Abstract

A holographic technique used to fabricate three-dimensional photonic crystals with a two-beam interference method is presented. In the optical setup of fabrication one beam is incident on the recording plate in the direction of the plate normal and the other beam with an angle to the normal. Three exposures were taken. Between each exposure, the recording plate was rotated 120° on axis until three exposures were completed. Good three-dimensional lattice structures have been obtained. Theoretical analysis, computer simulations, and experimental results are presented.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. Y. J. Lee, S. H. Kim, and J. Huh, "A high-extraction-efficiency nanopatterned organic light-emitting diode," Phys. Rev. Lett. 82, 3779-3781 (2003).
  4. S. Y. Lin, E. Chow, and V. Hietala, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
    [CrossRef] [PubMed]
  5. J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
    [CrossRef]
  6. M. D. B. Charlton, S. W. Roberts, and G. J. Parker, "Guided mode analysis and fabrication of a 2-dimensional visible photonic band structure confined within a planar semiconductor waveguide," Mater. Sci. Eng. B 49, 155-165 (1997).
    [CrossRef]
  7. A. Y. Vlasov, X. Bo, and C. J. Sturm, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 6861, 289-293 (2001).
    [CrossRef]
  8. E. Özbay, E. Michel, and G. Tuttle, "Micromachined millimeter-wave photonic band-gap crystals," Appl. Phys. Lett. 64, 2059-2061 (1994).
    [CrossRef]
  9. M. Campbell, N. D. Sharp, and T. M. Harrison, "Fabrication of photonic crystals for the visible spectrum by holography," Nature 6773, 53-56 (2000).
  10. V. Y. Miklyaev, C. D. Meisel, and A. Blanco, "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]
  11. D. N. Sharp, M. Campbell, and R. E. Dedman, "Photonic crystal for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
    [CrossRef]
  12. L. Z. Cai, X. I. Yang, and Y. R. Wang, "Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams," J. Opt. Soc. Am. A 19, 2238-2244 (2002).
    [CrossRef]
  13. I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
    [CrossRef]

2003 (3)

Y. J. Lee, S. H. Kim, and J. Huh, "A high-extraction-efficiency nanopatterned organic light-emitting diode," Phys. Rev. Lett. 82, 3779-3781 (2003).

V. Y. Miklyaev, C. D. Meisel, and A. Blanco, "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]

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
[CrossRef]

2002 (2)

D. N. Sharp, M. Campbell, and R. E. Dedman, "Photonic crystal for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

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

2001 (2)

J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
[CrossRef]

A. Y. Vlasov, X. Bo, and C. J. Sturm, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 6861, 289-293 (2001).
[CrossRef]

2000 (1)

M. Campbell, N. D. Sharp, and T. M. Harrison, "Fabrication of photonic crystals for the visible spectrum by holography," Nature 6773, 53-56 (2000).

1998 (1)

S. Y. Lin, E. Chow, and V. Hietala, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

1997 (1)

M. D. B. Charlton, S. W. Roberts, and G. J. Parker, "Guided mode analysis and fabrication of a 2-dimensional visible photonic band structure confined within a planar semiconductor waveguide," Mater. Sci. Eng. B 49, 155-165 (1997).
[CrossRef]

1994 (1)

E. Özbay, E. Michel, and G. Tuttle, "Micromachined millimeter-wave photonic band-gap crystals," Appl. Phys. Lett. 64, 2059-2061 (1994).
[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]

Blanco, A.

V. Y. Miklyaev, C. D. Meisel, and A. Blanco, "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]

Bo, X.

A. Y. Vlasov, X. Bo, and C. J. Sturm, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 6861, 289-293 (2001).
[CrossRef]

Cai, L. Z.

Campbell, M.

D. N. Sharp, M. Campbell, and R. E. Dedman, "Photonic crystal for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

M. Campbell, N. D. Sharp, and T. M. Harrison, "Fabrication of photonic crystals for the visible spectrum by holography," Nature 6773, 53-56 (2000).

Charlton, M. D. B.

M. D. B. Charlton, S. W. Roberts, and G. J. Parker, "Guided mode analysis and fabrication of a 2-dimensional visible photonic band structure confined within a planar semiconductor waveguide," Mater. Sci. Eng. B 49, 155-165 (1997).
[CrossRef]

Chow, E.

S. Y. Lin, E. Chow, and V. Hietala, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Crespi, V. H.

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
[CrossRef]

Dedman, R. E.

D. N. Sharp, M. Campbell, and R. E. Dedman, "Photonic crystal for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Divliansky, I.

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
[CrossRef]

Harrison, T. M.

M. Campbell, N. D. Sharp, and T. M. Harrison, "Fabrication of photonic crystals for the visible spectrum by holography," Nature 6773, 53-56 (2000).

Hietala, V.

S. Y. Lin, E. Chow, and V. Hietala, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Holliday, K. S.

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
[CrossRef]

Huh, J.

Y. J. Lee, S. H. Kim, and J. Huh, "A high-extraction-efficiency nanopatterned organic light-emitting diode," Phys. Rev. Lett. 82, 3779-3781 (2003).

John, S.

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

Kim, S. H.

Y. J. Lee, S. H. Kim, and J. Huh, "A high-extraction-efficiency nanopatterned organic light-emitting diode," Phys. Rev. Lett. 82, 3779-3781 (2003).

Lee, Y. J.

Y. J. Lee, S. H. Kim, and J. Huh, "A high-extraction-efficiency nanopatterned organic light-emitting diode," Phys. Rev. Lett. 82, 3779-3781 (2003).

Lin, S. Y.

S. Y. Lin, E. Chow, and V. Hietala, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

Matthias, S.

J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
[CrossRef]

Mayer, T. S.

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
[CrossRef]

Meisel, C. D.

V. Y. Miklyaev, C. D. Meisel, and A. Blanco, "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]

Michel, E.

E. Özbay, E. Michel, and G. Tuttle, "Micromachined millimeter-wave photonic band-gap crystals," Appl. Phys. Lett. 64, 2059-2061 (1994).
[CrossRef]

Miklyaev, V. Y.

V. Y. Miklyaev, C. D. Meisel, and A. Blanco, "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]

Muller, F.

J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
[CrossRef]

Özbay, E.

E. Özbay, E. Michel, and G. Tuttle, "Micromachined millimeter-wave photonic band-gap crystals," Appl. Phys. Lett. 64, 2059-2061 (1994).
[CrossRef]

Parker, G. J.

M. D. B. Charlton, S. W. Roberts, and G. J. Parker, "Guided mode analysis and fabrication of a 2-dimensional visible photonic band structure confined within a planar semiconductor waveguide," Mater. Sci. Eng. B 49, 155-165 (1997).
[CrossRef]

Roberts, S. W.

M. D. B. Charlton, S. W. Roberts, and G. J. Parker, "Guided mode analysis and fabrication of a 2-dimensional visible photonic band structure confined within a planar semiconductor waveguide," Mater. Sci. Eng. B 49, 155-165 (1997).
[CrossRef]

Schilling, J.

J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
[CrossRef]

Sharp, D. N.

D. N. Sharp, M. Campbell, and R. E. Dedman, "Photonic crystal for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Sharp, N. D.

M. Campbell, N. D. Sharp, and T. M. Harrison, "Fabrication of photonic crystals for the visible spectrum by holography," Nature 6773, 53-56 (2000).

Sturm, C. J.

A. Y. Vlasov, X. Bo, and C. J. Sturm, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 6861, 289-293 (2001).
[CrossRef]

Tuttle, G.

E. Özbay, E. Michel, and G. Tuttle, "Micromachined millimeter-wave photonic band-gap crystals," Appl. Phys. Lett. 64, 2059-2061 (1994).
[CrossRef]

Vlasov, A. Y.

A. Y. Vlasov, X. Bo, and C. J. Sturm, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 6861, 289-293 (2001).
[CrossRef]

Wang, Y. R.

Wehrspohn, R. B.

J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
[CrossRef]

Yablonovitch, E.

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

Yang, X. I.

Appl. Phys. Lett. (4)

J. Schilling, F. Muller, S. Matthias, and R. B. Wehrspohn, "Three-dimensional photonic crystals based on macroporous silicon with modulated pore diameter," Appl. Phys. Lett. 78, 1180-1182 (2001).
[CrossRef]

E. Özbay, E. Michel, and G. Tuttle, "Micromachined millimeter-wave photonic band-gap crystals," Appl. Phys. Lett. 64, 2059-2061 (1994).
[CrossRef]

V. Y. Miklyaev, C. D. Meisel, and A. Blanco, "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]

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, "Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography," Appl. Phys. Lett. 82, 1667-1669 (2003).
[CrossRef]

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

Mater. Sci. Eng. B (1)

M. D. B. Charlton, S. W. Roberts, and G. J. Parker, "Guided mode analysis and fabrication of a 2-dimensional visible photonic band structure confined within a planar semiconductor waveguide," Mater. Sci. Eng. B 49, 155-165 (1997).
[CrossRef]

Nature (2)

A. Y. Vlasov, X. Bo, and C. J. Sturm, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 6861, 289-293 (2001).
[CrossRef]

M. Campbell, N. D. Sharp, and T. M. Harrison, "Fabrication of photonic crystals for the visible spectrum by holography," Nature 6773, 53-56 (2000).

Opt. Quantum Electron. (1)

D. N. Sharp, M. Campbell, and R. E. Dedman, "Photonic crystal for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

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]

Y. J. Lee, S. H. Kim, and J. Huh, "A high-extraction-efficiency nanopatterned organic light-emitting diode," Phys. Rev. Lett. 82, 3779-3781 (2003).

Science (1)

S. Y. Lin, E. Chow, and V. Hietala, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
[CrossRef] [PubMed]

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 (4)

Fig. 1
Fig. 1

Schematic diagram showing the optical setup of four-beam interference.

Fig. 2
Fig. 2

Optical geometry of the two-beam interference system.

Fig. 3
Fig. 3

Computer simulations of fcc PhCs obtained from two-beam interference with three exposures. Only the regions with an intensity lower than 42% of the maximum value are displayed. (b) Simulation with a d/2 shift along the z axis from (a).

Fig. 4
Fig. 4

SEM images of the fcc PhC fabricated with two-beam interference. (a) (111) plane, scale bar 500 nm. (b) (111) plane with a d/2 shift from (a) along the z axis, scale bar 1 μm. (c) Lattice structure of the plane perpendicular to the (111) plane, scale bar 1 μm. (d) Lattice structure fabricated by arranging the surface of the recording plate 5° from the (111) plane, scale bar 2 μm.

Equations (13)

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

I ( r ) = [ j = 1 n E j ( r ) exp ( i k j r + i ϕ j ) ] [ j = 1 n E j ( r ) exp ( i k j r i ϕ j ) ]
= j = 1 n | E j | 2 + i < j n E i E j     exp [ i ( k i k j ) r + i ϕ i j ] ,
G i j = k i k j .
I ( r ) = i , j 4 a i , j exp ( i G i j r )
= a 11 + a 22 + a 33 + a 44 + a 12 exp ( i G 12 r ) + a 12 exp ( i G 12 r ) + a 13 exp ( i G 13 r ) + a 13 exp ( i G 13 r ) + a 14 exp ( i G 14 r ) + a 14 exp ( i G 14 r ) + a 23 exp ( i G 23 r ) + a 23 exp ( i G 23 r ) + a 24 exp ( i G 24 r ) + a 24 exp ( i G 24 r ) + a 34 exp ( i G 34 r ) + a 34     exp ( i G 34 r ) ,
G 1 i r = ( k 1 k i ) r = 2 π l i ,   for   i = 2 4 ,
I 12 ( r ) = a 11 + a 22 + a 12 exp ( i G 12 r ) + a 12 exp ( i G 12 r ) .
I ( r ) = I 12 ( r ) + I 13 ( r ) + I 14 ( r )
= 3 a 11 + a 22 + a 33 + a 44 + a 12 exp ( i G 12 r ) + a 12 exp ( i G 12 r ) + a 13 exp ( i G 13 r ) + a 13 exp ( i G 13 r ) + a 14 exp ( i G 14 r ) + a 14 exp ( i G 14 r ) .
k ^ 1 = e ^ z ,
k ^ 2 = sin φ cos θ e ^ x + sin φ sin θ e ^ y + cos φ e ^ z ,
I = 6 + 2 cos ( x k sin φ z k cos φ + z k ) + 2 cos [ z k k ( 1 2 x sin φ 3 2 y sin φ + z cos φ ) ]
+ 2 cos [ z k k ( 1 2 x sin φ + 3 2 y sin φ + z cos φ ) ] ,

Metrics