Abstract

We propose a theoretical model for a laser cooled continuous-wave fiber amplifier. The amplification process takes place in the Yb3+-doped core of a fluoride ZBLAN (ZrF4BaF2LaF3AlF3NaF) glass fiber, while the cooling process takes place in the cladding, which is doped with thulium. It is shown that for each value of the pump power and amplified signal there is an optimum distribution of the concentration of the Tm3+ along the length of the fiber amplifier, which provides optimum athermal operation. The influence of a small deviation in the input signal power on the temperature of the fiber with a fixed distribution of the Tm3+ ions in the fiber cladding is investigated.

© 2009 Optical Society of America

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References

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  1. R. Paschotts, Encyclopedia of Laser Physics and Technology (Wiley-VCH, 2008).
  2. D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158 μJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier,” Opt. Lett. 22, 378-380 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
  4. S. R. Bowman, “Laser without internal heat generation,” IEEE J. Quantum Electron. 35, 115-122 (1999).
    [CrossRef]
  5. P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenzund temperature-strahlung,” Z. Phys. 57, 739-746 (1929).
    [CrossRef]
  6. R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
    [CrossRef]
  7. E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.
  8. P. C. Becker, N. A. Olsson, and J. B. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).
  9. T. R. Gosnell, “Laser cooling of a solid by 65 K starting from room temperature,” Opt. Lett. 24, 1041-1043 (1999).
    [CrossRef]
  10. T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
    [CrossRef]
  11. D. C. Brown, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” IEEE J. Quantum Electron. 37, 207-217 (2001).
    [CrossRef]
  12. J. Y. Allain, M. Monerie, and H. Poignant, “Ytterbium-doped fluoride fiber laser operating at 1.02 μm,” Electron. Lett. 28, 988-989 (1992).
    [CrossRef]
  13. C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
    [CrossRef] [PubMed]

2008 (1)

2001 (1)

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

2000 (1)

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

1999 (2)

S. R. Bowman, “Laser without internal heat generation,” IEEE J. Quantum Electron. 35, 115-122 (1999).
[CrossRef]

T. R. Gosnell, “Laser cooling of a solid by 65 K starting from room temperature,” Opt. Lett. 24, 1041-1043 (1999).
[CrossRef]

1997 (1)

1996 (1)

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

1995 (1)

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

1992 (1)

J. Y. Allain, M. Monerie, and H. Poignant, “Ytterbium-doped fluoride fiber laser operating at 1.02 μm,” Electron. Lett. 28, 988-989 (1992).
[CrossRef]

1929 (1)

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenzund temperature-strahlung,” Z. Phys. 57, 739-746 (1929).
[CrossRef]

Allain, J. Y.

J. Y. Allain, M. Monerie, and H. Poignant, “Ytterbium-doped fluoride fiber laser operating at 1.02 μm,” Electron. Lett. 28, 988-989 (1992).
[CrossRef]

Anderson, J. E.

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. B. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

Bowman, S. R.

S. R. Bowman, “Laser without internal heat generation,” IEEE J. Quantum Electron. 35, 115-122 (1999).
[CrossRef]

Brown, D. C.

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

Buchwald, M. I.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

Caplen, J. E.

Dong, L.

Edwards, B. C.

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

Epstein, R. I.

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

Gosnell, T. R.

T. R. Gosnell, “Laser cooling of a solid by 65 K starting from room temperature,” Opt. Lett. 24, 1041-1043 (1999).
[CrossRef]

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

Hakimi, F.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.

Hoyt, C. W.

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

Kanamori, T.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Kashyap, R.

McCollum, B. C.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.

Monerie, M.

J. Y. Allain, M. Monerie, and H. Poignant, “Ytterbium-doped fluoride fiber laser operating at 1.02 μm,” Electron. Lett. 28, 988-989 (1992).
[CrossRef]

Mungan, C. E.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

Nemova, G.

Ohishi, Y.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. B. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

Paschotts, R.

R. Paschotts, Encyclopedia of Laser Physics and Technology (Wiley-VCH, 2008).

Penty, R. V.

Po, H.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.

Poignant, H.

J. Y. Allain, M. Monerie, and H. Poignant, “Ytterbium-doped fluoride fiber laser operating at 1.02 μm,” Electron. Lett. 28, 988-989 (1992).
[CrossRef]

Pringsheim, P.

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenzund temperature-strahlung,” Z. Phys. 57, 739-746 (1929).
[CrossRef]

Richardson, D. J.

Sakamoto, T.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Sheik-Bahae, M.

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

Shimizu, M.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Simpson, J. B.

P. C. Becker, N. A. Olsson, and J. B. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

Snitzer, E.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.

Sudo, S.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Taverner, D.

Terunuma, Y.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Tumminelli, R.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.

Williams, K.

Yamada, M.

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

Electron. Lett. (1)

J. Y. Allain, M. Monerie, and H. Poignant, “Ytterbium-doped fluoride fiber laser operating at 1.02 μm,” Electron. Lett. 28, 988-989 (1992).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

S. R. Bowman, “Laser without internal heat generation,” IEEE J. Quantum Electron. 35, 115-122 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Sakamoto, M. Shimizu, M. Yamada, T. Kanamori, Y. Ohishi, Y. Terunuma, and S. Sudo, “35 dB gain Tm-doped ZBLZN fiber amplifier operating at 1.65 μm,” IEEE Photon. Technol. Lett. 8, 349-351 (1996).
[CrossRef]

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

Nature (1)

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser-induced fluorescent cooling of a solid,” Nature 377, 500-502 (1995).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

C. W. Hoyt, M. Sheik-Bahae, R. I. Epstein, B. C. Edwards, and J. E. Anderson, “Observation of anti-Stokes fluorescence cooling in thulium-doped glass,” Phys. Rev. Lett. 85, 3600-3603 (2000).
[CrossRef] [PubMed]

Z. Phys. (1)

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenzund temperature-strahlung,” Z. Phys. 57, 739-746 (1929).
[CrossRef]

Other (3)

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset-core Nd fiber laser,” Proceedings of the Conference on Optical Fiber Sensors, Postdeadline paper PD5, New Orleans, LA, January 1988.

P. C. Becker, N. A. Olsson, and J. B. Simpson, Erbium-Doped Fiber Amplifiers (Academic Press, 1999).

R. Paschotts, Encyclopedia of Laser Physics and Technology (Wiley-VCH, 2008).

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Figures (6)

Fig. 1
Fig. 1

Structure under consideration. The curves in the cladding illustrate the distribution of Tm 3 + ions.

Fig. 2
Fig. 2

Pump power depletion and signal power amplification along the length of the fiber amplifier.

Fig. 3
Fig. 3

Distribution of the temperature of the fiber as a function of length of the fiber amplifier without laser cooling of the cladding. P p ( 0 ) = 170   W and P s ( 0 ) = 1   W .

Fig. 4
Fig. 4

Concentrations of the Tm 3 + ions in the cladding of the fiber as functions of the length of the fiber for different values of the input pump powers, P p ( 0 ) . P p cool ( 0 ) = 300   W and P s ( 0 ) = 1   W .

Fig. 5
Fig. 5

Distribution of the temperature of the fiber along the length of the fiber amplifier for different input cooling pump powers, P p cool ( 0 ) . P p ( 0 ) = 170   W and P s ( 0 ) = 1.2   W .

Fig. 6
Fig. 6

Concentrations of the Tm 3 + ions in the cladding of the fiber as functions of the length of the amplifier. P p cool ( 0 ) = 300   W , P p ( 0 ) = 170   W , and P s ( 0 ) = 1   W .

Equations (8)

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P cool ( z ) = A eff cl I s N Tm ( z ) σ abs Tm 1 + σ se Tm σ abs Tm + A eff cl I s P p cool ( z ) ( λ p cool λ f Tm 1 ) ,
P p cool ( 0 ) P p cool ( z ) exp ( P p cool ( 0 ) P p cool ( z ) P Sat cool ) exp ( σ abs Tm N Tm z ) = 0 ,
1 r r ( r T co ( r ) r ) = Q heat κ ,     0 r R co
1 r r ( r T cl ( r ) r ) = Q cool κ ,     R co r R cl
T co ( r ) = T r Q cool 2 R cl ( R cl 2 κ + 1 H ) + ( Q heat + Q cool ) R co 2 2 [ 1 H R cl + 1 2 κ 1 κ ln ( R co R cl ) ] Q heat 4 κ r 2 , 0 r R co
T cl ( r ) = T r Q cool 2 R cl ( R cl 2 κ + 1 H ) + ( Q heat + Q cool ) R co 2 2 [ 1 H R cl + 1 2 κ 1 κ ln ( R co R cl ) ] ( Q heat + Q cool ) 4 κ R co 2 + R co 2 2 κ ( Q heat + Q cool ) ln ( R co ) R co 2 2 κ ( Q heat + Q cool ) ln ( r ) + Q cool 4 κ ( r 2 ) , R co r R cl
T av = 0 R co T co ( r ) d r + R co R cl T cl ( r ) d r 0 R cl d r .
T av = T r + Q heat [ R co 2 2 κ + R co 2 2 H R cl R co 3 3 κ R cl ] + Q cool [ R co 2 2 κ + R co 2 2 H R cl R co 3 3 κ R cl R cl 2 H R cl 2 6 κ ] .

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