Abstract

We describe the creation of general photonic crystals by means of holography with an experimental demonstration. The recordings of periodic variations of amplitude and phase by the interference of coherent laser beams offer a natural means for the creation of one- two- or three-dimensional photonic crystals. Based on the principle of the interference of four noncoplanar beams, we present a comparative analysis of two different approaches for creating photonic crystals and use numerical simulated lattice structures to illustrate the differences between these two approaches. We then use a specific symmetrical optical architecture and select the proper approach to create holographic photonic crystals. The advantages and constraints of this holographic method are discussed.

© 2004 Optical Society of America

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  1. 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]
  2. 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]
  3. 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]
  4. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  5. J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
    [CrossRef]
  6. 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]
  7. S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
    [CrossRef] [PubMed]
  8. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
    [CrossRef]
  9. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
    [CrossRef]
  10. A. Sharkawy, S. Shi, D. W. Prather, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt. 40, 2247–2252 (2001).
    [CrossRef]
  11. C. C. Cheng, A. Scherer, R.-C. 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]
  12. A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
    [CrossRef]
  13. 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]
  14. 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]

2002

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]

A. Sharkawy, S. Shi, D. W. Prather, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt. 40, 2247–2252 (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]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

1998

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

1997

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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

C. C. Cheng, A. Scherer, R.-C. 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]

1987

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

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.-C. 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]

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[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.-C. 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.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

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

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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]

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

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]

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[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]

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

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]

Prather, D. W.

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.-C. 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]

Sharkawy, A.

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]

Shi, S.

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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]

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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. C. Cheng, A. Scherer, R.-C. 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.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

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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M. C. Wanke, O. Lehmann, K. Müller, Q. Wen, M. Stuke, “Laser rapid prototyping of photonic band-gap microstructures,” Science 275, 1284–1286 (1997).
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A. van Blaaderen, R. Ruel, P. Wiltzius, “Template-directed colloidal crystallization,” Nature 385, 321–324 (1997).
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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).
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C. C. Cheng, A. Scherer, R.-C. Tyan, Y. Fainman, G. Witzgall, E. Yablonovitch, “New fabrication techniques for high quality photonic crystals,” J. Vac. Sci. Technol. B 15, 2764–2767 (1997).
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C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
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C. C. Cheng, A. Scherer, R.-C. 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]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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).
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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).
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[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Concept diagram of an optical architecture. In aperture array 1, the length and width are L M and L R . The location of the opening aperture is (m, r). In aperture array 2, the length and width are L P and L Q . The location of the opening aperture is (p, q). The focal lengths of lenses 1 and 2 are f 1 and f 2, respectively.

Fig. 2
Fig. 2

For approach A, (m, r) = (1, 1), (8, 1), (1, 8); f 1 = 5 cm, (p, q) = (8, 8); f 2 = 15 cm; and λ = 650 nm. (a) A 3-D plot of the four noncoplanar beams. The circle denotes the interference region. (b) The interference pattern of these beams. The inset is the projected intensity distribution between any two neighboring spheres in the interference pattern.

Fig. 3
Fig. 3

For approach A, (m, r) = (1, 4), (4, 1), (8, 4); f 1 = 5 cm, (p, q) = (4, 8); f 2 = 10 cm; and λ = 650 nm. (a) A 3-D plot of the four noncoplanar beams. The circle denotes the interference region. (b) The interference pattern of these beams.

Fig. 4
Fig. 4

For approach A, (m, r) = (4, 1), (4, 8); f 1 = 5 cm; (p, q) = (1, 4), (8, 4); f 2 = 10 cm; and λ = 650 nm. (a) A 3-D plot of the four noncoplanar beams. The circle denotes the interference region. (b) The interference pattern of these beams.

Fig. 5
Fig. 5

By using approach B we obtained (a) a 3-D plot of the four noncoplanar beams for primitive lattice constant vectors Ā = (1, 0, 0), = (0, 1, 0), = (0, 0, 1) in micrometers. The circle indicates the interference region. (b) The interference pattern (simple cubic) of these beams.

Fig. 6
Fig. 6

By using approach B we obtained (a) a 3-D plot of the four noncoplanar beams for primitive lattice constant vectors Ā = (1, 0, 0), = (0.5, 0.866, 0), = (0, 0, 1) in micrometers. The circle indicates the interference region. (b) The interference pattern (simple hexagonal) of these beams.

Fig. 7
Fig. 7

Experimental system used to create holographic photonic crystals. The system is a realization of the concept of the optical architecture shown in Fig. 1: M, mirror; BS, beam splitter; AG, array generator; AA, aperture array; HRM, holographic recording medium; L, lens; SF, spatial filter; Ir, iris.

Fig. 8
Fig. 8

Microscope image at 1000× in the x-z plane of a 2-D photonic crystal: (a) the exposure time is 0.5 s, a = 5.662 μm and b = 5.360 μm. (b) The exposure time is 0.25 s, a = 5.826 μm and b = 5.412 μm. Note, we refer to the y axis as the axis of propagation instead of the z axis as is conventionally done.

Fig. 9
Fig. 9

(a) Microscope image at 200× in the x-z plane of a 3-D photonic crystal: a = 8.497 μm, b = 14.063 μm, where color dispersion is visible. (b) Same image as in (a) but color enhanced.

Equations (43)

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Ej¯=Ej expiKj¯·r¯+φojej¯, j=1, 2, 3, 4,
Kj¯=Kjx, Kjy, Kjz=2πλsj, tj, uj,
I=j Ej2+i<j 2EiEj cos θij×cosKi¯-Kj¯·r¯+φoi-φoj,
K1¯-K2¯r¯=2lπ,
K1¯-K3¯r¯=2mπ,
K1¯-K4¯r¯=2nπ,
K2¯-K3¯r¯=2pπ,
K2¯-K4¯r¯=2qπ,
K3¯-K4¯r¯=2rπ,
s12x+t12y+u12z=λl,
s13x+t13y+u13z=λm,
s14x+t14y+u14z=λn.
x=λlt12u12λmt13u13λnt14u14Δ,
y=s12λlu12s13λmu13s14λnu14Δ,
z=s12t12λls13t13λms14t14λnΔ,
Δ=s12t12u12s13t13u13s14t14u14.
A¯=λΔt13u13t14u14, u13s13u14s14, s13t13s14t14,
B¯=λΔt14u14t12u12, u14s14u12s12, s14t14s12t12,
C¯=λΔt12u12t13u13, u12s12u13s13, s12t12s13t13.
K1¯=2πλs1, t1, u1, K2¯=2πλs2, t2, u2, K3¯=2πλs3, t3, u3, K4¯=2πλs4, t4, u4.
K1¯=-0.27, 0.93, -0.27,K2¯=0.27, 0.93, -0.27,K3¯=-0.27, 0.93, 0.27,K4¯=0.14, -0.98, 0.14.
A¯=-1.21, -0.26, 0,B¯=0, -0.26, -1.21,C¯=0, 0.34, 0.
K1¯=-0.27, 0.93, -0.04,K2¯=-0.04, 0.93, -0.27,K3¯=0.27, 0.93, -0.04,K4¯=-0.02, -0.98, 0.14.
A¯=0, 0.28, 2.83,B¯=-1.21, -0.27, -1.21,C¯=0, 0.34, 0.
K1¯=-0.04, 0.96, -0.28,K2¯=-0.04, 0.96, 0.28,K3¯=-0.14, -0.99, -0.02,K4¯=0.14, -0.99, -0.02.
A¯=0, -0.15, -1.17,B¯=2.27, 0.21, 0,C¯=-2.27, 0.12, 0.
A¯=a1, a2, a3,B¯=b1, b2, b3,C¯=c1, c2, c3.
K1¯=2πλs1, t1, u1,
K2¯=2πλs1-s12, t1-t12, u1-u12,
K3¯=2πλs1-s13, t1-t13, u1-u13,
K4¯=2πλs1-s14, t1-t14, u1-u14.
s12+t12+u12=1,
s1-s122+t1-t122+u1-u122=1,
s1-s132+t1-t132+u1-u132=1,
s1-s142+t1-t142+u1-u142=1.
A¯=1, 0, 0, B¯=0, 1, 0, C¯=0, 0, 1.
λ=1.15 μm, K1¯=2πλ0.58, 0.58, 0.58,K2¯=2πλ-0.58, 0.58, 0.58,K3¯=2πλ0.58, -0.58, 0.58,K4¯=2πλ0.58, 0.58, -0.58.
A¯=1, 0, 0,B¯=0.5, 0.86, 0,C¯=0, 0, 1.
λ=0.79 μm,K1¯=2πλ0.80, 0.46, 0.40,K2¯=2πλ0, 0.92, 0.40,K3¯=2πλ0.80-0.46, 0.40,K4¯=2πλ0.80, 0.46, -0.40.
K1¯=0.0560, 0.9969, -0.0560,K2¯=-0.0560, 0.9969, 0.0560,K3¯=0.0560, 0.9969, 0.0560.
A¯=5.804, 0, 0, B¯=0, 0, 5.804.
K1¯=0.0187, 0.9996, -0.0187,K2¯=-0.0187, 0.9982, 0.0562,K3¯=0.0562, 0.9982, 0.0187,K4¯=0.0398, -0.9984, -0.0398.
A¯=5.786, -0.339, -5.790,B¯=-11.573, 0.170, -5.786,C¯=0.004, 0.325, 0.008.

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