Abstract

We present a three-dimensional (3D) analysis of a hybrid photonic crystal-conventional waveguide 90° bend proposed previously [Opt. Express 10, 1334 (2002)] as an ultracompact component for large-scale planar lightwave circuit integration. Both rigorous 3D finite-difference time-domain modeling and a simple perfect mirror model analysis were carried out for different Si post heights in the photonic crystal region. Results show that the bend efficiency increases rapidly with Si post height. For a post height of 6.5 μm, this structure yields a bend efficiency of 97.3% at a wavelength of 1.55 μm for 90° bends in 2 μm × 2 μm square channel conventional waveguides with a refractive index contrast of 3.55%, which is very close to the bend efficiency of 98.2% for the corresponding two-dimensional problem. Our 3D analysis permits the examination of issues such as out-of-plane scattering loss and the effects of finite Si post height that are not considered in two dimensions.

© 2004 Optical Society of America

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  1. H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
    [CrossRef]
  2. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
    [CrossRef]
  3. P. Lalanne, H. Benistry, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
    [CrossRef]
  4. A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
    [CrossRef]
  5. P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
    [CrossRef]
  6. M. Tokushima, H. Yamada, “Light propagation in a photonic-crystal-slab line-defect waveguide,” IEEE J. Quantum Electron. 38, 753–759 (2002).
    [CrossRef]
  7. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Properties of the slab modes in photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1554–1564 (2000).
    [CrossRef]
  8. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
    [CrossRef]
  9. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, U. Oesterle, “Improved 60° bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Lightwave Technol. 20, 1198–1203 (2002).
    [CrossRef]
  10. G. P. Nordin, S. Kim, J. Cai, J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Opt. Express 10, 1334–1341 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  11. M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).
  12. C. Guiffaut, K. Mahdjoubi, “A parallel FDTD algorithm using the MPI Library,” IEEE Antennas Propag. Mag. 43, 94–102 (2001).
    [CrossRef]
  13. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).
  14. K. Okamoto, Fundamentals of Optical Waveguides (Academic, New York, 2000).
  15. http://oedcad.jlu.edu.cn .
  16. E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. QE-22, 988–993 (1986).
    [CrossRef]
  17. R. Syms, J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, New York, 1992).

2002 (5)

P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
[CrossRef]

M. Tokushima, H. Yamada, “Light propagation in a photonic-crystal-slab line-defect waveguide,” IEEE J. Quantum Electron. 38, 753–759 (2002).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, U. Oesterle, “Improved 60° bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Lightwave Technol. 20, 1198–1203 (2002).
[CrossRef]

G. P. Nordin, S. Kim, J. Cai, J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Opt. Express 10, 1334–1341 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

2001 (3)

C. Guiffaut, K. Mahdjoubi, “A parallel FDTD algorithm using the MPI Library,” IEEE Antennas Propag. Mag. 43, 94–102 (2001).
[CrossRef]

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

P. Lalanne, H. Benistry, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

2000 (3)

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Properties of the slab modes in photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1554–1564 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

1986 (1)

E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. QE-22, 988–993 (1986).
[CrossRef]

Adibi, A.

Baets, R.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

Benistry, H.

P. Lalanne, H. Benistry, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Benisty, H.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, U. Oesterle, “Improved 60° bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Lightwave Technol. 20, 1198–1203 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Beraud, A.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Bienstman, P.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

Bogaerts, W.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

Cai, J.

Cassagne, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Chutinan, A.

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Cozens, J.

R. Syms, J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, New York, 1992).

Dongarra, J.

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).

Guiffaut, C.

C. Guiffaut, K. Mahdjoubi, “A parallel FDTD algorithm using the MPI Library,” IEEE Antennas Propag. Mag. 43, 94–102 (2001).
[CrossRef]

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Houdre, R.

Huss-Lederman, S.

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).

Jiang, J.

Jouanin, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Kim, S.

Krauss, T. F.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, U. Oesterle, “Improved 60° bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Lightwave Technol. 20, 1198–1203 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Labilloy, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Lalanne, P.

P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
[CrossRef]

P. Lalanne, H. Benistry, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Lee, R. K.

Mahdjoubi, K.

C. Guiffaut, K. Mahdjoubi, “A parallel FDTD algorithm using the MPI Library,” IEEE Antennas Propag. Mag. 43, 94–102 (2001).
[CrossRef]

Marcatili, E.

E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. QE-22, 988–993 (1986).
[CrossRef]

Noda, S.

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Nordin, G. P.

Notomi, M.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Oesterle, U.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, New York, 2000).

Olivier, S.

Otto, S.

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).

Scherer, A.

Shinya, A.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Smith, C. J. M.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, U. Oesterle, “Improved 60° bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Lightwave Technol. 20, 1198–1203 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Snir, M.

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).

Syms, R.

R. Syms, J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, New York, 1992).

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

Taillaert, D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

Takahashi, C.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Takahashi, J.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Tokushima, M.

M. Tokushima, H. Yamada, “Light propagation in a photonic-crystal-slab line-defect waveguide,” IEEE J. Quantum Electron. 38, 753–759 (2002).
[CrossRef]

Walker, D.

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).

Weisbuch, C.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, R. Houdre, U. Oesterle, “Improved 60° bend transmission of submicron-width waveguides defined in two-dimensional photonic crystals,” J. Lightwave Technol. 20, 1198–1203 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Xu, Y.

Yamada, H.

M. Tokushima, H. Yamada, “Light propagation in a photonic-crystal-slab line-defect waveguide,” IEEE J. Quantum Electron. 38, 753–759 (2002).
[CrossRef]

Yamada, K.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Yariv, A.

Yokohama, I.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

Zutter, D. D.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Beraud, C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

C. Guiffaut, K. Mahdjoubi, “A parallel FDTD algorithm using the MPI Library,” IEEE Antennas Propag. Mag. 43, 94–102 (2001).
[CrossRef]

IEEE J. Quantum Electron. (4)

P. Lalanne, “Electromagnetic analysis of photonic crystal waveguides operating above the light cone,” IEEE J. Quantum Electron. 38, 800–804 (2002).
[CrossRef]

M. Tokushima, H. Yamada, “Light propagation in a photonic-crystal-slab line-defect waveguide,” IEEE J. Quantum Electron. 38, 753–759 (2002).
[CrossRef]

E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. QE-22, 988–993 (1986).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, I. Yokohama, “Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs,” IEEE J. Quantum Electron. 38, 736–742 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets, D. D. Zutter, “Out-of-plane scattering in photonic crystal slabs,” IEEE Photon. Technol. Lett. 13, 565–567 (2001).
[CrossRef]

J. Appl. Phys. (1)

P. Lalanne, H. Benistry, “Out-of-plane losses of two-dimensional photonic crystals waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (1)

Phys. Rev. B (1)

A. Chutinan, S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Other (5)

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, Mass., 2000).

K. Okamoto, Fundamentals of Optical Waveguides (Academic, New York, 2000).

http://oedcad.jlu.edu.cn .

R. Syms, J. Cozens, Optical Guided Waves and Devices (McGraw-Hill, New York, 1992).

M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI—The Complete Reference (MIT Press, Cambridge, Mass., 2000).

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Figures (6)

Fig. 1
Fig. 1

Hybrid PhC-CWG 90° bend. See text for details.

Fig. 2
Fig. 2

Cross section of a waveguide with (a) E y amplitude and (b) Poynting vector z components of the sourcing mode. (c), (d) Comparisons in the x and y directions, respectively, of mode profiles obtained by bootstrapping and the mode solver package oedcad.

Fig. 3
Fig. 3

Case 1 (5.0-μm post height) and case 2 (3.0-μm post height). (a) E y amplitude, y = 0 μm, case 1. (b) E y amplitude, y = 0 μm, case 2. (c) y component of Poynting vector, y = 3.3 μm, case 1. (d) y component of Poynting vector, y = 3.3 μm, case 2.

Fig. 4
Fig. 4

Case 1 (5.0-μm post height), case 2 (3.0-μm post height). (a) z component of Poynting vector, z = 5.1 μm, case 1. (b) z component of Poynting vector, z = 5.1 μm, case 2. (c) E y amplitude, x = 5.0 μm, case 1. (d) E y amplitude, x = 5.0 μm, case 2.

Fig. 5
Fig. 5

Efficiency as a function of post height.

Fig. 6
Fig. 6

Clipping of a mode by a perfect mirror. (a) Mode clipped by a perfect mirror 3 μm tall in the y dimension. (b) Clipped field profile along the dotted line in (a). Dashed curve, clipped part of the mode.

Tables (1)

Tables Icon

Table 1 Efficiencies for Several Post Heights

Equations (2)

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ηbend=ηcorner×ηc,
ηc= Ep*×Hq+Eq×Hp*ds2 Ep*×Hp+Ep×Hp*ds Eq*×Hq+Eq×Hq*ds,

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