Abstract

A 3-dimenstional (3D) heat flow model of laser diode (LD) pumped short-length Er3+/Yb3+ heavily co-doped phosphate fiber laser that includes the energy-transfer upconversion (ETU) effects has been developed. The fully 3D analytical solution with the consideration of longitudinal heat flow has been given to describe the temperature distribution in phosphate fiber. The calculated results show that both ETU processes and longitudinal heat conduction have a great influence on the fiber laser performance. Finally, we have validated the analytical expression by measuring the temperature distribution of an end-pumped short-length Er3+/Yb3+ co-doped fiber laser, which was placed into the copper tube.

© 2009 Optical Society of America

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  1. J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
    [CrossRef]
  2. P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
    [CrossRef]
  3. J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
    [CrossRef]
  4. W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
    [CrossRef]
  5. V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
    [CrossRef]
  6. M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
    [CrossRef]
  7. M. Pollnau, "Analysis of Heat Generation and Thermal Lensing in Erbium 3-?m Lasers," IEEE J. Quantum. Electron. 39, 350-357 (2003)
    [CrossRef]
  8. D. C. Brown and H. J. Hoffman, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum. Electron. 37, 207-217 (2001).
    [CrossRef]
  9. P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
    [CrossRef]
  10. L. Li, H. Li, T. Qiu, V. L. Temyanko, M. M. Morrell, and A. Schulzgen, "3-Dimensional thermal analysis and active cooling of short-length high-power fiber lasers," Opt. Express 13, 3420-3428 (2005).
    [CrossRef] [PubMed]
  11. X. Huai and Z. G. Li, "Thermal stress analysis of Nd:YVO4 laser medium end pumped by a Gaussian beam," Appl. Phys. Lett. 92, 1121-1122 (2008).
    [CrossRef]
  12. M. Sabaeian, H. Nadgaran, and L. Mousave, "Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser," Appl. Opt. 47, 2317-2325 (2008).
    [CrossRef] [PubMed]
  13. F. Song, S. Liu, Z. H. Wu, H. Cai, X. Zhang, L. Teng, and J. G. Tian, "Determination of the thermal loading in laser-diode-pumped erbium-ytterbium-codoped phosphate glass microchip laser, " J. Opt. Soc. Am. B 24, 2327-2332 (2007)
    [CrossRef]
  14. S. Bjurshagen, J. E. Hellstrom, V. Pasiskevicius, M. C. Pujol, M. Aguilo, and F. Díaz, "Fluorescence dynamics and rate equation analysis in Er3+ and Yb3+ doped double tungstates, " Appl. Opt. 45, 4715-4725 (2006)
    [CrossRef] [PubMed]
  15. F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
    [CrossRef]
  16. G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
    [CrossRef]
  17. Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)
  18. M. Karasek, "Optimum design of Er3+-Yb3+ co-doped fibers for large-signal high-pump-power applications," IEEE J. Quantum. Electron. 33, 1699-1705 (1997).
    [CrossRef]
  19. D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
    [CrossRef]
  20. C. E. Chryssou, F. D. Pasquale, and C. W. Pitt, "Improved gain performance in Yb3+-sensitized Er3+-doped alumina (Al2O3) channel optical waveguide amplifiers," J. Lightwave Technol. 19, 345-349 (2001).
    [CrossRef]
  21. I. Kelson and A. A. Hardy, "Strongly Pumped Fiber Lasers," IEEE J. Quantum. Electron. 34, 1570-1577 (1998).
    [CrossRef]
  22. Y. Wang, C. Q. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
    [CrossRef]
  23. S. Bjurshagen and R. Koch, "Modeling of energy-transfer upconversion and thermal effects in end-pumped quasi-three-level lasers," Appl. Opt. 43, 4753-4767 (2004).
    [CrossRef] [PubMed]
  24. Y. P. Lan, Y. F. Chen, and S. C. Wang, "Repetition-rate dependence of thermal loading in diode-end-pumped Q-switched lasers: influence of energy-transfer upconversion," Appl. Phys. B 71, 27-31 (2000).
  25. 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]
  26. S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
    [CrossRef]

2008 (4)

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

X. Huai and Z. G. Li, "Thermal stress analysis of Nd:YVO4 laser medium end pumped by a Gaussian beam," Appl. Phys. Lett. 92, 1121-1122 (2008).
[CrossRef]

M. Sabaeian, H. Nadgaran, and L. Mousave, "Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser," Appl. Opt. 47, 2317-2325 (2008).
[CrossRef] [PubMed]

2007 (2)

F. Song, S. Liu, Z. H. Wu, H. Cai, X. Zhang, L. Teng, and J. G. Tian, "Determination of the thermal loading in laser-diode-pumped erbium-ytterbium-codoped phosphate glass microchip laser, " J. Opt. Soc. Am. B 24, 2327-2332 (2007)
[CrossRef]

P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
[CrossRef]

2006 (1)

2005 (2)

L. Li, H. Li, T. Qiu, V. L. Temyanko, M. M. Morrell, and A. Schulzgen, "3-Dimensional thermal analysis and active cooling of short-length high-power fiber lasers," Opt. Express 13, 3420-3428 (2005).
[CrossRef] [PubMed]

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

2004 (2)

Y. Wang, C. Q. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

S. Bjurshagen and R. Koch, "Modeling of energy-transfer upconversion and thermal effects in end-pumped quasi-three-level lasers," Appl. Opt. 43, 4753-4767 (2004).
[CrossRef] [PubMed]

2003 (2)

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

M. Pollnau, "Analysis of Heat Generation and Thermal Lensing in Erbium 3-?m Lasers," IEEE J. Quantum. Electron. 39, 350-357 (2003)
[CrossRef]

2002 (1)

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

2001 (3)

D. C. Brown and H. J. Hoffman, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum. Electron. 37, 207-217 (2001).
[CrossRef]

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

C. E. Chryssou, F. D. Pasquale, and C. W. Pitt, "Improved gain performance in Yb3+-sensitized Er3+-doped alumina (Al2O3) channel optical waveguide amplifiers," J. Lightwave Technol. 19, 345-349 (2001).
[CrossRef]

2000 (2)

Y. P. Lan, Y. F. Chen, and S. C. Wang, "Repetition-rate dependence of thermal loading in diode-end-pumped Q-switched lasers: influence of energy-transfer upconversion," Appl. Phys. B 71, 27-31 (2000).

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

1999 (1)

S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
[CrossRef]

1998 (2)

I. Kelson and A. A. Hardy, "Strongly Pumped Fiber Lasers," IEEE J. Quantum. Electron. 34, 1570-1577 (1998).
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

1997 (2)

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]

M. Karasek, "Optimum design of Er3+-Yb3+ co-doped fibers for large-signal high-pump-power applications," IEEE J. Quantum. Electron. 33, 1699-1705 (1997).
[CrossRef]

1993 (1)

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

1989 (1)

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Aguilo, M.

Archambault, J. L.

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

Ballato, J.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Barnes, W. L.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Bass, M.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Bjurshagen, S.

Brown, D. C.

D. C. Brown and H. J. Hoffman, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum. Electron. 37, 207-217 (2001).
[CrossRef]

Cai, H.

Chen, M.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Chen, T.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Chen, Y.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Chen, Y. F.

Y. P. Lan, Y. F. Chen, and S. C. Wang, "Repetition-rate dependence of thermal loading in diode-end-pumped Q-switched lasers: influence of energy-transfer upconversion," Appl. Phys. B 71, 27-31 (2000).

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]

Chryssou, C. E.

Clarkson, W. A.

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

Denker, B.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Díaz, F.

Driver, J.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Fontaine, N.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Funk, D. S.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Galagan, B.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Hanna, D. C.

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

Hardman, P. J.

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

Hardy, A. A.

I. Kelson and A. A. Hardy, "Strongly Pumped Fiber Lasers," IEEE J. Quantum. Electron. 34, 1570-1577 (1998).
[CrossRef]

Hardy, C.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Hayden, J. S.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Hellstrom, J. E.

Hoffman, H. J.

D. C. Brown and H. J. Hoffman, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum. Electron. 37, 207-217 (2001).
[CrossRef]

Huai, X.

X. Huai and Z. G. Li, "Thermal stress analysis of Nd:YVO4 laser medium end pumped by a Gaussian beam," Appl. Phys. Lett. 92, 1121-1122 (2008).
[CrossRef]

Jiang, D. S.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Karasek, M.

M. Karasek, "Optimum design of Er3+-Yb3+ co-doped fibers for large-signal high-pump-power applications," IEEE J. Quantum. Electron. 33, 1699-1705 (1997).
[CrossRef]

Karlsson, G.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Kelson, I.

I. Kelson and A. A. Hardy, "Strongly Pumped Fiber Lasers," IEEE J. Quantum. Electron. 34, 1570-1577 (1998).
[CrossRef]

Kern, M. A.

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

Koch, R.

Kringlebotn, J. T.

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

Lan, Y. P.

Y. P. Lan, Y. F. Chen, and S. C. Wang, "Repetition-rate dependence of thermal loading in diode-end-pumped Q-switched lasers: influence of energy-transfer upconversion," Appl. Phys. B 71, 27-31 (2000).

Laporta, P.

S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
[CrossRef]

Laurell, F.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Li, G.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Li, H.

Li, L.

Li, P. X.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Li, Z. G.

X. Huai and Z. G. Li, "Thermal stress analysis of Nd:YVO4 laser medium end pumped by a Gaussian beam," Appl. Phys. Lett. 92, 1121-1122 (2008).
[CrossRef]

Liu, S.

Liu, S. J.

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Liu, W. C.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Longhi, S.

S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
[CrossRef]

Mayers, J.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Mccomb, T.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Meng, F.

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

Moloney, J.

P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
[CrossRef]

Morkel, P. R.

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

Morrell, M. M.

Mousave, L.

Myers, M.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

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]

Nadgaran, H.

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]

Obarski, G. E.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Osiko, V.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Pasiskevicius, V.

Pasquale, F. D.

Payne, D. N.

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Peskin, A. P.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Peters, P. M.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Peyghambarian, N.

P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
[CrossRef]

Pitt, C. W.

Po, H.

Y. Wang, C. Q. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Pollnau, M.

M. Pollnau, "Analysis of Heat Generation and Thermal Lensing in Erbium 3-?m Lasers," IEEE J. Quantum. Electron. 39, 350-357 (2003)
[CrossRef]

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

Polynkin, P.

P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
[CrossRef]

Poole, S. B.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Pujol, M. C.

Qin, B.

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Qiu, T.

Reekie, L.

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Richardson, M.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Sabaeian, M.

Sanford, N. A.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Schulzgen, A.

Shang, M. R.

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

Siegman, A. E.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Song, F.

F. Song, S. Liu, Z. H. Wu, H. Cai, X. Zhang, L. Teng, and J. G. Tian, "Determination of the thermal loading in laser-diode-pumped erbium-ytterbium-codoped phosphate glass microchip laser, " J. Opt. Soc. Am. B 24, 2327-2332 (2007)
[CrossRef]

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

Sorbello, G.

S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
[CrossRef]

Su, J.

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Sudesh, V.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Sverchkov, S.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Taccheo, S.

S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
[CrossRef]

Tan, H.

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

Tate, R.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Taylor, D. J.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Tellefsen, J.

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Temyanko, V.

P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
[CrossRef]

Temyanko, V. L.

Teng, L.

Tian, J. G.

F. Song, S. Liu, Z. H. Wu, H. Cai, X. Zhang, L. Teng, and J. G. Tian, "Determination of the thermal loading in laser-diode-pumped erbium-ytterbium-codoped phosphate glass microchip laser, " J. Opt. Soc. Am. B 24, 2327-2332 (2007)
[CrossRef]

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Townsend, J. E.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

Veasey, D. L.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Walter, S.N. H.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Wang, S. C.

Y. P. Lan, Y. F. Chen, and S. C. Wang, "Repetition-rate dependence of thermal loading in diode-end-pumped Q-switched lasers: influence of energy-transfer upconversion," Appl. Phys. B 71, 27-31 (2000).

Wang, Y.

Y. Wang, C. Q. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Wu, R.

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Wu, Z. H.

F. Song, S. Liu, Z. H. Wu, H. Cai, X. Zhang, L. Teng, and J. G. Tian, "Determination of the thermal loading in laser-diode-pumped erbium-ytterbium-codoped phosphate glass microchip laser, " J. Opt. Soc. Am. B 24, 2327-2332 (2007)
[CrossRef]

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Xu, C. Q.

Y. Wang, C. Q. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Yang, J.

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

Young, M.

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

Zhang, D. Y.

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Zhang, G. Y.

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

Zhang, X.

Zhao, H.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Zhu, C.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Zou, S. Z.

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Acta Phys. Sin. (1)

Z. H. Wu, F. Song, S. J. Liu, B. Qin, J. Su, J. G. Tian, and D. Y. Zhang, "Er3+, Yb3+ co-doped phosphate glass lasers, " Acta Phys. Sin. 54, 5637-5641 (2005)

Appl. Opt. (3)

Appl. Phys. B (3)

G. Karlsson, F. Laurell, J. Tellefsen, B. Denker, B. Galagan, V. Osiko, and S. Sverchkov, "Development and characterization of Yb-Er laser glass for high average power laser diode pumping," Appl. Phys. B 75, 41-46 (2002)
[CrossRef]

Y. P. Lan, Y. F. Chen, and S. C. Wang, "Repetition-rate dependence of thermal loading in diode-end-pumped Q-switched lasers: influence of energy-transfer upconversion," Appl. Phys. B 71, 27-31 (2000).

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, "Diode-pumped 200?m diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008)
[CrossRef]

Appl. Phys. Lett. (3)

P. Polynkin, V. Temyanko, J. Moloney, and N. Peyghambarian, "Dramatic change of guiding properties in heavily Yb-doped, soft-glass active fibers caused by optical pumping," Appl. Phys. Lett. 90, 2411061-2411063 (2007).
[CrossRef]

X. Huai and Z. G. Li, "Thermal stress analysis of Nd:YVO4 laser medium end pumped by a Gaussian beam," Appl. Phys. Lett. 92, 1121-1122 (2008).
[CrossRef]

F. Song, G. Y. Zhang, M. R. Shang, H. Tan, J. Yang, and F. Meng, "Three-photon phenomena in the upconversion luminescence of erbirum-ytterbium-codoped phosphate glass," Appl. Phys. Lett. 79, 1748-1750 (2001)
[CrossRef]

IEEE J. Lightwave Technol. (2)

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]

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, "Er3+-Yb3+ and Er3+ doped fiber lasers," IEEE J. Lightwave Technol. 7, 1461-1465 (1989).
[CrossRef]

IEEE J. Quantum. Electron. (4)

M. Pollnau, "Analysis of Heat Generation and Thermal Lensing in Erbium 3-?m Lasers," IEEE J. Quantum. Electron. 39, 350-357 (2003)
[CrossRef]

D. C. Brown and H. J. Hoffman, "Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers," IEEE J. Quantum. Electron. 37, 207-217 (2001).
[CrossRef]

I. Kelson and A. A. Hardy, "Strongly Pumped Fiber Lasers," IEEE J. Quantum. Electron. 34, 1570-1577 (1998).
[CrossRef]

M. Karasek, "Optimum design of Er3+-Yb3+ co-doped fibers for large-signal high-pump-power applications," IEEE J. Quantum. Electron. 33, 1699-1705 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. T. Kringlebotn, P. R. Morkel, L. Reekie, J. L. Archambault, and D. N. Payne, "Efficient diode-pumped single frequency erbium: ytterbium fiber laser," IEEE Photon. Technol. Lett. 5, 1162-1164 (1993).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

Y. Wang, C. Q. Xu, and H. Po, "Analysis of Raman and thermal effects in kilowatt fiber lasers," Opt. Commun. 242, 487-502 (2004).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

P. X. Li, C. Zhu, S. Z. Zou, H. Zhao, D. S. Jiang, G. Li, and M. Chen, "Theoretical and experimental investigation of thermal effects in a high power Yb3+-doped double-clad fiber laser," Opt. Laser Technol. 40, 360-364 (2008).
[CrossRef]

Opt. Quantum Electron. (1)

S. Taccheo, G. Sorbello, S. Longhi, and P. Laporta, "Measurement of the energy transfer and upconversion constants in Er-Yb-doped phosphate glass," Opt. Quantum Electron. 31, 249-262 (1999).
[CrossRef]

Phys. Rev. B (1)

M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, and D. C. Hanna, "Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG," Phys. Rev. B 58, 16076-16092,1998
[CrossRef]

Proc. SPIE (1)

J. Mayers, R. Wu, T. Chen, M. Myers, C. Hardy, J. Driver, and R. Tate, "New high-power rare-earth-doped fiber laser materials and architectures," Proc. SPIE 4974, 177-183 (2003)
[CrossRef]

Silids (1)

D. L. Veasey, D. S. Funk, P. M. Peters, N. A. Sanford, G. E. Obarski, N. Fontaine, M. Young, A. P. Peskin,W. C. Liu, S.N. H. Walter, and J. S. Hayden, " Yb/Er-codoped and Yb-doped waveguide lasers in phosphate glass," J. Non-Cryst.Silids 263, 369-381 (2000)
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

Energy-level scheme of the Er3+/Yb3+ co-doped system including ETU processes: UC1, UC2, cumulative upconversion; UC3, cooperative upconversion; M, multiphonon relaxation; F, fluorescence process; L, 1535 nm laser emission.

Fig. 2.
Fig. 2.

Schematic illustration of phosphate fiber laser

Fig. 3.
Fig. 3.

Pump and signal powers as a function of the position along the fiber length: (a) pump power along the fiber length; (b) signal power in positive and negative directions along the fiber length.

Fig. 4.
Fig. 4.

The theoretical calculation and experimental results on signal laser output versus pump power. The best fit parameters k1, k2, and Cup are 2.56×10-22 m3 s-1 , 0.85×10-22 m3 s-1, 1.67×10-24 m3 s-1, respectively.

Fig. 5.
Fig. 5.

Temperature field distribution in phosphate fiber

Fig. 6.
Fig. 6.

The end-surface temperature distribution along active fiber radial coordinate: (a) without considering longitudinal heat conduction; (b) with longitudinal heat conduction.

Fig. 7.
Fig. 7.

The end-surface temperature distribution along radial coordinate when the pump power is 100 mW: (a) with upconversion; (b) without upconversion.

Fig. 8.
Fig. 8.

The maximum temperatures in active fiber core vs. pump power with and without considering ETU.

Fig. 9.
Fig. 9.

The fractional thermal loading at different pump powers.

Fig. 10.
Fig. 10.

The fiber cross-section inside the tube

Fig. 11.
Fig. 11.

The signal vs. absorbed pump power plot

Fig. 12.
Fig. 12.

The inner surface temperature of the copper tube at different pump power.

Fig. 13.
Fig. 13.

Calculated values vs. experimental values at different pump power.

Tables (2)

Tables Icon

Table 1. The related parameters used in this paper

Tables Icon

Table 2. Nonradiative transition rate and total spontaneous radiative transitions rate of Er3+ upconversion levels

Equations (61)

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

UC1:Yb3+(F522)+Er3+(I1124)Yb3+(F722)+Er3+(F724)
UC2:Yb3+(F522)+Er3+(I1324)Yb3+(F722)+Er3+(F924)
UC3:Er3+(I1324)+Er3+(I1324)Er3+(I1524)+Er3+(I924)
N2yt=W12yN1yW21yN2yN2yτyk1N2yN1ek2N2yN2e=0
N2et=W12eN1e+A32eN3eW21eN2ek2N2eN2yN2eτe2CupN2e2=0
N3et=k1N1eN2y+A43eN4eA32eN3e=0
N4et=CupN2e2A43eN4e=0
NEr=N1e+N2e+N3e+N4e
NYb=N1y+N2y
W12ezt=Γsσas(υs)Ps(z)hυsAcoreW21ezt=Γsσes(υs)Ps(z)hυsAcore
W12yzt=Γpσap(υp)Pp(z)hυpAcoreW21yzt=Γpσep(υp)Pp(z)hυpAcore
1rr[rTrzr]+2Trzz2=Qrzk,0rr1
1rr[rTrzr]+2Trzz2=0,r1rr2
kTrzr=c[TcTrz],r=r2
T1=T2,T1r=T2r,r=r1
Trzz=0,z=0,z=L
Qrz=2(αaη+αps)[Pp+(z)+Pp(z)]+2αs[Ps+(z)+Ps(z)]πωp2exp(2r2ωp2)
T1rz=Tc+C0lnr1+D0+n=1m=1Anmcos(Lz)J0(μn(0)r1r)+m=1[CmI0(Lr1)+DmK0(Lr1)]cos(Lz)
T2rz=Tc+C0lnr+D0+m=1[CmI0(Lr)+DmK0(Lr)]cos(Lz)
kC0r2=c(C0lnr2+D0),C0r1=n=1An0μn(0)r1 J1 (μn(0))
k(L)[CmI1(Lr2)DmK1(Lr2)]=c[CmI0(Lr2)+DmK0(Lr2)]
(L)[CmI1(Lr1)DmK1(Lr1)]=n=1Anmμn(0)r1J1(μn(0))
An0=4kL(μn(0))2J12(μn(0))0r1exp(2r2ωp2)J0(μn(0)r1r)rdr×
0L (αaη+αps)[Pp+(z)+Pp(z)]+αs[Ps+(z)+Ps(z)]πωp2 dz
Anm=8Lk[m2π2r12+L2(μn(0))2]J12(μn(0))0L(αaη+αps)[Pp+(z)+Pp(z)]+αs[Ps+(z)+Ps(z)]πωp2cos(Lz)dz×
0r1exp(2r2ωp2)J0(μn(0)r1r)rdr2r12()2[m2π2r12+L2(μn(0))2]J1(μn(0))μn(0)[CmI0(Lr1)+DmK0(Lr1)]
FETU=(n0n)n0
η=FETU+(1FETU)(1λpλs)
1rr[rθrzr]+2θrzz2=Qrzk,0rr1
1rr[rθrzr]+2θrzz2=0,r1rr2
kθrzr+cθrz=0,r=r2
θ1=θ2,θ1r=θ2r,r=r1
θrzz=0,z=0,z=L
θ2rz=C0lnr+D0+m=1[CmI0(Lr)+DmK0(Lr)]cos(Lz)
2trzr2+1rtrzr+2trzz2=Qrzk2θ2r1zz2
trz=0,tr=θ2r,r=r1
tzrz=0,z=0,z=L
θ2r1z=C0lnr1+D0+m=1[CmI0(Lr1)+DmK0(Lr1)]cos(Lz)
t=n=1m=0Anmcos(Lz)J0(μn(0)r1r)
1rr[rTrzr]=Qrzk , (0rr1)
1rr[rTrzr]=0,(r1rr2)
kTrzr=c[TcTrz],r=r2
T1=T2,T1r=T2r,r=r1
T1rz=Tc+αaη[Pp+(z)+Pp(z)]+αs[Ps+(z)+Ps(z)]4kπm=1(2)mm![(rr1)2m1m+2lnr1r22khr2](0rr1)
T2rz=Tc+αaη[Pp+(z)+Pp(z)]+αs[Ps+(z)+Ps(z)]2kπm=1(2)mm!(lnrr2khr2)(r1rr2)
1rr[rTrzr]+2Trzz2=Qrzk,(0rr1 )
1rr[rTrzr]+2Trzz2=0,(r1rr2 )
2Trzr2+1rTrzr+2Trzz2=0,(r2rr3)
kcuTrzr=c[TcTrz],r=r3
T2=T3,kT2r=kcuT3r,r=r2
T1=T2,T1r=T2r,r=r1
Trzz=0,z=0,z=L
T1rz=Tc+C0lnr1+D0+n=1m=0Anmcos(Lz)J0(μn(0)r1r)+m=1[CmI0(Lr1)+DmK0(Lr1)]cos(Lz)
T2rz=Tc+C0lnr+D0+m=1[CmI0(Lr)+DmK0(Lr)]cos(Lz)
T3rz=Tc+A0lnr+B0+m=1[AmI0(Lr)+BmK0(Lr)]cos(Lz)
kcuA0r2=c(A0lnr3+B0)A0lnr2+B0=C0lnr2+D0
kcuA0=kC0C0r1=n=1An0μn(0)r1J1(μn(0))
kcu(L)[AmI1(Lr3)BmK1(Lr3)]=c[AmI0(Lr3)+BmK0(Lr3)]
AmI0(Lr2)+BmK0(Lr2)=CmI0(Lr2)+DmK0(Lr2)
kcu[AmI1(Lr2)BmK1(Lr2)]=k[CmI1(Lr2)DmK1(Lr2)]
(L)[CmI1(Lr1)DmK1(Lr1)]=n=1Anmμn(0)r1J1(μn(0))

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