Abstract

We propose a stabilization method to numerically calculate the dispersion relations and quality factors of optically confined finite structures. For the coupled resonator optical waveguide (CROW) made in a photonic-crystal slab (PCS) used as an example, the dispersion curve is normally not well defined due to the appearance of discontinuities, which do not occur in a two-dimensional CROW with infinite slab height. Therefore, there is less effort devoted to the calculation of quasi dispersion curves of the CROW in a slab. The dispersion relation of the PCS CROW can only be obtained by theoretical fitting to the experimental data under the tight-binding approximation. Here, we demonstrate the use of a stabilization method to calculate the quasi dispersion relation of a PCS CROW accurately. From the stabilization graph, we can calculate the quality factor for an eigenfrequency and properly choose the size of the simulation cell to avoid coupling the CROW modes with the unconfined modes and to accurately calculate the dispersion curve of the PCS CROW using the plane-wave expansion method. The proposed method and results not only provide important information for designing practical photonic devices such as slow-light optical waveguides and nonlinear photonic devices for the PCS CROWs but also can be applied to compute the quality factors and resonance frequencies of microcavities or nanocavities.

© 2012 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission on solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef]
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    [CrossRef]
  3. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
    [CrossRef]
  4. D. N. Christodoulides and N. K. Efremidis, “Discrete temporal solitons along a chain of nonlinear coupled microcavities embedded in photonic crystals,” Opt. Lett. 27, 568–570 (2002).
    [CrossRef]
  5. C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
    [CrossRef]
  6. K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
    [CrossRef]
  7. M. Bayindir and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247–R2250 (2000).
    [CrossRef]
  8. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
    [CrossRef]
  9. M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa, F. N. A. Xia, D. K. Gifford, and S. Mookherjea, “Waveguide dispersion effects in silicon-on-insulator coupled-resonator optical waveguides,” Opt. Lett. 35, 3030–3032 (2010).
    [CrossRef]
  10. 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, 104004 (2010).
    [CrossRef]
  11. A. Talneau, “Slow light modes for optical delay lines: 2D photonic crystal-based design structures, performances and challenges,” J. Opt. 12, 104005 (2010).
    [CrossRef]
  12. C. H. Huang, Y. H. Lai, S. C. Cheng, and W. F. Hsieh, “Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides,” Opt. Express 17, 1299–1307 (2009).
    [CrossRef]
  13. C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
    [CrossRef]
  14. D. P. Fussell and M. M. Dignam, “Quantum-dot photon dynamics in a coupled-cavity waveguide: observing band-edge quantum optics,” Phys. Rev. A 76, 053801 (2007).
    [CrossRef]
  15. M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photon. 2, 741–747 (2008).
    [CrossRef]
  16. C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
    [CrossRef]
  17. H. C. Liu and A. Yariv, “Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs),” Opt. Express 19, 17653–17668 (2011).
    [CrossRef]
  18. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
    [CrossRef]
  19. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  20. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).
  21. S. G. Johnson, and J. D. Joannopoulos, Photonic Crystals: the Road from Theory to Practice (Kluwer Academic, 2002), pp. 99–112.
  22. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [CrossRef]
  23. V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993).
    [CrossRef]
  24. D. M. T. Kuo and Y. C. Chang, “Electron tunneling rate in quantum dots under a uniform electric field,” Phys. Rev. B 61, 11051–11056 (2000).
    [CrossRef]
  25. E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
    [CrossRef]
  26. C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
    [CrossRef]

2011 (3)

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
[CrossRef]

H. C. Liu and A. Yariv, “Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs),” Opt. Express 19, 17653–17668 (2011).
[CrossRef]

2010 (5)

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
[CrossRef]

M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa, F. N. A. Xia, D. K. Gifford, and S. Mookherjea, “Waveguide dispersion effects in silicon-on-insulator coupled-resonator optical waveguides,” Opt. Lett. 35, 3030–3032 (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, 104004 (2010).
[CrossRef]

A. Talneau, “Slow light modes for optical delay lines: 2D photonic crystal-based design structures, performances and challenges,” J. Opt. 12, 104005 (2010).
[CrossRef]

2009 (2)

C. H. Huang, Y. H. Lai, S. C. Cheng, and W. F. Hsieh, “Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides,” Opt. Express 17, 1299–1307 (2009).
[CrossRef]

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

2008 (1)

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

2007 (1)

D. P. Fussell and M. M. Dignam, “Quantum-dot photon dynamics in a coupled-cavity waveguide: observing band-edge quantum optics,” Phys. Rev. A 76, 053801 (2007).
[CrossRef]

2004 (1)

2002 (2)

2001 (1)

2000 (4)

D. M. T. Kuo and Y. C. Chang, “Electron tunneling rate in quantum dots under a uniform electric field,” Phys. Rev. B 61, 11051–11056 (2000).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

M. Bayindir and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247–R2250 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

1993 (1)

V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission on solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Agger, C.

C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
[CrossRef]

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Arora, W.

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

Assefa, S.

Barbastathis, G.

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

Bayindir, M.

M. Bayindir and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247–R2250 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Beggs, D. M.

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, 104004 (2010).
[CrossRef]

Bur, J.

Chang, Y. C.

D. M. T. Kuo and Y. C. Chang, “Electron tunneling rate in quantum dots under a uniform electric field,” Phys. Rev. B 61, 11051–11056 (2000).
[CrossRef]

Cheng, S. C.

C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
[CrossRef]

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

C. H. Huang, Y. H. Lai, S. C. Cheng, and W. F. Hsieh, “Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides,” Opt. Express 17, 1299–1307 (2009).
[CrossRef]

Chow, E.

S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, “Low-loss, wide-angle Y splitter ∼1.6  μm wavelengths built with a two-dimensional photonic crystal,” Opt. Lett. 27, 1400–1402 (2002).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Christodoulides, D. N.

Cooper, M. L.

Dignam, M. M.

D. P. Fussell and M. M. Dignam, “Quantum-dot photon dynamics in a coupled-cavity waveguide: observing band-edge quantum optics,” Phys. Rev. A 76, 053801 (2007).
[CrossRef]

Dong, B. Q.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Efremidis, N. K.

Fan, S. H.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Fussell, D. P.

D. P. Fussell and M. M. Dignam, “Quantum-dot photon dynamics in a coupled-cavity waveguide: observing band-edge quantum optics,” Phys. Rev. A 76, 053801 (2007).
[CrossRef]

Gifford, D. K.

Green, W. M. J.

Gregersen, N.

C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
[CrossRef]

Gupta, G.

Hong, J.

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

Hou, H.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Hsieh, W. F.

C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
[CrossRef]

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

C. H. Huang, Y. H. Lai, S. C. Cheng, and W. F. Hsieh, “Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides,” Opt. Express 17, 1299–1307 (2009).
[CrossRef]

Hu, X. H.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Huang, C. H.

C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
[CrossRef]

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

C. H. Huang, Y. H. Lai, S. C. Cheng, and W. F. Hsieh, “Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides,” Opt. Express 17, 1299–1307 (2009).
[CrossRef]

Huang, Y. Y.

Joannopoulos, J. D.

S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, “Low-loss, wide-angle Y splitter ∼1.6  μm wavelengths built with a two-dimensional photonic crystal,” Opt. Lett. 27, 1400–1402 (2002).
[CrossRef]

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

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).

S. G. Johnson, and J. D. Joannopoulos, Photonic Crystals: the Road from Theory to Practice (Kluwer Academic, 2002), pp. 99–112.

Johnson, S. G.

S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, “Low-loss, wide-angle Y splitter ∼1.6  μm wavelengths built with a two-dimensional photonic crystal,” Opt. Lett. 27, 1400–1402 (2002).
[CrossRef]

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

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).

S. G. Johnson, and J. D. Joannopoulos, Photonic Crystals: the Road from Theory to Practice (Kluwer Academic, 2002), pp. 99–112.

Kolodziejski, L. A.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

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, 104004 (2010).
[CrossRef]

Kuo, D. M. T.

D. M. T. Kuo and Y. C. Chang, “Electron tunneling rate in quantum dots under a uniform electric field,” Phys. Rev. B 61, 11051–11056 (2000).
[CrossRef]

Kuramochi, E.

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

Lai, Y. H.

Lee, P. Y.

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

Lee, R. K.

Lin, S. Y.

S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, “Low-loss, wide-angle Y splitter ∼1.6  μm wavelengths built with a two-dimensional photonic crystal,” Opt. Lett. 27, 1400–1402 (2002).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Liu, H. C.

Liu, X. H.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Mandelshtam, V. A.

V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).

Melloni, 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, 104004 (2010).
[CrossRef]

Mookherjea, S.

Mork, J.

C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
[CrossRef]

Notomi, M.

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

O’Faolain, L.

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, 104004 (2010).
[CrossRef]

Ouyang, C. F.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Ozbay, E.

M. Bayindir and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247–R2250 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Paloczi, G. T.

Poon, J. K. S.

Ravuri, T. R.

V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993).
[CrossRef]

Scherer, A.

Scheuer, J.

Schneider, M. A.

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, 104004 (2010).
[CrossRef]

Skovgard, T. S.

C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
[CrossRef]

Takahashi, S.

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

Talneau, A.

A. Talneau, “Slow light modes for optical delay lines: 2D photonic crystal-based design structures, performances and challenges,” J. Opt. 12, 104005 (2010).
[CrossRef]

Tanabe, T.

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

Taylor, H. S.

V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

Tian, K. H.

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Villeneuve, P. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Wendt, J. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

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, 104004 (2010).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).

Wu, J. N.

C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
[CrossRef]

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

Xia, F. N. A.

Xiong, Z. Q.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission on solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Yariv, A.

Zhao, F. Y.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Zi, J.

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

Zubrzycki, W.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Comput. Phys. Commun. (1)

C. H. Huang, J. N. Wu, S. C. Cheng, and W. F. Hsieh, “The evolution of solitons in coupled resonator optical waveguides and photonic-crystal waveguides,” Comput. Phys. Commun. 182, 232–236 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Agger, T. S. Skovgard, N. Gregersen, and J. Mork, “Modeling of mode-locked coupled-resonator optical waveguide lasers,” IEEE J. Quantum Electron. 46, 1804–1812 (2010).
[CrossRef]

J. Opt. (2)

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, 104004 (2010).
[CrossRef]

A. Talneau, “Slow light modes for optical delay lines: 2D photonic crystal-based design structures, performances and challenges,” J. Opt. 12, 104005 (2010).
[CrossRef]

J. Phys. D (1)

C. H. Huang, J. N. Wu, P. Y. Lee, W. F. Hsieh, and S. C. Cheng, “The properties and design concepts of photonic directional couplers made of photonic crystal slabs,” J. Phys. D 43, 465103 (2010).
[CrossRef]

Nat. Photon. (1)

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

Nature (1)

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. A (2)

C. F. Ouyang, Z. Q. Xiong, F. Y. Zhao, B. Q. Dong, X. H. Hu, X. H. Liu, and J. Zi, “Slow light with low group-velocity dispersion at the edge of photonic graphene,” Phys. Rev. A 84, 015801 (2011).
[CrossRef]

D. P. Fussell and M. M. Dignam, “Quantum-dot photon dynamics in a coupled-cavity waveguide: observing band-edge quantum optics,” Phys. Rev. A 76, 053801 (2007).
[CrossRef]

Phys. Rev. B (4)

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

K. H. Tian, W. Arora, S. Takahashi, J. Hong, and G. Barbastathis, “Dynamic group velocity control in a mechanically tunable photonic-crystal coupled-resonator optical waveguide,” Phys. Rev. B 80, 134305 (2009).
[CrossRef]

M. Bayindir and E. Ozbay, “Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal,” Phys. Rev. B 62, R2247–R2250 (2000).
[CrossRef]

D. M. T. Kuo and Y. C. Chang, “Electron tunneling rate in quantum dots under a uniform electric field,” Phys. Rev. B 61, 11051–11056 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission on solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

V. A. Mandelshtam, T. R. Ravuri, and H. S. Taylor, “Calculation of the density of resonance states using the stabilization method,” Phys. Rev. Lett. 70, 1932–1935 (1993).
[CrossRef]

Other (2)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Modeling the Flow of Light (Princeton University, 2008).

S. G. Johnson, and J. D. Joannopoulos, Photonic Crystals: the Road from Theory to Practice (Kluwer Academic, 2002), pp. 99–112.

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Figures (4)

Fig. 1.
Fig. 1.

Structures of the coupled resonator optical waveguide (CROW) made of photonic-crystal slabs with (a) dielectric rods and (b) air holes. a and aL are the lattice constants of photonic crystals and CROWs, respectively.

Fig. 2.
Fig. 2.

Dispersion curves of a CROW made of (a) a 2D dielectric-rod photonic crystal and (b) a photonic-crystal slab (PCS) calculated using a super cell of size 2a×9a×4a. The insets in (b) illustrate the intensity distribution of the electric field.

Fig. 3.
Fig. 3.

(a) Dispersion relation of the CROW at kx=0 using a simulation cell 412a in the z direction and (b) its resonant density. The flat curves in (a) are contributed by one cavity-guided mode (CGM) with f around 0.389c/a and several slab-confined modes (SCMs) in the allowed bands. The curves vary with simulation cell contributions from the unconfined modes (UCMs). (c) The eigenfrequency and spectral width Δf at each wave vector.

Fig. 4.
Fig. 4.

Comparison of dispersion curves of 2D CROWs and PCS CROWs made of either dielectric rods or air holes in a dielectric having a dielectric constant of 12. (a) Dielectric-rod CROWs with rod radius of 0.2a in the PC and a defect rod radius rd ranging from 0.06 to 0.1a. The slab height for the PCS is 2a; (b) Air-hole CROWs with a hole radius of 0.3a in the triangular-lattice PC and a defect hole radius rd ranging from 0.46 to 0.5a. The slab height for the PCS is a; (c) Same PC as in (b) with a radius of defect holes rd ranging from 0 to 0.1a. The inset in (b) shows a comparison of group velocities of the two structures with rd=0.5a. The inset in (c) illustrates the intensity distribution of an EM wave for rd=0.1a.

Equations (4)

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

ρz(f)=1Δzz0Δz/2z0+Δz/2iδ(ffi(z))dz=1Δzi|dfi(z)dz|fi(z0)=f1.
dzδ(ffi(z))=|dfi(z)dz|fi(z0)=f1,
ρz(f)=ρzP(f)+ρQ(f),
ρQ(f)Δf/2(ff0)2+Δf2/4,

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