Abstract

A numerical method was developed by combining a plane-wave-based transfer matrix method and a robust rational function interpolation algorithm. The optical properties of three-dimensional photonic crystal cavities were extracted in a short computation time with high numerical accuracy.

© 2006 Optical Society of America

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  1. J. C. Knight, T. A. Birks, P. St. J. Russel, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
    [Crossref] [PubMed]
  2. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulous, Phys. Rev. Lett. 77, 3787 (1996).
    [Crossref] [PubMed]
  3. S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
    [Crossref] [PubMed]
  4. A. Chutinan and S. Noda, Appl. Phys. Lett. 75, 3739 (1999).
    [Crossref]
  5. E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
    [Crossref]
  6. M. Okano, A. Chutinan, and S. Noda, Phys. Rev. B 66, 165211 (2002).
    [Crossref]
  7. J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
    [Crossref]
  8. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).
  9. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981).
    [Crossref]
  10. L. L. Lin, Z. Y. Li, and K. M. Ho, J. Appl. Phys. 94, 811 (2003).
    [Crossref]
  11. W. H. Press, Numerical Recipes (Cambridge U. Press, 1992).
  12. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, 1980).
  13. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [Crossref] [PubMed]
  14. R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).
  15. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  16. Ph. Lalanne, J. P. Hugonin, and J. M. Gerard, Appl. Phys. Lett. 84, 4726 (2004).
    [Crossref]
  17. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
    [Crossref]
  18. Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.
  19. S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
    [Crossref]
  20. S. Dey and R. Mittra, IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
    [Crossref]
  21. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
    [Crossref] [PubMed]
  22. O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
    [Crossref]
  23. K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002).
    [PubMed]
  24. Ph. Lalanne, S. Mias, and J. P. Hugonin, Opt. Express 12, 458 (2004).
    [Crossref] [PubMed]

2004 (3)

Ph. Lalanne, J. P. Hugonin, and J. M. Gerard, Appl. Phys. Lett. 84, 4726 (2004).
[Crossref]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

Ph. Lalanne, S. Mias, and J. P. Hugonin, Opt. Express 12, 458 (2004).
[Crossref] [PubMed]

2003 (1)

L. L. Lin, Z. Y. Li, and K. M. Ho, J. Appl. Phys. 94, 811 (2003).
[Crossref]

2002 (3)

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

M. Okano, A. Chutinan, and S. Noda, Phys. Rev. B 66, 165211 (2002).
[Crossref]

K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002).
[PubMed]

2001 (1)

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

1999 (1)

A. Chutinan and S. Noda, Appl. Phys. Lett. 75, 3739 (1999).
[Crossref]

1998 (2)

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

S. Dey and R. Mittra, IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[Crossref]

1996 (2)

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

J. C. Knight, T. A. Birks, P. St. J. Russel, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[Crossref] [PubMed]

1995 (1)

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

1994 (2)

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

1987 (1)

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

1981 (1)

Adler, R. B.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

Atkin, D. M.

Birks, T. A.

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

Bulirsch, R.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, 1980).

Cao, J. R.

Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

Chen, J. C.

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

Chow, E.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

Chu, L. J.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

Chutinan, A.

M. Okano, A. Chutinan, and S. Noda, Phys. Rev. B 66, 165211 (2002).
[Crossref]

A. Chutinan and S. Noda, Appl. Phys. Lett. 75, 3739 (1999).
[Crossref]

Dapkus, P. D.

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

Dey, S.

S. Dey and R. Mittra, IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[Crossref]

Fan, S.

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

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

Fano, R. M.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

Gaylord, T. K.

Gerard, J. M.

Ph. Lalanne, J. P. Hugonin, and J. M. Gerard, Appl. Phys. Lett. 84, 4726 (2004).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Hietala, V.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

Ho, K. M.

L. L. Lin, Z. Y. Li, and K. M. Ho, J. Appl. Phys. 94, 811 (2003).
[Crossref]

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.

Hu, X.

Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.

Hugonin, J. P.

Ph. Lalanne, J. P. Hugonin, and J. M. Gerard, Appl. Phys. Lett. 84, 4726 (2004).
[Crossref]

Ph. Lalanne, S. Mias, and J. P. Hugonin, Opt. Express 12, 458 (2004).
[Crossref] [PubMed]

Imada, M.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

Joannopoulos, J. D.

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

Joannopoulous, J. D.

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

Knight, J. C.

Kurland, I.

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

Lalanne, Ph.

Ph. Lalanne, J. P. Hugonin, and J. M. Gerard, Appl. Phys. Lett. 84, 4726 (2004).
[Crossref]

Ph. Lalanne, S. Mias, and J. P. Hugonin, Opt. Express 12, 458 (2004).
[Crossref] [PubMed]

Li, Ming

Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.

Li, Z. Y.

L. L. Lin, Z. Y. Li, and K. M. Ho, J. Appl. Phys. 94, 811 (2003).
[Crossref]

Lin, L. L.

L. L. Lin, Z. Y. Li, and K. M. Ho, J. Appl. Phys. 94, 811 (2003).
[Crossref]

Lin, S. Y.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

Mekis, A.

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

Mias, S.

Mittra, R.

S. Dey and R. Mittra, IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[Crossref]

Miyawaki, M.

Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.

Moharam, M. G.

Noda, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

M. Okano, A. Chutinan, and S. Noda, Phys. Rev. B 66, 165211 (2002).
[Crossref]

A. Chutinan and S. Noda, Appl. Phys. Lett. 75, 3739 (1999).
[Crossref]

O'Brien, J. D.

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

Ogawa, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

Okano, M.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

M. Okano, A. Chutinan, and S. Noda, Phys. Rev. B 66, 165211 (2002).
[Crossref]

Özbay, E.

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

Painter, O.

K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002).
[PubMed]

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

Pendry, J. B.

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[Crossref]

Press, W. H.

W. H. Press, Numerical Recipes (Cambridge U. Press, 1992).

Russel, P. St. J.

Scherer, A.

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

Sigalas, M.

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

Soukoulis, C. M.

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

Srinivasan, K.

K. Srinivasan and O. Painter, Opt. Express 10, 670 (2002).
[PubMed]

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

Stoer, J.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, 1980).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

Tuttle, G.

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

Villeneuve, P. R.

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

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

Yablonovitch, E.

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

Yoshimoto, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

A. Chutinan and S. Noda, Appl. Phys. Lett. 75, 3739 (1999).
[Crossref]

Ph. Lalanne, J. P. Hugonin, and J. M. Gerard, Appl. Phys. Lett. 84, 4726 (2004).
[Crossref]

IEEE Microwave Guid. Wave Lett. (1)

S. Dey and R. Mittra, IEEE Microwave Guid. Wave Lett. 8, 415 (1998).
[Crossref]

J. Appl. Phys. (1)

L. L. Lin, Z. Y. Li, and K. M. Ho, J. Appl. Phys. 94, 811 (2003).
[Crossref]

J. Mod. Opt. (1)

J. B. Pendry, J. Mod. Opt. 41, 209 (1994).
[Crossref]

J. Opt. A (1)

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, J. Opt. A 3, S161 (2001).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (3)

E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, Phys. Rev. B 51, 13961 (1995).
[Crossref]

M. Okano, A. Chutinan, and S. Noda, Phys. Rev. B 66, 165211 (2002).
[Crossref]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[Crossref]

Phys. Rev. Lett. (2)

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

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

Science (2)

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, Science 305, 227 (2004).
[Crossref] [PubMed]

S. Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, Science 282, 274 (1998).
[Crossref] [PubMed]

Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[Crossref]

Other (6)

Ming Li, J. R. Cao, X. Hu, M. Miyawaki, and K. M. Ho, "Fano peaks in the bandgap of 3D layer-by-layer photonic crystal," to be submitted to Opt. Express.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2000).

W. H. Press, Numerical Recipes (Cambridge U. Press, 1992).

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, 1980).

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Figures (4)

Fig. 1
Fig. 1

Left, 5 × 5 PC cavity supercell structures; right, cross section of the cavity layer.

Fig. 2
Fig. 2

The z directional transmission spectrum (solid curve) across the full bandgap range with its estimated error term (light gray curve). Left inset, enlarged linear plot of the Lorentzian resonant transmission peak, with its peak frequency and Q value labeled. Right inset, enlarged view of an asymmetric transmission feature, with 26 confirmation TMM frequency points (crosses).

Fig. 3
Fig. 3

Spectra for varying supercell sizes.

Fig. 4
Fig. 4

(a) Extracted from the spectra in Fig. 3; the cavity resonant mode frequency and Q value vary and stabilize as the supercell size increases. (b) Cavity mode resonant frequency and Q value plotted as functions of the total number of layers along the z direction.

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