Abstract

A systematic and comprehensive analysis of the interference of four umbrellalike beams (IFUB) is provided based on the reciprocal space theory. The concept of pattern contrast is extended to the case of the IFUB, and it is indicated that a uniform contrast for all the interference terms can be obtained by properly choosing the beam ratio and the polarization of each beam. Different polarization combinations, including linear light and linear light, circular light and circular light, and linear light and circular light, have been discussed for the purpose of maximum uniform contrast. It is shown that the use of circular light may generally improve the uniform contrast. This study may lay a theoretical foundation for holographic fabrication of three-dimensional (3D) periodic microstructures, such as simple cubic, body-centered cubic, face-centered cubic, or trigonal lattice.

© 2002 Optical Society of America

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    [CrossRef]
  2. T. F. Krauss, R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
    [CrossRef]
  3. C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
    [CrossRef]
  4. A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
    [CrossRef]
  5. M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
    [CrossRef] [PubMed]
  6. B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
    [CrossRef]
  7. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
    [CrossRef] [PubMed]
  8. T. Kondo, S. Matsuo, S. Juodkazis, 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, Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001).
    [CrossRef]
  10. L. Z. Cai, X. L. Yang, Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49, 1663–1672 (2002).
    [CrossRef]
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    [CrossRef]
  12. X. L. Yang, L. Z. Cai, “Wave design of the interference of three noncoplanar beams for microfiber fabrication,” Opt. Commun. 208, 293–297 (2002).
    [CrossRef]
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  14. K. I. Petsas, A. B. Coates, G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50, 5173–5789 (1994).
    [CrossRef] [PubMed]
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2002

L. Z. Cai, X. L. Yang, Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49, 1663–1672 (2002).
[CrossRef]

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

X. L. Yang, L. Z. Cai, “Wave design of the interference of three noncoplanar beams for microfiber fabrication,” Opt. Commun. 208, 293–297 (2002).
[CrossRef]

2001

T. Kondo, S. Matsuo, S. Juodkazis, 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]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001).
[CrossRef]

2000

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

1999

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

T. F. Krauss, R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

1997

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
[CrossRef] [PubMed]

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

1994

K. I. Petsas, A. B. Coates, G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50, 5173–5789 (1994).
[CrossRef] [PubMed]

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Barlow, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Cai, L. Z.

L. Z. Cai, X. L. Yang, Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49, 1663–1672 (2002).
[CrossRef]

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

X. L. Yang, L. Z. Cai, “Wave design of the interference of three noncoplanar beams for microfiber fabrication,” Opt. Commun. 208, 293–297 (2002).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of three-dimensional periodical microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A (to be published).

Campbell, M.

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

Cheng, C. C.

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

Coates, A. B.

K. I. Petsas, A. B. Coates, G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50, 5173–5789 (1994).
[CrossRef] [PubMed]

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

Denning, R. G.

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

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Fainman, Y.

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

Fan, S.

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

Grynberg, G.

K. I. Petsas, A. B. Coates, G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50, 5173–5789 (1994).
[CrossRef] [PubMed]

Harrison, M. T.

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

Hecht, E.

E. Hecht, A. Zajac, Optics. (Addison-Wesley, Reading, Massachusetts1974).

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Joannopoulos, J. D.

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

Juodkazis, S.

T. Kondo, S. Matsuo, S. Juodkazis, 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]

Kondo, T.

T. Kondo, S. Matsuo, S. Juodkazis, 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]

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, “Photonic crystals in the optical regime—past, present and future,” Prog. Quantum Electron. 23, 51–96 (1999).
[CrossRef]

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Lee, I. Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Lehmann, O.

M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
[CrossRef] [PubMed]

Marder, S. R.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Matsuo, S.

T. Kondo, S. Matsuo, S. Juodkazis, 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]

McCord-Maughon, D.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Misawa, H.

T. Kondo, S. Matsuo, S. Juodkazis, 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]

Müller, K.

M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
[CrossRef] [PubMed]

Perry, J. W.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Petsas, K. I.

K. I. Petsas, A. B. Coates, G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50, 5173–5789 (1994).
[CrossRef] [PubMed]

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Röckel, H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Ruel, R.

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

Rumi, M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Scherer, A.

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

Sharp, D. N.

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

Stuke, M.

M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
[CrossRef] [PubMed]

Turberfield, A. J.

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

Tyan, R.

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

van Blaaderen, A.

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

Villeneuve, P. R.

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

Wang, Y. R.

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

L. Z. Cai, X. L. Yang, Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49, 1663–1672 (2002).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of three-dimensional periodical microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A (to be published).

Wanke, M. C.

M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
[CrossRef] [PubMed]

Wen, Q.

M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
[CrossRef] [PubMed]

Wiltzius, P.

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

Witzgall, G.

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

Wu, X. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. L. Wu, S. R. Marder, J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Yablonovitch, E.

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

Yang, X. L.

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

X. L. Yang, L. Z. Cai, “Wave design of the interference of three noncoplanar beams for microfiber fabrication,” Opt. Commun. 208, 293–297 (2002).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49, 1663–1672 (2002).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26, 1858–1860 (2001).
[CrossRef]

L. Z. Cai, X. L. Yang, Y. R. Wang, “Formation of three-dimensional periodical microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A (to be published).

Zajac, A.

E. Hecht, A. Zajac, Optics. (Addison-Wesley, Reading, Massachusetts1974).

Appl. Phys. Lett.

T. Kondo, S. Matsuo, S. Juodkazis, 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. Mod. Opt.

L. Z. Cai, X. L. Yang, Y. R. Wang, “Interference of three noncoplanar beams: patterns, contrast and polarization optimization,” J. Mod. Opt. 49, 1663–1672 (2002).
[CrossRef]

J. Vac. Sci. Technol. B

C. C. Cheng, A. Scherer, R. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
[CrossRef]

Nature

A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
[CrossRef]

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

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Figures (2)

Fig. 1
Fig. 1

Umbrellalike symmetric recording geometry and the coordinate system used for calculation.

Fig. 2
Fig. 2

Comparison of the maximum uniform contrasts obtained from different combinations of polarization states in IFUB.

Tables (3)

Tables Icon

Table 1 Calculation Results of Maximum Uniform Contrast of IFUB for Different Polarization Combinations

Tables Icon

Table 2 Uniform Contrast and Beam Ratio for Different Polarization Combinations in IFUB

Tables Icon

Table 3 Optimized Polarization Combinations in IFUB for Different Ranges of θ

Equations (40)

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cos η=123 cos2 θ-1.
k10=l, m, n 0<l<1, -1<m<0, n=cos θ
k20=-l, m, n, k30=0, 1-n21/2, n, k40=0, 0, 1.
l=31-n21/22, m=-1-n21/22.
a1=2πb2×b3Ω*, a2=2πb3×b1Ω*, a3=2πb1×b2Ω*,
Ω*=b1  b2×b3,
ai  bj=2πδij=2π,i=j0,ij.
b1=2πλk10-k40, b2=2πλk20-k40, b3=2πλk30-k40.
a1=λ31/231-n21/2, -131-n21/2, 13n-1, a2=λ-31/231-n21/2, -131-n21/2, 13n-1, a3=λ0, 231-n21/2, 13n-1.
A=1+cos θ5-3 cos θ1/23 sin2 θ λ,
cos φ=3 cos θ-1-3 cos θ+5.
Ej=Ej expikj  r+φj0ej, j=14,
kj=2πλkj0=2πλlj, mj, nj.
I=j=14 Ej2+2 i<j EiEjeij coski-kj  r+φi0-φj0+δij, i, j=14,
Vij=2EiEjeijE12+E22+E32+E42, i, j=14, i<j.
e12e34=e13e24=e14e23,
E2E1=e13e23, E3E1=e12e23, E4E1=e12e24.
V=Vij=2e12e13e23e122+e132+e232+e132e232/e342, i, j=14, i<j.
eL=12ex+iey, eR=12ex-iey,
eL=12sin α-1sin αcos α cosβ-i cos γ-1sin αcos α cosγ+i cos β, eR=eL*.
eL1  eL2*=12sin α1 sin α2+1sin α1 sin α2×1+cos α1 cos α2cos β1 cos β2+cos γ1 cos γ2+icos α1+cos α2×cos β1 cos γ2-cos β2 cos γ1.
eL1,L2=|eL1  eL2*| =121+cos α1 cos α2+cos β1 cos β2+cos γ1 cos γ2 =121+cos δ,
eR1,R2=|eR1  eR2*|=121+cos δ
eL,R=|eL  eR*|=121-cos δ
esL=esR=12,
epL=epR=12 |cos δ|,
e12=e13=e23=1+cos η2=1+3 cos2 θ4, e14=e24=e34=1+cos θ2.
E1=E2=E3, E4E1=e12e24=1+3 cos2 θ21+cos θ
V=1+3 cos2 θ6+21+3 cos2 θ21+cos θ2.
e12=e13=e23=1+3 cos2 θ4, e14=e24=e34=1-cos θ2.
V=1+3 cos2 θ6+21+3 cos2 θ21-cos θ2,
E1=E2=E3, E4E1=e12e24=1+3 cos2 θ21-cos θ
l2+m2+n2=1, e4  k4=0, e14=e24=e34.
e12=e13=e23=cos 60°=12,
e14=e24=e34=12.
E1=E2=E3, E4E1=e12e24=12
e1=-32cos θ12cos θsin θ, e2=32cos θ12cos θsin θ, e3=0-cos θsin θ, e4=121i0
e12=e13=e23=|2-3 cos2 θ|2, e14=e24=e34=|cos θ|2.
V=|2-3 cos2 θ|3+22-3 cos2 θ2 cos θ2
E1=E2=E3=2 cos θ22-3 cos2 θE4.

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