Abstract

This paper simulates the photonic band structure in face-centered-orthorhombic and face-centered-tetragonal woodpile-type photonic crystals and shows the fabrication feasibility of these crystals with phase mask based holographic lithography. The experimental demonstration on SU-8 photoresist indicates that a single optical element can replace a complex optical setup for the holographic fabrication of woodpile-type photonic crystals. Photonic band gap calculation predicts the existence of full band gap in these crystals. Optimum band gap sizes are studied for crystals formed under various experimental conditions.

© 2006 Optical Society of America

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References

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Appl. Phys. Lett. (3)

S. Shoji, H. Sun, and S. Kawata, "Photofabrication of wood-pile three-dimensional photonic crystals using four-beam laser interference," Appl. Phys. Lett. 83, 608-710 (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]

Cheng Lu, X. K. Hu, I. V. Mitchell, and R. H. Lipson, "Diffraction element assisted lithography: Pattern control for photonic crystal fabrication," Appl. Phys. Lett. 86, 193110/1-3 (2005).
[CrossRef]

Chem. Commun. (1)

H. Miguez, N. Tetreault, B. Hatton, S. M.Yang, D. Perovic, G. A. Ozin, "Mechanical stability enhancement by pore size and connectivity control in colloidal crystals by layer-by-layer growth of oxide," Chem. Commun. (Cambridge) 22, 2736-2737 (2002).
[CrossRef]

J. Appl. Phys. (2)

Y. Lin, P. R. Herman, and E. L. Abolghasemi, "Proposed single-exposure holographic fabrication of microsphere-type photonic crystal through phase mask techniques," J. Appl. Phys. 97, 096102/1-3 (2005).
[CrossRef]

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[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 holographic lithography," Nature (London) 404, 53-56 (2000).
[CrossRef] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, "Photonics crystals: putting a new twist on light," Nature (London) 386, 143-147 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

D. N. Sharp, A. J. Turberfield, and R. G. Denning, "Holographic photonic crystals with diamond symmetry," Phys. Rev. B 68, 205102-6 (2003).
[CrossRef]

Phys. Rev. E (1)

Y. M. Chan, O. Toader, and S. John, "Photonic band gap templating using optical interference lithography," Phys. Rev. E 71, 046605/1-18 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

O. Toader, T. Y. M. Chan, and S. John, "Photonic band gap architectures for holographic lithography," Phys. Rev. Lett. 92, 043905/1-4 (2004).
[CrossRef]

Other (1)

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).

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Figures (4)

Fig. 1.
Fig. 1.

(left) phase mask based interference. A phase mask can replace a complex optical setup for a generation of interference pattern; (middle) a simulated woodpile-type photonic structure formed in the doubly-exposed photoresist; (right) a schematic illustration of woodpile-type photonic structure with orthorhombic or tetragonal symmetry and its lattice constants.

Fig. 2.
Fig. 2.

(left) First Brillouin surface of face-centered-orthorhombic lattice; (right) photonic band structure for an orthorhombic photonic crystal. λphoton is the wavelength of photons in the photonic band

Fig. 3.
Fig. 3.

(left) Photonic band gap size as a function of rotation angles for photonic crystal with c/L=2.3 and c/L=2.0. (right) photonic band gap size in face-centered-tetragonal structures (α=90 degree) and in face-centered-orthorhombic structures (α less than 90 degree) for various structures with a different c/L value.

Fig. 4.
Fig. 4.

(left) an arrangement of the phase mask and the photoresist. The interface between the backside of the phase mask and the photoresist is wetted with an index-match fluid; (right) SEM top-view of a woodpile-type structure in SU-8TM photoresist formed through the phase mask based holographic lithography. The insert is a side-view of the SU-8 structure.

Equations (6)

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

E 1 ( r , t ) = E 1 cos ( ( k cos θ ) z ( k sin θ ) x ωt + δ 1 ) ,
E 2 ( r , t ) = E 2 cos ( ( k cos θ ) z + ( k sin θ ) x ωt + δ 2 ) ,
E 3 ( r , t ) = E 3 cos ( kz ωt + δ 3 ) .
I = 1 2 E 1 2 + 1 2 E 3 2 + 1 2 E 2 3 + ( E 1 E 2 ) cos ( ( 2 k sin θ ) x + ( δ 2 δ 1 ) )
+ ( E 1 E 3 ) cos ( ( 2 k sin 2 ( θ 2 ) z + ( k sin θ ) x + ( δ 3 δ 1 ) )
+ ( E 2 E 3 ) cos ( ( 2 k sin 2 ( θ 2 ) ) z - ( k sin θ ) x + ( δ 3 δ 2 ) )

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