Abstract

A numerical model for erbium-doped waveguide amplifiers (EDWAs) containing bent waveguides was developed. The model uses rate-propagation equations and takes into account bend-induced losses in the waveguide with a varying radius of curvature. It is applied to the design of tightly packed erbium-doped waveguide amplifiers under two constraints: minimization of the area required to obtain a predetermined gain and maximization of the gain available from a given area. Numerical calculations based on realistic waveguide parameters demonstrate the possibility of fabricating high-gain, small-size EDWAs. Simple design rules, based on geometric formulas and consideration of bend losses, are given and compared with the results of numerical calculations.

© 2005 Optical Society of America

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  1. J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.
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    [CrossRef]
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    [CrossRef]
  4. S. F. Wong, E. Y. B. Pun, P. S. Chung, “Er3+-Yb3+ codoped phosphate glass waveguide amplifier using Ag+-Li+ ion exchange,” IEEE Photonics Technol. Lett. 14, 80–82 (2002).
    [CrossRef]
  5. D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.
  6. G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
    [CrossRef]
  7. J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
    [CrossRef]
  8. T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.
  9. K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.
  10. K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
    [CrossRef]
  11. T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
    [CrossRef]
  12. G. N. van den Hoven, R. J. I. Koper, A. Polman, “Net optical gain at 1.53 µm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68, 1886–1888 (1996).
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    [CrossRef]
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    [CrossRef]
  16. O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
    [CrossRef]
  17. K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
    [CrossRef]
  18. M. V. D. Vermelho, U. Peschel, S. Aitchison, “Simple and accurate procedure for modeling erbium-doped waveguide amplifiers with high concentration,” J. Lightwave Technol. 18, 401–408 (2000).
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  19. P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
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  23. J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
    [CrossRef]
  24. K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
    [CrossRef]
  25. E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell. Syst. Tech. J. 48, 2103–2132 (1969).
    [CrossRef]

2002 (2)

S. F. Wong, E. Y. B. Pun, P. S. Chung, “Er3+-Yb3+ codoped phosphate glass waveguide amplifier using Ag+-Li+ ion exchange,” IEEE Photonics Technol. Lett. 14, 80–82 (2002).
[CrossRef]

D. Lowe, R. Syms, W. Huang, “Layout optimization for erbium-doped waveguide amplifiers,” J. Lightwave Technol. 20, 454–462 (2002).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

1996 (2)

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

G. N. van den Hoven, R. J. I. Koper, A. Polman, “Net optical gain at 1.53 µm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68, 1886–1888 (1996).
[CrossRef]

1995 (3)

F. Di Pasquale, M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[CrossRef]

P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
[CrossRef]

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

1994 (1)

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

1993 (3)

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

O. Lumholt, A. Bjarklev, T. Rasmussen, “Modeling of extremely high concentration erbium-doped silica waveguides,” Electron. Lett. 29, 495–496 (1993).
[CrossRef]

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

1992 (1)

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

1991 (1)

1969 (1)

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

Aitchison, J. S.

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

Aitchison, S.

Barbier, D.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

Becker, P. C.

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

Bjarklev, A.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

O. Lumholt, A. Bjarklev, T. Rasmussen, “Modeling of extremely high concentration erbium-doped silica waveguides,” Electron. Lett. 29, 495–496 (1993).
[CrossRef]

A. Bjarklev, Optical Fiber Amplifiers: Design and System Application (Artech House, Boston, Mass., 1993), pp. 97–98.

Bogert, G. A.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Bonar, J. R.

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

Brener, I.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Bruce, A. J.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Bruno, P.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

Cassagnettes, C.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

Chiang, K. S.

Chung, P. S.

S. F. Wong, E. Y. B. Pun, P. S. Chung, “Er3+-Yb3+ codoped phosphate glass waveguide amplifier using Ag+-Li+ ion exchange,” IEEE Photonics Technol. Lett. 14, 80–82 (2002).
[CrossRef]

Clauss, G.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Delavaux, J.-M. P.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

Di Pasquale, F.

F. Di Pasquale, M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[CrossRef]

Federighi, M.

F. Di Pasquale, M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[CrossRef]

Granlund, S.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Haner, M.

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

Hansen, P. B.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Hattori, K.

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.

Hisaaki, H.

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

Horiguchi, M.

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.

Huang, W.

Hyde, R. L.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

Jacobson, D. C.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Kevorkian, A.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Kitagawa, T.

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

Kobayashi, M.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

Koper, R. J. I.

G. N. van den Hoven, R. J. I. Koper, A. Polman, “Net optical gain at 1.53 µm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68, 1886–1888 (1996).
[CrossRef]

Laskowski, E. J.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Lenz, G.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Lester, C.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

Lowe, D.

Lumholt, O.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

O. Lumholt, A. Bjarklev, T. Rasmussen, “Modeling of extremely high concentration erbium-doped silica waveguides,” Electron. Lett. 29, 495–496 (1993).
[CrossRef]

Marcatili, E. A. J.

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

Marques, P. V. S.

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

McLaughlin, A. J.

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

Mizuhara, O.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Muehlner, D. J.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Murphy, E.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Nagel, J. A.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Nielsen, T. N.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Nykolak, G.

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

Oguma, M.

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.

Ohmori, Y.

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.

Pal, B. P.

P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
[CrossRef]

Palai, P.

P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
[CrossRef]

Park, Y. K.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Paunescu, A.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Peschel, U.

Polman, A.

G. N. van den Hoven, R. J. I. Koper, A. Polman, “Net optical gain at 1.53 µm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68, 1886–1888 (1996).
[CrossRef]

Pun, E. Y. B.

S. F. Wong, E. Y. B. Pun, P. S. Chung, “Er3+-Yb3+ codoped phosphate glass waveguide amplifier using Ag+-Li+ ion exchange,” IEEE Photonics Technol. Lett. 14, 80–82 (2002).
[CrossRef]

Rasmussen, T.

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

O. Lumholt, A. Bjarklev, T. Rasmussen, “Modeling of extremely high concentration erbium-doped silica waveguides,” Electron. Lett. 29, 495–496 (1993).
[CrossRef]

Rattay, M.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

Roy, A. K.

P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
[CrossRef]

Ryazansky, I.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Shampine, L. F.

L. F. Shampine, Numerical Solutions of Ordinary Differential Equations (Chapman & Hall, New York, 1994), pp. 19–22.

Shmulovich, J.

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

J. Shmulovich, “Er-doped glass waveguide amplifiers on silicon,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 143–153 (1997).
[CrossRef]

Shuto, K.

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

Suzuki, S.

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

Syms, R.

Syms, R. R. A.

Temmyo, J.

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

Thyagarajan, K.

P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
[CrossRef]

Trouillon, M.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

van den Hoven, G. N.

G. N. van den Hoven, R. J. I. Koper, A. Polman, “Net optical gain at 1.53 µm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68, 1886–1888 (1996).
[CrossRef]

Vermelho, M. V. D.

M. V. D. Vermelho, U. Peschel, S. Aitchison, “Simple and accurate procedure for modeling erbium-doped waveguide amplifiers with high concentration,” J. Lightwave Technol. 18, 401–408 (2000).
[CrossRef]

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

White, A. E.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

Wong, S. F.

S. F. Wong, E. Y. B. Pun, P. S. Chung, “Er3+-Yb3+ codoped phosphate glass waveguide amplifier using Ag+-Li+ ion exchange,” IEEE Photonics Technol. Lett. 14, 80–82 (2002).
[CrossRef]

Wong, Y. H.

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

Yasu, M.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

G. N. van den Hoven, R. J. I. Koper, A. Polman, “Net optical gain at 1.53 µm in Er-doped Al2O3 waveguides on silicon,” Appl. Phys. Lett. 68, 1886–1888 (1996).
[CrossRef]

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)

O. Lumholt, A. Bjarklev, T. Rasmussen, “Modeling of extremely high concentration erbium-doped silica waveguides,” Electron. Lett. 29, 495–496 (1993).
[CrossRef]

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1550 nm WDM coupler,” Electron. Lett. 30, 856–857 (1994).
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, M. Horiguchi, “Amplification in erbium-doped silica-based planar lightwave circuits,” Electron. Lett. 28, 1818–1819 (1992).
[CrossRef]

K. Shuto, K. Hattori, T. Kitagawa, Y. Ohmori, M. Horiguchi, “Erbium-doped phosphosilicate glass waveguide amplifier fabricated by PECVD,” Electron. Lett. 29, 139–141 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

S. F. Wong, E. Y. B. Pun, P. S. Chung, “Er3+-Yb3+ codoped phosphate glass waveguide amplifier using Ag+-Li+ ion exchange,” IEEE Photonics Technol. Lett. 14, 80–82 (2002).
[CrossRef]

G. Nykolak, M. Haner, P. C. Becker, J. Shmulovich, Y. H. Wong, “Systems evaluation of an Er3+-doped planar waveguide amplifier,” IEEE Photonics Technol. Lett. 5, 1185–1187 (1993).
[CrossRef]

J. Appl. Phys. (1)

K. Hattori, T. Kitagawa, M. Oguma, H. Hisaaki, Y. Ohmori, “Optical amplification in Er3+-doped P2O5-SiO2 planar waveguides,” J. Appl. Phys. 80, 5301–5308 (1996).
[CrossRef]

J. Lightwave Technol. (5)

O. Lumholt, A. Bjarklev, T. Rasmussen, C. Lester, “Rare-earth doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275–282 (1995).
[CrossRef]

F. Di Pasquale, M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858–1864 (1995).
[CrossRef]

M. V. D. Vermelho, U. Peschel, S. Aitchison, “Simple and accurate procedure for modeling erbium-doped waveguide amplifiers with high concentration,” J. Lightwave Technol. 18, 401–408 (2000).
[CrossRef]

W. Huang, R. R. A. Syms, “Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines,” J. Lightwave Technol. 17, 2658–2664 (1999).
[CrossRef]

D. Lowe, R. Syms, W. Huang, “Layout optimization for erbium-doped waveguide amplifiers,” J. Lightwave Technol. 20, 454–462 (2002).
[CrossRef]

Opt. Commun. (1)

J. R. Bonar, M. V. D. Vermelho, P. V. S. Marques, A. J. McLaughlin, J. S. Aitchison, “Fluorescence lifetime measurements of aerosol doped erbium in phosphosilicate planar waveguides,” Opt. Commun. 149, 27–32 (1998).
[CrossRef]

Opt. Fiber Technol. (1)

P. Palai, K. Thyagarajan, A. K. Roy, B. P. Pal, “Role of bends on the optimization of 980-nm-pumped erbium-doped fiber amplifier,” Opt. Fiber Technol. 1, 341–345 (1995).
[CrossRef]

Opt. Lett. (1)

Other (8)

A. Bjarklev, Optical Fiber Amplifiers: Design and System Application (Artech House, Boston, Mass., 1993), pp. 97–98.

L. F. Shampine, Numerical Solutions of Ordinary Differential Equations (Chapman & Hall, New York, 1994), pp. 19–22.

J. Shmulovich, A. J. Bruce, G. Lenz, P. B. Hansen, T. N. Nielsen, D. J. Muehlner, G. A. Bogert, I. Brener, E. J. Laskowski, A. Paunescu, I. Ryazansky, D. C. Jacobson, A. E. White, “Integrated planar waveguide amplifier with 15 dB net gain at 1550 nm,” in Optical Fiber Communication Conference 1999, and the International Conference on Integrated Optics and Optical Fiber Communication, OSA Technical Digest (Optical Society of America, Washington, D.C., 1999), paper PD42/1-3.
[CrossRef]

T. Kitagawa, K. Hattori, K. Shuto, M. Oguma, J. Temmyo, S. Suzuki, M. Horiguchi, “Erbium-doped silica-based planar amplifier module pumped by laser diodes,” in Proceedings of the European Conference on Optical Communication, ECOC'93 (Institute of Electrical and Electronics Engineers, New York, 1993), Vol. 3, pp. 41–44.

K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, M. Horiguchi, “Erbium-doped silica-based planar-waveguide amplifier integrated with a 980/1550 nm WDM coupler,” in Conference on Optical Fiber Communication, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 280–281.

D. Barbier, P. Bruno, C. Cassagnettes, M. Trouillon, R. L. Hyde, A. Kevorkian, J.-M. P. Delavaux, “Net gain of 27 dB with a 8.6 cm-long Er/Yb-doped glass-planar-amplifier,” in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 45–46.

J.-M. P. Delavaux, Y. K. Park, E. Murphy, S. Granlund, O. Mizuhara, D. Barbier, M. Rattay, G. Clauss, A. Kevorkian, J. A. Nagel, “High performance Er/Yb planar waveguide amplifiers as in-line and pre-amplifiers in 10 Gb/s fiber system experiments,” in Proceedings of the 22nd European Conference on Optical Communication, ECOC'96 (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 5, pp. 23–26.

J. Shmulovich, “Er-doped glass waveguide amplifiers on silicon,” in Rare-Earth-Doped Devices, S. Honkanen, ed., Proc. SPIE2996, 143–153 (1997).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Spiral waveguide configuration with a different number of coils n. (a) n = 1, (b) n = 2.

Fig. 2
Fig. 2

Three-level pump scheme of the Er3+ ion. The arrows represent transitions between energy bands: R, pump absorption; Wa, signal absorption; We, signal stimulated emission; A = 1/τ, spontaneous emission. τ is the lifetime of the metastable state 4I13/2. The dashed arrow represents fast nonradiative transition.

Fig. 3
Fig. 3

Illustration of the method of solving propagation equations for a curved waveguide with a varied radius of curvature. The waveguide is divided into segments with a constant radius of curvature. Pjout is the solution of the propagation equations at the jth segment. Tj is the transmission coefficient at the junction of the jth and (j + 1)th segments. Pj+1in is the initial value for the (j + 1)th segment.

Fig. 4
Fig. 4

Comparison of calculated (solid curve) and experimental (circles) results for a 7.5-cm-long straight erbium-doped phosphosilicate glass waveguide amplifier.17 The waveguide core area is 8 µm X 11 µm, the refractive-index difference is 1.6%, the erbium concentration is 3.7 × 1025 m−3, and the background loss is 0.17 dB/cm.

Fig. 5
Fig. 5

Chip area as a function of the number of coils for 20- and 10-cm-long spiral EDWAs and δR = 0, 100, and 200 µm.

Fig. 6
Fig. 6

Curvature radius R, internal Rmin, and external Rn radius of curvature for a 20-cm-long spiral EDWA and δR = 0, 50, and 200 µm.

Fig. 7
Fig. 7

Gain as a function of propagation distance for the 20-cm-long spiral EDWA δR = 50 and 200 µm.

Fig. 8
Fig. 8

Overall gain (triangles) and gain per unit area (circles) as functions of the number of coils for a 20-cm-long spiral EDWA and δR = 200 µm. The vertical dotted line indicates the number of coils corresponding to Smin′.

Fig. 9
Fig. 9

Overall gain as a function of the chip area for 10- and 20-cm-long spiral EDWAs and δR = 0, 100, and 200 µm.

Fig. 10
Fig. 10

Waveguide length (squares) and internal radius of curvature Rmin (circles) as functions of the number of coils for the chip area 60 mm2 and δR = 200 µm.

Fig. 11
Fig. 11

Overall gain as a function of waveguide length for a straight EDWA and a spiral EDWA fitted into area of 20, 60, and 100 mm2 with δR = 200 µm.

Tables (1)

Tables Icon

Table 1 Spectroscopic and Waveguide Parameters for the Erbium-Doped Phosphosilicate Planar Waveguides Used in the Calculations (taken from Refs. 16, 18, 23, 24)

Equations (11)

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

d N ( x , y , z ) d t = N ( x , y , z ) R ( x , y , z ) + N ( x , y , z ) W a ( x , y , z ) N ( x , y , z ) W e ( x , y , z ) N ( x , y , z ) τ , N ( x , y , z ) + N ( x , y , z ) = ρ ,
τ = τ 0 1 + [ N ( x , y , z ) / Q ] 2 ,
d P p ( z ) d z = [ S core σ pa ( ν p ) N ( x , y , z ) ψ p ( x , y ) d s + α p ( z ) ] P p ( z ) , d P s ( z ) d z = [ S core [ σ se ( ν s ) N ( x , y , z ) σ sa ( ν s ) N ( x , y , z ) ] ψ s ( x , y ) d s α s ( z ) ] P s ( z ) , ± d P ASE ± ( z , ν i ) d z = [ S core [ σ se ( ν i ) N ( x , y , z ) σ sa ( ν i ) N ( x , y , z ) ] ψ s ( x , y ) d s α s ( z ) ] P ASE ± ( z , ν i ) + k h ν i Δ ν S core σ se ( ν i ) N ( x , y , z ) ψ s ( x , y ) d s , i = 1 200 ,
P p ( 0 ) = P p in , P s ( 0 ) = P s in , P ASE + ( 0 , ν i ) = P ASE ( L , ν i ) = 0 ,
L = 2 ( R + 2 R n + π R n + π 2 R ) ,
R = L ( 2 + π ) ( 1 + 2 n ) ,
S = 8 R 2 .
L 2 { ( R min + n δ R ) + n [ ( 2 R min ) 2 + ( δ R ) 2 ] 1 / 2 + π i = 1 n R i + π 2 R min } ,
R i = R min + δ R ( i 1 ) .
R min L δ R [ π n 2 ( π 3 ) n ] ( 2 + π ) ( 1 + 2 n ) .
S 4 [ 2 R min + δ R ( n 1 ) ] ( R min + δ R n ) .

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