Abstract

The photonic bandgap of three-dimensional photonic crystals, formed by arranging circular spirals in face-centre-cubic lattice, was theoretically investigated. The structure was found to have a relative photonic bandgap of up to 25% in both direct and inversed configurations. The conditions under which the structure has a bandgap larger than 10% are described. Some considerations for optimizing such photonic crystal fabrication by two-photon polymerization are given. The theoretical results are implemented to fabricate polymeric structures that can be used as templates for photonic crystals with full photonic bandgap larger than 10% centered in the near-infrared region.

© 2007 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  3. B. Kurt, L. Stefan, W. Ralf, and B. Föll Helmut, Photonic Crystals (Wiley-VCH, Berlin, 2004).
  4. J.-M. Lourtioz, H.i Benisty, V. Berger, J.-M. Gerard, D. Maystre, A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer-Verlag Berlin and Heidelberg 2005).
  5. C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991).
    [CrossRef]
  6. C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
    [CrossRef]
  7. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
    [CrossRef]
  8. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
    [CrossRef] [PubMed]
  9. K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
    [CrossRef]
  10. A. Chutinan, and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev B 57, R2006 (1998).
    [CrossRef]
  11. K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
    [CrossRef]
  12. K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
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  13. S. G. Johnson "MIT Photonic-Bands," (Massachusetts Institute of Technology 2002), http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands>
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  15. H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999).
    [CrossRef]
  16. J. Serbin, A. Ovsianikov, and B. Chichkov, "Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties," Opt. Express 12, 5221 (2004).
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  17. H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
    [CrossRef]
  18. M. Deubel, G. V. 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 (2004).
    [CrossRef] [PubMed]
  19. N. Tétreault,  et al., "New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates," Adv. Mater. 18, 457-460 (2006).
    [CrossRef]
  20. S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, "Two-photon lithography of nanorods in SU-8 photoresist," Nanotechnology 16, 846-849 (2005).
    [CrossRef]
  21. D. Tan,  et al., "Reduction in feature size of two-photon polymerization using SCR500," Appl Phys Lett 90, 071106 (2007).
    [CrossRef]

2007 (1)

D. Tan,  et al., "Reduction in feature size of two-photon polymerization using SCR500," Appl Phys Lett 90, 071106 (2007).
[CrossRef]

2006 (2)

N. Tétreault,  et al., "New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates," Adv. Mater. 18, 457-460 (2006).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
[CrossRef]

2005 (2)

S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, "Two-photon lithography of nanorods in SU-8 photoresist," Nanotechnology 16, 846-849 (2005).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

2004 (3)

J. Serbin, A. Ovsianikov, and B. Chichkov, "Fabrication of woodpile structures by two-photon polymerization and investigation of their optical properties," Opt. Express 12, 5221 (2004).
[CrossRef] [PubMed]

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

2003 (1)

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
[CrossRef]

2001 (1)

2000 (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
[CrossRef] [PubMed]

1999 (1)

H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999).
[CrossRef]

1998 (1)

A. Chutinan, and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev B 57, R2006 (1998).
[CrossRef]

1994 (2)

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

1991 (1)

C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991).
[CrossRef]

1987 (2)

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

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

Biswas, R.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

Busch, K.

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
[CrossRef]

C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991).
[CrossRef]

Chichkov, B.

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
[CrossRef] [PubMed]

A. Chutinan, and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev B 57, R2006 (1998).
[CrossRef]

Datta, S.

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
[CrossRef]

Deubel, M.

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

Duan, X. M.

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
[CrossRef]

Freymann, G. V.

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

Ho, K. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
[CrossRef]

C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991).
[CrossRef]

Joannopoulos, J. D.

John, S.

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

Johnson, S. G.

Juodkazis, S.

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, "Two-photon lithography of nanorods in SU-8 photoresist," Nanotechnology 16, 846-849 (2005).
[CrossRef]

Kaneko, K.

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
[CrossRef]

Kawata, S.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
[CrossRef]

Kim, M. S.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

Lee, K. S.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

Matsuo, S.

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999).
[CrossRef]

Misawa, H.

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999).
[CrossRef]

Mizeikis, V.

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
[CrossRef] [PubMed]

A. Chutinan, and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev B 57, R2006 (1998).
[CrossRef]

Ovsianikov, A.

Pereira, S.

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

Seet, K. K.

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
[CrossRef]

Seet, K. K.

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

Serbin, J.

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
[CrossRef]

C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991).
[CrossRef]

Sun, H. B.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
[CrossRef]

H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999).
[CrossRef]

Suwa, T.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

Takada, K.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

Tan, D.

D. Tan,  et al., "Reduction in feature size of two-photon polymerization using SCR500," Appl Phys Lett 90, 071106 (2007).
[CrossRef]

Tétreault, N.

N. Tétreault,  et al., "New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates," Adv. Mater. 18, 457-460 (2006).
[CrossRef]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
[CrossRef] [PubMed]

Wegener, M.

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

Yablonovitch, E.

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

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
[CrossRef] [PubMed]

Zaccaria, R. P.

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

Adv. Mater. (2)

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-Dimensional Spiral-Architecture Photonic Crystals Obtained By Direct Laser Writing," Adv. Mater. 17, 541 (2005).
[CrossRef]

N. Tétreault,  et al., "New Route to Three-Dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates," Adv. Mater. 18, 457-460 (2006).
[CrossRef]

Appl Phys Lett (1)

D. Tan,  et al., "Reduction in feature size of two-photon polymerization using SCR500," Appl Phys Lett 90, 071106 (2007).
[CrossRef]

Appl Phys. Lett (1)

H. B. Sun, T. Suwa, K. Takada, R. P. Zaccaria, M. S. Kim, K. S. Lee, S. Kawata, "Shape precompensation in two-photon nanowriting of photonic lattices," Appl. Phys. Lett. 85, 3708 (2004).
[CrossRef]

Appl. Phys. Lett. (3)

H. B.  Sun, S.  Matsuo, and H.  Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett.  74, 786 (1999).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Juodkazis, and H. Misawa, "Three-dimensional horizontal circular spiral photonic crystals with stop gaps below 1 µm," Appl. Phys. Lett. 88, 221101 (2006).
[CrossRef]

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata," Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication," Appl. Phys. Lett. 83, 2091 (2003).
[CrossRef]

Europhys. Lett. (1)

C. T. Chan, K. M. Ho and C. M. Soukoulis, "Photonic bandgaps in experimentally realizable periodic dielectric structures," Europhys. Lett. 16, 563 (1991).
[CrossRef]

Nanotechnology (1)

S. Juodkazis1, V. Mizeikis1, K. Seet1, M. Miwa, and H. Misawa, "Two-photon lithography of nanorods in SU-8 photoresist," Nanotechnology 16, 846-849 (2005).
[CrossRef]

Nat. Mater. (1)

M. Deubel, G. V. 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 (2004).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev B (1)

A. Chutinan, and S. Noda, "Spiral three-dimensional photonic-band-gap structure," Phys. Rev B 57, R2006 (1998).
[CrossRef]

Phys. Rev. B (1)

C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, "A-7 structure: A family of photonic crystals," Phys. Rev. B 50, 1988 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

Science (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604 (2000).
[CrossRef] [PubMed]

Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic bandgaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413 (1994).
[CrossRef]

Other (3)

B. Kurt, L. Stefan, W. Ralf, and B. Föll Helmut, Photonic Crystals (Wiley-VCH, Berlin, 2004).

J.-M. Lourtioz, H.i Benisty, V. Berger, J.-M. Gerard, D. Maystre, A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer-Verlag Berlin and Heidelberg 2005).

S. G. Johnson "MIT Photonic-Bands," (Massachusetts Institute of Technology 2002), http://ab-initio.mit.edu/wiki/index.php/MIT_Photonic_Bands>

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Figures (4)

Fig. 1.
Fig. 1.

Sketch of a spiral and its parameters together with an array of 4 × 4 spirals that are arranged in fcc lattice. The lattice constant a is equal twice the distance between adjacent spirals. Each spiral has a pitch C, a diameter D and is made of rods with a width w and a length l.

Fig. 2.
Fig. 2.

(a) Two unit cells of the optimal fcc spiral structure in the direct configuration. (b) Photonic band structure of the fcc spiral structure made of n=3.5 material. (c) Sensitivity of the bandgap to the changes in the rod’s length (triangular), rod’s width (circular) and spiral’s diameter (rectangular). (left) direct configuration, (right) inverse configuration. (d) The distributions of the electric energy in the electromagnetic wave that propagates in the ΓZ direction. (top) ‘dielectric mode’ bellow the bandgap, (bottom) ‘air mode’ above the bandgap.

Fig. 3.
Fig. 3.

(a) The effect of the axial elongation on the maximal photonic bandgap for the inverse (left) and direct (right) architectures. (b) Bandgap map, i.e. bandgap as a function of spiral diameter and rod’s width of the inverse spiral structure. (c) The dependence of the photonic bandgap of the inverse architecture on the elongation factor for all structure configurations in the simulated range. (d) Parameters that optimize the photonic bandgap as a function of the elongation factor. Spiral diameter (black, rectangular), rod’s width (red, triangle), Relative size of the photonic bandgap (blue, circle).

Fig. 4.
Fig. 4.

(a) Side view of SEM image of 40μm × 40μm fcc spiral structure that was realized in SU8 resin. (b) Top view. (c) ΓZU band structure for n=3.5 refractive index (left) and polymeric n=1.6 refractive index (right). (d) Sketch describes the formation of sinusoidal lines by the overlapping spirals. The arrows indicate the winding direction of the spirals which are segmented in such a way that the colors represent ¼ pitch length sequential layers.

Equations (4)

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[ w d , l d , D d , C d ] = [ ( 0.15 a : 0.35 a ) , ( 0.15 a : 0.4 a ) , ( 0.3 a : 0.5 a ) , ~a ]
[ w i , l i , D i , C i ] = [ ( 0.3 a : 0.55 a ) , ( 0.15 a : 0.75 a ) , ( 0.3 a : 0.45 a ) , ~a ]
f d = 0.17 ln ( wl ) + 0.005
f i = 1.22 wl + 0.225

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