Abstract

A theoretical model of the group velocity, dispersion parameter, and dispersion slope of coupled-cavity waveguides in photonic crystals is reported. Results arising from closed-form expressions show a good agreement with simulation results obtained by employing a plane-wave expansion method. Coupled-cavity waveguides present interesting dispersion properties that may be employed in applications such as optical signal processing, dispersion compensation, and optical delay lines.

© 2003 Optical Society of America

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Corrections

Alejandro Martı́nez, Andrés Garcı́a, Pablo Sanchis, and Javier Martı́, "Group velocity and dispersion model of coupled-cavity waveguides in photonic crystals: erratum," J. Opt. Soc. Am. A 21, 160-160 (2004)
https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-21-1-160

References

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, New Brunswick, N.J., 1995).
  4. T. F. Krauss, R. M. de la Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
    [CrossRef]
  5. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
    [CrossRef]
  6. N. Stefanou, A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
    [CrossRef]
  7. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).
  8. M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
    [CrossRef] [PubMed]
  9. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, U. Oesterle, “Miniband transmission in a photonic crystal coupled-resonator optical waveguide,” Opt. Lett. 26, 1019–1021 (2001).
    [CrossRef]
  10. V. Yannopapas, A. Modinos, N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 23501-1–235201-6 (2002).
    [CrossRef]
  11. S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express. 8, 173–190 (2001); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  12. A. Taflove, Computational Electrodynamics (Artech House, Boston, Mass., 1995).
  13. A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
    [CrossRef]
  14. V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
    [CrossRef]

2002 (1)

V. Yannopapas, A. Modinos, N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 23501-1–235201-6 (2002).
[CrossRef]

2001 (2)

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

S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdre, U. Oesterle, “Miniband transmission in a photonic crystal coupled-resonator optical waveguide,” Opt. Lett. 26, 1019–1021 (2001).
[CrossRef]

2000 (3)

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

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

1999 (1)

1998 (1)

N. Stefanou, A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

1996 (1)

T. F. Krauss, R. M. de la Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

1987 (2)

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

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

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

Astratov, V. N.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

Bayindir, M.

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

Benisty, H.

Brand, S.

T. F. Krauss, R. M. de la Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Chutinan, A.

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Culshaw, I. S.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

de la Rue, R. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

T. F. Krauss, R. M. de la Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Houdre, R.

Joannopoulos, J. D.

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

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, New Brunswick, N.J., 1995).

John, S.

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

Johnson, S. G.

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

Krauss, T.

Krauss, T. F.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

T. F. Krauss, R. M. de la Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Lee, R. K.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, New Brunswick, N.J., 1995).

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

Modinos, A.

V. Yannopapas, A. Modinos, N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 23501-1–235201-6 (2002).
[CrossRef]

N. Stefanou, A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Noda, S.

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Oesterle, U.

Olivier, S.

Ozbay, E.

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

Rattier, M.

Scherer, A.

Skolnick, M. S.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

Smith, C.

Stefanou, N.

V. Yannopapas, A. Modinos, N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 23501-1–235201-6 (2002).
[CrossRef]

N. Stefanou, A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

Stevenson, R. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics (Artech House, Boston, Mass., 1995).

Temelkuran, B.

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

Weisbuch, C.

Whittaker, D. M.

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, New Brunswick, N.J., 1995).

Xu, Y.

Yablonovitch, E.

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

Yannopapas, V.

V. Yannopapas, A. Modinos, N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 23501-1–235201-6 (2002).
[CrossRef]

Yariv, A.

Appl. Phys. Lett. (1)

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. de la Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[CrossRef]

Nature (1)

T. F. Krauss, R. M. de la Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Opt. Express. (1)

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

Opt. Lett. (2)

Phys. Rev. B (3)

V. Yannopapas, A. Modinos, N. Stefanou, “Waveguides of defect chains in photonic crystals,” Phys. Rev. B 65, 23501-1–235201-6 (2002).
[CrossRef]

N. Stefanou, A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
[CrossRef]

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

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

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

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

Other (3)

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, New Brunswick, N.J., 1995).

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

A. Taflove, Computational Electrodynamics (Artech House, Boston, Mass., 1995).

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Figures (5)

Fig. 1
Fig. 1

Schematic view of the hexagonal lattice used in simulations. A CCW with intercavity separation of Δ=2a is created along the ΓK direction. The supercell used in PWE simulations is highlighted by a dashed rectangle. The electric field component parallel to the rods of the guided mode at k=K is shown in grayscale. On the right is shown the Brillouin zone of the supercell used in PWE and FDTD calculations. The high-symmetry points along the waveguide direction are Γ (0, 0) and K(0, π/Δ).

Fig. 2
Fig. 2

Dispersion relation of the TM guided mode in the proposed structure (r/a=0.2, Δ=2a): TB model [Eq. (1)] (solid curve), PWE method (open circles) and 2D FDTD method (dots). Calculations are carried out for wave vectors between Γ (0, 0) and K(0, π/Δ).

Fig. 3
Fig. 3

Group velocity vg in units of the speed of light in vacuum for three CCWs with different radii (rdef/r=0, 0.2 and 0.3) of the rods in the cavities obtained from Eq. (3) (solid curves) and from the differentiation of PWE results (dots). The lattice constant is a=475 nm.

Fig. 4
Fig. 4

Cavity group delay τΔ for the three considered CCWs from Eq. (4): (rdef/r=0, solid curve; rdef/r=0.2, dashed–dotted curve; rdef/r=0.3, dashed curve) and from PWE simulations (rdef/r=0, squares; rdef/r=0.2, triangles; rdef/r=0.3, circles).

Fig. 5
Fig. 5

Dispersion parameter D in a CCW with rdef/r=0 as a function of the wavelength: The solid curves represent Eq. (5), and open circles represent results obtained from the differentiation of the PWE calculations. (b) Detailed view of the central region. (c) Detailed view of the highly negative dispersion zone.

Equations (7)

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ω(k)=Ω[1+κ cos(kΔ)],
k(ω)=1Δ arccosω-ΩκΩ.
vg(λ)=1dk/dω=-2πcΔ [(κλ)2-(λ0-λ)2]1/2λλ0,
τΔ(λ)=Δvg=-λλ02πc[(κλ)2-(λ0-λ)2]1/2.
D(λ)=ddλ 1vg=-λ02(λ-λ0)2πcΔ[(κλ)2-(λ0-λ)2]3/2,
S(λ)=dDdλ=-λ02[(2κλ)2-4(λ0-λ)2-3κλ0λ]2πcΔ[(κλ)2-(λ0-λ)2]5/2.
Ω=ω(Γ)+ω(K)2,κ=ω(Γ)-ω(K)ω(Γ)+ω(K).

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