Abstract

We propose a new type of optical waveguide that consists of a sequence of coupled high-Q resonators. Unlike other types of optical waveguide, waveguiding in the coupled-resonator optical waveguide (CROW) is achieved through weak coupling between otherwise localized high-Q optical cavities. Employing a formalism similar to the tight-binding method in solid-state physics, we obtain the relations for the dispersion and the group velocity of the photonic band of the CROW’s and find that they are solely characterized by coupling factor κ1. We also demonstrate the possibility of highly efficient nonlinear optical frequency conversion and perfect transmission through bends in CROW’s.

© 1999 Optical Society of America

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References

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
    [CrossRef]
  3. S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  4. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
    [CrossRef]
  5. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
    [CrossRef]
  6. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  7. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  8. See, for example, N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).
  9. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
    [CrossRef] [PubMed]
  10. A. Yariv, Optical Electronics in Modern Communications (Oxford University, New York, 1997).

1996 (2)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

1994 (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

1992 (1)

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

1987 (2)

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1976 (1)

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

Alerhand, O. L.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

Ashcroft, N. W.

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

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Devenyi, A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

Joannopoulos, J. D.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Kash, K.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Levi, A. F.

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Logan, R. L.

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Meade, R. D.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Mermin, N. D.

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

Pearton, S. J.

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Smith, D. A.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

Villeneuve, P. R.

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yariv, A.

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

A. Yariv, Optical Electronics in Modern Communications (Oxford University, New York, 1997).

Yeh, P.

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Appl. Phys. Lett. (1)

S. L. McCall, A. F. Levi, R. E. Slusher, S. J. Pearton, and R. L. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

J. Appl. Phys. (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, J. Appl. Phys. 75, 4753 (1994).
[CrossRef]

Opt. Commun. (1)

P. Yeh and A. Yariv, Opt. Commun. 19, 427 (1976).
[CrossRef]

Phys. Rev. B (1)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Other (3)

A. Yariv, Optical Electronics in Modern Communications (Oxford University, New York, 1997).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

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

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Figures (3)

Fig. 1
Fig. 1

Three types of waveguiding: (a) waveguiding achieved through total internal reflection at the interface between a dielectric medium with a high refractive index n2 and a low refractive index n1. (b) Bragg waveguiding achieved by reflection from periodic Bragg stacks. (c) CROW, with waveguiding that is due to coupling between individual microdisks. R is the size of a unit cell, and ez is the direction of the periodicity for the coupled resonators. (d) CROW realized by coupling of the individual defect cavities in a 2D photonic crystal. R and ez are defined the same as in (c).

Fig. 2
Fig. 2

Dispersion diagram of a CROW band. The dispersion relation is plotted according to Eq.  (5), with Δα=0 and κ1=-0.03. Ω is the resonant frequency of the single high-Q cavity. K is the wave vector of the CROW band.

Fig. 3
Fig. 3

Two realizations of the CROW bend with complete transmission. The gray regions represent the microcavi-ties that are coupled together to form the CROW. The black regions inside the individual microcavities represent the high-Q optical modes in each microcavity, which have n-fold rotational symmetry. (a) n=4, (b) n=6.

Equations (10)

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

EKr,t=E0expiωKtnexp-inKR×EΩr-nRez.
××EK=ϵrωK2c2EK,
ωK2=Ω21+n0exp-inKRβn1+Δα+n0exp-inKRαn,
αn=d3rϵrEΩr·EΩr-nRez,n0,
βn=d3rϵ0r-nRezEΩr·EΩr-nRez,n0,
Δα=d3rϵr-ϵ0rEΩr·EΩr.
ωK=Ω1-Δα2+κ1cosKR,
κ1=β1-α1=d3rϵ0r-Rez-ϵr-Rez×EΩr·EΩr-Rez.
vgK=dωKdK=-ΩRκ1sinKR,
P=18πRvω,gE02.

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