C. Vassallo, "About coupled-mode theories for dielectric waveguides," IEEE J. Lightwave Technol. 6, 294-303 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum. Electron. (1)

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, "Light Localizations in Photonic Crystal Line Defect Waveguides," IEEE J. Sel. Top. Quantum. Electron. 10, 484-491 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Ma and C. Jiang, "Demonstration of Ultraslow Modes in Asymmetric Line-Defect Photonic Crystal Waveguides," IEEE Photon. Technol. Lett. 20, 1237-1239 (2008).
[CrossRef]

J. Appl. Phys. (2)

Y. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 (2004).
[CrossRef]

H. Benisty, "Modal analysis of optical guides with two-dimensional photonic band-gap boundaries," J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

M. Mulot, A. Säynätjoki, S. Arpiainen, H. Lipsanen, and J. Ahopelto, "Slow light propagation in photonic crystal waveguides with ring-shaped holes," J. Opt. A: Pure Appl. Opt. 9, S415-S418 (2007).
[CrossRef]

J. Opt. Soc. B (1)

H. Kurt, H. Benisty, T. Melo, O. Khayam, and C. Cambournac, "Slow-light regime and critical coupling in highly multimode corrugated waveguides," J. Opt. Soc. B 25, C1-C14 (2008).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

J. Quantum Electron. (2)

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

A. Yariv, "Coupled mode theory for guided wave optics," J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

Nature (1)

Y. A. Vlasov, M. O'Boyle, H. F. Hamman, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Nature Photon. (2)

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Takasumi, "Large-scale arrays of ultrahigh-Q coupled nanocavities," Nature Photon. 2, 741-747 (2008).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. (1)

M. L. Cohen and T. K. Bergstresser, "Band Structures and Pseudopotential Form Factors for Fourteen Semiconductors of the Diamond and Zinc-blende Structures," Phys. Rev. 141, 556 (1966).

Phys. Rev. B (2)

O. Khayam, H. Benisty, and C. Cambournac, "Experimental observation of minigap stripes in periodically corrugated broad photonic wires," Phys. Rev. B 78, 153107 (2008).
[CrossRef]

H. Benisty, "Graphene nanoribbons: Photonic crystal waveguide analogy and minigap stripes," Phys. Rev. B 79, 155409 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

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

H. Gersen, T. J. Karle, J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, "Real-space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Other (2)

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, "Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal," Phys. Rev. B 63, 113311 (113311-113316) (2001).
[CrossRef]

H. Benisty, "Single-material coupling-tolerant semi-planar microresonator using Littrow diffraction," PNFA (2009).

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Figures (9)

Fig. 1.
Fig. 1.

Slow light mechanisms in PhC waveguide. (a) Oscillation patterns of 1. Fabry-Perot, 2. BZ-edge Littrow and 3. inside-BZ anticrossing modes and (b) their positions on a schematic dispersion diagram. (c) A flatband is formed near BZ edge by increasing the coupling strength κ, and hence the gap width Δωab, at anticrossings 2 and 3. (d) The spread Δkz of the flatband corresponds to the slow mode angular bandwidth Δθ inside the waveguide. The arrows show the resonance path of the flatband mode at BZ-edge (black arrows) and near BZ-edge (grey arrows).

Fig. 2.
Fig. 2.

Evolution of equidistant and linear bands with increase in coupling strength. The interaction region is enclosed in a lozenge (dotted lines). At critical coupling, the gap width increases to half of the FSR.

Fig. 3.
Fig. 3.

(a–c) Dispersion diagrams at different coupling coefficient values obtained from the CMT model of PhC waveguide modes. (a) κ=0 case (b) κ>0 case with parity-independent and (c) parity-dependent coupling (d) actual W7 raw dispersion diagram calculated with the PWE supercell method (only the discretization of PhC air and dielectric bands depends on the supercell size). The minigap-stripes and the necklace dispersion branches are perfectly mimicked by the CMT model.

Fig. 4.
Fig. 4.

Dispersion diagrams at critical coupling in (a) parity-dependent and (b) parity-independent schemes. The red lozenge encloses the flatband region. FSRΔ inside the lozenge is approximately 0.75 in (a) and 0.375 in (b), FSR0 being taken as unity.

Fig. 5.
Fig. 5.

Classification of PhC waveguide variants according to their coupling strength as compared to that of the uncoupled DT-PhC waveguide modes.

Fig. 6.
Fig. 6.

(a). A standard W9 ST-PhC waveguide, its first Fourier component dielectric profile and (b) its dispersion diagram. The dark triangular regions at the corners represent the light cone. (c) Evolution of the average group velocity with the change in hole size, labeled through f and through the overlap integral. The curve dips by an order of magnitude at the critical overlap value obtained from the simple Eq(5). (d) W9 ST-PhC waveguide with modified hole size and (e) its actual flattened band diagram. The flatbands are highlighted in the red lozenge, where the quantity plotted in (c) is extracted.

Fig. 7.
Fig. 7.

(a). Standard W5 ST-PhC waveguide and (b) its band diagram and light cone (dark solid regions). (c) Evolution of the average group velocity with the change in hole’s dielectric constant, again labeled also by the overlap integral. The group velocity dips close to the expected critical value ≈0.647. (d) W5 ST-PhC waveguide with modified hole dielectric and (e) Flattened band diagram at εhole=2.25. The flatbands are highlighted in the red lozenge.

Fig. 8.
Fig. 8.

(a). Standard W2 ST-PhC waveguide and (b) its band diagram with light cone (dark solid regions). (c) Evolution of the average group velocity with the shift in first row of holes labeled by parameter s (“shift”, see text). The group velocity dips near the critical overlap value. (d) W2 ST-PhC waveguide with modified hole position (e) Flattened band diagram at s=0.6. The flatbands are highlighted in the red lozenge.

Fig. 9.
Fig. 9.

Evolution of band structure of a PhC waveguide with increasing boundary perturbation; (a,c,e) Sketch of waveguides and dielectric first Fourier harmonic profile, (b,d,f) band structures highlighting the mode coupling region around the BZ edge.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

(iddz+δma)αm(z)+Σm'=0NPκmmbm(z)=0 , where {m:0mN}
(iddz+δma)αm(z)+Σm=0NPκmmαm(z)=0 , where {m:0mN}
ddzM=i C M
καb=k022kzEα(x)Eb(x)ε̂1(x)dxEα(x)Eb(x)dx=k022kzΓx=2πΛu2Γx
Γxcritical=ngFSRuu2π

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