Abstract

We report the use of a (4+1)-beam optical interference holography technique to fabricate woodpile structures in photo-resists. The configuration consists of 4 linearly polarized side beams arranged symmetrically around a circularly polarized central beam with all the beams from the same half space, making it easily accessible experimentally. The fabricated woodpile structures are in good agreement with model simulations. Furthermore, woodpiles with the diamond symmetry are also obtained by exploiting the shrinkage of the photo-resists. Bandgaps in the visible range are also observed for the samples with and without the correct stacking of the woodpile structures.

© 2006 Optical Society of America

Full Article  |  PDF Article
Related Articles
Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties

Jesper Serbin, Aleksandr Ovsianikov, and Boris Chichkov
Opt. Express 12(21) 5221-5228 (2004)

Translation of interference pattern by phase shift for diamond photonic crystals

Jun Hyuk Moon, Shu Yang, David J. Pine, and Seung-Man Yang
Opt. Express 13(24) 9841-9846 (2005)

Holographic design and band gap evolution of photonic crystals formed with five-beam symmetric umbrella configuration

G. Y. Dong, L. Z. Cai, X. L. Yang, X. X. Shen, X. F. Meng, X. F. Xu, and Y. R. Wang
Opt. Express 14(18) 8096-8102 (2006)

References

  • View by:
  • |
  • |
  • |

  1. C. M. Soukoulis, “Photonic band gap material,” (Kluwer, Dordrecht, 1996).
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  3. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic crystals,” (Princeton, 1995).
  5. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
    [Crossref] [PubMed]
  6. J. Maddox, “Photonic band-gaps bite the dust,” Nature 348, 481 (1990).
    [Crossref]
  7. E. Yablonovitch, T. 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]
  8. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
    [Crossref]
  9. M. Maldovan and E. L. Thomas, “Diamond-structured photonic crystal,” Nature Materials 3, 593–600 (2004).
    [Crossref] [PubMed]
  10. J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in Titania,” Science 281, 802–804 (1998).
    [Crossref]
  11. E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
    [Crossref]
  12. W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
    [Crossref]
  13. F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
    [Crossref]
  14. A. Chutinan and S. Noda, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Phys. Rev. B 57, R2006–R2008 (1998).
    [Crossref]
  15. O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals,” Science 292, 1133–1135 (2001).
    [Crossref] [PubMed]
  16. N. Yamamoto, S. Noda, and A. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997).
    [Crossref]
  17. 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]
  18. A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
    [Crossref]
  19. 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]
  20. S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
    [Crossref]
  21. L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Optics Lett. 27, 900–902 (2002).
    [Crossref]
  22. Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
    [Crossref]
  23. X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
    [Crossref]
  24. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
    [Crossref]
  25. X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
    [Crossref]
  26. Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
    [Crossref] [PubMed]
  27. M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
    [Crossref]
  28. M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
    [Crossref]
  29. S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003).
    [Crossref]
  30. D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (2003).
    [Crossref]
  31. C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004).
    [Crossref]
  32. M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
    [Crossref]
  33. C. K. Ullal, M. Maldovan, M. Wohlgemuth, and E. L. Thomas, “Triply periodic bicontinuous structures through interference lithography: a level set approach,” J. Opt. Soc. Am. 20, 948–954 (2003).
    [Crossref]
  34. D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004).
    [Crossref]
  35. T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005).
    [Crossref]
  36. O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004).
    [Crossref]
  37. Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
    [Crossref]
  38. W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

2006 (1)

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

2005 (4)

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005).
[Crossref]

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

2004 (6)

M. Maldovan and E. L. Thomas, “Diamond-structured photonic crystal,” Nature Materials 3, 593–600 (2004).
[Crossref] [PubMed]

O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004).
[Crossref]

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004).
[Crossref]

D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004).
[Crossref]

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
[Crossref]

2003 (7)

S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003).
[Crossref]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (2003).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

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

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

2002 (4)

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Optics Lett. 27, 900–902 (2002).
[Crossref]

2001 (2)

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
[Crossref]

O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals,” Science 292, 1133–1135 (2001).
[Crossref] [PubMed]

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 404, 53–56 (2000).
[Crossref] [PubMed]

1998 (3)

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]

A. Chutinan and S. Noda, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Phys. Rev. B 57, R2006–R2008 (1998).
[Crossref]

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

1997 (1)

N. Yamamoto, S. Noda, and A. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997).
[Crossref]

1994 (1)

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[Crossref]

1991 (1)

E. Yablonovitch, T. 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 (2)

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

J. Maddox, “Photonic band-gaps bite the dust,” Nature 348, 481 (1990).
[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]

Aizenberg, J.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

Arsh, A.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

Belmonte, M.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[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]

Blanco, A.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

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]

Busch, K.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Cai, L. Z.

L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Optics Lett. 27, 900–902 (2002).
[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]

Chaikin, P. M.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

Chan, C. T.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 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 a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Chan, T. Y. M.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005).
[Crossref]

O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004).
[Crossref]

Chen, G.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004).
[Crossref]

Chen, J. M.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

Chen, Y. L.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Chutinan, A.

A. Chutinan and S. Noda, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Phys. Rev. B 57, R2006–R2008 (1998).
[Crossref]

Datta, S.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[Crossref]

Denning, R. G.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (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 404, 53–56 (2000).
[Crossref] [PubMed]

Deubel, M.

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Deuble, M.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

Enkrich, C.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Feigel, A.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[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]

García-Santamaría, F.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

Gmitter, T.

E. Yablonovitch, T. 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]

Han, Y.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004).
[Crossref]

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]

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]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 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 a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

Hoffmann, J.

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
[Crossref]

Ibisate, M.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic crystals,” (Princeton, 1995).

John, S.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005).
[Crossref]

O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004).
[Crossref]

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
[Crossref]

O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals,” Science 292, 1133–1135 (2001).
[Crossref] [PubMed]

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

Kaso, A.

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
[Crossref]

Kawata, S.

S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003).
[Crossref]

Klebanov, M.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

Koch, W.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

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]

Lee, H. F.

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

Lee, J. C. W.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

Leung, K. M.

E. Yablonovitch, T. 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]

Li, J.

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

Li, W.

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

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]

López, C.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

Lyubin, V.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

Maddox, J.

J. Maddox, “Photonic band-gaps bite the dust,” Nature 348, 481 (1990).
[Crossref]

Maldovan, M.

M. Maldovan and E. L. Thomas, “Diamond-structured photonic crystal,” Nature Materials 3, 593–600 (2004).
[Crossref] [PubMed]

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

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic crystals,” (Princeton, 1995).

Megens, M.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

Meisel, D. C.

D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Meseguer, F.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

Miklyaev, Yu. V.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Miyazaki, H. T.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

Ng, C. Y.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

Noda, S.

A. Chutinan and S. Noda, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Phys. Rev. B 57, R2006–R2008 (1998).
[Crossref]

N. Yamamoto, S. Noda, and A. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997).
[Crossref]

Palacios-Lidón, E.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

Pang, Y. K.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Pereira, S.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

Russel, W. B.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

Sánchez-Dehesa, J.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

Sasaki, A.

N. Yamamoto, S. Noda, and A. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997).
[Crossref]

Sfez, B.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

Sharp, D. N.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (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 404, 53–56 (2000).
[Crossref] [PubMed]

Sheng, P

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

Sheng, P.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

Shinya, N.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

Shoji, S.

S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003).
[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]

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]

Soukoulis, C. M.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 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 a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref] [PubMed]

C. M. Soukoulis, “Photonic band gap material,” (Kluwer, Dordrecht, 1996).

Su, H. M.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Su, N. M.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

Sun, G.

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

Sun, H.

S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003).
[Crossref]

Tam, W. Y.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

Tang, F.

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

Thomas, E. L.

M. Maldovan and E. L. Thomas, “Diamond-structured photonic crystal,” Nature Materials 3, 593–600 (2004).
[Crossref] [PubMed]

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

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
[Crossref]

Toader, O.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005).
[Crossref]

O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004).
[Crossref]

O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals,” Science 292, 1133–1135 (2001).
[Crossref] [PubMed]

Turberfield, A. J.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (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 404, 53–56 (2000).
[Crossref] [PubMed]

Ullal, C. K.

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

Urquía, A.

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

Veinger, M.

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

Von Freymann, G.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Vos, W. L.

J. E. G. 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.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Wang, X.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Wang, Y. R.

L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Optics Lett. 27, 900–902 (2002).
[Crossref]

Wegener, M.

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
[Crossref]

D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Wijnhoven, J. E. G. J.

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

Wiltzius, P.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic crystals,” (Princeton, 1995).

Wohlgemuth, M.

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

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
[Crossref]

Xu, J.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Xu, J. F.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, T. 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. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997).
[Crossref]

Yang, S.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004).
[Crossref]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

Yang, X. L.

L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Optics Lett. 27, 900–902 (2002).
[Crossref]

Yufa, N.

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
[Crossref]

Zeng, Z. H.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

Zhong, Y. C.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

Zhu, S. A.

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[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]

Adv. Mat. (1)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional Mesoscale Quasi-crystals,” Adv. Mat. 15, 1526–1528 (2003).
[Crossref]

Adv. Mater. (1)

F. García-Santamaría, H. T. Miyazaki, A. Urquía, M. Ibisate, M. Belmonte, N. Shinya, F. Meseguer, and C. López, “Nanorobotic manipulation of microspheres for on-chip diamond architectures,” Adv. Mater. 4, 1144–1147 (2002).
[Crossref]

App. Phys. Lett. (2)

A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” App. Phys. Lett. 83, 4480–4482 (2003).
[Crossref]

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of Slanted Pore photonic crystals,” App. Phys. Lett. 85, 1895–1897 (2004).
[Crossref]

Appl. Phys. Lett. (7)

S. Shoji, H. Sun, and S. Kawata, “Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference,” Appl. Phys. Lett. 83, 608–610 (2003).
[Crossref]

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. Han, and S. Yang, “Photonic crystals through holographic lithography: simple cubic, diamond-like, and gyroid-like structures,” Appl. Phys. Lett. 84, 5434–5436 (2004).
[Crossref]

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88, 051901 (2006).
[Crossref]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Threedimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82, 2212–2214 (2003).
[Crossref]

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, C. López, and J. Sánchez-Dehesa, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81, 4925–4927 (2002).
[Crossref]

Y. C. Zhong, S. A. Zhu, N. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, “Photonic crystal with diamondlike structure fabricated by holographic lithography,” Appl. Phys. Lett. 87, 061103-1/3 (2005).
[Crossref]

Chem. Mat. (1)

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14, 2831–2833 (2002).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Phys. Condens. Matter. (1)

W. Li, G. Sun, F. Tang, W. Y. Tam, J. Li, C. T. Chan, and P Sheng, “Fabrication and optical characterization of gold-infiltrated silica opals,” J. Phys. Condens. Matter. 17, 2177–2190 (2005).
[Crossref]

Jpn. J. Appl. Phys. (1)

N. Yamamoto, S. Noda, and A. Sasaki, “Development of one period of a three-dimensional photonic crystal in the 5–10 µm wavelength region by wafer fusion and laser beam diffraction pattern observation techniques,” Jpn. J. Appl. Phys. 36, 1907–1911 (1997).
[Crossref]

Maromol. (1)

M. Wohlgemuth, N. Yufa, J. Hoffmann, and E. L. Thomas, “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Maromol. 34, 6083–6089 (2001).
[Crossref]

Nat. Mater. (1)

M. Deuble, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref]

Nature (3)

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. 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]

J. Maddox, “Photonic band-gaps bite the dust,” Nature 348, 481 (1990).
[Crossref]

Nature Materials (1)

M. Maldovan and E. L. Thomas, “Diamond-structured photonic crystal,” Nature Materials 3, 593–600 (2004).
[Crossref] [PubMed]

Optics Express (1)

Y. K. Pang, J. C. W. Lee, H. F. Lee, W. Y. Tam, C. T. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Optics Express 13, 7615–7620 (2005).
[Crossref] [PubMed]

Optics Lett. (1)

L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Optics Lett. 27, 900–902 (2002).
[Crossref]

Phys. Rev. B (4)

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, “A-7 structure: a family of photonic crystals,” Phys. Rev. B 50, 1988–1991 (1994).
[Crossref]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, “Holographic photonic crystals with diamond symmetry,” Phys. Rev. B 68, 205102-1/6 (2003).
[Crossref]

D. C. Meisel, M. Wegener, and K. Busch, “Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps,” Phys. Rev. B 70, 165104-1/10 (2004).
[Crossref]

A. Chutinan and S. Noda, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Phys. Rev. B 57, R2006–R2008 (1998).
[Crossref]

Phys. Rev. E (1)

T. Y. M. Chan, O. Toader, and S. John, “Photonic band gap templating using optical interference. Lithography,” Phys. Rev. E 71, 046605-1/18 (2005).
[Crossref]

Phys. Rev. Lett. (5)

O. Toader, T. Y. M. Chan, and S. John, “Photonic band gap architectures for holographic lithography,” Phys. Rev. Lett. 92, 043905-1/4 (2004).
[Crossref]

E. Yablonovitch, T. 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]

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

Science (2)

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

O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals,” Science 292, 1133–1135 (2001).
[Crossref] [PubMed]

Other (3)

C. M. Soukoulis, “Photonic band gap material,” (Kluwer, Dordrecht, 1996).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic crystals,” (Princeton, 1995).

W. Y. Tam, “Woodpile and diamond structures by optical interference holography,” http://arxiv.org/ftp/physics/papers/0607/0607092.pdf (2006).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

(a). (4+1)-beam configuration for the woodpile structure. (b) Superposition of x-rods and y-rods obtained by the interference of ( k 0, k 2, k 4) and ( k 0, k 1, k 3), respectively. (c) Woodpile structure shown as intensity contour surfaces with a 50% cut-off by the interference of ( k 0, k 1, k 2, k 3, k 4) beams with equal phases and using φ=41.8°. The structure is compressed by 40% and expanded by 10% along the z and in the xy-directions, respectively, to simulate the deformations observed in the experiment. (Same result is obtained using φ=70.53° but without the deformations as reported in Ref. [38].) The insets, upper-right (50% cut-off) and lower-right (95% cut-off), are views of the top and the unit cell of the diamond structure, respectively. (d) Contour surfaces with a 40% intensity cut-off for the 5-beam interference similar to (c) but with k 2 180° out of phase w.r.t. the other beams. The insets, upper-right (40% cut-off) and lower-right (60% cut-off), are views of the top and the unit cell, respectively.

Fig. 2.
Fig. 2.

(a). 3D SEM image of woodpile structure. The upper-left inset shows the expanded view of the woodpile structure. (b)–(d) SEM images for the woodpile structures with a/b=0.72, 0.88, and 0.82, respectively. Note that (b) and (c) show the favorable results with the x- and y-rods properly interlaced while (d) shows the unfavorable result with the x-and y-rods in the same plane for each layer. The upper-right insets (size 1.5×1.0µm2) are the expanded front views while the lower-left insets (size 1.8×1.8µm2) are the top views of the structures. The scale bars (white) are all 1.0 µm.

Fig. 3.
Fig. 3.

(a)-(c). Normal reflectance (in blue) and transmittance (in red) for the samples in Fig. 2(b)-(d), respectively. The insets are white light reflection photos. The dashed circles (17 µm diameter) are regions where optical spectra are obtained.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

[ k 0 = k ( 0 , 0 , 1 ) k 1 = k ( sin φ , 0 , cos φ ) k 2 = k ( 0 , sin φ , cos φ ) k 3 = k ( sin φ , 0 , cos φ ) k 4 = k ( 0 , sin φ , cos φ ) ] ,
I ( r ) = l , m E l · E m * e i q lm · r i ( δ l δ m )

Metrics