Abstract

Theoretical analysis has shown that a two-dimensional (2D) lattice with circular columns connected by veins can produce a large complete bandgap when the radius of the columns and the width of the veins are properly chosen. We propose a holographic method to fabricate a similar 2D structure of irregular columns that can yield a 2D complete bandgap for a wide range of dielectric contrasts and a bandgap as large as 15.0% for ϵ=11.4 and 15.8% for ϵ=13.6. The specific problems of interference beam design, intensity threshold selection, and the effect of the shape and size of the unit cells on the final bandgap are discussed. This analysis demonstrates the unique features and advantages of the holographic method in bandgap engineering and gives a guideline for practical fabrication.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2005

2004

L. Carretero, M. Unibarrena, P. Acebal, S. Blaya, R. Madrigal, and A. Fimia, "Multiplexed holographic gratings for fabricating 3D photonic crystals in BB640 photographic emulsions," Opt. Express 12, 2903-2908 (2004).
[CrossRef] [PubMed]

X. L. Yang, L. Z. Cai, Q. Liu, and H. K. Liu, "Theoretical bandgap modeling of two-dimensional square photonic crystals fabricated by interference technique of three noncoplanar beams," J. Opt. Soc. Am. B 21, 1699-1702 (2004).
[CrossRef]

R. C. Gauthier and K. M. Mnaymneh, "Design of photonic band gap structures through a dual-beam multiple exposure techniques," Opt. Laser Technol. 36, 625-633 (2004).
[CrossRef]

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetry and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
[CrossRef]

2003

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

2002

2000

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]

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]

M. Qiu and S. He, "Optimal design of two-dimensional photonic crystal of square lattice with large complete two-dimensional bandgap," J. Opt. Soc. Am. B 17, 1027-1030 (2000).
[CrossRef]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519-15522 (2000).
[CrossRef]

1999

X. H. Wang, B. Y. Gu, Z. Y. Li, and G. Z. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417-11421 (1999).
[CrossRef]

1998

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gaps in two-dimensional anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

1996

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2952 (1996).
[CrossRef] [PubMed]

1994

S. Y. Lin, G. Arjavalingam, and W. M. Robertson, "Investigation of absolute photonic band-gaps in 2-dimensional dielectric structures," J. Mod. Opt. 41, 385-393 (1994).
[CrossRef]

1993

1992

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannapoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

P. R. Villeneuve and M. Piche, "Phonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992).
[CrossRef]

P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square lattices: square and circular lattices," Phys. Rev. B 46, 4973-4975 (1992).
[CrossRef]

1990

K. M. Leung and Y. F. Liu, "Photon band structures: the plane-wave method," Phys. Rev. B 41, 10188-10190 (1990).
[CrossRef]

1987

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]

Acebal, P.

Agio, M.

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519-15522 (2000).
[CrossRef]

Anderson, C. M.

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2952 (1996).
[CrossRef] [PubMed]

Andreani, L. C.

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519-15522 (2000).
[CrossRef]

Arjavalingam, G.

S. Y. Lin, G. Arjavalingam, and W. M. Robertson, "Investigation of absolute photonic band-gaps in 2-dimensional dielectric structures," J. Mod. Opt. 41, 385-393 (1994).
[CrossRef]

Blanco, A.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Blaya, S.

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannapoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

Bullock, D. L.

Busch, K.

D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetry and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
[CrossRef]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (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 holographic lithography," Nature 404, 53-56 (2000).
[CrossRef] [PubMed]

Carretero, L.

Chan, T. Y. M.

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

Chen, G.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Denning, R. G.

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]

Deubel, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Dong, G. Y.

Driel, H. M. V.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Encrich, C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Feng, C. S.

Fimia, A.

Freymann, G.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Gauthier, R. C.

R. C. Gauthier and K. M. Mnaymneh, "Design of photonic band gap structures through a dual-beam multiple exposure techniques," Opt. Laser Technol. 36, 625-633 (2004).
[CrossRef]

Giapis, K. P.

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2952 (1996).
[CrossRef] [PubMed]

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Gu, B. Y.

X. H. Wang, B. Y. Gu, Z. Y. Li, and G. Z. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417-11421 (1999).
[CrossRef]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gaps in two-dimensional anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Han, Y. J.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

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 holographic lithography," Nature 404, 53-56 (2000).
[CrossRef] [PubMed]

He, M. Z.

He, S.

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Joannapoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannapoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

Joannopoulos, J. D.

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

John, S.

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

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Kawata, S.

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.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Leonard, S. W.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Leung, K. M.

K. M. Leung and Y. F. Liu, "Photon band structures: the plane-wave method," Phys. Rev. B 41, 10188-10190 (1990).
[CrossRef]

Li, Z. Y.

X. H. Wang, B. Y. Gu, Z. Y. Li, and G. Z. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417-11421 (1999).
[CrossRef]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gaps in two-dimensional anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Lin, S. Y.

S. Y. Lin, G. Arjavalingam, and W. M. Robertson, "Investigation of absolute photonic band-gaps in 2-dimensional dielectric structures," J. Mod. Opt. 41, 385-393 (1994).
[CrossRef]

Liu, H. K.

Liu, Q.

Liu, Y. F.

K. M. Leung and Y. F. Liu, "Photon band structures: the plane-wave method," Phys. Rev. B 41, 10188-10190 (1990).
[CrossRef]

Lopez, C.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Madrigal, R.

Maldovan, M.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

Margulies, R. S.

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannapoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

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

Meisel, D. C.

D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetry and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
[CrossRef]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Meng, X. F.

Meseguer, F.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Miguez, H.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Miklyaev, Y. V.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Mnaymneh, K. M.

R. C. Gauthier and K. M. Mnaymneh, "Design of photonic band gap structures through a dual-beam multiple exposure techniques," Opt. Laser Technol. 36, 625-633 (2004).
[CrossRef]

Mondia, J. P.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Ozin, G. A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Piche, M.

P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square lattices: square and circular lattices," Phys. Rev. B 46, 4973-4975 (1992).
[CrossRef]

P. R. Villeneuve and M. Piche, "Phonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992).
[CrossRef]

Qiu, M.

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannapoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[CrossRef]

Robertson, W. M.

S. Y. Lin, G. Arjavalingam, and W. M. Robertson, "Investigation of absolute photonic band-gaps in 2-dimensional dielectric structures," J. Mod. Opt. 41, 385-393 (1994).
[CrossRef]

Sharp, D. N.

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]

Shih, C.

Shoji, S.

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]

Thomas, E. L.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

Toader, O.

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

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[CrossRef] [PubMed]

Turberfield, A. J.

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]

Ullal, C. K.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

Unibarrena, M.

Villeneuve, P. R.

P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square lattices: square and circular lattices," Phys. Rev. B 46, 4973-4975 (1992).
[CrossRef]

P. R. Villeneuve and M. Piche, "Phonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992).
[CrossRef]

Wang, X. H.

X. H. Wang, B. Y. Gu, Z. Y. Li, and G. Z. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417-11421 (1999).
[CrossRef]

Wang, Y. R.

Wegener, M.

D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetry and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
[CrossRef]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

Winn, J. N.

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

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E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yang, G. Z.

X. H. Wang, B. Y. Gu, Z. Y. Li, and G. Z. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417-11421 (1999).
[CrossRef]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gaps in two-dimensional anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Yang, S.

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

Yang, X. L.

Yu, X. Q.

Appl. Phys. Lett.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannapoulos, "Existence of a photonic band gap in two dimensions," Appl. Phys. Lett. 61, 495-497 (1992).
[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]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Koch, C. Encrich, M. Deubel, and M. Wegener, "Three-dimensional face-centered-cubic photonic crystals templates by laser holography: fabrication: optical characterization, and band-structure calculations," Appl. Phys. Lett. 82, 1284-1286 (2003).
[CrossRef]

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: simple cubic diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

J. Mod. Opt.

S. Y. Lin, G. Arjavalingam, and W. M. Robertson, "Investigation of absolute photonic band-gaps in 2-dimensional dielectric structures," J. Mod. Opt. 41, 385-393 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. V. Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-439 (2000).
[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. Express

Opt. Laser Technol.

R. C. Gauthier and K. M. Mnaymneh, "Design of photonic band gap structures through a dual-beam multiple exposure techniques," Opt. Laser Technol. 36, 625-633 (2004).
[CrossRef]

Opt. Lett.

Phys. Rev. B

K. M. Leung and Y. F. Liu, "Photon band structures: the plane-wave method," Phys. Rev. B 41, 10188-10190 (1990).
[CrossRef]

D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetry and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
[CrossRef]

P. R. Villeneuve and M. Piche, "Phonic band gaps in two-dimensional square and hexagonal lattices," Phys. Rev. B 46, 4969-4972 (1992).
[CrossRef]

P. R. Villeneuve and M. Piche, "Photonic band gaps in two-dimensional square lattices: square and circular lattices," Phys. Rev. B 46, 4973-4975 (1992).
[CrossRef]

X. H. Wang, B. Y. Gu, Z. Y. Li, and G. Z. Yang, "Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices," Phys. Rev. B 60, 11417-11421 (1999).
[CrossRef]

M. Agio and L. C. Andreani, "Complete photonic band gap in a two-dimensional chessboard lattice," Phys. Rev. B 61, 15519-15522 (2000).
[CrossRef]

Phys. Rev. E

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

Phys. Rev. Lett.

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]

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2952 (1996).
[CrossRef] [PubMed]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gaps in two-dimensional anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2577 (1998).
[CrossRef]

Other

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

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Figures (7)

Fig. 1
Fig. 1

Relation between threshold intensity I t and the filling ratio f of dielectric material when c = 0.16 , where curve (A) is for the normal structure and curve (B) is for the inverse structure.

Fig. 2
Fig. 2

Variation of the shape and size of the cross section of dielectric columns with different I t when c = 0.16 . (a) I t = 2.69 , f = 0.378 ; (b) I t = 2.72 , f = 0.416 ; (c) I t = 2.75 , f = 0.443 ; (d) I t = 2.79 , f = 0.469 .

Fig. 3
Fig. 3

Variation of the relative bandgap with filling ratio for the inverse structure in the case of c = 0.16 and ϵ = 11.4 .

Fig. 4
Fig. 4

Gap map for the inverse structure when c = 0.16 and ϵ = 11.4 .

Fig. 5
Fig. 5

Photonic band structure in the optimized case I t = 2.72 when c = 0.16 and ϵ = 11.4 . The solid curves are for p polarization, and the dashed curves are for s polarization.

Fig. 6
Fig. 6

Relation between the value of c and the corresponding maximum relative bandwidth when ϵ = 11.4 .

Fig. 7
Fig. 7

Optimized column shapes yielding maximum PBG for different ϵ. (a) ϵ = 8.9 , c = 0.13 , I t = 2.75 , and f = 0.424 ; (b) ϵ = 13.6 , c = 0.18 , I t = 2.71 , and f = 0.416 .

Equations (1)

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I ( x , y ) = 3 + cos ( 2 π x a ) + cos ( 2 π y a ) c { cos [ 4 π ( x + y ) a ] + cos [ 4 π ( x y ) a ] } ,

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