Abstract

A rate equation approach is used to model an experimentally realized $\sim {2}~\mu{\rm m}~{\rm Tm}^{3+}$-doped tellurite fiber laser utilizing an in-band pumping scheme $({}^{3}H_{6}\ura{}{} ^{3}F_{4})$. Excellent agreement between the theoretically predicted and experimentally measured slope efficiency is obtained. It is shown that in order to achieve agreement between the predicted and measured thresholds it is important to include cross-relaxation mechanisms with the ${}^{3}H_{4}$ level, even with the in-band pumping scheme. By fitting the results of the model with level lifetime measurements and the threshold pump powers we have extracted the cross-relaxation parameters of Tm-doped tellurite glass.

© 2009 IEEE

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  1. B. Richards, Y. Tsang, D. Binks, J. Lousteau, A. Jha, "Efficient $\sim {2}~\mu{\rm m}~{\rm Tm}^{3+}$-doped tellurite fiber laser," Opt. Lett. 33, 402-404 (2008).
  2. L. Huang, S. Shen, A. Jha, "Near infrared spectroscopic investigation of ${\rm Tm}^{3+}-{\rm Yb}^{3+}$ co-doped tellurite glasses," J. Non-Cryst. Solids 345–346, 349-353 (2004).
  3. A. Jha, S. Shen, M. Naftaly, "Structural origin of spectral broadening of 1.5-$\mu{\rm m}$ emission in ${\rm Er}^{3+}$-doped tellurite glasses," Phys. Rev. B 62, 6215-6227 (2000).
  4. J. S. Wang, E. M. Vogel, E. Snitzer, "Tellurite glass: A new candidate for fiber devices," Opt. Mat. 3, 187-203 (1994).
  5. S. D. Jackson, T. A. King, "Theoretical modeling of Tm-doped silica fiber lasers," J. Lightw. Technol. 17, 948-956 (1999).
  6. H. Lin, K. Lui, L. Lin, Y. Hou, D. Yang, T. Ma, E. Y. B. Pun, Q. An, J. Yu, S. Tanabe, "Optical parameters and upconversion fluorescence in ${\rm Tm}^{3+}/{\rm Yb}^{3+}$-doped alkali-barium-bismuth-tellurite glasses," Spectrochim. Acta A 65, 702-707 (2006).
  7. A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge Univ. Press, 1998).
  8. J. Wang, M. Ahmad, T. A. King, "Theoretical modeling of thulium-sensitized holmium continuous-wave fibre lasers," J. Mod. Opt. 41, 1457-1472 (1994).
  9. B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, U. N. Singh, "Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent ${\rm Tm}^{3+}$ and ${\rm Ho}^{3+}$ in ${\rm YLiF}_{4}$ and ${\rm LuLiF}_{4}$," J. Appl. Phys. 95, 3255-3271 (2004).
  10. Y. Huo, P. K. Cheo, G. G. King, "Modeling and experiments of actively $q$-switched ${\rm Er}^{3+}$–${\rm Yb}^{3+}$ codoped clad-pumped fiber lasers," IEEE J. Quantum Electron. 41, 573-580 (2005).
  11. J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, N. P. Barnes, "Efficient thulium-doped 2-$\mu{\rm m}$ germanate fiber laser," IEEE Photon. Technol. Lett. 18, 334-336 (2006).
  12. D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, G. Monnom, "Energy transfer up-conversion in ${\rm Tm}^{3+}$-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).
  13. L. B. Shaw, R. S. F. Chang, N. Djeu, "Measurement of up-conversion energy-transfer probabilities in ${\rm Ho:Y}_{3}{\rm Al}_{5}{\rm O}_{12}$ and ${\rm Tm:Y}_{3}{\rm Al}_{5}{\rm O}_{12}$," Phys. Rev. B 50, 6609-6619 (1994).
  14. G. Armagan, B. M. Walsh, N. P. Barnes, E. A. Modlin, A. M. Buoncristiani, "Determination of Tm-Ho rate coefficients from spectroscopic measurements," OSA Proc. Adv. Solid State Lasers, Opt. Soc. Amer 20, 141-145 (1994).
  15. M. Falconieri, A. Lanzi, G. Salvetti, A. Toncelli, "Fluorescence dynamics in an optically-excited Tm-Ho:YAG crystal," Opt. Mater. 7, 135-143 (1997).
  16. R. R. Petrin, M. G. Jani, R. C. Powell, M. Kokta, "Spectral dynamics of laser-pumped ${\rm Y}_{3}{\rm Al}_{5}{\rm O}_{12}$: Tm, Ho lasers," Opt. Mat. 1, 111-124 (1992).
  17. M. Naftaly, S. Shen, A. Jha, "${\rm Tm}^{3+}$-doped tellurite glass for a broadband amplifier at ${1.47}~\mu{\rm m}$," App. Opt. 39, 4979-4984 (2000).
  18. R. S. Quimby, "Range of validity of McCumber theory in relating absorption and emission cross sections," J. Appl. Phys. 92, 180-187 (2002).
  19. E. M.-C. M. J. F. Digonnet, D. G. Falquier, "Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers," IEEE. J. Quantum Electron. 38, 1629-1637 (2002).
  20. R. M. Martin, R. S. Quimby, "Experimetnal evidence of the validity of the McCumber theory relating emission and absorption for rare-earth glasses," J. Opt. Soc. Am. B 23, 1770-1775 (2006).
  21. P. C. Becker, N. A. Olsen, J. Simpson, Erbium Doped Fiber Amplifiers: Fundamentals and Technology (Academic Press, 1999) pp. 105.
  22. M. Digonnet, Rare Earth Doped Fiber Lasers and Amplifiers (Marcel Dekker, 2001) pp. 36-37.
  23. E. R. Taylor, L. N. Ng, N. P. Sessions, H. Buerger, "Spectroscopy of ${\rm Tm}^{3+}$-doped tellurite glasses for 1470 nm fiber amplifier," J. Appl. Phys. 92, 112-117 (2002).
  24. G. A. Kumar, E. D. La Rosa-Cruz, A. Martinez, N. V. Unnikrishnan, K. Ueda, "Influence of borate content on the radiative properties of ${\rm Nd}^{3+}$ ions in fluorophosphate glasses," J. Phys. Chem. Sol. 64, 69-76 (2003).
  25. J. R. Engholm, U. Happek, A. J. Sievers, "Observation of site-dependent relaxation of the OH vibrational stretch mode in fused silica," Chem. Phys. Lett. 249, 387-391 (1996).
  26. N. K. Giri, A. K. Singh, S. B. Rai, "Judd-Ofelt analysis of Tm and energy transfer studies between Tm and Er codoped in lithium tellurite network," Spec. Acta. Part A 68, 117-122 (2007).
  27. G. Turri, V. Sudesh, M. Richardson, M. Bass, A. Toncelli, M. Tonelli, "Temperature-dependent spectroscopic properties of ${\rm Tm}^{3+}$ in germanate, silica, and phosphate glasses: A comparative study," J. Appl. Phys. 103, 1-7 (2008).
  28. S. D. Jackson, "Cross relaxation and energy transfer upconversion processes relevant to the functioning of ${2}~\mu{\rm m}~{\rm Tm}^{3+}$-doped silica fibre lasers," Opt. Comms. 230, 197-203 (2004).

2008 (2)

G. Turri, V. Sudesh, M. Richardson, M. Bass, A. Toncelli, M. Tonelli, "Temperature-dependent spectroscopic properties of ${\rm Tm}^{3+}$ in germanate, silica, and phosphate glasses: A comparative study," J. Appl. Phys. 103, 1-7 (2008).

B. Richards, Y. Tsang, D. Binks, J. Lousteau, A. Jha, "Efficient $\sim {2}~\mu{\rm m}~{\rm Tm}^{3+}$-doped tellurite fiber laser," Opt. Lett. 33, 402-404 (2008).

2007 (1)

N. K. Giri, A. K. Singh, S. B. Rai, "Judd-Ofelt analysis of Tm and energy transfer studies between Tm and Er codoped in lithium tellurite network," Spec. Acta. Part A 68, 117-122 (2007).

2006 (4)

R. M. Martin, R. S. Quimby, "Experimetnal evidence of the validity of the McCumber theory relating emission and absorption for rare-earth glasses," J. Opt. Soc. Am. B 23, 1770-1775 (2006).

H. Lin, K. Lui, L. Lin, Y. Hou, D. Yang, T. Ma, E. Y. B. Pun, Q. An, J. Yu, S. Tanabe, "Optical parameters and upconversion fluorescence in ${\rm Tm}^{3+}/{\rm Yb}^{3+}$-doped alkali-barium-bismuth-tellurite glasses," Spectrochim. Acta A 65, 702-707 (2006).

J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, N. P. Barnes, "Efficient thulium-doped 2-$\mu{\rm m}$ germanate fiber laser," IEEE Photon. Technol. Lett. 18, 334-336 (2006).

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, G. Monnom, "Energy transfer up-conversion in ${\rm Tm}^{3+}$-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).

2005 (1)

Y. Huo, P. K. Cheo, G. G. King, "Modeling and experiments of actively $q$-switched ${\rm Er}^{3+}$–${\rm Yb}^{3+}$ codoped clad-pumped fiber lasers," IEEE J. Quantum Electron. 41, 573-580 (2005).

2004 (3)

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, U. N. Singh, "Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent ${\rm Tm}^{3+}$ and ${\rm Ho}^{3+}$ in ${\rm YLiF}_{4}$ and ${\rm LuLiF}_{4}$," J. Appl. Phys. 95, 3255-3271 (2004).

L. Huang, S. Shen, A. Jha, "Near infrared spectroscopic investigation of ${\rm Tm}^{3+}-{\rm Yb}^{3+}$ co-doped tellurite glasses," J. Non-Cryst. Solids 345–346, 349-353 (2004).

S. D. Jackson, "Cross relaxation and energy transfer upconversion processes relevant to the functioning of ${2}~\mu{\rm m}~{\rm Tm}^{3+}$-doped silica fibre lasers," Opt. Comms. 230, 197-203 (2004).

2003 (1)

G. A. Kumar, E. D. La Rosa-Cruz, A. Martinez, N. V. Unnikrishnan, K. Ueda, "Influence of borate content on the radiative properties of ${\rm Nd}^{3+}$ ions in fluorophosphate glasses," J. Phys. Chem. Sol. 64, 69-76 (2003).

2002 (3)

R. S. Quimby, "Range of validity of McCumber theory in relating absorption and emission cross sections," J. Appl. Phys. 92, 180-187 (2002).

E. M.-C. M. J. F. Digonnet, D. G. Falquier, "Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers," IEEE. J. Quantum Electron. 38, 1629-1637 (2002).

E. R. Taylor, L. N. Ng, N. P. Sessions, H. Buerger, "Spectroscopy of ${\rm Tm}^{3+}$-doped tellurite glasses for 1470 nm fiber amplifier," J. Appl. Phys. 92, 112-117 (2002).

2000 (2)

M. Naftaly, S. Shen, A. Jha, "${\rm Tm}^{3+}$-doped tellurite glass for a broadband amplifier at ${1.47}~\mu{\rm m}$," App. Opt. 39, 4979-4984 (2000).

A. Jha, S. Shen, M. Naftaly, "Structural origin of spectral broadening of 1.5-$\mu{\rm m}$ emission in ${\rm Er}^{3+}$-doped tellurite glasses," Phys. Rev. B 62, 6215-6227 (2000).

1999 (1)

S. D. Jackson, T. A. King, "Theoretical modeling of Tm-doped silica fiber lasers," J. Lightw. Technol. 17, 948-956 (1999).

1997 (1)

M. Falconieri, A. Lanzi, G. Salvetti, A. Toncelli, "Fluorescence dynamics in an optically-excited Tm-Ho:YAG crystal," Opt. Mater. 7, 135-143 (1997).

1996 (1)

J. R. Engholm, U. Happek, A. J. Sievers, "Observation of site-dependent relaxation of the OH vibrational stretch mode in fused silica," Chem. Phys. Lett. 249, 387-391 (1996).

1994 (4)

J. S. Wang, E. M. Vogel, E. Snitzer, "Tellurite glass: A new candidate for fiber devices," Opt. Mat. 3, 187-203 (1994).

J. Wang, M. Ahmad, T. A. King, "Theoretical modeling of thulium-sensitized holmium continuous-wave fibre lasers," J. Mod. Opt. 41, 1457-1472 (1994).

L. B. Shaw, R. S. F. Chang, N. Djeu, "Measurement of up-conversion energy-transfer probabilities in ${\rm Ho:Y}_{3}{\rm Al}_{5}{\rm O}_{12}$ and ${\rm Tm:Y}_{3}{\rm Al}_{5}{\rm O}_{12}$," Phys. Rev. B 50, 6609-6619 (1994).

G. Armagan, B. M. Walsh, N. P. Barnes, E. A. Modlin, A. M. Buoncristiani, "Determination of Tm-Ho rate coefficients from spectroscopic measurements," OSA Proc. Adv. Solid State Lasers, Opt. Soc. Amer 20, 141-145 (1994).

1992 (1)

R. R. Petrin, M. G. Jani, R. C. Powell, M. Kokta, "Spectral dynamics of laser-pumped ${\rm Y}_{3}{\rm Al}_{5}{\rm O}_{12}$: Tm, Ho lasers," Opt. Mat. 1, 111-124 (1992).

App. Opt. (1)

M. Naftaly, S. Shen, A. Jha, "${\rm Tm}^{3+}$-doped tellurite glass for a broadband amplifier at ${1.47}~\mu{\rm m}$," App. Opt. 39, 4979-4984 (2000).

Chem. Phys. Lett. (1)

J. R. Engholm, U. Happek, A. J. Sievers, "Observation of site-dependent relaxation of the OH vibrational stretch mode in fused silica," Chem. Phys. Lett. 249, 387-391 (1996).

IEEE Photon. Technol. Lett. (1)

J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, N. P. Barnes, "Efficient thulium-doped 2-$\mu{\rm m}$ germanate fiber laser," IEEE Photon. Technol. Lett. 18, 334-336 (2006).

IEEE J. Quantum Electron. (1)

Y. Huo, P. K. Cheo, G. G. King, "Modeling and experiments of actively $q$-switched ${\rm Er}^{3+}$–${\rm Yb}^{3+}$ codoped clad-pumped fiber lasers," IEEE J. Quantum Electron. 41, 573-580 (2005).

IEEE. J. Quantum Electron. (1)

E. M.-C. M. J. F. Digonnet, D. G. Falquier, "Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers," IEEE. J. Quantum Electron. 38, 1629-1637 (2002).

J. Appl. Phys. (1)

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, U. N. Singh, "Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent ${\rm Tm}^{3+}$ and ${\rm Ho}^{3+}$ in ${\rm YLiF}_{4}$ and ${\rm LuLiF}_{4}$," J. Appl. Phys. 95, 3255-3271 (2004).

J. Phys. Chem. Sol. (1)

G. A. Kumar, E. D. La Rosa-Cruz, A. Martinez, N. V. Unnikrishnan, K. Ueda, "Influence of borate content on the radiative properties of ${\rm Nd}^{3+}$ ions in fluorophosphate glasses," J. Phys. Chem. Sol. 64, 69-76 (2003).

J. Appl. Phys. (3)

E. R. Taylor, L. N. Ng, N. P. Sessions, H. Buerger, "Spectroscopy of ${\rm Tm}^{3+}$-doped tellurite glasses for 1470 nm fiber amplifier," J. Appl. Phys. 92, 112-117 (2002).

G. Turri, V. Sudesh, M. Richardson, M. Bass, A. Toncelli, M. Tonelli, "Temperature-dependent spectroscopic properties of ${\rm Tm}^{3+}$ in germanate, silica, and phosphate glasses: A comparative study," J. Appl. Phys. 103, 1-7 (2008).

R. S. Quimby, "Range of validity of McCumber theory in relating absorption and emission cross sections," J. Appl. Phys. 92, 180-187 (2002).

J. Lightw. Technol. (1)

S. D. Jackson, T. A. King, "Theoretical modeling of Tm-doped silica fiber lasers," J. Lightw. Technol. 17, 948-956 (1999).

J. Mod. Opt. (1)

J. Wang, M. Ahmad, T. A. King, "Theoretical modeling of thulium-sensitized holmium continuous-wave fibre lasers," J. Mod. Opt. 41, 1457-1472 (1994).

J. Non-Cryst. Solids (2)

L. Huang, S. Shen, A. Jha, "Near infrared spectroscopic investigation of ${\rm Tm}^{3+}-{\rm Yb}^{3+}$ co-doped tellurite glasses," J. Non-Cryst. Solids 345–346, 349-353 (2004).

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, G. Monnom, "Energy transfer up-conversion in ${\rm Tm}^{3+}$-doped silica fiber," J. Non-Cryst. Solids 352, 136-141 (2006).

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

Opt. Comms. (1)

S. D. Jackson, "Cross relaxation and energy transfer upconversion processes relevant to the functioning of ${2}~\mu{\rm m}~{\rm Tm}^{3+}$-doped silica fibre lasers," Opt. Comms. 230, 197-203 (2004).

Opt. Lett. (1)

Opt. Mat. (2)

J. S. Wang, E. M. Vogel, E. Snitzer, "Tellurite glass: A new candidate for fiber devices," Opt. Mat. 3, 187-203 (1994).

R. R. Petrin, M. G. Jani, R. C. Powell, M. Kokta, "Spectral dynamics of laser-pumped ${\rm Y}_{3}{\rm Al}_{5}{\rm O}_{12}$: Tm, Ho lasers," Opt. Mat. 1, 111-124 (1992).

Opt. Mater. (1)

M. Falconieri, A. Lanzi, G. Salvetti, A. Toncelli, "Fluorescence dynamics in an optically-excited Tm-Ho:YAG crystal," Opt. Mater. 7, 135-143 (1997).

OSA Proc. Adv. Solid State Lasers, Opt. Soc. Amer (1)

G. Armagan, B. M. Walsh, N. P. Barnes, E. A. Modlin, A. M. Buoncristiani, "Determination of Tm-Ho rate coefficients from spectroscopic measurements," OSA Proc. Adv. Solid State Lasers, Opt. Soc. Amer 20, 141-145 (1994).

Phys. Rev. B (1)

A. Jha, S. Shen, M. Naftaly, "Structural origin of spectral broadening of 1.5-$\mu{\rm m}$ emission in ${\rm Er}^{3+}$-doped tellurite glasses," Phys. Rev. B 62, 6215-6227 (2000).

Phys. Rev. B (1)

L. B. Shaw, R. S. F. Chang, N. Djeu, "Measurement of up-conversion energy-transfer probabilities in ${\rm Ho:Y}_{3}{\rm Al}_{5}{\rm O}_{12}$ and ${\rm Tm:Y}_{3}{\rm Al}_{5}{\rm O}_{12}$," Phys. Rev. B 50, 6609-6619 (1994).

Spec. Acta. Part A (1)

N. K. Giri, A. K. Singh, S. B. Rai, "Judd-Ofelt analysis of Tm and energy transfer studies between Tm and Er codoped in lithium tellurite network," Spec. Acta. Part A 68, 117-122 (2007).

Spectrochim. Acta A (1)

H. Lin, K. Lui, L. Lin, Y. Hou, D. Yang, T. Ma, E. Y. B. Pun, Q. An, J. Yu, S. Tanabe, "Optical parameters and upconversion fluorescence in ${\rm Tm}^{3+}/{\rm Yb}^{3+}$-doped alkali-barium-bismuth-tellurite glasses," Spectrochim. Acta A 65, 702-707 (2006).

Other (3)

A. Ghatak, K. Thyagarajan, Introduction to Fiber Optics (Cambridge Univ. Press, 1998).

P. C. Becker, N. A. Olsen, J. Simpson, Erbium Doped Fiber Amplifiers: Fundamentals and Technology (Academic Press, 1999) pp. 105.

M. Digonnet, Rare Earth Doped Fiber Lasers and Amplifiers (Marcel Dekker, 2001) pp. 36-37.

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