Abstract

We present laser interference patterning of three-dimensional photonic lattice structures with three-step three-beam irradiation. In contrast to one-step four-beam interference patterning, the proposed method makes it possible to continuously tune the lattice constant and the photonic band gap without distortion of the lattice shape. We analytically show that all fourteen Bravais lattices are possible to be produced by choosing proper incident vectors of laser beams. A simple routine to seek the geometrical configuration of the incident beams for producing arbitrary Bravais lattices is shown. Furthermore, We experimentally demonstrate the fabrication of three-dimensional photonic lattices in the photoresist SU-8. Significant photonic band gap effects have been observed from the well-defined photonic lattices.

© 2006 Optical Society of America

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References

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  1. J. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997).
    [CrossRef]
  2. L. Z. Cai, X. L. Yang, and Y. R. Wang, "All fourteen Bravais lattices can be formed by interference of four noncoplanar beams," Opt. Lett. 27, 900-902 (2002).
    [CrossRef]
  3. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographiclithography," Nature (London) 404, 53-56 (2000).
    [CrossRef]
  4. S. Shoji and S. Kawata, "Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin," Appl. Phys. Lett. 76, 2668-2670 (2000).
    [CrossRef]
  5. D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68, 205102 (2003).
    [CrossRef]
  6. S. Shoji, H.-B. 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]
  7. G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
    [CrossRef]
  8. S. Shoji, H.-B. Sun, and S. Kawata, "Multi-Beam Interference Laser Fabrication of an Inverse Structure of Yablonovite Photonic Crystal," Technical Digest of International Symposium on Photonic and Electromagnetic Crystal Structures V (PECS-V), 34 (2004).
  9. L. Z. Cai, X. L. Yang, and Y. R. Wang, "Formation of a microfiber bundle by interference of three noncoplanar beams," Opt. Lett. 26, 1858-1860 (2001).
    [CrossRef]
  10. L. Yuan, G. P. Wang, and X. Huang, "Arrangements of four beams for any Bravais lattice," Opt. Lett. 28, 1769-1771 (2003).
    [CrossRef] [PubMed]
  11. 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 (2003).
    [CrossRef]
  12. E. Yablonovitch, T. J. 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]

2005 (1)

G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
[CrossRef]

2003 (4)

L. Yuan, G. P. Wang, and X. Huang, "Arrangements of four beams for any Bravais lattice," Opt. Lett. 28, 1769-1771 (2003).
[CrossRef] [PubMed]

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 (2003).
[CrossRef]

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68, 205102 (2003).
[CrossRef]

S. Shoji, H.-B. 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]

2002 (1)

2001 (1)

2000 (2)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographiclithography," Nature (London) 404, 53-56 (2000).
[CrossRef]

S. Shoji and S. Kawata, "Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin," Appl. Phys. Lett. 76, 2668-2670 (2000).
[CrossRef]

1997 (1)

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

1991 (1)

E. Yablonovitch, T. J. 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]

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 (2003).
[CrossRef]

Busch, K.

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 (2003).
[CrossRef]

Cai, L. Z.

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 holographiclithography," Nature (London) 404, 53-56 (2000).
[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 (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 holographiclithography," Nature (London) 404, 53-56 (2000).
[CrossRef]

Deubel, M.

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 (2003).
[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 (2003).
[CrossRef]

Fan, S.

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

Gmitter, T. J.

E. Yablonovitch, T. J. 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]

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 holographiclithography," Nature (London) 404, 53-56 (2000).
[CrossRef]

Huang, X.

Joannopoulos, J.

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

Kawata, S.

S. Shoji, H.-B. 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]

S. Shoji and S. Kawata, "Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin," Appl. Phys. Lett. 76, 2668-2670 (2000).
[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 (2003).
[CrossRef]

Leung, K. M.

E. Yablonovitch, T. J. 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]

Meisel, D. 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 (2003).
[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 (2003).
[CrossRef]

Murakowski, J. A.

G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
[CrossRef]

Prather, D. W.

G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
[CrossRef]

Schneider, G. J.

G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
[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 (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 holographiclithography," Nature (London) 404, 53-56 (2000).
[CrossRef]

Shoji, S.

S. Shoji, H.-B. 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]

S. Shoji and S. Kawata, "Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin," Appl. Phys. Lett. 76, 2668-2670 (2000).
[CrossRef]

Sun, H.-B.

S. Shoji, H.-B. 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]

Turberfield, A. J.

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68, 205102 (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 holographiclithography," Nature (London) 404, 53-56 (2000).
[CrossRef]

Villeneuve, P. R.

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

von Freymann, G.

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 (2003).
[CrossRef]

Wang, G. P.

Wang, Y. R.

Wegener, M.

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 (2003).
[CrossRef]

Wetzel, E. D.

G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. 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]

Yang, X. L.

Yuan, L.

Appl. Phys. Lett. (3)

S. Shoji and S. Kawata, "Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin," Appl. Phys. Lett. 76, 2668-2670 (2000).
[CrossRef]

S. Shoji, H.-B. 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]

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 (2003).
[CrossRef]

Nature (London) (2)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographiclithography," Nature (London) 404, 53-56 (2000).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. B (1)

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68, 205102 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. 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]

Proc. SPIE (1)

G. J. Schneider, E. D. Wetzel, J. A. Murakowski, and D. W. Prather, "Fabrication of three-dimensional Yablonovite photonic crystals by multiple-exposure UV interference lithography," Proc. SPIE 5720, 9 (2005).
[CrossRef]

Other (1)

S. Shoji, H.-B. Sun, and S. Kawata, "Multi-Beam Interference Laser Fabrication of an Inverse Structure of Yablonovite Photonic Crystal," Technical Digest of International Symposium on Photonic and Electromagnetic Crystal Structures V (PECS-V), 34 (2004).

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Figures (6)

Fig. 1.
Fig. 1.

Three-dimensional simple-cubic lattices created by three-step three-beam laser interference. In the calculation, the wavelength of laser light is 355 nm, the size of calculation space is 5 μm. The inclination angle of the laser beams θ is (a)10° and (b)15°.

Fig. 2.
Fig. 2.

Three dimensional light pattern created by three-step three-beam laser interference. (a)body-centered cubic(bcc) lattice and (b)face-centered cubic(fcc) lattice. The initial wavevectors of laser beams before linear transformation is the same as those for Fig. 1(b). The wavelength of laser light is 355 nm, the size of calculation space is 5 μm.

Fig. 3.
Fig. 3.

Optical setup for the three-beam three-times laser interference patterning.

Fig. 4.
Fig. 4.

The scanning electron microscope image of the scaffold type a fcc optical lattice. The lattice constant is about 1.5 μm. (a)A bird’s eye view. (b,c)Magnified images of (b)top surface of the structure, and (c)cross section of a crack in the rim of the structure. (d,e)Simulated cross section of fcc lattice in (a)< 1,1,1 > and (b)< 1,1,-1 >.

Fig. 5.
Fig. 5.

The transmittance(black thick line) and the reflectance(gray line)spectra of the fabricated structure. The thin black line shows the transmittance spectrum of a SU-8 film as a reference.

Fig. 6.
Fig. 6.

The photonic band diagram for our fabricated structure. The Brillouin zone of fcc structure and the definition of the symmetry points can be found in ref.12. The gap opens in the Γ-L3 direction at a frequency of 4500 cm-1.

Equations (20)

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

k 11 = ( k sin θ 2 , k sin θ 2 , k cos θ ) ,
k 12 = ( k sin θ 2 , k sin θ 2 , k cos θ ) ,
k 13 = ( k sin θ 2 , k sin θ 2 , k cos θ ) .
I ( r ) = i = 1 3 0 j < j ' 3 E ij E ij ' exp [ i { ( k ij k ij ' ) r + ϕ i j ϕ i j ' } ] .
R = u 1 a 1 + u 2 a 2 + u 3 a 3 .
Δ = ( δ 1 x δ 2 x δ 3 x δ 1 y δ 2 y δ 3 y δ 1 z δ 2 z δ 3 z ) .
A = Δ A 0
= ( δ 1 x δ 2 x δ 3 x δ 1 y δ 2 y δ 3 y δ 1 z δ 2 z δ 3 z ) ( a 0 0 0 a 0 0 0 a ) .
Δ bcc = ( 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 ) .
k i j = Δ 1 k i j .
Δ bcc 1 = ( 1 1 0 1 0 1 0 1 1 ) .
k 11 = ( 2 k 2 sin θ , k 2 ( sin θ + 2 cos θ ) , k 2 ( sin θ + 2 cos θ ) ) ,
k 12 = ( 0 , k 2 ( sin θ + 2 cos θ ) , k 2 ( sin θ + 2 cos θ ) ) ,
k 13 = ( 0 , k 2 ( sin θ + 2 cos θ ) , k 2 ( sin θ + 2 cos θ ) ) ,
k 21 = ( k 2 ( sin θ + 2 cos θ ) , 2 k 2 sin θ , k 2 ( sin θ + 2 cos θ ) ) ,
k 22 = ( k 2 ( sin θ + 2 cos θ ) , 0 , k 2 ( sin θ + 2 cos θ ) ) ,
k 23 = ( k 2 ( sin θ + 2 cos θ ) , 0 , k 2 ( sin θ + 2 cos θ ) ) ,
k 31 = ( k 2 ( sin θ + 2 cos θ ) , k 2 ( sin θ + 2 cos θ ) , 2 k 2 sin θ ) ,
k 32 = ( k 2 ( sin θ + 2 cos θ ) , k 2 ( sin θ + 2 cos θ ) , 0 ) ,
k 33 = ( k 2 ( sin θ + 2 cos θ ) , k 2 ( sin θ + 2 cos θ ) , 0 ) .

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