Abstract

A rigorous, full-vectorial and computationally efficient finite-element-based modal solution, together with junction analysis and beam propagation approaches have been used to study bending loss, transition loss, mode coupling, and polarization coupling in bent optical waveguides. The waveguide offset and their widths have been optimized to reduce the transition loss and the mode beating.

© 2008 Optical Society of America

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  2. M. Zirngibl, C. H. Joyner, L. W. Stulz, Th. Gaiffe, and C. Dragone, “Polarization independent 8×8 waveguide grating multiplexers on InP,” Electron. Lett. 29, 201-202 (1993).
    [CrossRef]
  3. R. R. Hayes and D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523-528(1993).
    [CrossRef]
  4. X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
    [CrossRef]
  5. W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130-132 (1978).
    [CrossRef]
  6. E. C. M. Pennings, G. H. Manhoudt, and M. K. Smit, “Low-loss bends in planar optical ridge waveguides,” Electron. Lett. 24, 998-999 (1988).
    [CrossRef]
  7. V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
    [CrossRef]
  8. M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Characterization of low-loss waveguide bends with offset optimisation for compact photonic integrated circuits,” IEE Proc.-Optoelectron. 147, 382-388 (2000).
    [CrossRef]
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    [CrossRef]
  10. C. Yeung, T. Rozzi, and G. Cerri, “Crosspolarisation coupling in curved dielectric rib waveguides,” IEE Proc.-Optoelectron. 135, 281-284 (1988).
    [CrossRef]
  11. C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
    [CrossRef]
  12. W. W. Lui, T. Hirono, K. Yokoyama, and W. P. Huang, “Polarization rotation in semiconductor bending waveguides: a coupled-mode theory formulation,” J. Lightwave Technol. 16, 929-936 (1998).
    [CrossRef]
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    [CrossRef]
  14. S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikati, “Improved design of a polarization converter based on semiconductor optical waveguide bends,” Appl. Opt. 40, 5395-5401 (2001).
    [CrossRef]
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    [CrossRef]
  16. S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Analysis of polarisation rotation in cascaded optical waveguide bends,” IEE Proc.-Optoelectron. 149, 75-80 (2002).
    [CrossRef]
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    [CrossRef]
  18. B. M. A. Rahman and J. B. Davies, “Analysis of optical waveguide discontinuities,” J. Lightwave Technol. 6, 52-57 (1988).
    [CrossRef]
  19. S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikati, “New full-vectorial numerically efficient propagation algorithm based on the finite element method,” J. Lightwave Technol. 18, 409-415 (2000).
    [CrossRef]
  20. E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103-2132 (1969).
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    [CrossRef]
  22. M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75-83 (1975).
    [CrossRef]
  23. P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
    [CrossRef]
  24. J. Gu, P. Besse, and H. Melchior, “Novel method for analysis of curved optical rib-waveguides,” Electron. Lett. 25, 278-280(1989).
    [CrossRef]
  25. R. Pregla, “The method of lines for analysis of dielectric waveguide bends,” J. Lightwave Technol. 14, 634-639 (1996).
    [CrossRef]
  26. S. Kim and A. Gopinath, “Vector analysis of optical dielectric waveguide bends using finite-difference method,” J. Lightwave Technol. 14, 2085-2092 (1996).
    [CrossRef]
  27. A. Nesterov and U. Troppenz, “A plane-wave boundary method for analysis of bent optical waveguides,” J. Lightwave Technol. 21, 2434-2437 (2003).
    [CrossRef]
  28. F. Wassmann, “Modal field analysis of circularly bent single-mode fibers,” J. Lightwave Technol. 17, 957-968 (1999).
    [CrossRef]
  29. K. Thyagarajan, M. R. Shenoy, and A. K. Ghatak, “Accurate numerical method for the calculation of bending loss in optical waveguides using a matrix approach,” Opt. Lett. 12, 296-298 (1987).
    [CrossRef] [PubMed]
  30. W. Berglund and A. Gopinath, “WKB analysis of bend losses in optical waveguides,” J. Lightwave Technol. 18, 1161-1166(2000).
    [CrossRef]
  31. R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
    [CrossRef]
  32. R. Baets and P. E. Lagasse, “Loss calculation and design of arbitrarily curved integrated-optic waveguides,” J. Opt. Soc. Am. 73, 177-182 (1983).
    [CrossRef]
  33. T. Yamamoto and M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579-1583 (1993).
    [CrossRef]
  34. R. Jedidi and R. Pierre, “High-order finite-element method for the computation of bending loss in optical waveguides,” J. Lightwave Technol. 25, 2618-2630 (2007).
    [CrossRef]
  35. Y. Tsuji and M. Koshiba, “Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions,” Electromagnetics 24, 39-48 (2004).
    [CrossRef]
  36. L. Prkna, M. Hubalek, and J. Ctyroky, “Field modelling of circular microresonators by film mode matching,” IEEE J. Sel. Top. Quantum Electron. 11, 217-223 (2005).
    [CrossRef]
  37. K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14, 11128-11141 (2006).
    [CrossRef] [PubMed]
  38. N. H. Vu, I-K. Hwang, and Y-H. Lee, “Bending loss analyses of photonic crystal fibers based on the finite-difference time-domain method,” Opt. Lett. 33, 119-121 (2008).
    [CrossRef] [PubMed]
  39. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200(1994).
    [CrossRef]
  40. M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Design of compact optical bends with a trench by use of finite element and beam propagation methods,” Appl. Opt. 39, 4946-4953 (2000).
    [CrossRef]
  41. S. Tomlijenovic-Hanic, J. D. Love, and A. Ankiewicz, “Effect of additional layers on bend loss in buried channel waveguides,” IEE Proc.-Optoelectron. 150, 259-265 (2003).
    [CrossRef]

2008

2007

R. Jedidi and R. Pierre, “High-order finite-element method for the computation of bending loss in optical waveguides,” J. Lightwave Technol. 25, 2618-2630 (2007).
[CrossRef]

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

2006

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14, 11128-11141 (2006).
[CrossRef] [PubMed]

2005

L. Prkna, M. Hubalek, and J. Ctyroky, “Field modelling of circular microresonators by film mode matching,” IEEE J. Sel. Top. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

2004

Y. Tsuji and M. Koshiba, “Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions,” Electromagnetics 24, 39-48 (2004).
[CrossRef]

2003

S. Tomlijenovic-Hanic, J. D. Love, and A. Ankiewicz, “Effect of additional layers on bend loss in buried channel waveguides,” IEE Proc.-Optoelectron. 150, 259-265 (2003).
[CrossRef]

A. Nesterov and U. Troppenz, “A plane-wave boundary method for analysis of bent optical waveguides,” J. Lightwave Technol. 21, 2434-2437 (2003).
[CrossRef]

2002

N. Somasiri, B. M. A. Rahman, and S. S. A. Obayya, “Fabrication tolerance study of a compact passive polarization rotator,” J. Lightwave Technol. 20, 751-757 (2002).
[CrossRef]

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Analysis of polarisation rotation in cascaded optical waveguide bends,” IEE Proc.-Optoelectron. 149, 75-80 (2002).
[CrossRef]

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

2001

2000

1999

1998

1997

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

1996

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

R. Pregla, “The method of lines for analysis of dielectric waveguide bends,” J. Lightwave Technol. 14, 634-639 (1996).
[CrossRef]

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

1994

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

1993

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

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

R. R. Hayes and D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523-528(1993).
[CrossRef]

1989

J. Gu, P. Besse, and H. Melchior, “Novel method for analysis of curved optical rib-waveguides,” Electron. Lett. 25, 278-280(1989).
[CrossRef]

1988

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

E. C. M. Pennings, G. H. Manhoudt, and M. K. Smit, “Low-loss bends in planar optical ridge waveguides,” Electron. Lett. 24, 998-999 (1988).
[CrossRef]

C. Yeung, T. Rozzi, and G. Cerri, “Crosspolarisation coupling in curved dielectric rib waveguides,” IEE Proc.-Optoelectron. 135, 281-284 (1988).
[CrossRef]

1987

1984

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

1983

1978

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130-132 (1978).
[CrossRef]

1976

1975

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

1969

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

Ankiewicz, A.

S. Tomlijenovic-Hanic, J. D. Love, and A. Ankiewicz, “Effect of additional layers on bend loss in buried channel waveguides,” IEE Proc.-Optoelectron. 150, 259-265 (2003).
[CrossRef]

Baets, R

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

Baets, R.

Berenger, J. P.

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

Berglund, W.

Besse, P.

J. Gu, P. Besse, and H. Melchior, “Novel method for analysis of curved optical rib-waveguides,” Electron. Lett. 25, 278-280(1989).
[CrossRef]

Bienstman, P.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

Boyd, J. T.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

Cerri, G.

C. Yeung, T. Rozzi, and G. Cerri, “Crosspolarisation coupling in curved dielectric rib waveguides,” IEE Proc.-Optoelectron. 135, 281-284 (1988).
[CrossRef]

Chu, S. T.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Cole, J. H.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

Ctyroky, J.

L. Prkna, M. Hubalek, and J. Ctyroky, “Field modelling of circular microresonators by film mode matching,” IEEE J. Sel. Top. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

Davies, J. B.

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

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

De Brabander, G. N.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

Dragone, C.

M. Zirngibl, C. H. Joyner, L. W. Stulz, Th. Gaiffe, and 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, K. T. V. Grattan, and H. A. El-Mikathi, “Analysis of polarisation rotation in cascaded optical waveguide bends,” IEE Proc.-Optoelectron. 149, 75-80 (2002).
[CrossRef]

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Characterization of low-loss waveguide bends with offset optimisation for compact photonic integrated circuits,” IEE Proc.-Optoelectron. 147, 382-388 (2000).
[CrossRef]

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Design of compact optical bends with a trench by use of finite element and beam propagation methods,” Appl. Opt. 39, 4946-4953 (2000).
[CrossRef]

El-Mikati, H. A.

Feng, W.

Feuerstein, R. J.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Gaiffe, Th.

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

Gambling, W. A.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130-132 (1978).
[CrossRef]

Ghatak, A. K.

Gopinath, A.

W. Berglund and A. Gopinath, “WKB analysis of bend losses in optical waveguides,” J. Lightwave Technol. 18, 1161-1166(2000).
[CrossRef]

S. Kim and 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.

Groen, F. H.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Gu, J.

J. Gu, P. Besse, and H. Melchior, “Novel method for analysis of curved optical rib-waveguides,” Electron. Lett. 25, 278-280(1989).
[CrossRef]

Hamacher, M.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Hao, Y.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Harris, J. H.

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

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Hayes, R. R.

R. R. Hayes and D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523-528(1993).
[CrossRef]

Heiblum, M.

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

Heidrich, H.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Hirono, T.

Huang, W. P.

Hubalek, M.

L. Prkna, M. Hubalek, and J. Ctyroky, “Field modelling of circular microresonators by film mode matching,” IEEE J. Sel. Top. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

Hwang, I-K.

Jedidi, R.

Jiang, X.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Joyner, C. H.

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

Kakihara, K.

Kim, S.

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

Kono, N.

Koshiba, M.

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14, 11128-11141 (2006).
[CrossRef] [PubMed]

Y. Tsuji and M. Koshiba, “Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions,” Electromagnetics 24, 39-48 (2004).
[CrossRef]

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

Lagasse, P. E.

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Lee, Y-H.

Lin, S.

Little, B. E.

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Love, J. D.

S. Tomlijenovic-Hanic, J. D. Love, and A. Ankiewicz, “Effect of additional layers on bend loss in buried channel waveguides,” IEE Proc.-Optoelectron. 150, 259-265 (2003).
[CrossRef]

Lui, W. W.

Manhoudt, G. H.

E. C. M. Pennings, G. H. Manhoudt, and M. K. Smit, “Low-loss bends in planar optical ridge waveguides,” Electron. Lett. 24, 998-999 (1988).
[CrossRef]

Marcatili, E. A. J.

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

Marcuse, D.

Matsumura, H.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130-132 (1978).
[CrossRef]

Melchior, H.

J. Gu, P. Besse, and H. Melchior, “Novel method for analysis of curved optical rib-waveguides,” Electron. Lett. 25, 278-280(1989).
[CrossRef]

Moerman, I.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Naghski, D. H.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

Nesterov, A.

Obayya, S. S. A.

Pascher, W. W.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Pennings, E. C. M.

E. C. M. Pennings, G. H. Manhoudt, and M. K. Smit, “Low-loss bends in planar optical ridge waveguides,” Electron. Lett. 24, 998-999 (1988).
[CrossRef]

Pierre, R.

Powelson, J. C.

Pregla, R.

R. Pregla, “The method of lines for analysis of dielectric waveguide bends,” J. Lightwave Technol. 14, 634-639 (1996).
[CrossRef]

Prkna, L.

L. Prkna, M. Hubalek, and J. Ctyroky, “Field modelling of circular microresonators by film mode matching,” IEEE J. Sel. Top. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

Qi, W.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Ragdale, C. M.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130-132 (1978).
[CrossRef]

Rahman, B. M. A.

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Analysis of polarisation rotation in cascaded optical waveguide bends,” IEE Proc.-Optoelectron. 149, 75-80 (2002).
[CrossRef]

N. Somasiri, B. M. A. Rahman, and S. S. A. Obayya, “Fabrication tolerance study of a compact passive polarization rotator,” J. Lightwave Technol. 20, 751-757 (2002).
[CrossRef]

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikati, “Improved design of a polarization converter based on semiconductor optical waveguide bends,” Appl. Opt. 40, 5395-5401 (2001).
[CrossRef]

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Design of compact optical bends with a trench by use of finite element and beam propagation methods,” Appl. Opt. 39, 4946-4953 (2000).
[CrossRef]

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

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Characterization of low-loss waveguide bends with offset optimisation for compact photonic integrated circuits,” IEE Proc.-Optoelectron. 147, 382-388 (2000).
[CrossRef]

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

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

Rajarajan, M.

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Characterization of low-loss waveguide bends with offset optimisation for compact photonic integrated circuits,” IEE Proc.-Optoelectron. 147, 382-388 (2000).
[CrossRef]

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Design of compact optical bends with a trench by use of finite element and beam propagation methods,” Appl. Opt. 39, 4946-4953 (2000).
[CrossRef]

Roelens, M.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

Rozzi, T.

C. Yeung, T. Rozzi, and G. Cerri, “Crosspolarisation coupling in curved dielectric rib waveguides,” IEE Proc.-Optoelectron. 135, 281-284 (1988).
[CrossRef]

Saitoh, K.

Schermer, R. T.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

Shenoy, M. R.

Six, E.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

Smit, M. K.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

E. C. M. Pennings, G. H. Manhoudt, and M. K. Smit, “Low-loss bends in planar optical ridge waveguides,” Electron. Lett. 24, 998-999 (1988).
[CrossRef]

Somasiri, N.

Spiekman, L. H.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Stulz, L. W.

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

Subramaniam, V.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

Tang, Y.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Thyagarajan, K.

Tomic, D.

Tomlijenovic-Hanic, S.

S. Tomlijenovic-Hanic, J. D. Love, and A. Ankiewicz, “Effect of additional layers on bend loss in buried channel waveguides,” IEE Proc.-Optoelectron. 150, 259-265 (2003).
[CrossRef]

Troppenz, U.

Tsuji, Y.

Y. Tsuji and M. Koshiba, “Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions,” Electromagnetics 24, 39-48 (2004).
[CrossRef]

van Dam, C.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

van der Tol, J. J. G. M.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

van Ham, F. P. G. M.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Vanwolleghem, M.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

Vu, N. H.

Wang, M.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Wassmann, F.

Weinert, C. M.

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

Yamamoto, T.

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

Yang, J.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Yap, D.

R. R. Hayes and D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523-528(1993).
[CrossRef]

Yeung, C.

C. Yeung, T. Rozzi, and G. Cerri, “Crosspolarisation coupling in curved dielectric rib waveguides,” IEE Proc.-Optoelectron. 135, 281-284 (1988).
[CrossRef]

Yokoyama, K.

Zhang, H.

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
[CrossRef]

Zirngibl, M.

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

Appl. Opt.

Bell Syst. Tech. J.

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

Electromagnetics

Y. Tsuji and M. Koshiba, “Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions,” Electromagnetics 24, 39-48 (2004).
[CrossRef]

Electron. Lett.

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

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14, 130-132 (1978).
[CrossRef]

E. C. M. Pennings, G. H. Manhoudt, and M. K. Smit, “Low-loss bends in planar optical ridge waveguides,” Electron. Lett. 24, 998-999 (1988).
[CrossRef]

J. Gu, P. Besse, and H. Melchior, “Novel method for analysis of curved optical rib-waveguides,” Electron. Lett. 25, 278-280(1989).
[CrossRef]

IEE Proc.-Optoelectron.

S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Analysis of polarisation rotation in cascaded optical waveguide bends,” IEE Proc.-Optoelectron. 149, 75-80 (2002).
[CrossRef]

M. Rajarajan, S. S. A. Obayya, B. M. A. Rahman, K. T. V. Grattan, and H. A. El-Mikathi, “Characterization of low-loss waveguide bends with offset optimisation for compact photonic integrated circuits,” IEE Proc.-Optoelectron. 147, 382-388 (2000).
[CrossRef]

C. Yeung, T. Rozzi, and G. Cerri, “Crosspolarisation coupling in curved dielectric rib waveguides,” IEE Proc.-Optoelectron. 135, 281-284 (1988).
[CrossRef]

S. Tomlijenovic-Hanic, J. D. Love, and A. Ankiewicz, “Effect of additional layers on bend loss in buried channel waveguides,” IEE Proc.-Optoelectron. 150, 259-265 (2003).
[CrossRef]

IEEE J. Quantum Electron.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron.

L. Prkna, M. Hubalek, and J. Ctyroky, “Field modelling of circular microresonators by film mode matching,” IEEE J. Sel. Top. Quantum Electron. 11, 217-223 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164-166 (2002).
[CrossRef]

C. van Dam, L. H. Spiekman, F. P. G. M. van Ham, F. H. Groen, J. J. G. M. van der Tol, I. Moerman, W. W. Pascher, M. Hamacher, H. Heidrich, C. M. Weinert, and M. K. Smit, “Novel compact polarization converters based on ultra short bends,” IEEE Photon. Technol. Lett. 8, 1346-1348 (1996).
[CrossRef]

B. E. Little and S. T. Chu, “Theory of polarization rotation and conversion in vertically coupled microresonators,” IEEE Photon. Technol. Lett. 12, 401-403 (2000).
[CrossRef]

X. Jiang, W. Qi, H. Zhang, Y. Tang, Y. Hao, J. Yang, and M. Wang, “Loss crosstalk 1×2 thermooptic digital optical switch with integrated S-bend attenuator,” IEEE Photon. Technol. Lett. 18, 610-612 (2006).
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J. Comput. Phys.

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

J. Lightwave Technol.

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

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

W. Berglund and A. Gopinath, “WKB analysis of bend losses in optical waveguides,” J. Lightwave Technol. 18, 1161-1166(2000).
[CrossRef]

F. Wassmann, “Modal field analysis of circularly bent single-mode fibers,” J. Lightwave Technol. 17, 957-968 (1999).
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W. W. Lui, T. Hirono, K. Yokoyama, and W. P. Huang, “Polarization rotation in semiconductor bending waveguides: a coupled-mode theory formulation,” J. Lightwave Technol. 16, 929-936 (1998).
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J. C. Powelson, W. Feng, S. Lin, R. J. Feuerstein, and D. Tomic, “Crosstalk of passive directional couplers,” J. Lightwave Technol. 16, 2020-2027 (1998).
[CrossRef]

N. Somasiri, B. M. A. Rahman, and S. S. A. Obayya, “Fabrication tolerance study of a compact passive polarization rotator,” J. Lightwave Technol. 20, 751-757 (2002).
[CrossRef]

A. Nesterov and U. Troppenz, “A plane-wave boundary method for analysis of bent optical waveguides,” J. Lightwave Technol. 21, 2434-2437 (2003).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

R. R. Hayes and D. Yap, “GaAs spiral optical waveguides for delay-line applications,” J. Lightwave Technol. 11, 523-528(1993).
[CrossRef]

R. Pregla, “The method of lines for analysis of dielectric waveguide bends,” J. Lightwave Technol. 14, 634-639 (1996).
[CrossRef]

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

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

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

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

R. Jedidi and R. Pierre, “High-order finite-element method for the computation of bending loss in optical waveguides,” J. Lightwave Technol. 25, 2618-2630 (2007).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

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Figures (13)

Fig. 1
Fig. 1

Schematic cross-section of the bent optical waveguide.

Fig. 2
Fig. 2

(a) Dominant H y field profile of the fundamental quasi-TE mode of a straight waveguide. (b) Nondominant H x field profile of the fundamental quasi-TE mode of a straight waveguide.

Fig. 3
Fig. 3

(a) Dominant H y field profile of the fundamental quasi-TE mode of a bent waveguide. (b) Nondominant H x field profile of the fundamental quasi-TE mode of a bent waveguide.

Fig. 4
Fig. 4

Variation of the power loss along the axial distance for a straight-to-bent waveguide.

Fig. 5
Fig. 5

Variation of the spot size along the axial distance for a straight-to-bent waveguide.

Fig. 6
Fig. 6

Difference between two H y field profiles at two locations with a phase reversal.

Fig. 7
Fig. 7

Evolutions of the y and x-polarized powers along the axial distance.

Fig. 8
Fig. 8

Variations of power losses along the axial distance for bent-to-bent and straight-to-bent waveguides.

Fig. 9
Fig. 9

Variation of the power losses with the bending radius for straight-to-bent and bent-to-bent waveguides.

Fig. 10
Fig. 10

Variation of the polarization conversions with the bending radius.

Fig. 11
Fig. 11

Variation of the power loss for a straight-to-bent coupled waveguide with the waveguide offset, Δ x .

Fig. 12
Fig. 12

Variation of the power loss for a straight-to-bent waveguide with Δ w when the waveguide widths are unequal.

Fig. 13
Fig. 13

Variation of the spot size along the axial direction when an optimized value of Δ w is used.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ω 2 = [ ( × H ) * · ε 1 ( × H ) + p ( · H ) * ( · H ) ] Ω H * · μH Ω ,
n ( x , y ) = n m ( x , y ) ( 1 x / R ) ,
J = Ω | E t I E t I I | 2 + α · Z 0 2 | H t I H t I I | 2 Ω ,
× ( n 2 × H ) k 2 H = 0 ,

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