Abstract

We present an experimental and computational investigation of the dynamics in singly Er-doped and Er/Pr-codoped double-clad fluoride fiber lasers that are pulse-pumped with diode at 975 nm. Measurements that include time-dependent laser power and spectrum show multi-line operation with distinct initial line jumping in the Er fiber and spectral and power fluctuations in both fibers. Thermal effects are dismissed as the cause and the effects of homogeneous and inhomogeneous broadenings on the laser operation are studied by using a simulation that is based on the rate-equations. Simulation results show line jumping with accurate timing in both homogeneous and inhomogeneous models, and the best match with the experiment is achieved with the inhomogeneous model assuming independent lasing of two distinct ion classes.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  6. B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
    [CrossRef]
  29. A. K. Przhevuskii and N. V. Nikonorov, “Monte-Carlo simulation of upconversion processes in erbium-doped materials,” Opt. Mater. 21, 729–741 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]

2009 (3)

2007 (1)

2005 (1)

2004 (3)

L. Bigot, S. Choblet, A.-M. Jurdyc, and B. Jacquier, “Transient spectral hole burning in erbium-doped fluoride glasses,” J. Opt. Soc. Am. B 21, 307–312 (2004).
[CrossRef]

S. Guy, L. Bigot, I. Vasilief, B. Jacquier, B. Boulard, and Y. Gao, “Two crystallographic sites in erbium-doped fluoride glass by frequency-resolved and site-selective spectroscopies,” J. Non-Cryst. Solids 336, 165–172 (2004).
[CrossRef]

J. Tafoya, J. Pierce, R. K. Jain, and B. Wong, “Efficient and compact high-power mid-IR (∼3 μm) lasers for surgical applications,” Proc. SPIE 5312, 218–222 (2004).
[CrossRef]

2003 (2)

2002 (2)

M. Pollnau and S. D. Jackson, “Energy recycling versus lifetime quenching in erbium-doped 3-μm fiber lasers,” IEEE J. Quantum Electron. 38, 162–169 (2002).
[CrossRef]

H. Inoue, K. Soga, and A. Makishima, “Simulation of the optical properties of Er:ZBLAN glass,” J. Non-Cryst. Solids 298, 270–286 (2002).
[CrossRef]

2001 (3)

Y. D. Huang, M. Mortimer, and F. Auzel, “Stark level analysis for Er3+-doped ZBLAN glass,” Opt. Mater. 17, 501–511 (2001).
[CrossRef]

M. Pollnau and S. D. Jackson, “Erbium 3-μm fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 30–40 (2001).
[CrossRef]

B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
[CrossRef]

2000 (3)

S. D. Jackson, T. A. King, and M. Pollnau, “Modelling of high-power diode-pumped erbium 3 μm fibre lasers,” J. Mod. Opt. 47, 1987–1994 (2000).

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

B. Srinivasan, R. K. Jain, and G. Monnom, “Indirect measurement of the magnitude of ion clustering at high doping densities in Er:ZBLAN fibers,” J. Opt. Soc. Am. B 17, 178–181 (2000).
[CrossRef]

1999 (2)

S. D. Jackson and T. A. King, “Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers,” J. Opt. Soc. Am. B 16, 2178–2188 (1999).
[CrossRef]

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

1998 (2)

H. L. An, E. Y. B. Pun, H. D. Liu, and X. Z. Lin, “Effects of ion clusters on the performance of a heavily doped erbium-doped fiber laser,” J. Opt. Soc. Am. B 23, 1197–1199 (1998).

J. Daniel, J.-M. Costa, P. LeBoudec, G. Stephan, and F. Sanchez, “Generalized bistability in an erbium-doped fiber laser,” J. Opt. Soc. Am. B 15, 1291–1294 (1998).
[CrossRef]

1996 (2)

1994 (2)

Ch. Frerichs, “Efficient Er3+-doped cw fluorozirconate fiber laser operating at 2.7 μm pumped at 980 nm,” Int. J. Infrared Millim. Waves 15, 635–649 (1994).
[CrossRef]

J. Schneider, D. Hauschild, Ch. Frerichs, and L. Wetenkamp, “Highly efficient Er3+:Pr3+-codoped cw fluorozirconate fiber laser operating at 2.7 μm,” Int. J. Infrared Millim. Waves 15, 1907–1922 (1994).
[CrossRef]

1993 (2)

V. Lupei, S. Georgescu, and V. Florea, “On the dynamics of population inversion for 3 μmEr3+ lasers,” IEEE J. Quantum Electron. 29, 426–434 (1993).
[CrossRef]

F. Sanchez, P. LeBoudec, and P.-L. François, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

1992 (1)

L. Wetenkamp, G. F. West, and H. Többen, “Co-doping effects in erbium3+- and holmium3+-doped ZBLAN glasses,” J. Non-Cryst. Solids 140, 25–30 (1992).
[CrossRef]

An, H. L.

H. L. An, E. Y. B. Pun, H. D. Liu, and X. Z. Lin, “Effects of ion clusters on the performance of a heavily doped erbium-doped fiber laser,” J. Opt. Soc. Am. B 23, 1197–1199 (1998).

Auzel, F.

Y. D. Huang, M. Mortimer, and F. Auzel, “Stark level analysis for Er3+-doped ZBLAN glass,” Opt. Mater. 17, 501–511 (2001).
[CrossRef]

Barmenkov, Y. O.

Bernier, M.

Bigot, L.

S. Guy, L. Bigot, I. Vasilief, B. Jacquier, B. Boulard, and Y. Gao, “Two crystallographic sites in erbium-doped fluoride glass by frequency-resolved and site-selective spectroscopies,” J. Non-Cryst. Solids 336, 165–172 (2004).
[CrossRef]

L. Bigot, S. Choblet, A.-M. Jurdyc, and B. Jacquier, “Transient spectral hole burning in erbium-doped fluoride glasses,” J. Opt. Soc. Am. B 21, 307–312 (2004).
[CrossRef]

Bjarklev, A.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Boulard, B.

S. Guy, L. Bigot, I. Vasilief, B. Jacquier, B. Boulard, and Y. Gao, “Two crystallographic sites in erbium-doped fluoride glass by frequency-resolved and site-selective spectroscopies,” J. Non-Cryst. Solids 336, 165–172 (2004).
[CrossRef]

Bremberg, D.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Broeng, J.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Caron, N.

Chen, B.

B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
[CrossRef]

Cheng, L.

B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
[CrossRef]

Choblet, S.

Colin, S.

Contesse, E.

Copic, M.

M. Gorjan, M. Marinček, and M. Čopič, “Role of interionic processes in the efficiency and operation of erbium-doped fluoride fiber lasers,” IEEE J. Quantum Electron. 47 (to be published).

Costa, J. -M.

Daniel, J.

Dickinson, B. C.

B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
[CrossRef]

Faucher, D.

Florea, V.

V. Lupei, S. Georgescu, and V. Florea, “On the dynamics of population inversion for 3 μmEr3+ lasers,” IEEE J. Quantum Electron. 29, 426–434 (1993).
[CrossRef]

François, P. -L.

F. Sanchez, P. LeBoudec, and P.-L. François, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Frerichs, Ch.

Ch. Frerichs, “Efficient Er3+-doped cw fluorozirconate fiber laser operating at 2.7 μm pumped at 980 nm,” Int. J. Infrared Millim. Waves 15, 635–649 (1994).
[CrossRef]

J. Schneider, D. Hauschild, Ch. Frerichs, and L. Wetenkamp, “Highly efficient Er3+:Pr3+-codoped cw fluorozirconate fiber laser operating at 2.7 μm,” Int. J. Infrared Millim. Waves 15, 1907–1922 (1994).
[CrossRef]

Gao, Y.

S. Guy, L. Bigot, I. Vasilief, B. Jacquier, B. Boulard, and Y. Gao, “Two crystallographic sites in erbium-doped fluoride glass by frequency-resolved and site-selective spectroscopies,” J. Non-Cryst. Solids 336, 165–172 (2004).
[CrossRef]

Georgescu, S.

V. Lupei, S. Georgescu, and V. Florea, “On the dynamics of population inversion for 3 μmEr3+ lasers,” IEEE J. Quantum Electron. 29, 426–434 (1993).
[CrossRef]

Golding, P. S.

B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
[CrossRef]

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

Gorjan, M.

M. Gorjan, M. Marinček, and M. Čopič, “Role of interionic processes in the efficiency and operation of erbium-doped fluoride fiber lasers,” IEEE J. Quantum Electron. 47 (to be published).

Guy, S.

S. Guy, L. Bigot, I. Vasilief, B. Jacquier, B. Boulard, and Y. Gao, “Two crystallographic sites in erbium-doped fluoride glass by frequency-resolved and site-selective spectroscopies,” J. Non-Cryst. Solids 336, 165–172 (2004).
[CrossRef]

Hashida, M.

Hauschild, D.

J. Schneider, D. Hauschild, Ch. Frerichs, and L. Wetenkamp, “Highly efficient Er3+:Pr3+-codoped cw fluorozirconate fiber laser operating at 2.7 μm,” Int. J. Infrared Millim. Waves 15, 1907–1922 (1994).
[CrossRef]

Helmfrid, S.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Huang, Y. D.

Y. D. Huang, M. Mortimer, and F. Auzel, “Stark level analysis for Er3+-doped ZBLAN glass,” Opt. Mater. 17, 501–511 (2001).
[CrossRef]

Inoue, H.

H. Inoue, K. Soga, and A. Makishima, “Simulation of the optical properties of Er:ZBLAN glass,” J. Non-Cryst. Solids 298, 270–286 (2002).
[CrossRef]

Jackson, S. D.

M. Pollnau and S. D. Jackson, “Energy recycling versus lifetime quenching in erbium-doped 3-μm fiber lasers,” IEEE J. Quantum Electron. 38, 162–169 (2002).
[CrossRef]

M. Pollnau and S. D. Jackson, “Erbium 3-μm fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 30–40 (2001).
[CrossRef]

B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
[CrossRef]

S. D. Jackson, T. A. King, and M. Pollnau, “Modelling of high-power diode-pumped erbium 3 μm fibre lasers,” J. Mod. Opt. 47, 1987–1994 (2000).

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

S. D. Jackson and T. A. King, “Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers,” J. Opt. Soc. Am. B 16, 2178–2188 (1999).
[CrossRef]

Jacquier, B.

S. Guy, L. Bigot, I. Vasilief, B. Jacquier, B. Boulard, and Y. Gao, “Two crystallographic sites in erbium-doped fluoride glass by frequency-resolved and site-selective spectroscopies,” J. Non-Cryst. Solids 336, 165–172 (2004).
[CrossRef]

L. Bigot, S. Choblet, A.-M. Jurdyc, and B. Jacquier, “Transient spectral hole burning in erbium-doped fluoride glasses,” J. Opt. Soc. Am. B 21, 307–312 (2004).
[CrossRef]

Jain, R.

Jain, R. K.

J. Tafoya, J. Pierce, R. K. Jain, and B. Wong, “Efficient and compact high-power mid-IR (∼3 μm) lasers for surgical applications,” Proc. SPIE 5312, 218–222 (2004).
[CrossRef]

B. Srinivasan, R. K. Jain, and G. Monnom, “Indirect measurement of the magnitude of ion clustering at high doping densities in Er:ZBLAN fibers,” J. Opt. Soc. Am. B 17, 178–181 (2000).
[CrossRef]

James-Regàtegui, R.

Jarabo, S.

Jaskorzynska, B.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Jurdyc, A. -M.

King, T. A.

B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
[CrossRef]

S. D. Jackson, T. A. King, and M. Pollnau, “Modelling of high-power diode-pumped erbium 3 μm fibre lasers,” J. Mod. Opt. 47, 1987–1994 (2000).

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

S. D. Jackson and T. A. King, “Dynamics of the output of heavily Tm-doped double-clad silica fiber lasers,” J. Opt. Soc. Am. B 16, 2178–2188 (1999).
[CrossRef]

Kir’yanov, A. V.

LeBoudec, P.

Lin, X. Z.

H. L. An, E. Y. B. Pun, H. D. Liu, and X. Z. Lin, “Effects of ion clusters on the performance of a heavily doped erbium-doped fiber laser,” J. Opt. Soc. Am. B 23, 1197–1199 (1998).

Liu, H. D.

H. L. An, E. Y. B. Pun, H. D. Liu, and X. Z. Lin, “Effects of ion clusters on the performance of a heavily doped erbium-doped fiber laser,” J. Opt. Soc. Am. B 23, 1197–1199 (1998).

Lupei, V.

V. Lupei, S. Georgescu, and V. Florea, “On the dynamics of population inversion for 3 μmEr3+ lasers,” IEEE J. Quantum Electron. 29, 426–434 (1993).
[CrossRef]

Makishima, A.

H. Inoue, K. Soga, and A. Makishima, “Simulation of the optical properties of Er:ZBLAN glass,” J. Non-Cryst. Solids 298, 270–286 (2002).
[CrossRef]

Marincek, M.

M. Gorjan, M. Marinček, and M. Čopič, “Role of interionic processes in the efficiency and operation of erbium-doped fluoride fiber lasers,” IEEE J. Quantum Electron. 47 (to be published).

Monnom, G.

Mortimer, M.

Y. D. Huang, M. Mortimer, and F. Auzel, “Stark level analysis for Er3+-doped ZBLAN glass,” Opt. Mater. 17, 501–511 (2001).
[CrossRef]

Murakami, M.

Nikonorov, N. V.

A. K. Przhevuskii and N. V. Nikonorov, “Monte-Carlo simulation of upconversion processes in erbium-doped materials,” Opt. Mater. 21, 729–741 (2003).
[CrossRef]

Pálsdóttir, B.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Philipsen, J. L.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Pálsdóttir, “Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering,” IEEE J. Quantum Electron. 35, 1741–1749 (1999).
[CrossRef]

Pierce, J.

J. Tafoya, J. Pierce, R. K. Jain, and B. Wong, “Efficient and compact high-power mid-IR (∼3 μm) lasers for surgical applications,” Proc. SPIE 5312, 218–222 (2004).
[CrossRef]

Pisarchik, A. N.

Pollnau, M.

M. Pollnau and S. D. Jackson, “Energy recycling versus lifetime quenching in erbium-doped 3-μm fiber lasers,” IEEE J. Quantum Electron. 38, 162–169 (2002).
[CrossRef]

M. Pollnau and S. D. Jackson, “Erbium 3-μm fiber lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 30–40 (2001).
[CrossRef]

B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, and S. D. Jackson, “Investigation of a 791-nm pulse-pumped 2.7 μm Er-doped ZBLAN fibre laser,” Opt. Commun. 191, 315–321 (2001).
[CrossRef]

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

S. D. Jackson, T. A. King, and M. Pollnau, “Modelling of high-power diode-pumped erbium 3 μm fibre lasers,” J. Mod. Opt. 47, 1987–1994 (2000).

Przhevuskii, A. K.

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B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
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[CrossRef]

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B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
[CrossRef]

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L. Wetenkamp, G. F. West, and H. Többen, “Co-doping effects in erbium3+- and holmium3+-doped ZBLAN glasses,” J. Non-Cryst. Solids 140, 25–30 (1992).
[CrossRef]

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J. Schneider, D. Hauschild, Ch. Frerichs, and L. Wetenkamp, “Highly efficient Er3+:Pr3+-codoped cw fluorozirconate fiber laser operating at 2.7 μm,” Int. J. Infrared Millim. Waves 15, 1907–1922 (1994).
[CrossRef]

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J. Tafoya, J. Pierce, R. K. Jain, and B. Wong, “Efficient and compact high-power mid-IR (∼3 μm) lasers for surgical applications,” Proc. SPIE 5312, 218–222 (2004).
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B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
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B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
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H. Inoue, K. Soga, and A. Makishima, “Simulation of the optical properties of Er:ZBLAN glass,” J. Non-Cryst. Solids 298, 270–286 (2002).
[CrossRef]

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[CrossRef]

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J. Opt. Soc. Am. B (7)

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Opt. Express (1)

Opt. Lett. (3)

Opt. Mater. (3)

A. K. Przhevuskii and N. V. Nikonorov, “Monte-Carlo simulation of upconversion processes in erbium-doped materials,” Opt. Mater. 21, 729–741 (2003).
[CrossRef]

B. Wang, L. Cheng, H. Zhong, J. Sun, Y. Tian, X. Zhang, and B. Chen, “Excited state absorption cross sections of I413/2 of Er3+ in ZBLAN,” Opt. Mater. 31, 1658–1662 (2009).
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[CrossRef]

Phys. Rev. A (1)

F. Sanchez, P. LeBoudec, and P.-L. François, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48, 2220–2229 (1993).
[CrossRef] [PubMed]

Phys. Rev. B (1)

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

Phys. Rev. E (1)

F. Sanchez and G. Stephan, “General analysis of instabilities in erbium-doped fiber lasers,” Phys. Rev. E 55, 2110–2122 (1996).
[CrossRef]

Proc. SPIE (1)

J. Tafoya, J. Pierce, R. K. Jain, and B. Wong, “Efficient and compact high-power mid-IR (∼3 μm) lasers for surgical applications,” Proc. SPIE 5312, 218–222 (2004).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Experimental setup used for the measurements. Fiber-coupled diode pump beam is coupled to the laser fiber by two parabolic mirrors, and collimated output laser beam is reflected by dichroic mirror, put through a filter, and directed either to a fast diode or a spectrometer for the measurements. Pump pulses and data collection via computer or oscilloscope were synchronized.

Fig. 2
Fig. 2

Measured time-dependent power of Er-doped fiber laser at 40 W launched pump power is showing double relaxation oscillations at the beginning of the pulse (inset) and bursts of oscillations continue even after cw regime is reached.

Fig. 3
Fig. 3

Measured time difference between the appearance of the first two relaxation oscillations and rise time of laser oscillation to full power versus launched pump power in Er-doped fiber laser.

Fig. 4
Fig. 4

Measured time-dependent spectrum of Er-doped fiber laser at 40 W launched pump power is showing the beginning of lasing at lines 2771, 2782, and 2786 nm, quickly followed by jumps to multiple lines around 2790 nm. Later the redshift happens again, and the strongest line at 2793 nm dies out.

Fig. 5
Fig. 5

Measured time-dependent power of Er/Pr-codoped fiber laser at 20 W launched pump power is showing only single relaxation oscillations at the beginning of the pulse (inset), but they never die out completely even in the cw regime. Note that the recording resolution here was inadequate to properly show the oscillations in full time, but they are shown in full detail in the inset.

Fig. 6
Fig. 6

Measured time-dependent spectrum of Er/Pr-codoped fiber laser at 20 W launched pump power is showing lasing activity in multiple lines simultaneously. No line really dies out, but there is a constant energy redistribution among all lines.

Fig. 7
Fig. 7

Erbium energy levels and transitions in homogeneous broadening. Spectroscopic manifold notations are on the left, and level numbering in the simulation is on the right. Both lasing manifolds are split into two Stark levels, allowing for one major (thick double line) and three minor (thin double lines) laser transitions. Stark levels on each manifold are coupled in both ways (diamonds) according to their respective Boltzmann factors, while only the lowest laying Stark levels are coupled with all other manifolds through radiative and multiphonon relaxations (full straight lines) and three interionic transitions (curved lines).

Fig. 8
Fig. 8

Simulated spectral line dynamics in homogeneous broadening at 40 W launched pump power. Laser oscillation starts at minor line (4,2) and seamlessly jumps to the major line ((4,3)) producing no visual clue in the total power, i.e., sum of all lines. Note that the plot is trimmed in intensity at the beginning to show more detail.

Fig. 9
Fig. 9

Measured and calculated time difference between the appearance of the first two relaxation oscillations for homogeneous line broadening and inhomogeneous broadening with no line mixing.

Fig. 10
Fig. 10

Inhomogeneous broadening is modeled by using two homogeneously broadened ionic populations A and B. In the uniform case the interionic transitions are between both populations, while in the case of clustering the interionic transitions are only among the ions in population B. There is also line combining: pumping always affects both population equally, and we modeled two cases of laser line overlap and the case of no line overlap.

Fig. 11
Fig. 11

Simulated spectral line dynamics in inhomogeneous broadening with clustering at 40 W launched pump power and for three cases of Stark level overlap between the two ion populations. (a) Combining the major line ((4,3)) and a minor line (14,11) into ((4,3))-(14,11) helps it start, but later the major line ((13,12)) starts and wins. (b) Combining two minor lines ((4,3)) and (14,11) into (4,2)-(14,11) helps it start, but later both major lines ((4,3)) and ((13,12)) start and shut the combined line completely. (c) No line combining produces independent lasing on lines (4,2) and ((4,3)) for ion population A, and on lines (13,11) and ((13,12)) for ion population B like in homogeneous broadening. Note that the plot is trimmed in intensity at the beginning to show more detail.

Tables (2)

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Table 1 Values of the Spectroscopic Parameters for the Homogeneous Broadening a

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Table 2 Values of the Spectroscopic Parameters for the Inhomogeneous Broadening a

Equations (10)

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N ( z , t ) = [ N 1 , , N m ] ,
F ( z , t ) = [ F i j ± , i j 0 , i = j ] ,
d N d t = [ k T k 1 T 1 m T m 1 k T k 1 ] N + [ k , l w i j k l N j ] N ,
T i j = r i j + c Γ i j σ i j b i F i j ,
d F i j d t = c Γ i j σ i j ( b i F i j b j F j i ) N i + γ i j F i j + δ i j r i j N i ,
N ( z , t + d t ) = N ( z , t ) + d N ( z , t ) ,
F ± ( z , t + d t ) = F ± ( z 1 , t ) + d F ± ( z , t ) .
d t = n f L c 0 n .
F + ( z = 1 , t + d t ) = F P + R ± F ( z = 1 , t ) ,
F ( z = n , t + d t ) = R F + ( z = n , t ) ,

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