Abstract

We study theoretically the effects of structural fluctuations on the photonic bandgap during fabrication for the case of a photonic crystal with a finite number of periods. We use the transfer-matrix method to calculate the transmission spectra of the photonic crystals. The results of our calculations show that, even with a misalignment irregularity of 18%, the bandgap remains as large as 10%.

© 1999 Optical Society of America

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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. S. John and J. Wang, “Quantum electrodynamics near a photonic bandgap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
    [CrossRef] [PubMed]
  4. E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
    [CrossRef]
  5. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  6. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
    [CrossRef] [PubMed]
  7. K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
    [CrossRef]
  8. K. M. Leung, “Diamondlike photonic bandgap crystal with a sizable bandgap,” Phys. Rev. B 56, 3517–3519 (1997).
    [CrossRef]
  9. E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
    [CrossRef] [PubMed]
  10. H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
    [CrossRef]
  11. R. M. Hornreich, S. Shtrikman, and C. Sommers, “Photonic bandgaps in body-centered-cubic structures,” Phys. Rev. B 49, 10914–10917 (1994).
    [CrossRef]
  12. H. S. Sözüer and J. W. Haus, “Photonic bands: simple-cubic lattice,” J. Opt. Soc. Am. B 10, 296–302 (1993).
    [CrossRef]
  13. S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
    [CrossRef]
  14. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
    [CrossRef]
  15. A. Chutinan and S. Noda, “Spiral three-dimensional photonic-bandgap structure,” Phys. Rev. B 57, R2006–R2008 (1998).
    [CrossRef]
  16. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993).
    [CrossRef]
  17. E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
    [CrossRef]
  18. C. C. Cheng and A. Scherer, “Fabrication of photonic bandgap crystals,” J. Vac. Sci. Technol. B 13, 2696–2700 (1995).
    [CrossRef]
  19. S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys., Part 2 35, L909–L912 (1996).
    [CrossRef]
  20. N. Yamamoto and S. Noda, “Development of a period of three-dimensional photonic crystal operating at optical wavelength region,” presented at the 10th International Conference on Indium Phosphide and Related Materials, Tsukuba, Japan, May 11–15, 1998.
  21. N. Yamamoto, S. Noda, and A. Chutinan, “Development of one period of three-dimensional photonic crystal in 5–10 μm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 37, L1052–L1054 (1998).
    [CrossRef]
  22. S. Noda, N. Yamamoto, M. Imada, H. Kobayashi, and M. Okano, “Alignment and stacking of semiconductor photonic band gaps by wafer-fusion,” presented at the Workshop on Electromagnetic Crystal Structures, Design, Synthesis, and Applications, Laguna Beach, Calif., January 6–8 (1999).
  23. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
    [CrossRef]
  24. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
    [CrossRef]
  25. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Photonic band gap structures: studies of the transmission coefficient,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO Advanced Study Institute Series E: Applied Sciences (Academic, New York, 1996), pp. 173–202.
  26. M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
    [CrossRef]
  27. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
    [CrossRef]
  28. A. Chutinan and S. Noda, “Effect of structural fluctuations on the photonic bandgap during the photonic crystal fabrication,” J. Opt. Soc. Am. B 16, 240–244 (1999).
    [CrossRef]
  29. J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
    [CrossRef] [PubMed]
  30. N. Yamamoto and S. Noda, “100-nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
    [CrossRef]

1999

1998

M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
[CrossRef]

N. Yamamoto, S. Noda, and A. Chutinan, “Development of one period of three-dimensional photonic crystal in 5–10 μm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 37, L1052–L1054 (1998).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

N. Yamamoto and S. Noda, “100-nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-bandgap structure,” Phys. Rev. B 57, R2006–R2008 (1998).
[CrossRef]

1997

K. M. Leung, “Diamondlike photonic bandgap crystal with a sizable bandgap,” Phys. Rev. B 56, 3517–3519 (1997).
[CrossRef]

1996

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys., Part 2 35, L909–L912 (1996).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
[CrossRef]

1995

C. C. Cheng and A. Scherer, “Fabrication of photonic bandgap crystals,” J. Vac. Sci. Technol. B 13, 2696–2700 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

1994

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

R. M. Hornreich, S. Shtrikman, and C. Sommers, “Photonic bandgaps in body-centered-cubic structures,” Phys. Rev. B 49, 10914–10917 (1994).
[CrossRef]

1993

1992

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

1991

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

1990

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

S. John and J. Wang, “Quantum electrodynamics near a photonic bandgap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
[CrossRef] [PubMed]

1987

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]

Abeyta, A.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Brown, E. R.

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Chan, C. T.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Cheng, C. C.

C. C. Cheng and A. Scherer, “Fabrication of photonic bandgap crystals,” J. Vac. Sci. Technol. B 13, 2696–2700 (1995).
[CrossRef]

Chutinan, A.

A. Chutinan and S. Noda, “Effect of structural fluctuations on the photonic bandgap during the photonic crystal fabrication,” J. Opt. Soc. Am. B 16, 240–244 (1999).
[CrossRef]

N. Yamamoto, S. Noda, and A. Chutinan, “Development of one period of three-dimensional photonic crystal in 5–10 μm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 37, L1052–L1054 (1998).
[CrossRef]

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-bandgap structure,” Phys. Rev. B 57, R2006–R2008 (1998).
[CrossRef]

Datta, S.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
[CrossRef]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

Haus, J. W.

H. S. Sözüer and J. W. Haus, “Photonic bands: simple-cubic lattice,” J. Opt. Soc. Am. B 10, 296–302 (1993).
[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Hornreich, R. M.

R. M. Hornreich, S. Shtrikman, and C. Sommers, “Photonic bandgaps in body-centered-cubic structures,” Phys. Rev. B 49, 10914–10917 (1994).
[CrossRef]

Inguva, R.

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

Joannopoulos, J. D.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
[CrossRef]

John, S.

S. John and J. Wang, “Quantum electrodynamics near a photonic bandgap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
[CrossRef] [PubMed]

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

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Leung, K. M.

K. M. Leung, “Diamondlike photonic bandgap crystal with a sizable bandgap,” Phys. Rev. B 56, 3517–3519 (1997).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

MacKinnon, A.

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

Meade, R. D.

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Noda, S.

A. Chutinan and S. Noda, “Effect of structural fluctuations on the photonic bandgap during the photonic crystal fabrication,” J. Opt. Soc. Am. B 16, 240–244 (1999).
[CrossRef]

N. Yamamoto and S. Noda, “100-nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-bandgap structure,” Phys. Rev. B 57, R2006–R2008 (1998).
[CrossRef]

N. Yamamoto, S. Noda, and A. Chutinan, “Development of one period of three-dimensional photonic crystal in 5–10 μm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 37, L1052–L1054 (1998).
[CrossRef]

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys., Part 2 35, L909–L912 (1996).
[CrossRef]

Özbay, E.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Parker, C. D.

Pendry, J. B.

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

Sasaki, A.

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys., Part 2 35, L909–L912 (1996).
[CrossRef]

Scherer, A.

C. C. Cheng and A. Scherer, “Fabrication of photonic bandgap crystals,” J. Vac. Sci. Technol. B 13, 2696–2700 (1995).
[CrossRef]

Shtrikman, S.

R. M. Hornreich, S. Shtrikman, and C. Sommers, “Photonic bandgaps in body-centered-cubic structures,” Phys. Rev. B 49, 10914–10917 (1994).
[CrossRef]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Sommers, C.

R. M. Hornreich, S. Shtrikman, and C. Sommers, “Photonic bandgaps in body-centered-cubic structures,” Phys. Rev. B 49, 10914–10917 (1994).
[CrossRef]

Soukoulis, C. M.

M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
[CrossRef]

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

Soukouslis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Sözüer, H. S.

H. S. Sözüer and J. W. Haus, “Photonic bands: simple-cubic lattice,” J. Opt. Soc. Am. B 10, 296–302 (1993).
[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

Tringides, M.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Turner, D.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
[CrossRef]

Tuttle, G.

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
[CrossRef]

Wang, J.

S. John and J. Wang, “Quantum electrodynamics near a photonic bandgap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
[CrossRef] [PubMed]

Yablonovitch, E.

E. R. Brown, C. D. Parker, and E. Yablonovitch, “Radiation properties of a planar antenna on a photonic-crystal substrate,” J. Opt. Soc. Am. B 10, 404–407 (1993).
[CrossRef]

E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[CrossRef] [PubMed]

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

Yamamoto, N.

N. Yamamoto, S. Noda, and A. Chutinan, “Development of one period of three-dimensional photonic crystal in 5–10 μm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 37, L1052–L1054 (1998).
[CrossRef]

N. Yamamoto and S. Noda, “100-nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys., Part 2 35, L909–L912 (1996).
[CrossRef]

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Appl. Phys. Lett.

S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Appl. Phys. Lett. 65, 1466–1468 (1994).
[CrossRef]

J. Appl. Phys.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995).
[CrossRef]

J. Opt. Soc. Am. B

J. Vac. Sci. Technol. B

C. C. Cheng and A. Scherer, “Fabrication of photonic bandgap crystals,” J. Vac. Sci. Technol. B 13, 2696–2700 (1995).
[CrossRef]

Jpn. J. Appl. Phys.

N. Yamamoto, S. Noda, and A. Chutinan, “Development of one period of three-dimensional photonic crystal in 5–10 μm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 37, L1052–L1054 (1998).
[CrossRef]

N. Yamamoto and S. Noda, “100-nm-scale alignment using laser beam diffraction pattern observation techniques and wafer fusion for realizing three-dimensional photonic crystal structure,” Jpn. J. Appl. Phys. 37, 3334–3338 (1998).
[CrossRef]

Jpn. J. Appl. Phys., Part 2

S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys., Part 2 35, L909–L912 (1996).
[CrossRef]

Nature

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251–253 (1998).
[CrossRef]

Phys. Rev. B

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and D. Turner, “Localization of electromagnetic waves in two-dimensional disordered systems,” Phys. Rev. B 53, 8340–8348 (1996).
[CrossRef]

M. M. Sigalas, K. M. Ho, R. Biswas, and C. M. Soukoulis, “Theoretical investigation of defects in photonic crystals in the presence of dielectric losses,” Phys. Rev. B 57, 3815–3820 (1998).
[CrossRef]

E. Özbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, C. T. Chan, C. M. Soukoulis, and K. M. Ho, “Measurement of a three-dimensional photonic bandgap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945–1948 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[CrossRef]

A. Chutinan and S. Noda, “Spiral three-dimensional photonic-bandgap structure,” Phys. Rev. B 57, R2006–R2008 (1998).
[CrossRef]

H. S. Sözüer, J. W. Haus, and R. Inguva, “Photonic bands: convergence problems with the plane-wave method,” Phys. Rev. B 45, 13962–13972 (1992).
[CrossRef]

R. M. Hornreich, S. Shtrikman, and C. Sommers, “Photonic bandgaps in body-centered-cubic structures,” Phys. Rev. B 49, 10914–10917 (1994).
[CrossRef]

K. M. Leung, “Diamondlike photonic bandgap crystal with a sizable bandgap,” Phys. Rev. B 56, 3517–3519 (1997).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991).
[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]

S. John and J. Wang, “Quantum electrodynamics near a photonic bandgap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[CrossRef] [PubMed]

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772–2775 (1992).
[CrossRef] [PubMed]

Solid State Commun.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic bandgaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Other

N. Yamamoto and S. Noda, “Development of a period of three-dimensional photonic crystal operating at optical wavelength region,” presented at the 10th International Conference on Indium Phosphide and Related Materials, Tsukuba, Japan, May 11–15, 1998.

M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Photonic band gap structures: studies of the transmission coefficient,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO Advanced Study Institute Series E: Applied Sciences (Academic, New York, 1996), pp. 173–202.

S. Noda, N. Yamamoto, M. Imada, H. Kobayashi, and M. Okano, “Alignment and stacking of semiconductor photonic band gaps by wafer-fusion,” presented at the Workshop on Electromagnetic Crystal Structures, Design, Synthesis, and Applications, Laguna Beach, Calif., January 6–8 (1999).

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Figures (7)

Fig. 1
Fig. 1

Transmission spectra of EM waves propagating through eight layers of a stacked-bar structure (corresponds to two periods) in the stacking direction, calculated for four numbers of divisions n.

Fig. 2
Fig. 2

Transmittance and frequency at the minimum point of the transmission spectrum of the stacked-bar structure as a function of n-1.

Fig. 3
Fig. 3

Schematic depicting the stacked-bar structure with misalignment of two stripe positions and the incident angle of the EM wave. Misalignment δ of the stripe position is assumed for the third and the seventh layers in the +y and the -y directions, respectively. Incident angle ϕ is defined as the angle that lies within the xz plane, and θ lies within the yz plane.

Fig. 4
Fig. 4

Transmission spectra of a normally incident wave for polarization in which the electric field is parallel to the x axis, when δ varies from 0 to 0.5a.

Fig. 5
Fig. 5

Band edge frequencies in the stacking direction calculated by the PW method as a function of misalignment δ.

Fig. 6
Fig. 6

Transmission spectra when incident angle ϕ (in the xz plane) varies from 10° to 80° for (a) s polarization and (b) p polarization.

Fig. 7
Fig. 7

Transmission spectra when incident angle θ (in the yz plane) varies from 10° to 80° for (a) s polarization and (b) p polarization.

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