Abstract

An erbium-doped fiber ring laser is modeled by use of the standard propagation and rate equations of a homogeneous, two-level medium. A numerical model is obtained by development of a spectral analysis of erbium-doped fiber amplifiers. This approach is modified to account for the cyclical propagation of the field in the ring laser. Numerical simulations provide interesting information on the spectral behavior as well as important characteristics of the cavity, mainly the lasing wavelength and output power. The model also permits the study of competing modes’ gain and signal evolutions during the transient state of the ring laser cavity.

© 2000 Optical Society of America

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  1. O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
    [CrossRef]
  2. P. K. Cheo, L. Wang, and M. Ding, “Low-threshold, self-tuned and passively mode-locked coupled-cavity all-fiber lasers,” IEEE Photon. Technol. Lett. 8, 66–68 (1996).
    [CrossRef]
  3. W. L. Barnes, P. R. Morkel, L. Reekie, and D. N. Payne, “High quantum efficiency Er3+-fiber lasers pumped at 980 nm,” Opt. Lett. 14, 1002–1004 (1989).
    [CrossRef] [PubMed]
  4. J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
    [CrossRef]
  5. H. Schmuck, Th. Pfeiffer, and G. Veith, “Widely tunable narrow linewidth erbium-doped fibre ring laser,” Electron. Lett. 27, 2117–2119 (1991).
    [CrossRef]
  6. P. R. Morkel, G. J. Cowle, and D. N. Payne, “A travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
    [CrossRef]
  7. K. Iwatsuki, H. Okamura, and M. Saruwatari, “Er3+-doped fibre-ring-laser with less than 10 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
    [CrossRef]
  8. N. Park, J. W. Dawson, and K. J. Vahala, “All fiber low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with tandem fiber Fabry–Perot filter,” Appl. Phys. Lett. 59, 2369–2371 (1991).
    [CrossRef]
  9. P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
    [CrossRef]
  10. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
    [CrossRef]
  11. J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, and H. J. Shaw, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
    [CrossRef] [PubMed]
  12. B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
    [CrossRef]
  13. A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
    [CrossRef]
  14. P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” IEEE J. Lightwave Technol. 15, 112–120 (1997).
    [CrossRef]
  15. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art and Science of Scientific Computing (Cambridge U. Press, New York, 1986).
  16. S. R. Chinn, “Simplified modeling of transients in gain-clamped erbium-doped fiber amplifiers,” J. Lightwave Technol. 16, 1095–1100 (1998).
    [CrossRef]

1998

1997

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” IEEE J. Lightwave Technol. 15, 112–120 (1997).
[CrossRef]

1996

O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
[CrossRef]

P. K. Cheo, L. Wang, and M. Ding, “Low-threshold, self-tuned and passively mode-locked coupled-cavity all-fiber lasers,” IEEE Photon. Technol. Lett. 8, 66–68 (1996).
[CrossRef]

1993

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, and H. J. Shaw, “Effects of concentration and clusters in erbium-doped fiber lasers,” Opt. Lett. 18, 2014–2016 (1993).
[CrossRef] [PubMed]

1991

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

N. Park, J. W. Dawson, and K. J. Vahala, “All fiber low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with tandem fiber Fabry–Perot filter,” Appl. Phys. Lett. 59, 2369–2371 (1991).
[CrossRef]

P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
[CrossRef]

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

H. Schmuck, Th. Pfeiffer, and G. Veith, “Widely tunable narrow linewidth erbium-doped fibre ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[CrossRef]

1990

P. R. Morkel, G. J. Cowle, and D. N. Payne, “A travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[CrossRef]

K. Iwatsuki, H. Okamura, and M. Saruwatari, “Er3+-doped fibre-ring-laser with less than 10 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[CrossRef]

1989

Barnes, W. L.

Bayon, J.-F.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Bjarklev, A.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Blixt, P. M.

P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
[CrossRef]

Carlnas, T.

P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
[CrossRef]

Cheo, P. K.

P. K. Cheo, L. Wang, and M. Ding, “Low-threshold, self-tuned and passively mode-locked coupled-cavity all-fiber lasers,” IEEE Photon. Technol. Lett. 8, 66–68 (1996).
[CrossRef]

Chinn, S. R.

Chrostowski, J.

P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” IEEE J. Lightwave Technol. 15, 112–120 (1997).
[CrossRef]

Cowle, G. J.

P. R. Morkel, G. J. Cowle, and D. N. Payne, “A travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[CrossRef]

Cucinotta, A.

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

Dallargine, S.

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

Dawson, J. W.

N. Park, J. W. Dawson, and K. J. Vahala, “All fiber low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with tandem fiber Fabry–Perot filter,” Appl. Phys. Lett. 59, 2369–2371 (1991).
[CrossRef]

Delevaque, E.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Digiovanni, D. J.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Digonnet, M. J. F.

Ding, M.

P. K. Cheo, L. Wang, and M. Ding, “Low-threshold, self-tuned and passively mode-locked coupled-cavity all-fiber lasers,” IEEE Photon. Technol. Lett. 8, 66–68 (1996).
[CrossRef]

Dong, L.

O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
[CrossRef]

Dybdal, K.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Georges, T.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Graydon, O.

O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
[CrossRef]

Iwatsuki, K.

K. Iwatsuki, H. Okamura, and M. Saruwatari, “Er3+-doped fibre-ring-laser with less than 10 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[CrossRef]

Jaskorzynska, B.

P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
[CrossRef]

Laming, R. I.

O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
[CrossRef]

Lamouler, P.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Larsen, C. C.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Loh, W. H.

O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
[CrossRef]

Monerie, M.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

Morkel, P. R.

P. R. Morkel, G. J. Cowle, and D. N. Payne, “A travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[CrossRef]

W. L. Barnes, P. R. Morkel, L. Reekie, and D. N. Payne, “High quantum efficiency Er3+-fiber lasers pumped at 980 nm,” Opt. Lett. 14, 1002–1004 (1989).
[CrossRef] [PubMed]

Myslinski, P.

P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” IEEE J. Lightwave Technol. 15, 112–120 (1997).
[CrossRef]

Nguyen, D.

P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” IEEE J. Lightwave Technol. 15, 112–120 (1997).
[CrossRef]

Nilsson, J.

P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
[CrossRef]

Okamura, H.

K. Iwatsuki, H. Okamura, and M. Saruwatari, “Er3+-doped fibre-ring-laser with less than 10 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[CrossRef]

Park, N.

N. Park, J. W. Dawson, and K. J. Vahala, “All fiber low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with tandem fiber Fabry–Perot filter,” Appl. Phys. Lett. 59, 2369–2371 (1991).
[CrossRef]

Payne, D. N.

P. R. Morkel, G. J. Cowle, and D. N. Payne, “A travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[CrossRef]

W. L. Barnes, P. R. Morkel, L. Reekie, and D. N. Payne, “High quantum efficiency Er3+-fiber lasers pumped at 980 nm,” Opt. Lett. 14, 1002–1004 (1989).
[CrossRef] [PubMed]

Pedersen, B.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Pfeiffer, Th.

H. Schmuck, Th. Pfeiffer, and G. Veith, “Widely tunable narrow linewidth erbium-doped fibre ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[CrossRef]

Piccirilli, A.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Povlsen, J. H.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

Pramayon, P. E.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Presby, H. M.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Reekie, L.

Saruwatari, M.

K. Iwatsuki, H. Okamura, and M. Saruwatari, “Er3+-doped fibre-ring-laser with less than 10 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[CrossRef]

Schmuck, H.

H. Schmuck, Th. Pfeiffer, and G. Veith, “Widely tunable narrow linewidth erbium-doped fibre ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[CrossRef]

Selleri, S.

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

Shaw, H. J.

Stone, J.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Stultz, L. W.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Sulhoff, J. W.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Vahala, K. J.

N. Park, J. W. Dawson, and K. J. Vahala, “All fiber low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with tandem fiber Fabry–Perot filter,” Appl. Phys. Lett. 59, 2369–2371 (1991).
[CrossRef]

Veith, G.

H. Schmuck, Th. Pfeiffer, and G. Veith, “Widely tunable narrow linewidth erbium-doped fibre ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[CrossRef]

Wagener, J. L.

Wang, L.

P. K. Cheo, L. Wang, and M. Ding, “Low-threshold, self-tuned and passively mode-locked coupled-cavity all-fiber lasers,” IEEE Photon. Technol. Lett. 8, 66–68 (1996).
[CrossRef]

Wysocki, P. F.

Zilioli, C.

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

Zoboli, M.

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

Zyskind, J. L.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

Appl. Phys. Lett.

N. Park, J. W. Dawson, and K. J. Vahala, “All fiber low threshold, widely tunable single-frequency, erbium-doped fiber ring laser with tandem fiber Fabry–Perot filter,” Appl. Phys. Lett. 59, 2369–2371 (1991).
[CrossRef]

Electron. Lett.

J. L. Zyskind, J. W. Sulhoff, J. Stone, D. J. Digiovanni, L. W. Stultz, H. M. Presby, A. Piccirilli, and P. E. Pramayon, “Electrically tunable, diode-pumped erbium-doped fiber ring laser with fibre Fabry–Perot etalon,” Electron. Lett. 27, 1950–1951 (1991).
[CrossRef]

H. Schmuck, Th. Pfeiffer, and G. Veith, “Widely tunable narrow linewidth erbium-doped fibre ring laser,” Electron. Lett. 27, 2117–2119 (1991).
[CrossRef]

P. R. Morkel, G. J. Cowle, and D. N. Payne, “A travelling-wave erbium fibre ring laser with 60 kHz linewidth,” Electron. Lett. 26, 632–634 (1990).
[CrossRef]

K. Iwatsuki, H. Okamura, and M. Saruwatari, “Er3+-doped fibre-ring-laser with less than 10 kHz linewidth,” Electron. Lett. 26, 2033–2035 (1990).
[CrossRef]

IEEE J. Lightwave Technol.

P. Myslinski, D. Nguyen, and J. Chrostowski, “Effects of concentration on the performance of erbium-doped fiber amplifiers,” IEEE J. Lightwave Technol. 15, 112–120 (1997).
[CrossRef]

IEEE Photon. Tech. Lett.

P. M. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration dependent upconversion in Er-doped fiber amplifiers: experiments and modeling,” IEEE Photon. Tech. Lett. 3, 996–998 (1991).
[CrossRef]

IEEE Photon. Technol. Lett.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photon. Technol. Lett. 5, 73–75 (1993).
[CrossRef]

O. Graydon, W. H. Loh, R. I. Laming, and L. Dong, “Triple-frequency operation of an Er-doped twin core fiber loop laser,” IEEE Photon. Technol. Lett. 8, 63–65 (1996).
[CrossRef]

P. K. Cheo, L. Wang, and M. Ding, “Low-threshold, self-tuned and passively mode-locked coupled-cavity all-fiber lasers,” IEEE Photon. Technol. Lett. 8, 66–68 (1996).
[CrossRef]

J. Lightwave Technol.

B. Pedersen, A. Bjarklev, J. H. Povlsen, K. Dybdal, and C. C. Larsen, “The design of erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 1105–1112 (1991).
[CrossRef]

S. R. Chinn, “Simplified modeling of transients in gain-clamped erbium-doped fiber amplifiers,” J. Lightwave Technol. 16, 1095–1100 (1998).
[CrossRef]

Opt. Commun.

A. Cucinotta, S. Dallargine, S. Selleri, C. Zilioli, and M. Zoboli, “Modeling of erbium doped fiber ring laser,” Opt. Commun. 141, 21–24 (1997).
[CrossRef]

Opt. Lett.

Other

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art and Science of Scientific Computing (Cambridge U. Press, New York, 1986).

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Figures (8)

Fig. 1
Fig. 1

Energy-level diagram of erbium ions.

Fig. 2
Fig. 2

Schematic of the EDF ring laser.

Fig. 3
Fig. 3

Amplifier gain versus pump power for an EDF length of 12 m and an input signal power of -3.5 dBm. Dotted curve, model (k=0); solid curve, model (k=0.09); filled squares, experiment.

Fig. 4
Fig. 4

Calculated gain evolutions in the ring cavity before steady state for a 7-m-long EDF, pumped at 50-mW pump power with 50% reflectivity. Dotted curve, 1520 nm; thinner solid curve, 1531 nm; thicker solid curve, 1561 nm.

Fig. 5
Fig. 5

Calculated absolute signal power evolutions in the ring cavity before steady state for a 7-m-long EDF, pumped at 50-mW pump power with 50% reflectivity. Dotted curve, 1531; solid curve, 1561. The curves almost completely overlap.

Fig. 6
Fig. 6

Calculated output spectrum of the ring laser for a 8.14-m-long EDF, pumped at 115 mW pump power with 20% reflectivity.

Fig. 7
Fig. 7

Comparison of the calculated and measured values of the lasing wavelength of the ring laser versus reflectivity for an 8.14-m-long EDF pumped with 115-mW pump power. Filled squares, experiment; curve, model.

Fig. 8
Fig. 8

Comparison of the calculated and measured values of the output power of the ring laser versus reflectivity for an 8.14-m-long, EDF, pumped with 115-mW pump power. Filled squares, experiment; curve, model.

Equations (15)

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

Nc2(r, z)
=Nc Rpa(r, z)+Wsa(r, z)m[Rpa(r, z)+Wsa(r, z)]+Wse(r, z)+Ae,
Nc1(r, z)
=Nc-Nc2(r, z),
Ns2(r, z)
=Ns Rpa(r, z)+Wsa(r, z)Rpa(r, z)+Wsa(r, z)+Wse(r, z)+Ae,
Ns1(r, z)
=Ns-Ns2(r, z),
N1(r, z)
=Ns1(r, z)+Nc1(r, z),
N2(r, z)
=Ns2(r, z)+Nc2(r, z),
dPp(z)dz=-γa(νp, z)Pp(z),
dPs(z)dz=[γe(νs, z)-γa(νs, z)]Ps(z),
dSASE±(ν, z)dz=±2hνγe(ν, z)±[γe(ν, z)-γa(ν, z)]SASE±(ν, z),

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