Abstract

Periodic dielectric structures possessing large photonic band gaps have been based primarily on face-centered-cubic diamond symmetry. However, photonic crystals with large photonic band gaps are also found when neighboring lattice sites in the simple cubic lattice are connected to create a connected node dielectric network. Because of the inherent simplicity of this geometry, photonic crystals based on simple cubic symmetry can be more easily and economically produced. In this review, we show graphically and quantitatively the similarities among five photonic crystals having simple cubic lattice symmetry. Structural and photonic properties of this family of crystals are compared to reveal common characteristics. We provide three-dimensional (3-D) graphics to enable the reader to visualize the relationships amongst the various structures. We provide maps of the complete photonic band gaps as a function of the dielectric volume fraction for each structure to help researchers interested in the fabrication of the structures. We also discuss the basic origin of the 3-D complete photonic band gap for the simple cubic morphology in terms of dielectric modulations along principal directions. After reviewing the set of experimentally realized simple cubic structures, we feature the promising champion single P structure accessible through 3-D interference lithography.

© 2005 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. J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
    [CrossRef]
  4. E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
    [CrossRef] [PubMed]
  5. K. M. Leung and Y. F. Liu, "Full wave vector calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
    [CrossRef] [PubMed]
  6. Z. Zhang and S. Satpathy, "Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations," Phys. Rev. Lett. 65, 2650-2653 (1990).
    [CrossRef] [PubMed]
  7. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic band gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  8. M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3, 593-600 (2004).
    [CrossRef] [PubMed]
  9. H. S. Sozuer and J. W. Haus, "Photonic bands: simple-cubic lattice," J. Opt. Soc. Am. B 10, 296-302 (1993).
    [CrossRef]
  10. L. Zavieh and T. S. Mayer, "Demonstration of a three-dimensional simple-cubic infrared photonic crystal," Appl. Phys. Lett. 75, 2533-2525 (1999).
    [CrossRef]
  11. S. Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic bandgap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
    [CrossRef]
  12. C. K. Ullal, M. Maldovan, M. Wohlgemuth, C. A. White, S. Yang, and E. L. Thomas, "Triply periodic bicontinuous structures through interference lithography: a level set approach," J. Opt. Soc. Am. A 20, 948-954 (2003).
    [CrossRef]
  13. R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
    [CrossRef]
  14. M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
    [CrossRef]
  15. M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
    [CrossRef]
  16. L. Martin-Moreno, F. J. Garcia-Vidal, and A. M. Somoza, "Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials," Phys. Rev. Lett. 83, 73-75 (1999).
    [CrossRef]
  17. 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 404, 53-56 (2000).
    [CrossRef] [PubMed]
  18. O. Toader and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905 (2004).
    [CrossRef] [PubMed]
  19. M. Qiu and S. He, "Optimal design of a two-dimensional photonic crystal of a square lattice with a large complete two-dimensional band gap," J. Opt. Soc. Am. B 17, 1027-1030 (2000).
    [CrossRef]
  20. M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519 (2000).
    [CrossRef]
  21. M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
    [CrossRef]
  22. C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
    [CrossRef]

2004 (3)

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3, 593-600 (2004).
[CrossRef] [PubMed]

O. Toader and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905 (2004).
[CrossRef] [PubMed]

C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

2003 (1)

2002 (1)

R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
[CrossRef]

2001 (2)

S. Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic bandgap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
[CrossRef]

M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
[CrossRef]

2000 (4)

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 404, 53-56 (2000).
[CrossRef] [PubMed]

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

M. Qiu and S. He, "Optimal design of a two-dimensional photonic crystal of a square lattice with a large complete two-dimensional band gap," J. Opt. Soc. Am. B 17, 1027-1030 (2000).
[CrossRef]

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519 (2000).
[CrossRef]

1999 (2)

L. Zavieh and T. S. Mayer, "Demonstration of a three-dimensional simple-cubic infrared photonic crystal," Appl. Phys. Lett. 75, 2533-2525 (1999).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, and A. M. Somoza, "Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials," Phys. Rev. Lett. 83, 73-75 (1999).
[CrossRef]

1997 (2)

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

1993 (1)

1990 (3)

K. M. Leung and Y. F. Liu, "Full wave vector calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Z. Zhang and S. Satpathy, "Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations," Phys. Rev. Lett. 65, 2650-2653 (1990).
[CrossRef] [PubMed]

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

1989 (1)

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

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]

Agio , M.

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519 (2000).
[CrossRef]

Andreani, L. C.

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519 (2000).
[CrossRef]

Biswas, R.

R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
[CrossRef]

S. Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic bandgap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
[CrossRef]

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 404, 53-56 (2000).
[CrossRef] [PubMed]

Carter, W. C.

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

Chan, C. T.

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

Denning, R. G.

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 404, 53-56 (2000).
[CrossRef] [PubMed]

Doi, Y.

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

Fan, S. H.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

Fleming, J. G.

Garcia-Vidal, F. J.

L. Martin-Moreno, F. J. Garcia-Vidal, and A. M. Somoza, "Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials," Phys. Rev. Lett. 83, 73-75 (1999).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

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 404, 53-56 (2000).
[CrossRef] [PubMed]

Haus, J. W.

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

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

He, S.

Ho, K. M.

R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
[CrossRef]

S. Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic bandgap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
[CrossRef]

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

Hoffman, J.

M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
[CrossRef]

Inoue, K.

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

John, S.

O. Toader and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905 (2004).
[CrossRef] [PubMed]

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

Leung , K. M.

K. M. Leung and Y. F. Liu, "Full wave vector calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Lin, R.

Lin, S. Y.

R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
[CrossRef]

S. Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic bandgap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
[CrossRef]

Liu, Y. F.

K. M. Leung and Y. F. Liu, "Full wave vector calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Maldovan , M.

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3, 593-600 (2004).
[CrossRef] [PubMed]

Maldovan, M.

C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

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

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

Martin-Moreno, L.

L. Martin-Moreno, F. J. Garcia-Vidal, and A. M. Somoza, "Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials," Phys. Rev. Lett. 83, 73-75 (1999).
[CrossRef]

Mayer, T. S.

L. Zavieh and T. S. Mayer, "Demonstration of a three-dimensional simple-cubic infrared photonic crystal," Appl. Phys. Lett. 75, 2533-2525 (1999).
[CrossRef]

Qiu , M.

Satpathy, S.

Z. Zhang and S. Satpathy, "Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations," Phys. Rev. Lett. 65, 2650-2653 (1990).
[CrossRef] [PubMed]

Sharp, D. N.

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 404, 53-56 (2000).
[CrossRef] [PubMed]

Sigalas, M. M.

R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
[CrossRef]

S. Y. Lin, J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, "Complete three-dimensional photonic bandgap in a simple cubic structure," J. Opt. Soc. Am. B 18, 32-35 (2001).
[CrossRef]

Somoza, A. M.

L. Martin-Moreno, F. J. Garcia-Vidal, and A. M. Somoza, "Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials," Phys. Rev. Lett. 83, 73-75 (1999).
[CrossRef]

Soukoulis, C. M.

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

Sozuer , H. S.

Thomas, E. L.

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3, 593-600 (2004).
[CrossRef] [PubMed]

C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

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

M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
[CrossRef]

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

Toader , O.

O. Toader and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905 (2004).
[CrossRef] [PubMed]

Turberfield, A. J.

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 404, 53-56 (2000).
[CrossRef] [PubMed]

Ullal, C. K.

C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

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

Urbas, A. M.

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[CrossRef]

Wada, M.

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

White, C. A.

Wohlgemuth, M.

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

M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
[CrossRef]

Yablonovitch , E.

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

Yablonovitch, E.

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

Yang, S.

C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

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

Yuan, Z.

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

Yufa, N.

M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
[CrossRef]

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

Zavieh , L.

L. Zavieh and T. S. Mayer, "Demonstration of a three-dimensional simple-cubic infrared photonic crystal," Appl. Phys. Lett. 75, 2533-2525 (1999).
[CrossRef]

Zhang , Z.

Z. Zhang and S. Satpathy, "Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations," Phys. Rev. Lett. 65, 2650-2653 (1990).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

L. Zavieh and T. S. Mayer, "Demonstration of a three-dimensional simple-cubic infrared photonic crystal," Appl. Phys. Lett. 75, 2533-2525 (1999).
[CrossRef]

M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, "A simple cubic photonic lattice in silicon," Appl. Phys. Lett. 70, 2966-2968 (1997).
[CrossRef]

C. K. Ullal, M. Maldovan, S. Yang, and E. L. Thomas, "Photonic crystals through holographic lithography: simple cubic, diamond-like and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

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

J. Opt. Soc. Am. B (3)

Macromolecules (1)

M. Wohlgemuth, N. Yufa, J. Hoffman, and E. L. Thomas, "Triply periodic bicontinuous cubic microdomain morphologies by symmetries," Macromolecules 34, 6083-6089 (2001).
[CrossRef]

Nat. Mater. (1)

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3, 593-600 (2004).
[CrossRef] [PubMed]

Nature (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonic crystals: putting a new twist on light," Nature 386, 143-149 (1997).
[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 404, 53-56 (2000).
[CrossRef] [PubMed]

Phys. Rev. B (3)

R. Biswas, M. M. Sigalas, K. M. Ho, and S. Y. Lin, "Three-dimensional photonic band gaps in modified simple cubic lattices," Phys. Rev. B 65, 205121 (2002).
[CrossRef]

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2000).
[CrossRef]

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519 (2000).
[CrossRef]

Phys. Rev. Lett. (8)

O. Toader and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905 (2004).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, and A. M. Somoza, "Self-assembled triply periodic minimal surfaces as molds for photonic band gap materials," Phys. Rev. Lett. 83, 73-75 (1999).
[CrossRef]

E. Yablonovitch and T. J. Gmitter, "Photonic band structure: the face-centered-cubic case," Phys. Rev. Lett. 63, 1950-1953 (1989).
[CrossRef] [PubMed]

K. M. Leung and Y. F. Liu, "Full wave vector calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Z. Zhang and S. Satpathy, "Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations," Phys. Rev. Lett. 65, 2650-2653 (1990).
[CrossRef] [PubMed]

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

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

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[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

Air spheres in the simple cubic lattice. (a) The arrangement of air spheres at the corners of the unit cell creates a dielectric network that connects the sites of the simple cubic lattice. (b) Corresponding band diagram at dielectric volume fraction f=0.19, where the structure shows a maximum 7% complete gap. This structure presents a complete 5–6 gap and a 2–3 transition gap. (c) Gap map of the complete 5–6 photonic band gap as a function of the dielectric volume fraction.

Fig. 2
Fig. 2

Air cylinders in the simple cubic lattice. (a) The arrangement of air cylinders along the edges of the unit cell creates a dielectric network that connects the sites of the simple cubic lattice. The displayed structure is a good approximation of the actual morphology. (b) Corresponding band diagram at dielectric volume f=0.19, where the structure shows a maximum ∼10% complete 5–6 gap. (c) Gap map of the complete 5–6 photonic band gap as a function of the dielectric volume fraction.

Fig. 3
Fig. 3

Dielectric cylinders in the simple cubic lattice. (a) The dielectric cylinders create a dielectric network connecting the simple cubic lattice sites. (b) Corresponding band diagram at dielectric volume f=0.19, where the structure shows a maximum ∼7% complete gap. This simple cubic structure presents a 2–3 complete gap. (c) Complete 2–3 photonic band gap as a function of the dielectric volume fraction.

Fig. 4
Fig. 4

Modified simple cubic lattices. (a) Simple cubic structure made of dielectric spheres on the cubic lattice sites connected by cylinders. (b) Corresponding band diagram at dielectric volume f=0.21, where the structure shows a maximum 12% complete gap. This simple cubic structure presents a complete 5–6 photonic band gap. (c) Complete 5–6 photonic band gap as a function of the dielectric volume fraction.

Fig. 5
Fig. 5

Level-set simple cubic P. (a) The single P structure is given by the formula f(x, y, z)=sin(x)+sin(y)+sin(z). This 3-D surface connects the nearest-neighbor lattice sites in the simple cubic lattice. (b) Band diagram at f=0.26, where the structure shows a maximum 13% complete 5–6 gap. (c) Complete 5–6 photonic band gap as a function of the dielectric volume fraction.

Fig. 6
Fig. 6

2-D simple cubic structure. (a) A 2-D version of the simple cubic morphology involves the combination of dielectric veins and dielectric columns at the square lattice sites. (b) Photonic band diagram at f=0.36. Solid curves correspond to TE polarization, and dashed curves correspond to TM polarization. (c) Complete photonic band gap as a function of the dielectric volume fraction.

Fig. 7
Fig. 7

Photonic-band-gap clustering. (a) Complete 5–6 photonic band gaps for air spheres, air cylinders, modified simple cubic, and single P structure. The gaps cluster around a common frequency range, indicating that the common underlying dielectric network is primarily responsible for the gap.

Fig. 8
Fig. 8

Single P–3-D checkerboard analogy. (a) The first suggested photonic crystal, the 3-D checkerboard, was proposed by Yablonovitch1 as a 3-D generalization of 1-D dielectric modulations. Because 1-D dielectric modulations create gaps for light propagating at normal incidence, Yablonovitch envisioned a 3-D dielectric structure that can forbid the propagation of light for all directions. (b) The 1-D dielectric modulations can be described by f(x)=sin(x). A intuitive 3-D generalization is f(x)=sin(x)+sin(y)+sin(z), which corresponds to the single P structure. Unlike the 3-D checkerboard lattice, this photonic crystal presents a large 13% complete photonic band gap14 at volume fractions f0.26 for a refractive index n=3.6. Furthermore, this structure is accessible for fabrication by using 3-D interference lithography.12,18,22

Equations (2)

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(k+G)·[(k+G)×E(G)]
+ω2c2 G(G-G)E(G)=0,

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