Abstract

Three multiplexed holographic gratings were used to fabricate 3D photonic crystals without complete band gap using ultra-fine grain holographic emulsion as the storage material. Theoretical and experimental studies were carried out in order to characterize the crystals. Good agreement between theory and experimental results was obtained, showing that it is possible to obtain a band-pass filter for a fixed direction of illumination.

© 2004 Optical Society of America

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References

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  1. M. Campbell, D. Sharp, M. T. Harrison, R. G. Denning, and A. J. Tuberfield, ???Fabrication of photonic crystals for the visible spectrum by holographic lithography,??? Nature 404, 53???56 (2000).
    [CrossRef] [PubMed]
  2. Y. Zhicheng, J. Zheng, D. Liu, and P. Shouyong, ???Structures of photonic crystals and band gaps in volume holograms,??? Phys. Lett. A 299, 313???317 (2002).
    [CrossRef]
  3. D. T. Sharp, M. Campbell, E. Dedman, M. Harrison, D. R.G, and A. J. Tuberfield, ???Photonic crystals for the visible spectrum by holographic lithography,??? Opt. and Quantum Electronics 34, 3???12 (2002).
    [CrossRef]
  4. T. Ohira, T. Segawa, K. Nagai, K. Utaka, and M. Nakao, ???Large area InP submicron two-dimensional (2D) periodic structures fabricated by two-time laser holography,??? Jpn. J. Appl. Phys. 41, 1085???1089 (2002).
    [CrossRef]
  5. Y. Miklyaev, D. Meisel, A. Blanco, and G. Freymann, ???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]
  6. K. Saravanamuttu, C. Blanford, D. Sharp, E. Dedman, A. Tuberfield, and R. Denning, ???Sol-Gel Organic- Inorganic composites for 3-D holographic lithography of photonic crystals with submicron periodicity,??? Chem. Mater. 15, 2301???2304 (2003).
    [CrossRef]
  7. G.Wang, C. Tan, Y. Xi, and H. Shan, ???Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals with a single continuous wavelength laser beam,??? J. Mod. Opt 50, 2155???2161 (2003).
  8. L. Cai, L. Yang, and Y. Wang, ???Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,??? J. Opt. Soc. Am-A 19, 2238???2244 (2002).
    [CrossRef]
  9. M. Ulibarrena, L. Carretero, R. F. Madrigal, S. Blaya, and A. Fimia, ???Multiple band holographic reflection gratings recorded in new ultra-fine grain emulsion BBVPan,??? Opt. Express 11, 3385???3392 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3385">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3385</a>.
    [CrossRef] [PubMed]
  10. M. Ulibarrena, L. Carretero, R. F. Madrigal, S. Blaya, and A. Fimia, ???Nonlinear effects on holographic reflection gratings recorded with BB640 emulsions,??? Opt. Express 11, 1906???1917 (2003). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-16-1906">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-16-1906<a/>.
    [CrossRef] [PubMed]
  11. S. G. Johnson and J. D. Joannopoulos, ???Block-iterative frequency-domain methods for Maxwell???s equations in a planewave basis,??? Opt. Express 8, 173???190 (2001). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173<a/>.
    [CrossRef] [PubMed]
  12. <a href="http://www.colourholographic.com/">http://www.colourholographic.com/<a/>.
  13. Y. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, vol. MS 171 of Milestone Series, pp. 22???24 (SPIE, 2001).
  14. M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, ???New processing techniques for reflection holograms recorded on BB640 holographic emulsions,??? in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., pp. 65???74, SPIE (SPIE, 2003).

Appl. Phys. Lett

Y. Miklyaev, D. Meisel, A. Blanco, and G. Freymann, ???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]

Chem. Mater.

K. Saravanamuttu, C. Blanford, D. Sharp, E. Dedman, A. Tuberfield, and R. Denning, ???Sol-Gel Organic- Inorganic composites for 3-D holographic lithography of photonic crystals with submicron periodicity,??? Chem. Mater. 15, 2301???2304 (2003).
[CrossRef]

in Practical Holography XVII and Hologra

M. Ulibarrena, M. J. Méndez, S. Blaya, R. F. Madrigal, L. Carretero, and A. Fimia, ???New processing techniques for reflection holograms recorded on BB640 holographic emulsions,??? in Practical Holography XVII and Holographic Materials IX, T. H. Jeong and S. H. Stevenson, eds., pp. 65???74, SPIE (SPIE, 2003).

J. Mod. Opt

G.Wang, C. Tan, Y. Xi, and H. Shan, ???Holography for one-step fabrication of three-dimensional metallodielectric photonic crystals with a single continuous wavelength laser beam,??? J. Mod. Opt 50, 2155???2161 (2003).

J. Opt. Soc. Am-A

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

Jpn. J. Appl. Phys.

T. Ohira, T. Segawa, K. Nagai, K. Utaka, and M. Nakao, ???Large area InP submicron two-dimensional (2D) periodic structures fabricated by two-time laser holography,??? Jpn. J. Appl. Phys. 41, 1085???1089 (2002).
[CrossRef]

Milestone Series

Y. N. Denisyuk, Photographic reconstruction of the optical properties of an object in its own scattered radiation field, vol. MS 171 of Milestone Series, pp. 22???24 (SPIE, 2001).

Nature

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

Opt. and Quantum Electronics

D. T. Sharp, M. Campbell, E. Dedman, M. Harrison, D. R.G, and A. J. Tuberfield, ???Photonic crystals for the visible spectrum by holographic lithography,??? Opt. and Quantum Electronics 34, 3???12 (2002).
[CrossRef]

Opt. Express

Phys. Lett. A

Y. Zhicheng, J. Zheng, D. Liu, and P. Shouyong, ???Structures of photonic crystals and band gaps in volume holograms,??? Phys. Lett. A 299, 313???317 (2002).
[CrossRef]

Other

<a href="http://www.colourholographic.com/">http://www.colourholographic.com/<a/>.

Supplementary Material (1)

» Media 1: GIF (88 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

(a) Unit cell of the photonic crystal showed in Fig. 1(a), with vectors given by: a1=(492, 0, 0) nm, a2=(0, 492, 0) nm and a3=(0, 0, 204) nm. (b) Simulation of the isorefractive index surfaces of photonic crystal formed by multiplexing three diffraction gratings with vectors: G1=(0.013, 0, 0) nm -1, G2=(0, 0.013, 0) nm -1, G3=(0, 0, 0.031) nm -1.

Fig. 2.
Fig. 2.

Bands diagram generated by the photonic crystal with unit cell showed in figure 1(b). n 0=1.579, ni =0.03, G1=(0.013, 0, 0) nm -1, G2=(0, 0.013, 0) nm -1, G3=(0, 0, 0.031) nm -1

Fig. 3.
Fig. 3.

Experimental (a) and theoretical (b) bands diagrams generated by the photonic crystal with unit cell showed in Fig. 1(b) recorded in a photographic emulsion, with reconstruction direction along z axis.

Fig. 4.
Fig. 4.

(90 KB) Movie of the evolution of the transmission spectra of the band-pass filter starting with normal incidence along the Z axis and ending with the crystal rotated 48° around the Y axis, 9° around the X axis, 56° around the Z axis.

Equations (13)

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E vj = E vj 0 exp ( i K vj . r ) e ̂ vj
K vj = 2 π λ v ( l vj , m vj , n vj )
I = v = 1 3 ( ( E v 1 0 ) 2 + ( E v 2 0 ) 2 ) + 2 v = 1 3 E v 1 0 E v 2 0 Cos ( G v . r ) χ v , 12
G v = K v 1 K v 2
Cos ( G 1 . r ) = Cos ( G 2 . r ) = Cos ( G 3 . r ) = 1
L 1 . x + M 1 . y + N 1 . z = p 1 λ 1
L 2 . x + M 2 . y + N 2 . z = p 2 λ 2
L 3 . x + M 3 . y + N 3 . z = p 3 λ 3
a 1 = λ 1 det [ Q ] ( ( M 3 N 2 M 2 N 3 ) ( L 3 N 2 + L 2 N 3 ) ( L 3 M 2 L 2 M 3 ) )
a 2 = λ 2 det [ Q ] ( ( M 3 N 1 + M 1 N 3 ) ( L 3 N 1 L 1 N 3 ) ( L 3 M 1 + L 1 M 3 ) )
a 3 = λ 3 det [ Q ] ( ( M 2 N 1 M 1 N 2 ) ( L 2 N 1 + L 1 N 2 ) ( L 2 M 1 L 1 M 2 ) )
a 1 = a 2 = a ; a 3 = b ; a 1 . a 2 = 0 , a 1 . a 3 = 0 , a 2 . a 3 = 0 ;
n = n 0 + v = 1 3 n v Cos ( G v . r )

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