Abstract

We demonstrate the construction of diamond photonic crystal structures by the translation of a multi-beam interference pattern. Using phase shift of each beam, the double-exposed interference patterns can be aligned in the [111] direction for a face-centered cubic (FCC) and [210] direction for a body-centered cubic (BCC), respectively, producing diamond D from FCC and BCC-diamond like structure from BCC. The present result shows that the complete bandgap has been retained with slight deviation from ideal diamond symmetry.

© 2005 Optical Society of America

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Adv. Mater.

S. H. Park, D. Qin, and Y. Xia, "Crystallization of mesoscale particles over large areas," Adv. Mater. 10, 1028-1032 (1998).
[CrossRef]

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, "New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates," Adv. Mater. in press (2005).

Appl. Phys. Lett.

J. Qi, M. E. Sousa, A. K. Fontecchio, and G. P. Crawford, "Temporally multiplexed holographic polymer-dispersed liquid crystals," Appl. Phys. Lett. 82, 1652-1654 (2003).
[CrossRef]

S. H. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, "Design of 3-dimensional photonic crystals at submicron length scales," Appl. Phys. Lett. 65, 1466-1468 (1994).
[CrossRef]

J. H. Moon, S.-M. Yang, D. J. Pine, and W.-S. Chang, "Multiple-exposure holographic lithography with phase shift," Appl. Phys. Lett. 85, 4184-4186 (2004).
[CrossRef]

Chem. Mater.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, "Creating periodic three-dimensional structures by multibeam interference of visible laser," Chem. Mater. 14, 2831-2833 (2002).
[CrossRef]

J. Opt. A-Pure Appl. Op.

A. Chelnokov, S. Rowson, J. M. Lourtioz, V. Berger, and J. Y. Courtois, "An optical drill for the fabrication of photonic crystals," J. Opt. A-Pure Appl. Op. 1 (5), L3-L6 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

S. Noda, N. Yamamoto, and A. Sasaki, "New realization method for three-dimensional photonic crystal in optical wavelength region," Jpn. J. Appl. Phys. 35 (7B), L909-L912 (1996).
[CrossRef]

Nat. Mater.

M. Maldovan and E. L. Thomas, "Diamond-structured photonic crystals," Nat. Mater. 3 (9), 593-600 (2004).
[CrossRef] [PubMed]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, "Direct laser writing of three-dimensional photonic-crystal templates for telecommunications," Nat. Mater. 3, 444-447 (2004).
[CrossRef] [PubMed]

M. Maldovan, C. K. Ullal, W. C. Carter, and E. L. Thomas, "Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups," Nat. Mater. 2 (10), 664-667 (2003).
[CrossRef] [PubMed]

Nature

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices -Micromachines can be created with higher resolution using two-photon absorption," Nature 412, 697-698 (2001).
[CrossRef] [PubMed]

G. M. Gratson, M. J. Xu, and J. A. Lewis, "Microporiodis structures - Direct writing of three-dimensional webs," Nature 428, 386-386 (2004).
[CrossRef] [PubMed]

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

Opt. Lett.

Phys. Rev. B

M. Maldovan, A. M. Urbas, N. Yufa, W. C. Carter, and E. L. Thomas, "Photonic properties of bicontinuous cubic microphases," Phys. Rev. B 65, 165123 (2002).
[CrossRef]

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.

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92 (4), 043905 (2004).
[CrossRef] [PubMed]

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]

Science

O. Toader and S. John, "Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals," Science 292, 1133-1135 (2001).
[CrossRef] [PubMed]

Solid State Commun.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band-gaps in 3-dimensions - New layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Synth. Met.

J. H. Moon, A. Small, G.-R. Yi, S.-K. Lee, W.-S. Chang, D. J. Pine, and S.-M. Yang, "Patterned polymer photonic crystals using soft lithography and holographic lithography," Synth. Met. 148, 99-102 (2005).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Translation of (a) FCC interference pattern in the [111]direction and (b) BCC interference in the [210] direction.

Fig. 2.
Fig. 2.

The relative position of the FCC interference pattern (red) and the shifted pattern (blue) in the [111] direction by (a) 0.20d(1,1,1), (b) 0.25d(1,1,1), and (c) 0.29d(1,1,1). The level surface of each double-exposed FCC interference pattern with a filling fraction of 0.22 is shown in (d -f) for their respective cases.

Fig. 3.
Fig. 3.

Intensity profile of 8-term and 4-term interference patterns along [111] direction

Fig. 4.
Fig. 4.

The relative position of the BCC interference pattern (red) and the shifted pattern (blue) in the [210] direction by (a) 0.20d (1,1,1), (b) 0.25d (1,1,1), and (c) 0.29d (1,1,1). The level surface of each double-exposed BCC interference pattern with a filling fraction of 0.20 is shown in (d-f) for their respective cases.

Fig. 5.
Fig. 5.

Complete PBG of double-exposed (a) FCC and (b) BCC interference patterns as a function of the normalized pattern shift in [111] and [210], respectively.

Equations (17)

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I = n = 1 4 E n 2 + m < n 4 E n E m ε n · ε m * cos [ ( k n k m ) · r + ( ϕ n 0 ϕ m 0 ) ] .
I nm = E n E m ε n · ε m * cos [ ( k n k m ) · r + ( ϕ n 0 ϕ m 0 ) + ( ϕ n ϕ m ) ] .
I nm = E n E m ε n · ε m * cos [ ( k n k m ) · ( r + r ) + ( ϕ n 0 ϕ m 0 ) ] .
( ϕ n ϕ m ) = ( k n k m ) · r .
I nm ~ cos [ 2 π d ( x y + z ) + ( ϕ 1 ϕ 3 ) ] + cos [ 2 π d ( x + y + z ) + ( ϕ 1 ϕ 4 ) ]
+ cos [ 2 π d ( x y + z ) + ( ϕ 2 ϕ 3 ) ] + cos [ 2 π d ( x + y + z ) + ( ϕ 2 ϕ 4 ) ]
I nm ~ cos [ 4 π d ( y + z ) + ( ϕ 1 ϕ 2 ) ] + cos [ 4 π d ( x + y ) + ( ϕ 1 ϕ 3 ) ]
+ cos [ 4 π d ( x + z ) + ( ϕ 1 ϕ 4 ) ] + cos [ 4 π d ( x z ) + ( ϕ 2 ϕ 3 ) ]
+ cos [ 4 π d ( x y ) + ( ϕ 2 ϕ 4 ) ] + cos [ 4 π d ( y + z ) + ( ϕ 3 ϕ 4 ) ]
I nm ~ cos [ 2 π d ( x y + z ) ] + cos [ 2 π d ( x + y + z ) ]
+ cos [ 2 π d ( x y + z ) ] + cos [ 2 π d ( x + y + z ) ]
+ sin [ 2 π d ( x y + z ) ] sin [ 2 π d ( x + y + z ) ]
sin [ 2 π d ( x y + z ) ] + sin [ 2 π d ( x + y + z ) ]
I nm ~ cos [ 4 π d ( x + y ) ] + cos [ 4 π d ( y + z ) ]
+ cos [ 4 π d ( y + z ) ] + cos [ 4 π d ( x y ) ]
+ sin [ 4 π d ( x + y ) ] sin [ 4 π d ( y + z ) ]
sin [ 4 π d ( y + z ) ] sin [ 4 π d ( x y ) ]

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