Abstract

Photonic crystal microcavities, formed by local defects within an otherwise perfectly periodic structure, can be used as narrowband optical resonators and filters. The coupled-cavity waveguide (CCW) is a linear array of equally spaced identical microcavities. Tunneling of light between microcavities forms a guiding effect, with a central frequency and bandwidth controlled by the local defects’ parameters and spacing, respectively. We employ cavity perturbation theory to investigate the sensitivity of microcavities and CCWs to random structure inaccuracies. For the microcavity, we predict a frequency shift that is due to random changes in the lattice structure and show an approximate linear dependence between the standard deviation of the structure inaccuracy and that of the resonant frequency. The effect of structural inaccuracy on the CCW devices, however, is different; it has practically no effect on the CCW performance if it is below a certain threshold but may destroy the CCW if this threshold is exceeded.

© 2003 Optical Society of America

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References

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  1. E. Centeno, B. Guizal, D. Felbacq, “Multiplexing and demultiplexing with photonic crystals,” J. Opt. A Pure Appl. Opt. 1, L10–L13 (1999).
    [CrossRef]
  2. N. Stefanou, A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev. B 57, 12127–12133 (1998).
    [CrossRef]
  3. M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. B 61, 11855–11858 (2000).
    [CrossRef]
  4. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
    [CrossRef]
  5. A. Boag, M. Gafni, B. Z. Steinberg, “Bandwidth control for photonic bandgap waveguides,” in Proceedings of Bianisotropics 2000, the Eighth International Conference on Electromagnetics of Complex Media (Instituto Superior Tecnico, Lisbon, 2000), pp. 321–324.
  6. A. Boag, B. Z. Steinberg, “Narrow-band microcavity waveguides in photonic crystals,” J. Opt. Soc. Am. A 18, 2799–2805 (2001).
    [CrossRef]
  7. R. E. Peierls, Quantum Theory of Solids (Oxford Clarendon Press, Oxford, UK, 1955.
  8. R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw Hill, New York, 1961).
  9. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N. J.1995).
  10. P. Lancaster, M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, Orlando, Fla., 1985).

2001 (1)

2000 (1)

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. B 61, 11855–11858 (2000).
[CrossRef]

1999 (2)

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

E. Centeno, B. Guizal, D. Felbacq, “Multiplexing and demultiplexing with photonic crystals,” J. Opt. A Pure Appl. Opt. 1, L10–L13 (1999).
[CrossRef]

1998 (1)

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

Bayindir, M.

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. B 61, 11855–11858 (2000).
[CrossRef]

Boag, A.

A. Boag, B. Z. Steinberg, “Narrow-band microcavity waveguides in photonic crystals,” J. Opt. Soc. Am. A 18, 2799–2805 (2001).
[CrossRef]

A. Boag, M. Gafni, B. Z. Steinberg, “Bandwidth control for photonic bandgap waveguides,” in Proceedings of Bianisotropics 2000, the Eighth International Conference on Electromagnetics of Complex Media (Instituto Superior Tecnico, Lisbon, 2000), pp. 321–324.

Centeno, E.

E. Centeno, B. Guizal, D. Felbacq, “Multiplexing and demultiplexing with photonic crystals,” J. Opt. A Pure Appl. Opt. 1, L10–L13 (1999).
[CrossRef]

Felbacq, D.

E. Centeno, B. Guizal, D. Felbacq, “Multiplexing and demultiplexing with photonic crystals,” J. Opt. A Pure Appl. Opt. 1, L10–L13 (1999).
[CrossRef]

Gafni, M.

A. Boag, M. Gafni, B. Z. Steinberg, “Bandwidth control for photonic bandgap waveguides,” in Proceedings of Bianisotropics 2000, the Eighth International Conference on Electromagnetics of Complex Media (Instituto Superior Tecnico, Lisbon, 2000), pp. 321–324.

Guizal, B.

E. Centeno, B. Guizal, D. Felbacq, “Multiplexing and demultiplexing with photonic crystals,” J. Opt. A Pure Appl. Opt. 1, L10–L13 (1999).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw Hill, New York, 1961).

Joannopoulos, J. D.

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

Lancaster, P.

P. Lancaster, M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, Orlando, Fla., 1985).

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, Princeton, N. J.1995).

Modinos, A.

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

Ozbay, E.

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. B 61, 11855–11858 (2000).
[CrossRef]

Peierls, R. E.

R. E. Peierls, Quantum Theory of Solids (Oxford Clarendon Press, Oxford, UK, 1955.

Scherer, A.

Stefanou, N.

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

Steinberg, B. Z.

A. Boag, B. Z. Steinberg, “Narrow-band microcavity waveguides in photonic crystals,” J. Opt. Soc. Am. A 18, 2799–2805 (2001).
[CrossRef]

A. Boag, M. Gafni, B. Z. Steinberg, “Bandwidth control for photonic bandgap waveguides,” in Proceedings of Bianisotropics 2000, the Eighth International Conference on Electromagnetics of Complex Media (Instituto Superior Tecnico, Lisbon, 2000), pp. 321–324.

Temelkuran, B.

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. B 61, 11855–11858 (2000).
[CrossRef]

Tismenetsky, M.

P. Lancaster, M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, Orlando, Fla., 1985).

Winn, J. N.

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

Xu, Y.

Yariv, A.

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

E. Centeno, B. Guizal, D. Felbacq, “Multiplexing and demultiplexing with photonic crystals,” J. Opt. A Pure Appl. Opt. 1, L10–L13 (1999).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. B (2)

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

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. B 61, 11855–11858 (2000).
[CrossRef]

Other (5)

R. E. Peierls, Quantum Theory of Solids (Oxford Clarendon Press, Oxford, UK, 1955.

R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw Hill, New York, 1961).

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

P. Lancaster, M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, Orlando, Fla., 1985).

A. Boag, M. Gafni, B. Z. Steinberg, “Bandwidth control for photonic bandgap waveguides,” in Proceedings of Bianisotropics 2000, the Eighth International Conference on Electromagnetics of Complex Media (Instituto Superior Tecnico, Lisbon, 2000), pp. 321–324.

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