Abstract

Two-dimensional hexagonal photonic crystals can be recorded using the simple superimposition of two interference patterns rotated by 60°. Such process generates high contrast masks, however, it generates elliptical cross section structures instead of cylinders. We study the PBG properties of the experimentally feasible geometries, using this technique and we demonstrate that the effect of this asymmetric shape is a reduction in the PBG map area, for TE polarization, in comparison with cylindrical structures. On the other hand, it appears a PBG for TM polarization.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [PubMed]

2005

2004

2003

2002

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

M. Marrone, V. F. Rodriguez-Esquerre and H. E. Hernandez-Figueroa, "Novel numerical method for the analysis of 2D photonic crystals: the cell method," Opt. Express 10, 1299-1304 (2002).
[PubMed]

2001

E. Chow, S. Y. Lin, and J. R. Wendt, "Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ = 1.55μm wavelengths," Opt. Lett. 26, 286-288 (2001).
[CrossRef]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001)
[CrossRef] [PubMed]

2000

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

1999

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

1997

C. R. A. Lima, L. L. Soares, L. Cescato, M. A. R. Alves, and E. S. Braga, "Diffractive Structures Holographically Recorded in Amourphous Hydrogenated Carbon (a-C:H) films," Opt. Lett. 22,1805-1807 (1997).
[CrossRef]

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

1995

B. A. Mello, I. F. Costa, C. R. A. Lima, and L. Cescato, "Developed profile of holographically exposed photoresist gratings," Appl. Opt. 34,597 (1995).
[CrossRef]

C. C. Cheng and A. Scherer, "Fabrication of photonic band-gap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
[CrossRef]

1992

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

1988

Alleman, A

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

Alves, M. A. R.

Asakawa, K.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Benisty, H.

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Braga, E. S.

Cai, L. Z.

Campbell, M.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Carlsson, N.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Cescato, L.

Cheng, C. C.

C. C. Cheng and A. Scherer, "Fabrication of photonic band-gap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
[CrossRef]

Chow, E.

E. Chow, S. Y. Lin, and J. R. Wendt, "Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ = 1.55μm wavelengths," Opt. Lett. 26, 286-288 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001)
[CrossRef] [PubMed]

Costa, I. F.

de Carvalho, E. J.

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva, and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and eletroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

De La Rue, R. M.

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Decker, J. Y.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Dedman, E. R.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Denning, R. G.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Dong, G. Y.

Fan, D.

Feng, C. S.

Fernandez, A.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Frejlich, J.

Gutierrez-Rivera, L. E.

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva, and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and eletroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

Harrison, M. T.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

He, M. Z.

Herman, S. M.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Hernandez-Figueroa, H. E.

Hou, H.

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

Houdré, R.

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Hsu, C. C.

Ikeda, N.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Imada, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001)
[CrossRef] [PubMed]

Inoue, K.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Joannopoulos, J. D.

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

Jonhson, S. G.

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

Katayama, Y.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Kawai, N.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Krauss, T. F.

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Kuramochi, E.

M. Notomi, A. Shinya, and E. Kuramochi, "Photonic crystals: Towards ultrasmall lightwave circuits," NTT Tech. Rev. 2, 36-47 (2004).

Labilloy, D.

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Lai, N. D.

Liang, W. P.

Lima, C. R. A.

Lin, C. H.

Lin, J. H.

Lin, S. Y.

E. Chow, S. Y. Lin, and J. R. Wendt, "Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ = 1.55μm wavelengths," Opt. Lett. 26, 286-288 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

Marrone, M.

Mello, B. A.

Mendes, G. F.

Meng, X. F.

Mochizuki, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001)
[CrossRef] [PubMed]

Noda, S.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001)
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, A. Shinya, and E. Kuramochi, "Photonic crystals: Towards ultrasmall lightwave circuits," NTT Tech. Rev. 2, 36-47 (2004).

Oesterle, U.

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Olivier, S.

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

Peng, R.

Perry, M. D.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Phillion, D. W.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Piché, M.

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

Qian, L.

Rattier, M.

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

Rodriguez-Esquerre, V. F.

Scherer, A.

C. C. Cheng and A. Scherer, "Fabrication of photonic band-gap crystals," J. Vac. Sci. Technol. B 13, 2696-2700 (1995).
[CrossRef]

Sharp, D. N.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Shinya, A.

M. Notomi, A. Shinya, and E. Kuramochi, "Photonic crystals: Towards ultrasmall lightwave circuits," NTT Tech. Rev. 2, 36-47 (2004).

Silva, M. A.

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva, and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and eletroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

Smith, C. J. M.

S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

C. J. M. Smith, H. Benisty, D. Labilloy, U. Oesterle, R. Houdré, T. F. Krauss, R. M. De La Rue, and C. Weisbuch, "Near-infrared microcavities confined by two-dimensional photonic bandgap crystals," Electron. Lett. 35, 228-230 (1999).
[CrossRef]

Soares, L. L.

Sugimoto, Y.

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Sweeney, D. W.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney, and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
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N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

Tang, Z.

Turberfield, A. J.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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).
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E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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]

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[CrossRef]

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E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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).
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[CrossRef]

Nature

E. Chow, S. Y. Lin, S. G. Jonhson, P. R. 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).
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S. Olivier, H. Benisty, C. J. M. Smith, M. Rattier, C. Weisbuch, and T. F. Krauss, "Transmission properties of two-dimensional photonic crystal channel waveguides," Opt. Quantum Electron. 34, 171-181 (2002).
[CrossRef]

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

N. Carlsson, N. Ikeda, Y. Sugimoto, K. Asakawa, T. Takemori, Y. Katayama, N. Kawai, and K. Inoue, "Design, nano-fabication and analysis of near-infrared 2D photonic crystal air-bridge structures," Opt. Quantum Electron. 34, 123-131 (2002).
[CrossRef]

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

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S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001)
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Figures (8)

Fig. 1.
Fig. 1.

Simulated light intensity patterns resulting from the superimposition of two equal fringe patterns with a rotation of 90° (a) and 60° (b) between them. The lines represent the isointensity of the light pattern.

Fig. 2.
Fig. 2.

Scheme of the fabrication process.

Fig. 3.
Fig. 3.

Two-dimensional structures recorded by using double holographic exposures. (a) cubic lattice and (b) hexagonal lattice. The size of the scale bar is 0.5µm.

Fig. 4.
Fig. 4.

Two-dimensional structures with hexagonal lattice recorded in a-C:H film. The size of the scale bar is 1µm.

Fig. 5.
Fig. 5.

(a) Scheme of the unitary cell of circular structures used in the calculus and (b) corresponding Brillouin zone. The irreducible Brillouin zone is the triangle of vertices Γ, K e M.

Fig. 6.
Fig. 6.

(a) Scheme of the unitary cell of elliptical structures and (b) corresponding Brillouin zone. The irreducible zone of vertices Γ, K, M, K’ and M’ corresponds to ¼ of the Brillouin zone.

Fig. 7.
Fig. 7.

Band Diagram for the elliptical holes with r/a=0.37 in a dielectric material with n=2.

Fig. 8.
Fig. 8.

Gap map for a hexagonal lattices of: (a) circular holes and (b) elliptical holes (E=2), in a dielectric material with refractive index n=2.

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