Abstract

The spectroscopic properties of Tm3+/Yb3+ co-doped silica fibers under excitation at 980 nm are reported. Three distinct up-conversion fluorescence bands were observed in the visible to near infra-red regions. The blue and red fluorescence bands at 475 and 650 nm, respectively, were found to originate from the 1G4 level of Tm3+. A three step up-conversion process was established as the populating mechanism for these fluorescence bands. The fluorescence band at 800 nm was found to originate from two possible transitions in Tm3+; one being the transition from the 3H4 to 3H6 manifold which was found to dominate at low pump powers; the other being the transition from the 1G4 to 3H6 level which dominates at higher pump powers. The fluorescence lifetime of the 3H4 and 3F4 levels of Tm3+ and 2F5/2 level of Yb3+ were studied as a function of Yb3+ concentration, with no significant energy back transfer from Tm3+ to Yb3+ observed.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. Y. H. Tsang, D. J. Coleman, and T. A. King, "High power 1.9 µm Tm3+-silica fibre laser pumped at 1.09 µm by a Yb3+-silica fibre laser," Opt. Commun. 231, 357-364 (2004).
    [CrossRef]
  26. P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
    [CrossRef]
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    [CrossRef]
  30. A. S. L. Gomes, M. T. Carvalho, M. L. Sundheimer, C. J. A. Bastos, J. F. Martins, J. P. Von der Weid, W. Margulis, "Low-pump-power, short-fiber copropagating dual-pumped (800 and 1050 nm) thulium-doped fiber amplifier," Opt. Lett. 28, 334-336 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]

2007

B. Faure, W. Blanc, B. Dussardier and G. Monnom, "Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy," J. Non-Cryst. Solids 353, 2767-2773 (2007).
[CrossRef]

2006

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

R. Caspary, M. M. Kozak, D. Goebel, and W. Kowalsky, "Excited state absorption spectroscopy for thulium-doped zirconium fluoride fiber," Opt. Commun. 259, 154-157 (2006).
[CrossRef]

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

2005

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

2004

B. M. Walsh, and N. P. Barnes, "Comparison of Tm:ZBLAN and Tm:silica fiber lasers; spectroscopy and tunable pulsed laser operation around 1.9 µm," Appl. Phys. B, Lasers Opt. 78, 325-333 (2004).
[CrossRef]

Y. H. Tsang, D. J. Coleman, and T. A. King, "High power 1.9 µm Tm3+-silica fibre laser pumped at 1.09 µm by a Yb3+-silica fibre laser," Opt. Commun. 231, 357-364 (2004).
[CrossRef]

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

S. D. Jackson, "Cross relaxation and energy transfer upconversion processes relevant to the functioning of 2 µm Tm3+-doped silica fibre lasers," Opt. Commun. 230, 197-203 (2004).
[CrossRef]

2003

2002

2001

F. C. Guinhos, P. C. Nobrega, and P. A. Santa-Cruz, "Compositional dependence of up-conversion process in Tm3+-Yb3+ codoped oxyfluoride glasses and glass-ceramics," J. Alloys Compd. 323-324, 358-361 (2001).
[CrossRef]

T. Kasamatsu, Y. Yano, and T. Ono, "Laser-diode-pumped highly efficient gain-shifted thulium-doped fiber amplifier operating in the 1480-1510-nm band," IEEE Photon. Technol. Lett. 13, 433-435 (2001).
[CrossRef]

2000

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

1997

1995

B. Peng, and T. Izumitani, "Blue, green and 0.8 µm Tm3+,Ho3+ doped upconversion laser glasses, sensitized by Yb3+," Opt. Mater. 4, 701-711 (1995).
[CrossRef]

1994

1990

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

A. S. L. Gomes, C. B. de Araujo, B. J. Ainslie, and S. P. Craig-Ryan, "Amplified spontaneous emission in Tm3+-doped monomode optical fibers in the visible region," Appl. Phys. Lett. 57, 2169-2171 (1990).
[CrossRef]

1971

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

1969

R. A. Hewes, "Infrared excitation processes for visible luminescence of Er3+, Ho3+, and Tm3+ in Yb3+-sensitized rare-earth trifluorides," Phys. Rev. 182, 427 (1969).
[CrossRef]

D. L. Dexter, T. Forster, and R. S. Knox, "Radiationless transfer of energy of electronic excitation between impurity molecules in crystals," Phys. Status Solidi 34, 159 (1969).
[CrossRef]

Ainslie, B. J.

A. S. L. Gomes, C. B. de Araujo, B. J. Ainslie, and S. P. Craig-Ryan, "Amplified spontaneous emission in Tm3+-doped monomode optical fibers in the visible region," Appl. Phys. Lett. 57, 2169-2171 (1990).
[CrossRef]

Aozasa, S.

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

Barnes, N. P.

B. M. Walsh, and N. P. Barnes, "Comparison of Tm:ZBLAN and Tm:silica fiber lasers; spectroscopy and tunable pulsed laser operation around 1.9 µm," Appl. Phys. B, Lasers Opt. 78, 325-333 (2004).
[CrossRef]

W. A. Clarkson, N. P. Barnes, P. W. Turner, J. Nilsson, and D. C. Hanna, "High-power cladding-pumped Tm-doped silica fiber laser with wavelength tuning from 1860 to 2090 nm," Opt. Lett. 27, 1989-1991 (2002).
[CrossRef]

Bastos, C. J. A.

Baxter, G. W.

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

Blanc, W.

B. Faure, W. Blanc, B. Dussardier and G. Monnom, "Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy," J. Non-Cryst. Solids 353, 2767-2773 (2007).
[CrossRef]

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

Buddhudu, S.

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

Carvalho, M. T.

Caspary, R.

R. Caspary, M. M. Kozak, D. Goebel, and W. Kowalsky, "Excited state absorption spectroscopy for thulium-doped zirconium fluoride fiber," Opt. Commun. 259, 154-157 (2006).
[CrossRef]

Clarkson, W. A.

W. A. Clarkson, N. P. Barnes, P. W. Turner, J. Nilsson, and D. C. Hanna, "High-power cladding-pumped Tm-doped silica fiber laser with wavelength tuning from 1860 to 2090 nm," Opt. Lett. 27, 1989-1991 (2002).
[CrossRef]

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

Coleman, D. J.

Y. H. Tsang, D. J. Coleman, and T. A. King, "High power 1.9 µm Tm3+-silica fibre laser pumped at 1.09 µm by a Yb3+-silica fibre laser," Opt. Commun. 231, 357-364 (2004).
[CrossRef]

Collins, S. F.

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

Craig-Ryan, S. P.

A. S. L. Gomes, C. B. de Araujo, B. J. Ainslie, and S. P. Craig-Ryan, "Amplified spontaneous emission in Tm3+-doped monomode optical fibers in the visible region," Appl. Phys. Lett. 57, 2169-2171 (1990).
[CrossRef]

Curley, M.

Dawei, F.

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

de Araujo, C. B.

A. S. L. Gomes, C. B. de Araujo, B. J. Ainslie, and S. P. Craig-Ryan, "Amplified spontaneous emission in Tm3+-doped monomode optical fibers in the visible region," Appl. Phys. Lett. 57, 2169-2171 (1990).
[CrossRef]

Dexter, D. L.

D. L. Dexter, T. Forster, and R. S. Knox, "Radiationless transfer of energy of electronic excitation between impurity molecules in crystals," Phys. Status Solidi 34, 159 (1969).
[CrossRef]

Dussardier, B.

B. Faure, W. Blanc, B. Dussardier and G. Monnom, "Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy," J. Non-Cryst. Solids 353, 2767-2773 (2007).
[CrossRef]

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

Faure, B.

B. Faure, W. Blanc, B. Dussardier and G. Monnom, "Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy," J. Non-Cryst. Solids 353, 2767-2773 (2007).
[CrossRef]

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

Forster, T.

D. L. Dexter, T. Forster, and R. S. Knox, "Radiationless transfer of energy of electronic excitation between impurity molecules in crystals," Phys. Status Solidi 34, 159 (1969).
[CrossRef]

Geusic, J. E.

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

Gibbs, W. E. K.

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

Goebel, D.

R. Caspary, M. M. Kozak, D. Goebel, and W. Kowalsky, "Excited state absorption spectroscopy for thulium-doped zirconium fluoride fiber," Opt. Commun. 259, 154-157 (2006).
[CrossRef]

Gomes, A. S. L.

A. S. L. Gomes, M. T. Carvalho, M. L. Sundheimer, C. J. A. Bastos, J. F. Martins, J. P. Von der Weid, W. Margulis, "Low-pump-power, short-fiber copropagating dual-pumped (800 and 1050 nm) thulium-doped fiber amplifier," Opt. Lett. 28, 334-336 (2003).
[CrossRef] [PubMed]

A. S. L. Gomes, C. B. de Araujo, B. J. Ainslie, and S. P. Craig-Ryan, "Amplified spontaneous emission in Tm3+-doped monomode optical fibers in the visible region," Appl. Phys. Lett. 57, 2169-2171 (1990).
[CrossRef]

Grudinin, A. B.

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

Guinhos, F. C.

F. C. Guinhos, P. C. Nobrega, and P. A. Santa-Cruz, "Compositional dependence of up-conversion process in Tm3+-Yb3+ codoped oxyfluoride glasses and glass-ceramics," J. Alloys Compd. 323-324, 358-361 (2001).
[CrossRef]

Hanna, D. C.

W. A. Clarkson, N. P. Barnes, P. W. Turner, J. Nilsson, and D. C. Hanna, "High-power cladding-pumped Tm-doped silica fiber laser with wavelength tuning from 1860 to 2090 nm," Opt. Lett. 27, 1989-1991 (2002).
[CrossRef]

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Hayashi, H.

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

Hayward, A.

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

Hewes, R. A.

R. A. Hewes, "Infrared excitation processes for visible luminescence of Er3+, Ho3+, and Tm3+ in Yb3+-sensitized rare-earth trifluorides," Phys. Rev. 182, 427 (1969).
[CrossRef]

Hongping, M.

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

Hoshino, K.

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

Izumitani, T.

B. Peng, and T. Izumitani, "Blue, green and 0.8 µm Tm3+,Ho3+ doped upconversion laser glasses, sensitized by Yb3+," Opt. Mater. 4, 701-711 (1995).
[CrossRef]

Jackson, S. D.

Jenssen, H. P.

Ji, X. H.

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

Jiang, Z. H.

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

Johnson, L. F.

Kanamori, T.

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

Karasek, M.

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

Kasamatsu, T.

T. Kasamatsu, Y. Yano, and T. Ono, "Laser-diode-pumped highly efficient gain-shifted thulium-doped fiber amplifier operating in the 1480-1510-nm band," IEEE Photon. Technol. Lett. 13, 433-435 (2001).
[CrossRef]

King, T. A.

Y. H. Tsang, D. J. Coleman, and T. A. King, "High power 1.9 µm Tm3+-silica fibre laser pumped at 1.09 µm by a Yb3+-silica fibre laser," Opt. Commun. 231, 357-364 (2004).
[CrossRef]

Knox, R. S.

D. L. Dexter, T. Forster, and R. S. Knox, "Radiationless transfer of energy of electronic excitation between impurity molecules in crystals," Phys. Status Solidi 34, 159 (1969).
[CrossRef]

Kobayashi, K.

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

Kowalsky, W.

R. Caspary, M. M. Kozak, D. Goebel, and W. Kowalsky, "Excited state absorption spectroscopy for thulium-doped zirconium fluoride fiber," Opt. Commun. 259, 154-157 (2006).
[CrossRef]

Kozak, M. M.

R. Caspary, M. M. Kozak, D. Goebel, and W. Kowalsky, "Excited state absorption spectroscopy for thulium-doped zirconium fluoride fiber," Opt. Commun. 259, 154-157 (2006).
[CrossRef]

Lahoz, F.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Li, T.

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

Lozano-Gorrin, A. D.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Marcos, H. M.

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

Margulis, W.

Martin, I. R.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Martins, J. F.

J. F. Martins, "Dual-wavelength (1050 nm plus 1550 nm) pumped thulium-doped fiber amplifier characterization by optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 15, 24-26 (2003).
[CrossRef]

A. S. L. Gomes, M. T. Carvalho, M. L. Sundheimer, C. J. A. Bastos, J. F. Martins, J. P. Von der Weid, W. Margulis, "Low-pump-power, short-fiber copropagating dual-pumped (800 and 1050 nm) thulium-doped fiber amplifier," Opt. Lett. 28, 334-336 (2003).
[CrossRef] [PubMed]

Mendez-Ramos, J.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Monnom, G.

B. Faure, W. Blanc, B. Dussardier and G. Monnom, "Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy," J. Non-Cryst. Solids 353, 2767-2773 (2007).
[CrossRef]

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

Mossman, S.

Nilsson, J.

W. A. Clarkson, N. P. Barnes, P. W. Turner, J. Nilsson, and D. C. Hanna, "High-power cladding-pumped Tm-doped silica fiber laser with wavelength tuning from 1860 to 2090 nm," Opt. Lett. 27, 1989-1991 (2002).
[CrossRef]

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Nobrega, P. C.

F. C. Guinhos, P. C. Nobrega, and P. A. Santa-Cruz, "Compositional dependence of up-conversion process in Tm3+-Yb3+ codoped oxyfluoride glasses and glass-ceramics," J. Alloys Compd. 323-324, 358-361 (2001).
[CrossRef]

Noginov, M. A.

Ohara, S.

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

Ono, T.

T. Kasamatsu, Y. Yano, and T. Ono, "Laser-diode-pumped highly efficient gain-shifted thulium-doped fiber amplifier operating in the 1480-1510-nm band," IEEE Photon. Technol. Lett. 13, 433-435 (2001).
[CrossRef]

Ostermayer, F. W.

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Peng, B.

B. Peng, and T. Izumitani, "Blue, green and 0.8 µm Tm3+,Ho3+ doped upconversion laser glasses, sensitized by Yb3+," Opt. Mater. 4, 701-711 (1995).
[CrossRef]

Percival, R. M.

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Perry, I. R.

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Peterka, P.

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

Rodriguez, V. D.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Sakamoto, T.

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

Santa-Cruz, P. A.

F. C. Guinhos, P. C. Nobrega, and P. A. Santa-Cruz, "Compositional dependence of up-conversion process in Tm3+-Yb3+ codoped oxyfluoride glasses and glass-ceramics," J. Alloys Compd. 323-324, 358-361 (2001).
[CrossRef]

Shimizu, M.

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

Shiqing, X.

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

Simpson, D. A.

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

Smart, R. G.

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Soria, A. B.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Sugimoto, N.

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

Sundheimer, M. L.

Tamaoka, T.

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

Tanabe, S.

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

Thrash, R. J.

Townsend, J. E.

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Tropper, A. C.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Tsang, Y. H.

Y. H. Tsang, D. J. Coleman, and T. A. King, "High power 1.9 µm Tm3+-silica fibre laser pumped at 1.09 µm by a Yb3+-silica fibre laser," Opt. Commun. 231, 357-364 (2004).
[CrossRef]

Turner, P. W.

W. A. Clarkson, N. P. Barnes, P. W. Turner, J. Nilsson, and D. C. Hanna, "High-power cladding-pumped Tm-doped silica fiber laser with wavelength tuning from 1860 to 2090 nm," Opt. Lett. 27, 1989-1991 (2002).
[CrossRef]

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

Uitert, L. G.

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

van der Ziel, J. P.

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

Venkateswarlu, P.

Von der Weid, J. P.

Walsh, B. M.

B. M. Walsh, and N. P. Barnes, "Comparison of Tm:ZBLAN and Tm:silica fiber lasers; spectroscopy and tunable pulsed laser operation around 1.9 µm," Appl. Phys. B, Lasers Opt. 78, 325-333 (2004).
[CrossRef]

Williams, A.

Yano, Y.

T. Kasamatsu, Y. Yano, and T. Ono, "Laser-diode-pumped highly efficient gain-shifted thulium-doped fiber amplifier operating in the 1480-1510-nm band," IEEE Photon. Technol. Lett. 13, 433-435 (2001).
[CrossRef]

Zaixuan, Z.

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

Zhang, Q. Y.

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

Zhonghong, J.

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

Appl. Opt.

Appl. Phys. B

B. M. Walsh, and N. P. Barnes, "Comparison of Tm:ZBLAN and Tm:silica fiber lasers; spectroscopy and tunable pulsed laser operation around 1.9 µm," Appl. Phys. B, Lasers Opt. 78, 325-333 (2004).
[CrossRef]

Appl. Phys. Lett.

Q. Y. Zhang, T. Li, Z. H. Jiang, X. H. Ji, and S. Buddhudu, "980 nm laser-diode-excited intense blue upconversion in Tm3+/Yb3+-codoped gallate-bismuth-lead glasses," Appl. Phys. Lett. 87, 171911-171913 (2005).
[CrossRef]

A. S. L. Gomes, C. B. de Araujo, B. J. Ainslie, and S. P. Craig-Ryan, "Amplified spontaneous emission in Tm3+-doped monomode optical fibers in the visible region," Appl. Phys. Lett. 57, 2169-2171 (1990).
[CrossRef]

Electron. Lett.

A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, "Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm," Electron. Lett. 36, 711-712 (2000).
[CrossRef]

IEEE J. Quantum Electron.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Kasamatsu, Y. Yano, and T. Ono, "Laser-diode-pumped highly efficient gain-shifted thulium-doped fiber amplifier operating in the 1480-1510-nm band," IEEE Photon. Technol. Lett. 13, 433-435 (2001).
[CrossRef]

S. Aozasa, T. Sakamoto, T. Kanamori, K. Hoshino, K. Kobayashi, and M. Shimizu, "Tm-doped fiber amplifiers for 1470-nm-band WDM signals," IEEE Photon. Technol. Lett. 12, 1331-1333 (2000).
[CrossRef]

J. F. Martins, "Dual-wavelength (1050 nm plus 1550 nm) pumped thulium-doped fiber amplifier characterization by optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 15, 24-26 (2003).
[CrossRef]

J. Alloys Compd.

T. Tamaoka, S. Tanabe, S. Ohara, H. Hayashi, and N. Sugimoto, "Fabrication and blue upconversion characteristics of Tm-doped tellurite fiber for S-band amplifier," J. Alloys Compd. 408, 848-851 (2006).
[CrossRef]

F. C. Guinhos, P. C. Nobrega, and P. A. Santa-Cruz, "Compositional dependence of up-conversion process in Tm3+-Yb3+ codoped oxyfluoride glasses and glass-ceramics," J. Alloys Compd. 323-324, 358-361 (2001).
[CrossRef]

J. Lumin.

X. Shiqing, M. Hongping, F. Dawei, Z. Zaixuan, and J. Zhonghong, "Upconversion luminescence and mechanisms in Yb3+-sensitized Tm3+-doped oxyhalide tellurite glasses," J. Lumin. 117, 135-140 (2006).
[CrossRef]

J. Non-Cryst. Solids

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, "Energy transfer up-conversion in Tm3+-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
[CrossRef]

B. Faure, W. Blanc, B. Dussardier and G. Monnom, "Improvement of the Tm3+:3H4 level lifetime in silica optical fibers by lowering the local phonon energy," J. Non-Cryst. Solids 353, 2767-2773 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Mol. Phys.

J. Mendez-Ramos, F. Lahoz, I. R. Martin, A. B. Soria, A. D. Lozano-Gorrin, and V. D. Rodriguez, "Optical properties and upconversion in Yb3+-Tm3+/ co-doped oxyfluoride glasses and glass ceramics," Mol. Phys. 101, 1057-1065 (2003).
[CrossRef]

Opt. Commun.

R. Caspary, M. M. Kozak, D. Goebel, and W. Kowalsky, "Excited state absorption spectroscopy for thulium-doped zirconium fluoride fiber," Opt. Commun. 259, 154-157 (2006).
[CrossRef]

Y. H. Tsang, D. J. Coleman, and T. A. King, "High power 1.9 µm Tm3+-silica fibre laser pumped at 1.09 µm by a Yb3+-silica fibre laser," Opt. Commun. 231, 357-364 (2004).
[CrossRef]

S. D. Jackson, "Cross relaxation and energy transfer upconversion processes relevant to the functioning of 2 µm Tm3+-doped silica fibre lasers," Opt. Commun. 230, 197-203 (2004).
[CrossRef]

D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, and A. C. Tropper, "Frequency upconversion in Tm- and Yb:Tm-doped silica fibers," Opt. Commun. 78, 187-194 (1990).
[CrossRef]

Opt. Lett.

Opt. Mater.

B. Peng, and T. Izumitani, "Blue, green and 0.8 µm Tm3+,Ho3+ doped upconversion laser glasses, sensitized by Yb3+," Opt. Mater. 4, 701-711 (1995).
[CrossRef]

Opt. Quantum Electron.

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, "Theoretical modelling of S-band thulium-doped silica fibre amplifiers," Opt. Quantum Electron. 36, 201-212 (2004).
[CrossRef]

Phys. Rev.

R. A. Hewes, "Infrared excitation processes for visible luminescence of Er3+, Ho3+, and Tm3+ in Yb3+-sensitized rare-earth trifluorides," Phys. Rev. 182, 427 (1969).
[CrossRef]

Phys. Rev. B

F. W. Ostermayer, J. P. van der Ziel, H. M. Marcos, L. G. Uitert, and J. E. Geusic, "Frequency upconversion in YF3:Yb3+,Tm3+," Phys. Rev. B,  3, 2698-2705 (1971).
[CrossRef]

Phys. Status Solidi

D. L. Dexter, T. Forster, and R. S. Knox, "Radiationless transfer of energy of electronic excitation between impurity molecules in crystals," Phys. Status Solidi 34, 159 (1969).
[CrossRef]

Other

D. A. Simpson, "Spectroscopy of thulium doped silica glass," (Victoria University, Melbourne, 2008).

F. Yan, C. Xiaobo, S. Feng, L. Kun, and Z. Guangyin, "Upconversion luminescence of ZBLAN:Tm3+,Yb3+ glass pumped by a ~970 nm LD and its concentration effect," Proc. SPIE 116-120 (1998).

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Figures (12)

Fig. 1.
Fig. 1.

Double energy transfer mechanism between Tm3+ and Yb3+ ions, under 980 nm excitation.

Fig. 2.
Fig. 2.

Counter-propagating luminescence spectra of the Tm3+/Yb3+ co-doped fiber samples, under 980 nm excitation. Note: sample lengths were all kept to 20 cm and the incident pump power in each case was 128 mW.

Fig. 3.
Fig. 3.

Log/log plot of the 1800 nm luminescence from Tm3+ vs. the 1060 nm luminescence from Yb3+, for incident pump powers ranging from 3–108 mW. The 1800 nm measured data have been offset to aid comparison. Note: the errors associated with these measurements are not shown as they are smaller than the size of the individual data points in the plot.

Fig. 4.
Fig. 4.

Energy manifold labeling for the rate equation analysis of the Tm3+/Yb3+ co-doped system.

Fig. 5.
Fig. 5.

Log/log plot of the 475 nm luminescence from Tm3+ vs. the 1060 nm luminescence from Yb3+, for incident pump powers ranging from 3–108 mW. The 475 nm measured data have been offset to aid comparison. Note: the errors associated with these measurements are not shown as they are smaller than the size of the individual data points presented in the plot. The fits to the data are discussed in the text.

Fig. 6.
Fig. 6.

Spectral overlap of the Yb3+ fluorescence from the 2F5/22F7/2 transition with the calculated ESA transitions of Tm3+ [26]. Note: the Yb3+ fluorescence spectrum of the TmYb-1 sample was measured under 980 nm excitation.

Fig. 7.
Fig. 7.

Log/log plot of the 475 nm luminescence from Tm3+ vs. the 1060 nm luminescence from Yb3+, for incident pump powers ranging from 3–108 mW. The data were fitted with Eq. (13).

Fig. 8.
Fig. 8.

Log/log plot of the 810 nm luminescence from Tm3+ vs. the 1060 nm luminescence from Yb3+, for incident pump powers ranging from 3–108 mW. The 810 nm measured data have been offset to aid comparison. The solid lines represent the fit of a standard quadratic equation to the measured data.

Fig. 9.
Fig. 9.

Semi-log plot of the normalised 1060 ± 10 nm fluorescence decay waveform from the 2F5/2 manifold of sample TmYb-1 under 980 nm pulsed excitation.

Fig. 10.
Fig. 10.

Semi-log plot of the normalised fluorescence decay waveform from the 3F4 manifold of sample TmYb-3 under 980 nm excitation.

Fig. 11.
Fig. 11.

Semi-log plot of the normalised fluorescence decay from the 1G4 manifold under 980 nm excitation for sample TmYb-1. Note: decay waveforms were recorded using 50 ms pulses at a repetition rate of 10 Hz.

Fig. 12.
Fig. 12.

Semi-log plot of the normalised fluorescence decay at 810 nm under 980 nm excitation for sample TmYb-1. Note: decay waveforms were recorded using 50 ms pulses at a repetition rate of 10 Hz. The double exponential fit is discussed in the text.

Tables (8)

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Table 1. Core dopants of the Tm3+/Yb3+ co-doped silica fibers.

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Table 2. Experimental configuration for the measurement of fluorescence from the excited manifolds of Tm3+ and Yb3+.

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Table 3. Parameters obtained by fitting the steady state rate equation model to the 475 vs. 1060 nm luminescence data.

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Table 4. Fluorescence lifetimes of the 2F5/2 manifold under 980 nm excitation with an incident pump power of 9.3 mW.

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Table 5. Fluorescence lifetimes of the 3F4 and 3H4 manifolds under direct excitation at 1586 and 780 nm, respectively. Where τ1/e represents the lifetime obtained from the single exponential fit. Note: 30 µs pulses at 10 Hz were used for direct excitation of the 3F4 manifold, whilst 3 µs pulses at a repetition rate of 10 Hz were used to excite the 3H4 manifold directly.

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Table 6. Fluorescence lifetime of the 3F4 manifold under in-direct excitation at 980 nm. Note: 50 ms pulses at 10 Hz were used to excite the 3F4 manifold in-directly. The fluorescence lifetimes of the 3F4 and 2F5/2 manifolds under direct excitation at 1586 and 980 nm, respectively, are shown for comparison.Fluorescence lifetime of the 3F4 manifold under in-direct excitation at 980 nm. Note: 50 ms pulses at 10 Hz were used to excite the 3F4 manifold in-directly. The fluorescence lifetimes of the 3F4 and 2F5/2 manifolds under direct excitation at 1586 and 980 nm, respectively, are shown for comparison.

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Table 7. Fluorescence lifetime of the 1G4 manifold under in-direct excitation at 980 nm. Note: 50 ms pulses at 10 Hz were used to excite the 3F4 manifold.

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Table 8. Amplitude and characteristic lifetimes obtained from the double exponential fit of the 810 nm fluorescence decay for all three samples under in-direct pumping at 980 nm.

Equations (15)

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dN Y 1 dt = I σ Y 01 N Y 0 N Y 1 τ Y 1 ,
dN T 1 dt = W 1 N Y 1 N T 0 N T 1 τ T 1 W 2 N T 1 N T 1 ,
N Y 0 + N Y 1 = c Y ,
N T 0 + N T 1 + N T 2 + N T 3 = c T ,
N T 1 = W 1 N Y 1 c T τ T 1 1 + W 2 N Y 1 .
dN T 2 dt = W 2 N Y 1 N T 1 N T 2 τ T 2 W 3 N T 2 N Y 1 ,
dN T 3 dt = W 3 N Y 1 N T 2 N T 3 τ T 3 .
N T 2 = W 1 W 2 N Y 1 c T 2 τ T 1 τ T 2 1 + W 3 N Y 1 ,
N T 3 = W 1 W 2 W 3 N Y 1 c T 3 τ T 1 τ T 3 τ T 2 1 + W 3 N Y 1 .
N T 2 = W 1 W 2 N Y 1 c T 2 τ T 1 τ T 2 ,
N T 3 = W 1 W 2 W 3 N Y 1 c T 3 τ T 1 τ T 2 τ T 3 .
dN T 2 dt = I σ T 12 N T 1 + W 2 N Y 1 N T 1 N T 2 τ T 2 .
N T 3 = W 1 W 2 W 3 N Y 1 c T 3 τ T 1 τ T 2 τ T 3 + W 1 W 2 c T σ T 12 τ T 1 τ T 2 τ T 3 N Y 1 3 τ Y 1 σ Y 01 ( c Y N Y 1 ) .
dN T 3 ( t ) dt = W 3 N Y 1 ( t ) N T 2 ( t ) N T 3 τ T 3
N T 3 ( t ) = N T 3 ( 0 ) exp ( t τ T 3 )

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