Abstract

Interference lithography for the fabrication of photonic crystals is considered. A two-stage design method for realization of photonic bandgap structures with desired symmetries is developed. An optimal photonic crystal with a large bandgap is searched by adjusting some parameters while keeping some basic symmetry of the unit cell unchanged. A nonlinear programming method is then used to find the optimal electric field vectors of the laser beams and realize the desired interference pattern. The present method is useful for a rational and systematical design of new photonic bandgap structures.

©2004 Optical Society of America

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References

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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. J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ., Princeton, NJ, 1995).
  4. K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
    [Crossref]
  5. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
    [Crossref]
  6. V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60–64 (1997).
    [Crossref]
  7. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
    [Crossref]
  8. T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
    [Crossref]
  9. L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A 19, 2238–2244 (2002).
    [Crossref]
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    [Crossref]
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    [Crossref]
  12. L. Wu, F. Zhuang, and S. L. He, “Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps,” Phys. Rev. E 67, 026612 (2003).
    [Crossref]
  13. A. Fernandez and D. W. Phillion, “Effects of phase shifts on four-beam interference patterns,” Appl. Opt. 37, 473–478 (1998).
    [Crossref]
  14. H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  17. L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 1653156 (2002).
    [Crossref]
  18. I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
    [Crossref]
  19. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).
  20. D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102 (2003).
    [Crossref]

2003 (6)

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, “Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups,” Nature Mater. 2, 664–667 (2003).
[Crossref]

L. Wu, F. Zhuang, and S. L. He, “Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps,” Phys. Rev. E 67, 026612 (2003).
[Crossref]

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102 (2003).
[Crossref]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, and S. Yang, “Triply periodic bicontinuous structures through interference lithography: a level-set approach,” J. Opt. Soc. Am. A 20, 948–954 (2003).
[Crossref]

X. L. Yang, L. Z. Cai, and Q. Liu, “Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three-noncoplanar beams,” Opt. Express 11, 1050–1055 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1050.
[Crossref] [PubMed]

2002 (3)

L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A 19, 2238–2244 (2002).
[Crossref]

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 1653156 (2002).
[Crossref]

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

2001 (3)

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[Crossref] [PubMed]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
[Crossref]

2000 (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

1998 (2)

A. Fernandez and D. W. Phillion, “Effects of phase shifts on four-beam interference patterns,” Appl. Opt. 37, 473–478 (1998).
[Crossref]

J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[Crossref]

1997 (1)

V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

1987 (2)

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]

Aoki, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Aoyagi, Y.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Baba, T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Berger, V.

V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

Cai, L. Z.

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

Carter, W. C.

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, “Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups,” Nature Mater. 2, 664–667 (2003).
[Crossref]

Costard, E.

V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

Denning, R. G.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102 (2003).
[Crossref]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

Divliansky, I. B.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Fernandez, A.

Gauthier-Lafaye, O.

V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

Gill, P. E.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

He, S. L.

L. Wu, F. Zhuang, and S. L. He, “Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps,” Phys. Rev. E 67, 026612 (2003).
[Crossref]

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 1653156 (2002).
[Crossref]

Hirayama, H.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Inoshita, K.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Joannopoulos, J. D.

John, S.

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

Johnson, S. G.

Juodkazis, S.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
[Crossref]

Keating, C. D.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Khoo, I-C

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Kondo, T.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
[Crossref]

Liu, Q.

Maldovan, M.

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, “Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups,” Nature Mater. 2, 664–667 (2003).
[Crossref]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, and S. Yang, “Triply periodic bicontinuous structures through interference lithography: a level-set approach,” J. Opt. Soc. Am. A 20, 948–954 (2003).
[Crossref]

Mallouk, T. E.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Matsuo, S.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
[Crossref]

Mayer, T. S.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ., Princeton, NJ, 1995).

Misawa, H.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
[Crossref]

Miyazaki, H. T.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Murray, W.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).

Nishimura, S.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Pena, D.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Phillion, D. W.

Sharp, D. N.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102 (2003).
[Crossref]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

Shen, L. F.

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 1653156 (2002).
[Crossref]

Shinya, N.

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

Shishido, A.

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

Su, H. M.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

Thomas, E. L.

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, “Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups,” Nature Mater. 2, 664–667 (2003).
[Crossref]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, and S. Yang, “Triply periodic bicontinuous structures through interference lithography: a level-set approach,” J. Opt. Soc. Am. A 20, 948–954 (2003).
[Crossref]

Turberfield, A. J.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102 (2003).
[Crossref]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

Ullal, C. K.

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, “Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups,” Nature Mater. 2, 664–667 (2003).
[Crossref]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, and S. Yang, “Triply periodic bicontinuous structures through interference lithography: a level-set approach,” J. Opt. Soc. Am. A 20, 948–954 (2003).
[Crossref]

Vos, W. L.

J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[Crossref]

Wang, H. Z.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

Wang, X.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

Wang, Y. R.

White, C. A.

Wijnhoven, J.

J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[Crossref]

Winn, J.

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ., Princeton, NJ, 1995).

Wohlgemuth, M.

Wright, M. H.

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).

Wu, L.

L. Wu, F. Zhuang, and S. L. He, “Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps,” Phys. Rev. E 67, 026612 (2003).
[Crossref]

Xiao, S. S.

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 1653156 (2002).
[Crossref]

Xu, J. F.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

Yablonovitch, E.

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

Yang, S.

Yang, X. L.

Zheng, X. G.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

Zhong, Y. C.

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

Zhuang, F.

L. Wu, F. Zhuang, and S. L. He, “Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps,” Phys. Rev. E 67, 026612 (2003).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

I. B. Divliansky, A. Shishido, I-C Khoo, T. S. Mayer, D. Pena, S. Nishimura, C. D. Keating, and T. E. Mallouk, “Fabrication of two-dimensional photonic crystals using interference lithography and electrodeposition of CdSe,” Appl. Phys. Lett. 79, 3392–3394 (2001).
[Crossref]

K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, N. Shinya, and Y. Aoyagi, “Three-dimensional photonic crystals for optical wavelengths assembled by micromanipulation,” Appl. Phys. Lett. 81, 3122–3124 (2002).
[Crossref]

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79, 725–727 (2001).
[Crossref]

J. Appl. Phys. (1)

V. Berger, O. Gauthier-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82, 60–64 (1997).
[Crossref]

J. Opt. Soc. Am. A (2)

Nature (London) (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature (London) 404, 53–56 (2000).
[Crossref]

Nature Mater. (1)

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, “Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups,” Nature Mater. 2, 664–667 (2003).
[Crossref]

Opt. Express (2)

Phys. Rev. B (2)

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 1653156 (2002).
[Crossref]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102 (2003).
[Crossref]

Phys. Rev. E (2)

H. M. Su, Y. C. Zhong, X. Wang, X. G. Zheng, J. F. Xu, and H. Z. Wang, “Effects of polarization on laser holography for microstructure fabrication,” Phys. Rev. E 67, 056619 (2003).
[Crossref]

L. Wu, F. Zhuang, and S. L. He, “Degeneracy analysis for a supercell of a photonic crystal and its application to the creation of band gaps,” Phys. Rev. E 67, 026612 (2003).
[Crossref]

Phys. Rev. Lett. (2)

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]

Science (1)

J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281, 802–804 (1998).
[Crossref]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ., Princeton, NJ, 1995).

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).

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Figures (2)

Fig. 1.
Fig. 1. (a) Maximal absolute photonic bandgap between bands 3 and 4 and the corresponding threshold It when c 12 increases from 0.5 to 1.0. The other parameters are fixed as c 13=c 23=0.5. The two insets are the binarized patterns for (c 12=0.5,It =c 0-1.002) and (c 12=0.85,It =c 0-1.6886), respectively. (b) The band structures for both polarizations for the case of (c 12=0.85,It =c 0-1.6886).
Fig. 2.
Fig. 2. (a) Maximal absolute photonic bandgap between bands 2 and 3 and the corresponding threshold It when c 23 increases from -0.65 to -0.35. The other parameters are fixed as c 12=c 34=0 and c 13=c 14=c 24=0.5. The inset is the binarized pattern when (c 23=-0.5,It =c 0-1.0859). (b) The band structure for the case of (c 23=-0.5,It =c 0-1.0859).

Equations (17)

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I ( r ) = l , m = 1 N E l ( r ) · E m * ( r ) · exp [ i ( k l k m ) · r ]
I ( x , y ) = c 0 + 2 c 12 cos [ 4 π 3 a ( x 3 2 y 2 ) ]
+ 2 c 13 cos [ 4 π 3 a ( x 3 2 + y 2 ) ] + 2 c 23 cos [ 4 π 3 a y ]
I ( x , y , z ) = c 0 + 2 c 12 cos [ 4 π a x ] + 2 c 13 cos [ 2 π a ( x y + z ) ]
+ 2 c 14 cos [ 2 π a ( x + y + z ) ] + 2 c 23 cos [ 2 π a ( x + y z ) ]
+ 2 c 24 cos [ 2 π a ( x + y + z ) ] + 2 c 34 cos [ 4 π a y ]
c 0 = E 1 2 + E 2 2 + + E N 2
E l · k l = 0 , l = 1 , 2 , N
E l · E m * = c l m , 1 l < m N .
E 1 = [ 0.2768 , 0.6564 , 0.5536 ] ,
E 2 = [ 0.5667 , 0.7170 , 1.1335 ] ,
E 3 = [ 1.5880 , 0.1340 , 0.2681 ] ,
E 4 = [ 0.0748 , 0.2952 , 0.5905 ] .
E 1 = [ 0.2320 + 0.2326 i , 0.4047 + 0.4040 i , 0.4640 0.4651 i ] ,
E 2 = [ 0.0856 0.3178 i , 0.5478 + 0.1473 i 0.1711 0.6357 i ] ,
E 3 = [ 0.2551 + 0.9541 i , 0.1836 + 0.0491 i , 0.3673 + 0.0981 i ] ,
E 4 = [ 0.1837 0.0487 i , 0.0843 + 0.3182 i , 0.1686 0.6364 i ] .

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