Abstract

Topology optimization has been used to design a 60° bend in a single-mode planar photonic crystal waveguide. The design has been realized in a silicon-on-insulator material and we demonstrate a record-breaking 200nm transmission bandwidth with an average bend loss of 0.43±0.27 dB for the TE polarization. The experimental results agree well with 3D finite-difference-time-domain simulations.

©2004 Optical Society of America

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Topology optimization and fabrication of photonic crystal structures

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Opt. Express 12(9) 1996-2001 (2004)

Broadband topology-optimized photonic crystal components for both TE and TM polarizations

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Ultralow-loss 3-dB photonic crystal waveguide splitter

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx
Opt. Lett. 29(14) 1623-1625 (2004)

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  3. T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
    [Crossref]
  4. M. Thorhauge, L. H. Frandsen, and P. I. Borel, “Efficient Photonic Crystal Directional Couplers,” Opt. Lett. 28, 1525–1527 (2003).
    [Crossref] [PubMed]
  5. Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).
  6. L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
    [Crossref] [PubMed]
  7. T. Søndergaard, J. Arentoft, and M. Kristensen, “Theoretical Analysis of Finite-Height Semiconductor-on-Insulator-Based Planar Photonic Crystal Waveguides,” J. Lightwave Technol. 20, 1619–1626 (2002)
    [Crossref]
  8. C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
    [Crossref]
  9. P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
    [Crossref]
  10. A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys.Lett. 80, 1698–1700 (2002).
    [Crossref]
  11. J. Smajic, C. Hafner, and D. Erni, “Design and optimization of an achromatic photonic crystal bend,” Opt. Express 11, 1378–1384 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1378.
    [Crossref] [PubMed]
  12. P.I. Borel, A. Harpøth, L.H. Frandsen, M. Kristensen, P. Shi, J.S. Jensen, and O. Sigmund, “Topology Optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.
    [Crossref] [PubMed]
  13. A. Lavrinenko, P.I. Borel, L.H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, and T. Niemi, “Comprehensive FDTD Modelling of Photonic Crystal Waveguide Components,” Opt. Express 12, 234–248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234.
    [Crossref] [PubMed]
  14. P.I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, Y. X. Zhuang, M. Kristensen, and H. M. H. Chong, “Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light.” Opt. Express 11, 1757–1762 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757.
    [Crossref] [PubMed]
  15. A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
    [Crossref]
  16. E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ=1.55 µm wavelengths,” Opt. Lett. 26, 286–288 (2001).
    [Crossref]
  17. M. P. Bendsøe and O. Sigmund, Topology optimization — Theory, Methods and Applications (Springer-Verlag, 2003).
  18. K. Svanberg, “The method of moving asymptotes: a new method for structural optimization,” Int. J. Numer. Meth. Engng. 24, 359–373 (1987).
    [Crossref]
  19. J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022–2024 (2004).
    [Crossref]
  20. O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Phil. Trans. R. Soc. Lond. A 361, 1001–1019 (2003).
    [Crossref]
  21. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B, accepted (2004).
  22. R. L. Espinola, R. U. Ahmad, F. Pizzuto, M. J. Steel, and R. M. Osgood, “A study of high-index contrast 90° waveguide bend structures,” Opt. Express 8, 517–528 (2001), http://www.opticsexpress.org/abstract.cfm? URI=OPEX-8-9-517.
    [Crossref] [PubMed]

2004 (6)

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

P.I. Borel, A. Harpøth, L.H. Frandsen, M. Kristensen, P. Shi, J.S. Jensen, and O. Sigmund, “Topology Optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.
[Crossref] [PubMed]

A. Lavrinenko, P.I. Borel, L.H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, and T. Niemi, “Comprehensive FDTD Modelling of Photonic Crystal Waveguide Components,” Opt. Express 12, 234–248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234.
[Crossref] [PubMed]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022–2024 (2004).
[Crossref]

2003 (5)

2002 (3)

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys.Lett. 80, 1698–1700 (2002).
[Crossref]

T. Søndergaard, J. Arentoft, and M. Kristensen, “Theoretical Analysis of Finite-Height Semiconductor-on-Insulator-Based Planar Photonic Crystal Waveguides,” J. Lightwave Technol. 20, 1619–1626 (2002)
[Crossref]

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

2001 (2)

1996 (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

1987 (3)

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]

K. Svanberg, “The method of moving asymptotes: a new method for structural optimization,” Int. J. Numer. Meth. Engng. 24, 359–373 (1987).
[Crossref]

Agio, M.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

Ahmad, R. U.

Andreani, L.C.

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
[Crossref]

Arentoft, J.

Asakawa, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Baets, R.

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

Beckx, S.

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

Bendsøe, M. P.

M. P. Bendsøe and O. Sigmund, Topology optimization — Theory, Methods and Applications (Springer-Verlag, 2003).

Bogaerts, W.

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

Borel, P. I.

Borel, P.I.

Bouadma, N.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

Chong, H. M. H.

Chow, E.

Chutinan, A.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys.Lett. 80, 1698–1700 (2002).
[Crossref]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

Dumon, P.

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

Erni, D.

Espinola, R. L.

Frandsen, L. H.

Frandsen, L.H.

Gösele, U.

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
[Crossref]

Hafner, C.

Harpøth, A.

Hermann, C.

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
[Crossref]

Hess, O.

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
[Crossref]

Ikeda, N.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Inoue, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Ishida, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Ishikawa, H.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Jamois, C.

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
[Crossref]

Jensen, J. S.

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022–2024 (2004).
[Crossref]

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Phil. Trans. R. Soc. Lond. A 361, 1001–1019 (2003).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B, accepted (2004).

Jensen, J.S.

Joannopoulos, J. D.

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

Johnson, S. G.

Kafesaki, M.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

Kanamoto, K.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

Kristensen, M.

A. Lavrinenko, P.I. Borel, L.H. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, and T. Niemi, “Comprehensive FDTD Modelling of Photonic Crystal Waveguide Components,” Opt. Express 12, 234–248 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234.
[Crossref] [PubMed]

P.I. Borel, A. Harpøth, L.H. Frandsen, M. Kristensen, P. Shi, J.S. Jensen, and O. Sigmund, “Topology Optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.
[Crossref] [PubMed]

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultra-low-loss 3-dB Photonic Crystal Waveguide Splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

P.I. Borel, L. H. Frandsen, M. Thorhauge, A. Harpøth, Y. X. Zhuang, M. Kristensen, and H. M. H. Chong, “Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light.” Opt. Express 11, 1757–1762 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757.
[Crossref] [PubMed]

T. Søndergaard, J. Arentoft, and M. Kristensen, “Theoretical Analysis of Finite-Height Semiconductor-on-Insulator-Based Planar Photonic Crystal Waveguides,” J. Lightwave Technol. 20, 1619–1626 (2002)
[Crossref]

Lavrinenko, A.

Le Gouezigou, L.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

Leon, J.B.

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

Lin, S. Y.

Liu, H.

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

Nakamura, H.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Nakamura, Y.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Niemi, T.

Noda, S.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys.Lett. 80, 1698–1700 (2002).
[Crossref]

Ohkouchi, S.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Okano, M.

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys.Lett. 80, 1698–1700 (2002).
[Crossref]

Osgood, R. M.

Pizzuto, F.

Sasaki, H.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Shi, P.

Sigmund, O.

P.I. Borel, A. Harpøth, L.H. Frandsen, M. Kristensen, P. Shi, J.S. Jensen, and O. Sigmund, “Topology Optimization and fabrication of photonic crystal structures,” Opt. Express 12, 1996–2001 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996.
[Crossref] [PubMed]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022–2024 (2004).
[Crossref]

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Phil. Trans. R. Soc. Lond. A 361, 1001–1019 (2003).
[Crossref]

M. P. Bendsøe and O. Sigmund, Topology optimization — Theory, Methods and Applications (Springer-Verlag, 2003).

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B, accepted (2004).

Smajic, J.

Søndergaard, T.

Soukoulis, C.M.

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

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Sugimoto, Y.

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

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[Crossref]

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A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

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Thorhauge, M.

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Wehrspohn, R. B.

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
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Wiaux, V.

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P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
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Appl. Phys. Lett. (1)

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022–2024 (2004).
[Crossref]

Appl. Phys.Lett. (2)

A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys.Lett. 80, 1698–1700 (2002).
[Crossref]

A. Talneau, L. Le Gouezigou, N. Bouadma, M. Kafesaki, C.M. Soukoulis, and M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 µm,” Appl. Phys.Lett. 80, 547–549 (2002).
[Crossref]

Electron. Lett. (1)

P.I. Borel, L.H. Frandsen, A. Harpøth, J.B. Leon, H. Liu, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, W. Wiaux, J. Wouters, and S. Beckx, “Bandwidth tuning of photonic crystal waveguide bends,” Electron. Lett. 40, 1263–1264 (2004).
[Crossref]

IEICE Trans. Electron. (1)

Y. Sugimoto, Y. Tanaka, N. Ikeda, K. Kanamoto, Y. Nakamura, S. Ohkouchi, H. Nakamura, K. Inoue, H. Sasaki, Y. Watanabe, K. Ishida, H. Ishikawa, and K. Asakawa, “Two Dimensional Semiconductor-Based Photonic Crystal Slab Waveguides for Ultra-Fast Optical Signal Processing Devices,” IEICE Trans. Electron. E87-C, 316–327 (2004).

Int. J. Numer. Meth. Engng. (1)

K. Svanberg, “The method of moving asymptotes: a new method for structural optimization,” Int. J. Numer. Meth. Engng. 24, 359–373 (1987).
[Crossref]

J. Lightwave Technol. (1)

Nature (1)

T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Phil. Trans. R. Soc. Lond. A (1)

O. Sigmund and J. S. Jensen, “Systematic design of phononic band gap materials and structures by topology optimization,” Phil. Trans. R. Soc. Lond. A 361, 1001–1019 (2003).
[Crossref]

Photonics and Nanostructures - Fundamentals and Applications (1)

C. Jamois, R. B. Wehrspohn, L.C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photonics and Nanostructures - Fundamentals and Applications 1, 1–13 (2003).
[Crossref]

Phys. Rev. Lett. (2)

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]

Other (2)

M. P. Bendsøe and O. Sigmund, Topology optimization — Theory, Methods and Applications (Springer-Verlag, 2003).

J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: A high bandwidth low loss T-junction waveguide,” J. Opt. Soc. Am. B, accepted (2004).

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Figures (5)

Fig. 1.
Fig. 1. Schematics of photonic crystal waveguides containing two consecutive 60° bends. Left: Generic bend configuration. The red areas illustrate the chosen design domains in the topology optimization procedure. Right: Topology-optimized bends. The green areas highlight the optimized structures showing that a non-trivial smoothening has been applied to the bend.

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Fig. 2.
Fig. 2. Scanning electron micrographs of fabricated photonic crystal waveguides containing two consecutive 60° bends. The pitch of the triangular lattice is Λ≈400nm with hole diameter D≈275nm. Left: Waveguide with generic. Right: Waveguide with topology-optimized bends. The number, shape and size of the holes at each bend are designed using topology optimization. The contrast and brightness of the images have been changed for clarity.

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Fig. 3.
Fig. 3. Steady-state magnetic field distribution for the fundamental PBG mode simulated using 2D FDTD. The mode is incident from the bottom-left part of the waveguide. Left: Mode profile through the generic bends. Right: Mode profile through the topology-optimized bends.

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Fig. 4.
Fig. 4. Measured loss per bend for the un-optimized 60° bends (red) and the topology-optimized 60° bends (green). Both spectra have been normalized to the transmission through straight PhCWs of the same length to eliminate the coupling and the propagation loss in straight waveguides. Dotted line marks a bend loss of 1dB.

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Fig. 5.
Fig. 5. Experimental bend loss (green) compared to 3D FDTD calculated bend loss (blue). The 3D FDTD curve has been shifted 1.2% in absolute wavelength.

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