Abstract

We study theoretically the effect of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal. We consider irregularities such as misalignment of stripe position, deviation of intersecting angle, variation of layer thickness, and variation of stripe width. The results of our calculations show that misalignment of the stripes affects the width of the bandgap most. However, the photonic crystal is fairly robust to structural irregularities, so even with an irregularity of 15% the bandgap remains as large as 11%.

© 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 (1987).
  2. C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. B 13, 2696 (1995).
  3. 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 (1996).
  4. 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 (1998).
  5. 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 (1995).
  6. K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (1994).
  7. 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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).
  8. N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36, 1907 (1997).
  9. 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 (1998).
  10. K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646 (1990).
  11. J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772 (1992).
  12. A. Chutinan and S. Noda, “Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal: a study of the photonic crystal with finite period,” J. Opt. Soc. Am. B (to be published).
  13. H. L. Skriver, The LMTO Method (Springer-Verlag, Berlin, 1984).
  14. S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic system,” Phys. Rev. Lett. 78, 1888 (1997).

1998 (2)

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 (1998).

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 (1998).

1997 (2)

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic system,” Phys. Rev. Lett. 78, 1888 (1997).

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36, 1907 (1997).

1996 (1)

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 (1996).

1995 (2)

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. B 13, 2696 (1995).

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 (1995).

1994 (2)

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

1992 (1)

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772 (1992).

1990 (1)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646 (1990).

1987 (1)

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

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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Biswas, R.

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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (1994).

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Cheng, C. C.

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. B 13, 2696 (1995).

Chutinan, A.

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 (1998).

Fan, S.

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 (1995).

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Joannopoulos, J. D.

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 (1995).

John, S.

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic system,” Phys. Rev. Lett. 78, 1888 (1997).

Leung, K. M.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646 (1990).

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646 (1990).

MacKinnon, A.

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772 (1992).

Noda, S.

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 (1998).

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 (1998).

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36, 1907 (1997).

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 (1996).

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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Pendry, J. B.

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772 (1992).

Quang, T.

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic system,” Phys. Rev. Lett. 78, 1888 (1997).

Sasaki, A.

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36, 1907 (1997).

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 (1996).

Scherer, A.

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. B 13, 2696 (1995).

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (1994).

Soukoulis, C. 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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Soukouslis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (1994).

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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Villeneuve, P. R.

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 (1995).

Yablonovitch, E.

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

Yamamoto, N.

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 (1998).

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 (1998).

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36, 1907 (1997).

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 (1996).

J. Appl. Phys. (1)

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 (1995).

J. Vac. Sci. Technol. B (1)

C. C. Cheng and A. Scherer, “Fabrication of photonic band-gap crystals,” J. Vac. Sci. Technol. B 13, 2696 (1995).

Jpn. J. Appl. Phys. (3)

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 (1998).

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36, 1907 (1997).

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 (1998).

Jpn. J. Appl. Phys. Part 2 (1)

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 (1996).

Phys. Rev. B (1)

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 band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945 (1994).

Phys. Rev. Lett. (4)

S. John and T. Quang, “Collective switching and inversion without fluctuation of two-level atoms in confined photonic system,” Phys. Rev. Lett. 78, 1888 (1997).

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

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646 (1990).

J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relations,” Phys. Rev. Lett. 69, 2772 (1992).

Solid State Phys. (1)

K. M. Ho, C. T. Chan, C. M. Soukouslis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Phys. 89, 413 (1994).

Other (2)

A. Chutinan and S. Noda, “Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal: a study of the photonic crystal with finite period,” J. Opt. Soc. Am. B (to be published).

H. L. Skriver, The LMTO Method (Springer-Verlag, Berlin, 1984).

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