Abstract

We develop a detailed theoretical model for laser cooling in Yb3+:YAG. The expressions for the fluorescence power density removed from the system with spontaneous emission, the power density radiated with stimulated emission, as well as the heat power density generated in the system by nonradiative decays on the impurities of the host material have been calculated. The influence of each of these power densities on the cooling process has been analyzed. We show, for the first time to our knowledge, how the temperature dependences of the different parameters of the system as well as the concentration of the impurities in the host influence the final temperature of the cooled sample.

© 2014 Optical Society of America

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  1. P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung,” Z. Phys. 57, 739–746 (1929).
    [CrossRef]
  2. 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, 500–503 (1995).
    [CrossRef]
  3. S. D. Melgaard, D. V. Seletskiy, A. Di Lieto, M. Tonelli, and M. Sheik-Bahae, “Optical refrigeration to 119 K, below National Institute of Standards and Technology cryogenic temperature,” Opt. Lett. 38, 1588–1590 (2013).
    [CrossRef]
  4. M. Sheik-Bahae and R. I. Epstein, “Laser cooling of solids,” Laser Photon. Rev. 3, 67–84 (2009).
    [CrossRef]
  5. G. Nemova and R. Kashyap, “Laser cooling of solids,” Rep. Prog. Phys. 73, 086501 (2010).
    [CrossRef]
  6. D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photon. 4, 78–107 (2012).
    [CrossRef]
  7. X. Luo, M. D. Eisaman, and T. R. Gosnell, “Laser cooling of a solid by 21 K starting from room temperature,” Opt. Lett. 23, 639–641 (1998).
    [CrossRef]
  8. T. R. Gosnell, “Laser cooling of a solid by 65 K starting from room temperature,” Opt. Lett. 24, 1041–1043 (1999).
    [CrossRef]
  9. C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
    [CrossRef]
  10. F. E. Auzel, “Materials and devices using double-pumped-phosphors with energy transfer,” Proc. IEEE 61, 758–786 (1973).
    [CrossRef]
  11. F. Auzel, “Application of resonant energy transfers to the laser effect in Er-doped glasses,” Ann. Telecommun. 24, 363–376 (1969).
  12. F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
    [CrossRef]
  13. P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
    [CrossRef]
  14. C. Y. Chen, R. R. Petrin, D. C. Yeh, and W. A. Sibley, “Concentration-dependent energy-transfer processes in Er3+- and Tm3+-doped heavy-metal fluoride glass,” Opt. Lett. 14, 432–434 (1989).
    [CrossRef]
  15. S. R. Bowman and C. E. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
    [CrossRef]
  16. S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
    [CrossRef]
  17. D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Electron. 47, 3–12 (2011).
    [CrossRef]
  18. G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG:Yb3+crystals,” Laser Phys. 16, 1054–1057 (2006).
    [CrossRef]
  19. H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
    [CrossRef]
  20. F. Auzel, “On the maximum splitting of the (2F7/2) ground state inYb3+-doped solid state laser materials,” J. Lumin. 93, 129–135 (2001).
    [CrossRef]
  21. R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
    [CrossRef]
  22. E. Soares de Lima Filho, G. Nemova, S. Loranger, and R. Kashyap, “Laser-induced cooling of a Yb:YAG crystal in air at atmospheric pressure,” Opt. Express 21, 24711–24720 (2013).
    [CrossRef]
  23. M. Esmaeilzadeh, H. Roohbakhsh, and A. Ghaedzadeh, “Experimental study on temperature dependence of absorption and emission properties of Yb:YAG crystal as a disk laser medium,” World Acad. Sci. Eng. Technol. 63, 436–439 (2012).
  24. S. Georgescu, “Mathematical modeling of 3-μm erbium lasers,” in Proceedings of the First French-Romanian Colloquium of Numerical Physics, Bucharest, Romania, October30–31 (2002), pp. 71–103.
  25. B. Zandi, J. B. Gruber, D. K. Sardar, and T. H. Allik, “Modeling of Er in ceramic YAG and comparison with single-crystal YAG,” Proc. SPIE 5792, 26–33 (2005).
    [CrossRef]
  26. P. Goldner and M. Mortier, “Effect of rare earth impurities on fluorescent cooling in ZBLAN glass,” J. Non-Cryst. Solids 284, 249–254 (2001).
    [CrossRef]

2013 (2)

2012 (2)

M. Esmaeilzadeh, H. Roohbakhsh, and A. Ghaedzadeh, “Experimental study on temperature dependence of absorption and emission properties of Yb:YAG crystal as a disk laser medium,” World Acad. Sci. Eng. Technol. 63, 436–439 (2012).

D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photon. 4, 78–107 (2012).
[CrossRef]

2011 (1)

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Electron. 47, 3–12 (2011).
[CrossRef]

2010 (1)

G. Nemova and R. Kashyap, “Laser cooling of solids,” Rep. Prog. Phys. 73, 086501 (2010).
[CrossRef]

2009 (1)

M. Sheik-Bahae and R. I. Epstein, “Laser cooling of solids,” Laser Photon. Rev. 3, 67–84 (2009).
[CrossRef]

2006 (1)

G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG:Yb3+crystals,” Laser Phys. 16, 1054–1057 (2006).
[CrossRef]

2005 (1)

B. Zandi, J. B. Gruber, D. K. Sardar, and T. H. Allik, “Modeling of Er in ceramic YAG and comparison with single-crystal YAG,” Proc. SPIE 5792, 26–33 (2005).
[CrossRef]

2003 (1)

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

2002 (1)

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

2001 (4)

P. Goldner and M. Mortier, “Effect of rare earth impurities on fluorescent cooling in ZBLAN glass,” J. Non-Cryst. Solids 284, 249–254 (2001).
[CrossRef]

F. Auzel, “On the maximum splitting of the (2F7/2) ground state inYb3+-doped solid state laser materials,” J. Lumin. 93, 129–135 (2001).
[CrossRef]

R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
[CrossRef]

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
[CrossRef]

2000 (1)

S. R. Bowman and C. E. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[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, 500–503 (1995).
[CrossRef]

1992 (1)

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

1989 (1)

1973 (1)

F. E. Auzel, “Materials and devices using double-pumped-phosphors with energy transfer,” Proc. IEEE 61, 758–786 (1973).
[CrossRef]

1969 (1)

F. Auzel, “Application of resonant energy transfers to the laser effect in Er-doped glasses,” Ann. Telecommun. 24, 363–376 (1969).

1929 (1)

P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung,” Z. Phys. 57, 739–746 (1929).
[CrossRef]

Allik, T. H.

B. Zandi, J. B. Gruber, D. K. Sardar, and T. H. Allik, “Modeling of Er in ceramic YAG and comparison with single-crystal YAG,” Proc. SPIE 5792, 26–33 (2005).
[CrossRef]

Auzel, F.

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
[CrossRef]

F. Auzel, “On the maximum splitting of the (2F7/2) ground state inYb3+-doped solid state laser materials,” J. Lumin. 93, 129–135 (2001).
[CrossRef]

F. Auzel, “Application of resonant energy transfers to the laser effect in Er-doped glasses,” Ann. Telecommun. 24, 363–376 (1969).

Auzel, F. E.

F. E. Auzel, “Materials and devices using double-pumped-phosphors with energy transfer,” Proc. IEEE 61, 758–786 (1973).
[CrossRef]

Baldacchini, G.

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
[CrossRef]

Bonfigli, F.

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
[CrossRef]

Boulon, G.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Bowman, S. R.

S. R. Bowman and C. E. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[CrossRef]

Brown, D. C.

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Electron. 47, 3–12 (2011).
[CrossRef]

Brown, J. J.

R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
[CrossRef]

Bruesselbach, H. W.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[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, 500–503 (1995).
[CrossRef]

Byren, R. W.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Canibano, H.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Chase, L. L.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

Chen, C. Y.

Cohen-Adad, M. T.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Demirkhanyan, G. G.

G. G. Demirkhanyan, “Intensities of inter-Stark transitions in YAG:Yb3+crystals,” Laser Phys. 16, 1054–1057 (2006).
[CrossRef]

Deng, P.

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

Di Lieto, A.

Edwards, B. C.

R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
[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, 500–503 (1995).
[CrossRef]

Eisaman, M. D.

El Hassouni, A.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Epstein, R. I.

D. V. Seletskiy, M. P. Hehlen, R. I. Epstein, and M. Sheik-Bahae, “Cryogenic optical refrigeration,” Adv. Opt. Photon. 4, 78–107 (2012).
[CrossRef]

M. Sheik-Bahae and R. I. Epstein, “Laser cooling of solids,” Laser Photon. Rev. 3, 67–84 (2009).
[CrossRef]

R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
[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, 500–503 (1995).
[CrossRef]

Esmaeilzadeh, M.

M. Esmaeilzadeh, H. Roohbakhsh, and A. Ghaedzadeh, “Experimental study on temperature dependence of absorption and emission properties of Yb:YAG crystal as a disk laser medium,” World Acad. Sci. Eng. Technol. 63, 436–439 (2012).

Gagliari, S.

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
[CrossRef]

Georgescu, S.

S. Georgescu, “Mathematical modeling of 3-μm erbium lasers,” in Proceedings of the First French-Romanian Colloquium of Numerical Physics, Bucharest, Romania, October30–31 (2002), pp. 71–103.

Ghaedzadeh, A.

M. Esmaeilzadeh, H. Roohbakhsh, and A. Ghaedzadeh, “Experimental study on temperature dependence of absorption and emission properties of Yb:YAG crystal as a disk laser medium,” World Acad. Sci. Eng. Technol. 63, 436–439 (2012).

Gibbs, A.

R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
[CrossRef]

Goldner, P.

P. Goldner and M. Mortier, “Effect of rare earth impurities on fluorescent cooling in ZBLAN glass,” J. Non-Cryst. Solids 284, 249–254 (2001).
[CrossRef]

Gosnell, T. R.

Goutaudier, C.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Gruber, J. B.

B. Zandi, J. B. Gruber, D. K. Sardar, and T. H. Allik, “Modeling of Er in ceramic YAG and comparison with single-crystal YAG,” Proc. SPIE 5792, 26–33 (2005).
[CrossRef]

Guyot, Y.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Hehlen, M. P.

Ito, M.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Kashyap, R.

Krupke, W. F.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

Kway, W. L.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

Laversenne, L.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Lebbou, K.

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Loranger, S.

Luo, X.

Melgaard, S. D.

Mortier, M.

P. Goldner and M. Mortier, “Effect of rare earth impurities on fluorescent cooling in ZBLAN glass,” J. Non-Cryst. Solids 284, 249–254 (2001).
[CrossRef]

Mungan, C. E.

S. R. Bowman and C. E. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[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, 500–503 (1995).
[CrossRef]

Nemova, G.

Payne, S. A.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

Petrin, R. R.

Pringsheim, P.

P. Pringsheim, “Zwei Bemerkungen über den Unterschied von Lumineszenz- und Temperaturstrahlung,” Z. Phys. 57, 739–746 (1929).
[CrossRef]

Reeder, R. A.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Roohbakhsh, H.

M. Esmaeilzadeh, H. Roohbakhsh, and A. Ghaedzadeh, “Experimental study on temperature dependence of absorption and emission properties of Yb:YAG crystal as a disk laser medium,” World Acad. Sci. Eng. Technol. 63, 436–439 (2012).

Sardar, D. K.

B. Zandi, J. B. Gruber, D. K. Sardar, and T. H. Allik, “Modeling of Er in ceramic YAG and comparison with single-crystal YAG,” Proc. SPIE 5792, 26–33 (2005).
[CrossRef]

Seletskiy, D. V.

Sheik-Bahae, M.

Sibley, W. A.

Smith, L. K.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

Soares de Lima Filho, E.

Sumida, D. S.

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

Tonelli, M.

Vitali, V. A.

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Electron. 47, 3–12 (2011).
[CrossRef]

Yang, P.

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

Yeh, D. C.

Yin, Z.

P. Yang, P. Deng, and Z. Yin, “Concentration quenching in Yb:YAG,” J. Lumin. 97, 51–54 (2002).
[CrossRef]

Zandi, B.

B. Zandi, J. B. Gruber, D. K. Sardar, and T. H. Allik, “Modeling of Er in ceramic YAG and comparison with single-crystal YAG,” Proc. SPIE 5792, 26–33 (2005).
[CrossRef]

Adv. Opt. Photon. (1)

Ann. Chim. (1)

C. Goutaudier, K. Lebbou, Y. Guyot, M. Ito, H. Canibano, A. El Hassouni, L. Laversenne, M. T. Cohen-Adad, and G. Boulon, “Advances in fibre crystals: growth and optimization of spectroscopic properties for Yb3+-doped laser crystals,” Ann. Chim. 28, 73–88 (2003).
[CrossRef]

Ann. Telecommun. (1)

F. Auzel, “Application of resonant energy transfers to the laser effect in Er-doped glasses,” Ann. Telecommun. 24, 363–376 (1969).

Appl. Phys. B (1)

S. R. Bowman and C. E. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28, 2619–2630 (1992).
[CrossRef]

D. C. Brown and V. A. Vitali, “Yb:YAG kinetics model including saturation and power conservation,” IEEE J. Quantum Electron. 47, 3–12 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. W. Bruesselbach, D. S. Sumida, R. A. Reeder, and R. W. Byren, “Low-heat high-power scaling using InGaAs-diode-pumped Yb:YAG lasers,” IEEE J. Sel. Top. Quantum Electron. 3, 105–116 (1997).
[CrossRef]

J. Appl. Phys. (1)

R. I. Epstein, J. J. Brown, B. C. Edwards, and A. Gibbs, “Measurements of optical refrigeration in ytterbium-doped crystals,” J. Appl. Phys. 90, 4815–4819 (2001).
[CrossRef]

J. Lumin. (3)

F. Auzel, “On the maximum splitting of the (2F7/2) ground state inYb3+-doped solid state laser materials,” J. Lumin. 93, 129–135 (2001).
[CrossRef]

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001).
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

(a) Stark sublevel energies presented in [17] with radiative lifetimes calculated in [18] for Yb3+:YAG at room temperature. (b) Energy levels of the Yb3+ and Er3+ ions.

Fig. 2.
Fig. 2.

Boltzmann occupation factors in Yb:YAG: (a) f0i(i=14) of the manifold F27/2 and (b) f1j(j=13) of the manifold F25/2.

Fig. 3.
Fig. 3.

Radiative lifetime of the manifold F25/2 as a function of temperature. Yb:YAG is assumed free of self-quenching or impurities.

Fig. 4.
Fig. 4.

Mean fluorescence wavelength as a function of the temperature.

Fig. 5.
Fig. 5.

(a) Absorption and (b) emission cross sections at the pump wavelength λp=1030nm as functions of temperature.

Fig. 6.
Fig. 6.

Ratio of the energy transfer rate from Yb3+ ions to the Er3+ ions, CEY, and the energy back-transfer rate from Er3+ ions to the Yb3+ ions, CEY, as a function of temperature.

Fig. 7.
Fig. 7.

Cooling power density as a function of the temperature at the pump power Pp=0.5W. T is temperature of the samples with different Er3+ impurities concentrations, Ner.

Fig. 8.
Fig. 8.

Percentage of heat power density generated in the system with different concentrations of Er3+ impurity ions, NEr.

Fig. 9.
Fig. 9.

Pump power density, stimulated power density, spontaneous power density, and cooling power density as functions of temperature for pump powers (a) 0.5 W, (b) 2.45 W, (c) 4.9 W, and (d) 8.3 W. The Er3+ impurity concentration NEr=1.2×105μm3.

Fig. 10.
Fig. 10.

Ratio of cooling power density generated in the sample and the pump power density absorbed in the sample as a function of the temperature for different input pump powers.

Fig. 11.
Fig. 11.

Ratios of the stimulated emission and pump power densities and spontaneous emission and pump power densities as functions of temperature for pump powers (a) 0.5 W, (b) 2.45 W, (c) 4.9 W, and (d) 8.3 W. The Er3+ impurity concentration NEr=1.2×105μm3.

Fig. 12.
Fig. 12.

Dependence of the pump power and the temperature of the sample for different Er3+ impurity concentrations, NEr.

Fig. 13.
Fig. 13.

Cooling power density as a function of temperature and pump power. The Er3+ impurity concentration NEr=1.2×105μm3.

Tables (2)

Tables Icon

Table 1. Energies, E1j, and Radiative Lifetimes, τ1j, of the Stark Sublevels (1,j) of the F25/2 Manifold, j=1,2,3 and Energies, E0i, of the Stark Sublevels (0,i) of the F27/2 Manifold, i=1,2,3,4a

Tables Icon

Table 2. Energies of the Stark Sublevels of the I411/2 and I415/2 Manifolds of the Er3+:YAG at Different Concentrations of Er3+ Ions: Experimental (exp.) and Calculated (calc.) [25]

Equations (20)

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f0i=exp(E01E0ikBT)n=14exp(E01E0nkBT),
f1j=exp(E11E1jkBT)m=13exp(E11E0mkBT),
νf=j=13i=14f1jτ1jrβ0i1jν0i1j1τ1r,
1τ1r=j=13f1jτ1jr
Ts4=Tr4+D4εσBPcool(T),
τ1r=τ˜1tr(1+σlNYb)[1+92π(NYbNYb0)2],
dn1Ydt=Iphνp[σa(νp)n0Yσe(νp)n1Y]CYEn1Yn0E+CEYn2En0Ya10Yn1Yw10Yn1Y,dn1Edt=2ω11(n1E)2(a10+w10)n1E+k=25ak1nkE+w21n2E,dn2Edt=CYEn1Yn0ECEYn2En0Y2ω22(n2E)2+k=35ak2nkE+w32n3E(a20+a21+w21)n2E,dn3Edt=ω11(n1E)2+a53n5E+(a43+w43)n4E(k=02a3k+w32)n3E,dn4Edt=(a54+w54)n5E(k=03a4k+w43)n4E,dn5Edt=ω22(n2E)2(k=04a5k+w54)n5E,NYb=n0Y+n1Y,NEr=k=05nkE,
CEY=17.6R06(NEr+NYb)/τ1r,
CEYCYE=Z1YZ0EZ0YZ2Eexp[kBT(EZLErEZLYb)],
Pcool=PpumpPstimrPspontr+Pheat,
Ppump=Ip(νp)σa(νp)[NYbn1Yb].
Pstimr=Ip(νp)σe(νp)n1Yb.
Pspontr=hn1Ybj=13i=14f1jτ1jrν0i1jβ0i1j,
Pheat=hk=25nkEνk(k1)Ewk(k1),
w(T)=w(0)(nν+1)p,
nν=(exp(hν/kBT)1)1.
σa(νp)=σe(νp)Z1YZ0Yexp(hνpEZLYkBT).
λf(nm)=1012.2(nm)0.01(nm/K)·T(K).
σe(T)=[0.44+9.5exp(T/165)]×1020cm2.
Zm(T)=imexp(Em,iκT),

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