Abstract

A fast and simple quasi-analytic method to simulate mode characteristics in highly overmoded rectangular dielectric waveguide bends is presented. Fast mode-based bend models are necessary, since overmoded rectangular waveguides have become very popular in optical interconnects on printed circuit boards. The proposed method combines a simple mode solver with the formalism that was proposed by Melloni et al. [J. Lightwave Technol. 16, 571 (2001) ], yielding to a very convenient and accurate quasi-analytic formalism for the bend transfer function based on matrix notation. For that purpose, a simple method to approximate leaky modes is introduced. The model offers the ability to predict individual modal phases and amplitudes within a given bend as well as the calculation of coupling losses and was validated using three-dimensional beam-propagation-method simulation software.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.
  2. J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
    [CrossRef]
  3. E. Griese, “Modeling of highly multimode waveguides for time-domain simulation,” IEEE J. Sel. Top. Quantum Electron. 9, 433–442 (2003).
    [CrossRef]
  4. K. M. Patel, S. Ralph, “Enhanced multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Technol. Lett. 14, 393–395 (2002).
    [CrossRef]
  5. E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.
  6. H. R. Stuart, “Dispersive multiplexing in multimode optical fiber,” Science 289, 281–283 (2000).
    [CrossRef] [PubMed]
  7. T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.
  8. D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
    [CrossRef]
  9. D. Lenz, D. Erni, W. Bächtold, “Modal power loss coefficient for highly overmoded rectangular dielectric waveguides based on free space modes,” Opt. Express 12, 1150–1156 (2004).
    [CrossRef] [PubMed]
  10. W.-K. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
    [CrossRef]
  11. E. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
    [CrossRef]
  12. R. T. Deck, M. Mirkov, B. G. Bagley, “Determination of bending losses in rectangular waveguides,” J. Lightwave Technol. 16, 1703–1714 (1998).
    [CrossRef]
  13. A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in 1999 IEEE/Lasers and Electro-Optics Society Annual Meeting (IEEE, 1999), pp. 641–642.
  14. A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
    [CrossRef]
  15. A. Melloni, P. Monguzzi, R. Costa, M. Martinelli, “Design of curved waveguides: the matched bend,” J. Opt. Soc. Am. A 20, 130–137 (2003).
    [CrossRef]
  16. E. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2103 (1969).
    [CrossRef]
  17. D. Marcuse, Theory of Dielectric Optical Waveguides, Quantum Electronics—Principles and Applications, 2nd ed. (Academic, 1997).
  18. J. V. Roey, J. van der Donk, P. E. Lagasse, “Beam-propagation method: analysis and assessment,” J. Opt. Soc. Am. 71, 803–810 (1981).
    [CrossRef]
  19. D. W. Boertjes, J. N. McMullin, “Novel wide-angle 3-D BPM implemented on a path-based grid,” Microwave Opt. Technol. Lett. 20, 287–290 (1999).
    [CrossRef]
  20. R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
    [CrossRef]
  21. F. Ladouceur, J. D. Love, Silica-Based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

2004 (1)

2003 (2)

A. Melloni, P. Monguzzi, R. Costa, M. Martinelli, “Design of curved waveguides: the matched bend,” J. Opt. Soc. Am. A 20, 130–137 (2003).
[CrossRef]

E. Griese, “Modeling of highly multimode waveguides for time-domain simulation,” IEEE J. Sel. Top. Quantum Electron. 9, 433–442 (2003).
[CrossRef]

2002 (1)

K. M. Patel, S. Ralph, “Enhanced multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Technol. Lett. 14, 393–395 (2002).
[CrossRef]

2001 (1)

2000 (2)

H. R. Stuart, “Dispersive multiplexing in multimode optical fiber,” Science 289, 281–283 (2000).
[CrossRef] [PubMed]

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

1999 (1)

D. W. Boertjes, J. N. McMullin, “Novel wide-angle 3-D BPM implemented on a path-based grid,” Microwave Opt. Technol. Lett. 20, 287–290 (1999).
[CrossRef]

1998 (1)

1997 (2)

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

W.-K. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

1981 (1)

1969 (2)

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

E. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2103 (1969).
[CrossRef]

Alon, E.

E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.

Bächtold, W.

D. Lenz, D. Erni, W. Bächtold, “Modal power loss coefficient for highly overmoded rectangular dielectric waveguides based on free space modes,” Opt. Express 12, 1150–1156 (2004).
[CrossRef] [PubMed]

D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
[CrossRef]

Bagley, B. G.

Berger, C.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Bergmans, J.

T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.

Beyeler, R.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Boertjes, D. W.

D. W. Boertjes, J. N. McMullin, “Novel wide-angle 3-D BPM implemented on a path-based grid,” Microwave Opt. Technol. Lett. 20, 287–290 (1999).
[CrossRef]

Bogenberger, R.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Bona, G.-L.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Boyd, S.

E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.

Bristow, J.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Carniel, F.

A. Melloni, F. Carniel, R. Costa, M. Martinelli, “Determination of bend mode characteristics in dielectric waveguides,” J. Lightwave Technol. 19, 571–577 (2001).
[CrossRef]

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in 1999 IEEE/Lasers and Electro-Optics Society Annual Meeting (IEEE, 1999), pp. 641–642.

Costa, R.

Dangel, R.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Deck, R. T.

Dellmann, L.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Eldada, L.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Erni, D.

D. Lenz, D. Erni, W. Bächtold, “Modal power loss coefficient for highly overmoded rectangular dielectric waveguides based on free space modes,” Opt. Express 12, 1150–1156 (2004).
[CrossRef] [PubMed]

D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
[CrossRef]

Griese, E.

E. Griese, “Modeling of highly multimode waveguides for time-domain simulation,” IEEE J. Sel. Top. Quantum Electron. 9, 433–442 (2003).
[CrossRef]

Guttmann, J.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Horowitz, M.

E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.

Horst, F.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Huber, H.-P.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Kahn, J.

E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.

Khoe, G.-D.

T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.

Koonen, T.

T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.

Krumpholz, O.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Kuhn, K.-P.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Ladouceur, F.

F. Ladouceur, J. D. Love, Silica-Based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

Lagasse, P. E.

Lenz, D.

D. Lenz, D. Erni, W. Bächtold, “Modal power loss coefficient for highly overmoded rectangular dielectric waveguides based on free space modes,” Opt. Express 12, 1150–1156 (2004).
[CrossRef] [PubMed]

D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
[CrossRef]

Liu, Y.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Liu, Y. S.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Love, J. D.

F. Ladouceur, J. D. Love, Silica-Based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

Marcatili, E.

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

E. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2103 (1969).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, Quantum Electronics—Principles and Applications, 2nd ed. (Academic, 1997).

Martinelli, M.

McMullin, J. N.

D. W. Boertjes, J. N. McMullin, “Novel wide-angle 3-D BPM implemented on a path-based grid,” Microwave Opt. Technol. Lett. 20, 287–290 (1999).
[CrossRef]

Melloni, A.

Mirkov, M.

Moisel, J.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Monguzzi, P.

Muehlner, D. J.

W.-K. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

Offrein, B. J.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

Osgood, J. R. M.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Patel, K. M.

K. M. Patel, S. Ralph, “Enhanced multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Technol. Lett. 14, 393–395 (2002).
[CrossRef]

Ralph, S.

K. M. Patel, S. Ralph, “Enhanced multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Technol. Lett. 14, 393–395 (2002).
[CrossRef]

Rankov, B.

D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
[CrossRef]

Rode, M.

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Roey, J. V.

Rowlette, J.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Scotti, R.

W.-K. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

Stack, J.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Stojanovic, V.

E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.

Stuart, H. R.

H. R. Stuart, “Dispersive multiplexing in multimode optical fiber,” Science 289, 281–283 (2000).
[CrossRef] [PubMed]

van den Boom, H.

T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.

van der Donk, J.

Wang, W.-K.

W.-K. Wang, R. Scotti, D. J. Muehlner, “Phase compensation of bent silica-glass optical channel waveguide devices by vector-wave mode-matching method,” J. Lightwave Technol. 15, 538–545 (1997).
[CrossRef]

Willems, F.

T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.

Wittneben, A.

D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
[CrossRef]

Yardley, J. T.

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Bell Syst. Tech. J. (2)

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

E. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2103 (1969).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Griese, “Modeling of highly multimode waveguides for time-domain simulation,” IEEE J. Sel. Top. Quantum Electron. 9, 433–442 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. M. Patel, S. Ralph, “Enhanced multimode fiber link performance using a spatially resolved receiver,” IEEE Photon. Technol. Lett. 14, 393–395 (2002).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Microwave Opt. Technol. Lett. (1)

D. W. Boertjes, J. N. McMullin, “Novel wide-angle 3-D BPM implemented on a path-based grid,” Microwave Opt. Technol. Lett. 20, 287–290 (1999).
[CrossRef]

Opt. Eng. (Bellingham) (1)

J. Moisel, J. Guttmann, H.-P. Huber, O. Krumpholz, M. Rode, R. Bogenberger, K.-P. Kuhn, “Optical backplanes with integrated polymer waveguides,” Opt. Eng. (Bellingham) 39, 673–679 (2000).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

R. Scarmozzino, J. R. M. Osgood, L. Eldada, J. T. Yardley, Y. Liu, J. Bristow, J. Stack, J. Rowlette, Y. S. Liu, “Design and fabrication of passive optical polymer waveguide components for multimode parallel optical links,” Proc. SPIE 3005, 257–265 (1997).
[CrossRef]

Science (1)

H. R. Stuart, “Dispersive multiplexing in multimode optical fiber,” Science 289, 281–283 (2000).
[CrossRef] [PubMed]

Other (7)

T. Koonen, H. van den Boom, F. Willems, J. Bergmans, G.-D. Khoe, “Mode group diversity multiplexing for multi-service in-house networks using multi-mode polymer optical fibre,” in Proceedings of Symposium of IEEE/Lasers and Electro-Optics Society Benelux Chapter (IEEE, 2002), pp. 183–186.

D. Lenz, B. Rankov, D. Erni, W. Bächtold, A. Wittneben, “MIMO channel for modal multiplexing in highly overmoded optical waveguides,” in 2004 International Zurich Seminar on Communications (IEEE, 2004), pp. 196–199.
[CrossRef]

A. Melloni, R. Costa, F. Carniel, M. Martinelli, “An effective method for the analysis of bent dielectric waveguides,” in 1999 IEEE/Lasers and Electro-Optics Society Annual Meeting (IEEE, 1999), pp. 641–642.

L. Dellmann, R. Dangel, R. Beyeler, C. Berger, F. Horst, B. J. Offrein, G.-L. Bona, “Polymer waveguides for high-speed optical interconnects,” in EOS Topical Meeting Optics in Computing (European Optical Society, 2004), pp. 131–132.

E. Alon, V. Stojanovic, J. Kahn, S. Boyd, M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proceedings of IEEE Global Telecommunications Conference (IEEE, 2004), pp. 1023–1029.

F. Ladouceur, J. D. Love, Silica-Based Buried Channel Waveguides and Devices (Chapman & Hall, 1996).

D. Marcuse, Theory of Dielectric Optical Waveguides, Quantum Electronics—Principles and Applications, 2nd ed. (Academic, 1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Bent waveguide and the coordinate system used.

Fig. 2
Fig. 2

Artificially enlarged waveguide used in order to retrieve the quasi-leaky modes.

Fig. 3
Fig. 3

Schematic view of the transversal wavenumbers of the guided and the quasi-leaky modes of the multimode rectangular waveguide.

Fig. 4
Fig. 4

Bend as a transfer function: coupling from the straight waveguide to the bend, propagation within the bend, and coupling back to the following straight waveguide.

Fig. 5
Fig. 5

Absolute values of the modal amplitudes of a WG50 waveguide bend of radius R = 20 mm with fundamental mode excitation. Comparison between the 3D-BPM and the proposed method: diamonds, BPM values; solid curve, proposed model.

Fig. 6
Fig. 6

Field intensity I inside the core of a WG50 waveguide bend having a radius R = 20 mm along different angles: (a) θ = 0 ° , (b) θ = 1 ° , (c) θ = 2 ° , (d) θ = 3 ° , (e) θ = 4 ° , and (f) θ = 5 ° . The bend is excited by the fundamental mode of the corresponding straight input waveguide.

Fig. 7
Fig. 7

Absolute values of the modal amplitudes in a WG20 waveguide bend having radius R = 10 mm with mode 5-5 excited: diamonds, BPM values; solid curve, proposed model. QLM, quasi-leaky mode.

Fig. 8
Fig. 8

Overall coupling losses for a 20 × 20 μ m waveguide having different radii and extended over different angles θ.

Fig. 9
Fig. 9

Comparison of the coupling losses provided by three different methods as a function of the bending radius in a monomode waveguide.

Tables (2)

Tables Icon

Table 1 Calculated rms Values for Different Waveguides, Radii, and Mode 0-0 Excitation up to 5°

Tables Icon

Table 2 Calculated rms Values for a WG20 Waveguides with Different Radii and Mode 5-5 Excitation up to 5°

Equations (33)

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

E B ( j ) ( x , y ) θ = 0 = n = 1 N a n ( j ) ψ n ( x , y ) ,
E B ( j ) ( x , y , θ ) = exp ( i β b ( j ) R θ ) n = 1 N a n ( j ) ψ n ( x , y )
( R I + C ) G a = ν a ,
c n , m = ψ n ψ m * ( y b 2 ) d x d y ,
ψ n , x ( 1 ) = u n ( 1 ) sin [ k x ( n ) ( x + ξ ( n ) ) ] cos [ k y ( n ) ( y + η ( n ) ) ] .
c n , m = i = 1 5 c n , m ( i ) = i = 1 5 A i ψ n ( i ) ψ m * ( i ) ( y b 2 ) d x d y ,
u B ( j ) = i = 1 n κ i , j u i ,
κ i , j = E B ( j ) ( x , y ) , ψ i , x ( x , y ) E B ( j ) ( x , y ) , E B ( j ) ( x , y ) 1 2 ψ i , x ( x , y ) , ψ i , x ( x , y ) 1 2
κ i , j = a i * ( j ) ,
u B = K T u ,
u B = [ u B ( 1 ) , u B ( 2 ) , , u B ( n ) ] T ,
u = [ u 1 , u 2 , , u n ] T ,
K = [ κ 1 , 1 κ 2 , 1 κ 1 , n κ 2 , 1 κ n , 1 κ n , n ] = A * ,
u B ( θ ) = H B u B ( 0 ) ,
r k = j = 1 n n j k u B ( j ) exp ( i β b ( j ) R θ ) .
r = N T u B ( θ ) .
n i , k = a k ( i ) ,
N = A T .
r = N T u B ( θ ) = N T H B u B ( 0 ) = N T H B K T u = A H B A u ,
ψ n , x ( 4 ) = u n ( 4 ) sin [ k x ( n ) ( x + ξ ( n ) ) ] cos [ k y ( n ) ( b + η ( n ) ) ] exp [ γ 4 ( n ) ( y b ) ] ,
ψ n , x ( 5 ) = u n ( 5 ) sin [ k x ( n ) ( x + ξ ( n ) ) ] cos ( k y ( n ) η ( n ) ) exp ( γ 5 ( n ) y )
ψ n , x ( 2 ) = u n ( 2 ) cos [ k x ( n ) ( ξ ( n ) d ) ] cos [ k y ( n ) ( y + η ( n ) ) ] exp [ γ 2 ( n ) ( x + d ) ] ,
ψ n , x ( 3 ) = u n ( 3 ) cos ( k x ( n ) ξ ( n ) ) cos [ k y ( n ) ( y + η ( n ) ) ] exp ( γ 3 ( n ) x ) ,
u n ( 1 ) = i A k x ( n ) β ( n ) ( n 1 2 k 2 k x ( n ) 2 ) ,
u n ( 4 ) = u n ( 1 ) ( n 1 n 4 ) 2 ( n 4 2 k 2 k x ( n ) 2 n 1 2 k 2 k x ( n ) 2 ) ,
u n ( 5 ) = u n ( 1 ) ( n 1 n 5 ) 2 ( n 5 2 k 2 k x ( n ) 2 n 1 2 k 2 k x ( n ) 2 ) ,
u n ( 2 ) = u n ( 1 ) k x ( n ) γ 2 ( n ) ( γ 2 ( n ) 2 + n 2 2 k 2 n 1 2 k 2 k x ( n ) 2 ) ,
u n ( 3 ) = u n ( 1 ) k x ( n ) γ 3 ( n ) ( γ 3 ( n ) 2 + n 3 2 k 2 n 1 2 k 2 k x ( n ) 2 ) ,
c n , m ( 1 ) = 0 b d 0 ψ n , x ( 1 ) ψ m , x * ( 1 ) ( y b 2 ) d x d y ,
c n , m ( 2 ) = 0 b d ψ n , x ( 2 ) ψ m , x * ( 2 ) ( y b 2 ) d x d y ,
c n , m ( 3 ) = 0 b 0 ψ n , x ( 3 ) ψ m , x * ( 3 ) ( y b 2 ) d x d y ,
c n , m ( 4 ) = b d 0 ψ n , x ( 4 ) ψ m , x * ( 4 ) ( y b 2 ) d x d y ,
c n , m ( 5 ) = 0 d 0 ψ n , x ( 5 ) ψ m , x * ( 5 ) ( y b 2 ) d x d y .

Metrics