Abstract

We propose photonic crystal (PhC) structures in titanium dioxide (TiO2) material which is suitable for micro-nano structure optical device engineering and is a good candidate for visible light application. To provide a guideline for designing TiO2 based PhC, the comprehensive optical band gap maps of both the two-dimensional and three-dimensional structures are computed using the planewave expansion method. For 2D structures, besides the ideal infinite high 2D PhC and conventional air-bridge type slab, we also propose a “sandwich-type” PhC for better robustness and easier fabrication. The optimal thicknesses of both types of PhC slabs are investigated. In 3D PhC, we calculate the Yablonovite structure and its reverse which are made possible recently in our fabrication. For the first time to our knowledge, the computation results indicate that the reversed Yablonovite structure also shows a complete band gap characteristic, although it is smaller compared to that of the normal Yablonovite. The dependence of band gap width on the filling ratio and drilling angles for both types of Yablonovite structures are investigated.

© 2005 Optical Society of America

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Appl. Phys. Lett. (1)

G. Subramania, K. Constant, R. Biswas, M. M. Sigalas, and K.-M. Ho, �??Optical photonic crystals fabricated from colloidal systems,�?? Appl. Phys. Lett. 74, 3933-3935 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Noda, M. Imada, M. Okano, S. Ogawa, M. Mochizuki, and A. Chutinan, �??Semiconductor three-dimensional and two-dimensional photonic crystals and devices,�?? IEEE J. Quantum Electron. 38, 726�??735 (2002).
[CrossRef]

J. Phys. (Paris), Colloq. (1)

S. Yamasaki, N. Hata, T. Yoshida, H. Oheda, A. Matsuda, H. Okushi, and K. Tanaka, �??Annealing studies on low optical absorption of GD a-Si:H using photo-acoustic spectroscopy,�?? J. Phys. (Paris), Colloq. 42, C4-297 (1981).
[CrossRef]

J. Vac. Sci. Technol. B (1)

C. Cuisin, A. Chelnokov, J.-M. Lourtioz, D. Decanini and Y. Chen, �??Fabrication of three-dimensional photonic structures with submicrometer resolution by x-ray lithography,�?? J. Vac. Sci. Technol. B 18, 3505-3509 (2000).
[CrossRef]

Jpn. J. Appl. Phys. (1)

S. Shimada, K. Miyazawa and M. Kuwabara, �??An easy method for fabricating TiO2 gel photonic crystals using molds and highly concentrated alkoxide solutions,�?? Jpn. J. Appl. Phys. 41, L291�??L293 (2002).
[CrossRef]

Mat. Res. Soc. Symp. Proc. (1)

K. Awazu, M. Fujimaki, X. Wang, A. Sai, Y. Ohki, �??Fabrication of two-dimensional photonic structure of titanium dioxide with sub-micrometer resolution by deep x-ray lithography,�?? Mat. Res. Soc. Symp. Proc. 820, R4.5 (2004).
[CrossRef]

Nature (1)

E. Chow, S. Y. Lin, S. G. Johnson, P. B. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, �??Three-dimensional control of light in a two-dimensional photonic crystal slab,�?? Nature 407, 983�??986 (2000).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, �??Guided modes in photonic crystal slabs,�?? Phys. Rev. B 60, 5751�??5758 (1999).
[CrossRef]

K. Nomura, T. Nakanishi, Y. Nagasawa, Y. Ohki, K. Awazu, M. Fujimaki, N. Kobayashi, S. Ishii and K. Shima, �??Structural change induced in TiO2 by swift heavy ions and its application to three dimensional lithography,�?? Phys. Rev. B 68, 64106 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, �??Existence of a photonic gap in periodic dielectric structures,�?? Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

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]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, �??High transmission through sharp bends in photonic crystal waveguides,�?? Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

E. Yablonovitch and T. J. Gmitter, �??Photonic band structure: the face-centered-cubic case employing nonspherical atoms,�?? Phys. Rev. Lett. 67, 2295-2298 (1991).
[CrossRef] [PubMed]

Science (2)

J. E. G. J. Wijnhoven and W. L. Vos, �??Preparation of Photonic Crystals Made of Air Spheres in Titania,�?? Science 281, 802-804 (1998).
[CrossRef]

O. Painter, RK Lee, A. Yariv, A. Scherer, JD O'Brien, PD Dapkus, I. Kim, �??Two-dimensional photonic crystal defect laser,�?? Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Other (1)

J. D. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, New Jersey, 1995).

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Figures (15)

Fig. 1.
Fig. 1.

The reversed Yablonovite structure of titania fabricated by the liquid phase deposition method using a PMMA template (honeycomb lattice). Diameter of individual rod is 400nm.

Fig. 2.
Fig. 2.

An example of the band structure for a 2D PhC of triangular lattice air holes in TiO2 background. The hole radius is r=0.4a.

Fig. 3.
Fig. 3.

The optical band gap maps for two-dimensional TiO2 PhC of triangular lattice. (a) and (b) are for air holes in TiO2 background. (c) and (d) are for TiO2 rods in air.

Fig. 4.
Fig. 4.

The optical band gap maps for two-dimensional TiO2 PhC with square lattice ((a) and (b)) and honeycomb lattice ((c) and (d)). The TiO2 dielectric material is indicated in black in the insets.

Fig. 5.
Fig. 5.

The computational model of the air-bridge type PhC slab (Fig. (a)), and the computed TE-like band curves for r/a=0.4, h/a=0.6 slab (Fig. (b)).

Fig. 6.
Fig. 6.

The dependence of even-band gap width on the slab thickness for even mode at r/a=0.4.

Fig. 7.
Fig. 7.

The calculated TE transmission spectrum of the PhC slab for r/a=0.4 and h/a=0.6, by 3D FDTD.

Fig. 8.
Fig. 8.

(a) The proposed “sandwich-stucture” of TiO2 PhC slab on SiO2 substrate. (b) Its evenmode bandgap width against the slab thickness for different air-hole radii.

Fig. 9.
Fig. 9.

(a) The Yablonovite structure, (b) the unit cell for computation, and (c) the corresponding first Brillouin Zone.

Fig. 10.
Fig. 10.

(a) The band structures of TiO2 Yablonovite with drilling angle of 35.26° and air hole radius of 0.325a. (b) the band gap map for different air hole radii.

Fig. 11.
Fig. 11.

The dependence of band gap width of TiO2 Yablonovite on drilling angle for different hole radii.

Fig. 12.
Fig. 12.

The band structures of TiO2 Yablonovite with drilling angle of (a) 31.26°, (b) 39.26°.

Fig. 13.
Fig. 13.

The band structure of reversed Yablonovite in TiO2 with drilling angle=35.26°. (a) the structure image. (b) the band structure for r/a=0.19.

Fig. 14.
Fig. 14.

(a) The band gap map for different air hole radii. (b)The dependence of band gap width of TiO2 reversed Yablonovite on the drilling angle (r/a=0.19).

Fig. 15.
Fig. 15.

The band gap size of TiO2 Yablonovite with ellipsoidal holes. The gray line shows the corresponding optimal drilling angles.

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