Abstract

We address various approaches to the reduction of optical bending loss in photonic integrated circuits. Different methods, such as offsetting of waveguides and incorporation of the effect of an isolation trench on reduction of radiation loss, are demonstrated. A combination of the vectorial finite-element and the least-squares boundary residual methods is used to calculate transition losses and the required offset for their minimization. The semivectorial finite-element-based beam-propagation method is employed to calculate radiation loss. These vectorial approaches are also used to investigate several important properties, such as effects that are due to the sidewall slopes, rib heights, rib widths, and trench location, to optimize bend designs.

© 2000 Optical Society of America

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  1. M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
    [CrossRef]
  2. T. Krauss, P. J. R. Laybourn, J. Roberts, “CW operation of semiconductor ring lasers,” Electron. Lett. 26, 2095–2096 (1990).
    [CrossRef]
  3. R. R. Hayes, D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523–527 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. C. Seo, J. C. Chen, “Low transition losses in bent rib waveguide,” J. Lightwave Technol. 14, 2255–2259 (1992).
  7. J. Yamauchi, M. Ikegaya, H. Nakano, “Analysis of bent asymmetric slab waveguides by the beam propagation method,” Opt. Commun. 79, 291–294 (1990).
    [CrossRef]
  8. E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
    [CrossRef]
  9. M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–83 (1975).
    [CrossRef]
  10. E. C. M. Pennings, R. J. Deri, “Simple method for estimating usable bend radii of deeply etched optical rib waveguides,” Electron. Lett. 27, 1532–1534 (1990).
    [CrossRef]
  11. J. S. Gu, P. A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
    [CrossRef]
  12. S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
    [CrossRef]
  13. T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
    [CrossRef]
  14. S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikathi, “New full-vectorial numerically efficient propagation algorithm based on the finite element method,” J. Lightwave Technol. 18, 409–415 (2000).
    [CrossRef]
  15. B. M. A. Rahman, J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. LT-2, 682–688 (1984).
    [CrossRef]
  16. B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
    [CrossRef]
  17. H. E. Hernandez-Figueroa, F. A. Fernandez, J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett. 30, 2031–2032 (1994).
    [CrossRef]
  18. M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
    [CrossRef]
  19. C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
    [CrossRef]
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  22. C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1995).
    [CrossRef]
  23. K. Hayata, A. Misawa, M. Koshiba, “Split-step finite element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 9, 1772–1784 (1990).
    [CrossRef]
  24. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  25. M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.
  26. K. Smit, E. C. M. Pennings, H. Block, “Normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737–1742 (1993).
    [CrossRef]

2000 (1)

1998 (1)

1996 (2)

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

1995 (2)

C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
[CrossRef]

C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1995).
[CrossRef]

1994 (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

H. E. Hernandez-Figueroa, F. A. Fernandez, J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett. 30, 2031–2032 (1994).
[CrossRef]

1993 (4)

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

R. R. Hayes, D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523–527 (1993).
[CrossRef]

K. Smit, E. C. M. Pennings, H. Block, “Normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737–1742 (1993).
[CrossRef]

1992 (1)

C. Seo, J. C. Chen, “Low transition losses in bent rib waveguide,” J. Lightwave Technol. 14, 2255–2259 (1992).

1991 (1)

J. S. Gu, P. A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

1990 (4)

E. C. M. Pennings, R. J. Deri, “Simple method for estimating usable bend radii of deeply etched optical rib waveguides,” Electron. Lett. 27, 1532–1534 (1990).
[CrossRef]

J. Yamauchi, M. Ikegaya, H. Nakano, “Analysis of bent asymmetric slab waveguides by the beam propagation method,” Opt. Commun. 79, 291–294 (1990).
[CrossRef]

T. Krauss, P. J. R. Laybourn, J. Roberts, “CW operation of semiconductor ring lasers,” Electron. Lett. 26, 2095–2096 (1990).
[CrossRef]

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 9, 1772–1784 (1990).
[CrossRef]

1988 (1)

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

1984 (1)

B. M. A. Rahman, J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. LT-2, 682–688 (1984).
[CrossRef]

1983 (1)

M. W. Austin, P. G. Flavin, “Small-radii curved rib waveguides in GaAs/GaAlAs using electron-beam lithography,” J. Lightwave Technol. LT-1, 236–240 (1983).
[CrossRef]

1981 (1)

1980 (1)

1975 (1)

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–83 (1975).
[CrossRef]

1969 (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
[CrossRef]

Austin, M. W.

M. W. Austin, P. G. Flavin, “Small-radii curved rib waveguides in GaAs/GaAlAs using electron-beam lithography,” J. Lightwave Technol. LT-1, 236–240 (1983).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Besse, P. A.

J. S. Gu, P. A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

Block, H.

K. Smit, E. C. M. Pennings, H. Block, “Normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737–1742 (1993).
[CrossRef]

Chen, J. C.

C. Seo, J. C. Chen, “Low transition losses in bent rib waveguide,” J. Lightwave Technol. 14, 2255–2259 (1992).

Davies, J. B.

H. E. Hernandez-Figueroa, F. A. Fernandez, J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett. 30, 2031–2032 (1994).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. LT-2, 682–688 (1984).
[CrossRef]

Deri, R. J.

E. C. M. Pennings, R. J. Deri, “Simple method for estimating usable bend radii of deeply etched optical rib waveguides,” Electron. Lett. 27, 1532–1534 (1990).
[CrossRef]

Dragone, C.

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

El-Mikathi, H. A.

S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikathi, “New full-vectorial numerically efficient propagation algorithm based on the finite element method,” J. Lightwave Technol. 18, 409–415 (2000).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.

Feit, M. D.

Fernandez, F. A.

H. E. Hernandez-Figueroa, F. A. Fernandez, J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett. 30, 2031–2032 (1994).
[CrossRef]

Flavin, P. G.

M. W. Austin, P. G. Flavin, “Small-radii curved rib waveguides in GaAs/GaAlAs using electron-beam lithography,” J. Lightwave Technol. LT-1, 236–240 (1983).
[CrossRef]

Fleck, J. A.

Gaiffe, T.

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

Gopinath, A.

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

Grattan, K. T. V.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.

Gu, J. S.

J. S. Gu, P. A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

Hadjicharalabbous, A.

C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
[CrossRef]

Harris, J. H.

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–83 (1975).
[CrossRef]

Hayata, K.

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 9, 1772–1784 (1990).
[CrossRef]

Hayes, R. R.

R. R. Hayes, D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523–527 (1993).
[CrossRef]

Heiblum, M.

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–83 (1975).
[CrossRef]

Hernandez-Figueroa, H. E.

H. E. Hernandez-Figueroa, F. A. Fernandez, J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett. 30, 2031–2032 (1994).
[CrossRef]

Hirono, T.

Huang, W. P.

Ikegaya, M.

J. Yamauchi, M. Ikegaya, H. Nakano, “Analysis of bent asymmetric slab waveguides by the beam propagation method,” Opt. Commun. 79, 291–294 (1990).
[CrossRef]

Joyner, C. H.

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

Kim, S.

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

Koshiba, M.

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 9, 1772–1784 (1990).
[CrossRef]

Krauss, T.

T. Krauss, P. J. R. Laybourn, J. Roberts, “CW operation of semiconductor ring lasers,” Electron. Lett. 26, 2095–2096 (1990).
[CrossRef]

Lagasse, P. E.

Laybourn, P. J. R.

T. Krauss, P. J. R. Laybourn, J. Roberts, “CW operation of semiconductor ring lasers,” Electron. Lett. 26, 2095–2096 (1990).
[CrossRef]

Lee, C.

C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1995).
[CrossRef]

Lui, W. W.

Marcatili, E. A. J.

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
[CrossRef]

Melchior, H.

J. S. Gu, P. A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

Misawa, A.

K. Hayata, A. Misawa, M. Koshiba, “Split-step finite element method applied to nonlinear integrated optics,” J. Opt. Soc. Am. B 9, 1772–1784 (1990).
[CrossRef]

Nakano, H.

J. Yamauchi, M. Ikegaya, H. Nakano, “Analysis of bent asymmetric slab waveguides by the beam propagation method,” Opt. Commun. 79, 291–294 (1990).
[CrossRef]

Obayya, S. S. A.

S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikathi, “New full-vectorial numerically efficient propagation algorithm based on the finite element method,” J. Lightwave Technol. 18, 409–415 (2000).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.

Pennings, E. C. M.

K. Smit, E. C. M. Pennings, H. Block, “Normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737–1742 (1993).
[CrossRef]

E. C. M. Pennings, R. J. Deri, “Simple method for estimating usable bend radii of deeply etched optical rib waveguides,” Electron. Lett. 27, 1532–1534 (1990).
[CrossRef]

Rahman, B. M. A.

S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikathi, “New full-vectorial numerically efficient propagation algorithm based on the finite element method,” J. Lightwave Technol. 18, 409–415 (2000).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. LT-6, 52–57 (1988).
[CrossRef]

B. M. A. Rahman, J. B. Davies, “Finite-element solution of integrated optical waveguides,” J. Lightwave Technol. LT-2, 682–688 (1984).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.

Rajarajan, M.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.

Roberts, J.

T. Krauss, P. J. R. Laybourn, J. Roberts, “CW operation of semiconductor ring lasers,” Electron. Lett. 26, 2095–2096 (1990).
[CrossRef]

Roey, Van

Seo, C.

C. Seo, J. C. Chen, “Low transition losses in bent rib waveguide,” J. Lightwave Technol. 14, 2255–2259 (1992).

Smit, K.

K. Smit, E. C. M. Pennings, H. Block, “Normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737–1742 (1993).
[CrossRef]

Stulz, L. W.

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

Themistos, C.

C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
[CrossRef]

Van der Donk, J.

Voges, E.

C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1995).
[CrossRef]

Wongcharoen, T.

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

Yamamoto, T.

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

Yamauchi, J.

J. Yamauchi, M. Ikegaya, H. Nakano, “Analysis of bent asymmetric slab waveguides by the beam propagation method,” Opt. Commun. 79, 291–294 (1990).
[CrossRef]

Yap, D.

R. R. Hayes, D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523–527 (1993).
[CrossRef]

Yokoyama, K.

Zirngibl, M.

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
[CrossRef]

Electron. Lett. (4)

H. E. Hernandez-Figueroa, F. A. Fernandez, J. B. Davies, “Finite element approach for the modal analysis of open-boundary waveguides,” Electron. Lett. 30, 2031–2032 (1994).
[CrossRef]

M. Zirngibl, C. H. Joyner, L. W. Stulz, T. Gaiffe, C. Dragone, “Polarization independent 8 × 8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201–202 (1993).
[CrossRef]

T. Krauss, P. J. R. Laybourn, J. Roberts, “CW operation of semiconductor ring lasers,” Electron. Lett. 26, 2095–2096 (1990).
[CrossRef]

E. C. M. Pennings, R. J. Deri, “Simple method for estimating usable bend radii of deeply etched optical rib waveguides,” Electron. Lett. 27, 1532–1534 (1990).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. S. Gu, P. A. Besse, H. Melchior, “Method of lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEE J. Quantum Electron. 27, 531–537 (1991).
[CrossRef]

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–83 (1975).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Lightwave Technol. (13)

K. Smit, E. C. M. Pennings, H. Block, “Normalized approach to the design of low-loss optical waveguide bends,” J. Lightwave Technol. 11, 1737–1742 (1993).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, T. Wongcharoen, K. T. V. Grattan, “Accurate analysis of MMI devices with two-dimensional confinement,” J. Lightwave Technol. 14, 2078–2084 (1996).
[CrossRef]

C. Themistos, B. M. A. Rahman, A. Hadjicharalabbous, K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J. Lightwave Technol. 13, 1760–1765 (1995).
[CrossRef]

C. Lee, E. Voges, “Three-dimensional semi-vectorial wide-angle beam propagation method,” J. Lightwave Technol. 12, 215–225 (1995).
[CrossRef]

S. Kim, A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite difference method,” J. Lightwave Technol. 14, 2085–2092 (1996).
[CrossRef]

T. Yamamoto, M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

S. S. A. Obayya, B. M. A. Rahman, H. A. El-Mikathi, “New full-vectorial numerically efficient propagation algorithm based on the finite element method,” J. Lightwave Technol. 18, 409–415 (2000).
[CrossRef]

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[CrossRef]

Other (1)

M. Rajarajan, B. M. A. Rahman, K. T. V. Grattan, S. S. A. Obayya, H. A. El-Mikathi, “Characterization of ultrashort low-loss waveguidebends for compact photonic integrated circuits,” Digest of Topical Meeting on Integrated Photonic Research (Optical Society of America, Washington, D.C., 1999), pp. 46–48.

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Figures (11)

Fig. 1
Fig. 1

Schematic of (a) simulated rib structure and (b) slanted rib with trench.

Fig. 2
Fig. 2

Radiation loss as a function of bending radius for a rib structure with and without trench.

Fig. 3
Fig. 3

H y field profile for fundamental TE mode for (a) straight guide and (b) bent guide at R = 1.5 mm.

Fig. 4
Fig. 4

H y field profile of bent guide (a) at R = 200 µm and (b) at R = 100 µm with trench.

Fig. 5
Fig. 5

Variation of transmission and reflection coefficients with lateral offset for rib structures with and without trench.

Fig. 6
Fig. 6

Variation of transmission coefficients with lateral offset for structure with trench for two bending radii.

Fig. 7
Fig. 7

Graph showing radiation loss as function of bending radius for two different trench distances.

Fig. 8
Fig. 8

Graph showing transmission coefficients as function of lateral offset for two different trench distances.

Fig. 9
Fig. 9

Graph showing transmission and reflection coefficients as function of rib width of straight guide.

Fig. 10
Fig. 10

Graph showing transition loss as function of rib slope for slanted rib structure.

Fig. 11
Fig. 11

Graph showing radiation loss as function of bending radius for slanted and straight guides.

Equations (3)

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ω2=×H*ˆ-1·×HdΩ+α0 ·H*·H·dΩH*μˆ·H·dΩ,
Ax-ω2 Bx=0,
J=Ω|EtI-EtII|2+δ·Z02|HtI-HtII|2 dΩ,

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