Abstract

I present a model devoted to linking the properties of a quasi-three-level laser crystal to microscopic parameters. The role of the radiative diffusion is taken into account with a sample-size-dependent parameter, including the total internal reflections, allowing both radiative and nonradiative diffusions to be treated equally. The radiation self-trapping aspect is quantified with the number ηimp of imprisoned photons engendered by one absorbed pump photon. The losses toward the traps that are not always well known are described with the dipole–dipole interaction, giving a microscopic interpretation of the heat dispensed in the sample from the pump. One prediction is that the excited-state decay of the donor subsystem is exponential, in agreement with experiment. The main experimental data, which are the excited-state intrinsic and extrinsic lifetimes τ and τ and the extrinsic fractional thermal loading ξ, can be calculated by adjusting a small number of parameters. This number can be reduced by use of spectroscopy. I have shown that this model can be applied with a reasonable success to Yb3+-doped Y3Al5O12.

© 2006 Optical Society of America

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  1. E. A. Milne, "The diffusion of imprisoned radiation through a gas," J. Lond. Math. Soc. 1, 40-51 (1926).
    [CrossRef]
  2. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  3. T. Forster, "Experimentelle und theoretische untersuchung des zsischenmolekularen ubergangs von elektronenanregungsenergie," Z. Naturforsch. A 4, 321-327 (1949).
  4. D. L. Dexter, "A theory of sensitized luminescence in solids," J. Chem. Phys. 21, 836-850 (1953).
    [CrossRef]
  5. M. Inokuti and F. Hirayama, "Influence of energy transfer by the exchange mechanism on donor luminescence," J. Chem. Phys. 43, 1978-1989 (1965).
    [CrossRef]
  6. M. Yokota and O. Tanimoto, "Effects of diffusion on energy transfer by resonance," J. Phys. Soc. Jpn. 22, 779-784 (1967).
    [CrossRef]
  7. 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]
  8. M. J. Weber, "Luminescence decay by energy migration and transfer: observation of diffusion-limited relaxation," Phys. Rev. B 4, 2932-2939 (1971).
    [CrossRef]
  9. F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
    [CrossRef]
  10. F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
    [CrossRef]
  11. R. C. Powell, Physics of Solid-State Laser Materials (AIP Press, 1998).
    [CrossRef]
  12. A. I. Burshtein, "Hopping mechanism of energy transfer," Sov. Phys. JETP 35, 882-885 (1972).
  13. A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
    [CrossRef]
  14. H. Stehfest, "Numerical inversion of Laplace transforms," Commun. ACM 13, 47-49 (1970).
    [CrossRef]
  15. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
    [CrossRef]
  16. K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
    [CrossRef]
  17. A. Brenier, "A new evaluation of Yb3+-doped crystals for laser applications," J. Lumin. 92, 199-204 (2001).
    [CrossRef]
  18. L. Zhang and H. Hu, "The effect of OH− on IR emission of Nd3+, Yb3+ and Er3+ doped tetraphosphate glasses," J. Phys. Chem. Solids 63, 575-579 (2002).
    [CrossRef]
  19. D. A. Pinnow and T. C. Rich, "Development of a calorimetric method for making precision optical absorption measurements," Appl. Opt. 12, 984-992 (1973).
    [CrossRef] [PubMed]
  20. T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
    [CrossRef]
  21. D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).
  22. D. E. McCumber, "Einstein relations connecting broadband emission and absorption spectra," Phys. Rev. 136, A954-A957 (1964).
    [CrossRef]
  23. W. A. Shurcliff and R. C. Jones, "Trapping of fluorescent light produced within objects of high geometrical symmetry," J. Opt. Soc. Am. 39, 912-916 (1949).
    [CrossRef]

2003

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
[CrossRef]

2002

L. Zhang and H. Hu, "The effect of OH− on IR emission of Nd3+, Yb3+ and Er3+ doped tetraphosphate glasses," J. Phys. Chem. Solids 63, 575-579 (2002).
[CrossRef]

2001

A. Brenier, "A new evaluation of Yb3+-doped crystals for laser applications," J. Lumin. 92, 199-204 (2001).
[CrossRef]

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (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

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

1999

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

1993

T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
[CrossRef]

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

1973

1972

A. I. Burshtein, "Hopping mechanism of energy transfer," Sov. Phys. JETP 35, 882-885 (1972).

1971

M. J. Weber, "Luminescence decay by energy migration and transfer: observation of diffusion-limited relaxation," Phys. Rev. B 4, 2932-2939 (1971).
[CrossRef]

1970

H. Stehfest, "Numerical inversion of Laplace transforms," Commun. ACM 13, 47-49 (1970).
[CrossRef]

1967

M. Yokota and O. Tanimoto, "Effects of diffusion on energy transfer by resonance," J. Phys. Soc. Jpn. 22, 779-784 (1967).
[CrossRef]

1965

M. Inokuti and F. Hirayama, "Influence of energy transfer by the exchange mechanism on donor luminescence," J. Chem. Phys. 43, 1978-1989 (1965).
[CrossRef]

1964

D. E. McCumber, "Einstein relations connecting broadband emission and absorption spectra," Phys. Rev. 136, A954-A957 (1964).
[CrossRef]

1953

D. L. Dexter, "A theory of sensitized luminescence in solids," J. Chem. Phys. 21, 836-850 (1953).
[CrossRef]

1949

T. Forster, "Experimentelle und theoretische untersuchung des zsischenmolekularen ubergangs von elektronenanregungsenergie," Z. Naturforsch. A 4, 321-327 (1949).

W. A. Shurcliff and R. C. Jones, "Trapping of fluorescent light produced within objects of high geometrical symmetry," J. Opt. Soc. Am. 39, 912-916 (1949).
[CrossRef]

1926

E. A. Milne, "The diffusion of imprisoned radiation through a gas," J. Lond. Math. Soc. 1, 40-51 (1926).
[CrossRef]

Auzel, F.

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
[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]

Baldacchini, G.

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
[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]

Basun, S. A.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Betin, A. A.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

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.

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
[CrossRef]

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

Brenier, A.

A. Brenier, "A new evaluation of Yb3+-doped crystals for laser applications," J. Lumin. 92, 199-204 (2001).
[CrossRef]

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

Bruesselbach, H.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

Bryen, R.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

Burshtein, A. I.

A. I. Burshtein, "Hopping mechanism of energy transfer," Sov. Phys. JETP 35, 882-885 (1972).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chase, L. L.

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

DeLoach, D.

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

Dexter, D. L.

D. L. Dexter, "A theory of sensitized luminescence in solids," J. Chem. Phys. 21, 836-850 (1953).
[CrossRef]

Equall, R.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Fan, T. Y.

T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
[CrossRef]

Fornasiero, L.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Forster, T.

T. Forster, "Experimentelle und theoretische untersuchung des zsischenmolekularen ubergangs von elektronenanregungsenergie," Z. Naturforsch. A 4, 321-327 (1949).

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]

Hirayama, F.

M. Inokuti and F. Hirayama, "Influence of energy transfer by the exchange mechanism on donor luminescence," J. Chem. Phys. 43, 1978-1989 (1965).
[CrossRef]

Honea, E. C.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Hu, H.

L. Zhang and H. Hu, "The effect of OH− on IR emission of Nd3+, Yb3+ and Er3+ doped tetraphosphate glasses," J. Phys. Chem. Solids 63, 575-579 (2002).
[CrossRef]

Huber, G.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Hutcheson, R.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Inokuti, M.

M. Inokuti and F. Hirayama, "Influence of energy transfer by the exchange mechanism on donor luminescence," J. Chem. Phys. 43, 1978-1989 (1965).
[CrossRef]

Jones, R. C.

Krupke, W. F.

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

Kuch, S.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Kway, W. L.

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

Laversenne, L.

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
[CrossRef]

Lou, L.

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

Madej, C.

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

Mangir, M. S.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

Matthews, S.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

McCumber, D. E.

D. E. McCumber, "Einstein relations connecting broadband emission and absorption spectra," Phys. Rev. 136, A954-A957 (1964).
[CrossRef]

Milne, E. A.

E. A. Milne, "The diffusion of imprisoned radiation through a gas," J. Lond. Math. Soc. 1, 40-51 (1926).
[CrossRef]

Mix, E.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Patel, F. D.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Payne, S. A.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

Pédrini, C.

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

Petermann, K.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Peters, V.

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

Pinnow, D. A.

Powell, R. C.

R. C. Powell, Physics of Solid-State Laser Materials (AIP Press, 1998).
[CrossRef]

Reeder, R.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

Rich, T. C.

Shurcliff, W. A.

Smith, L. K.

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

Speth, J.

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

Stehfest, H.

H. Stehfest, "Numerical inversion of Laplace transforms," Commun. ACM 13, 47-49 (1970).
[CrossRef]

Sumida, D. S.

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

Tanimoto, O.

M. Yokota and O. Tanimoto, "Effects of diffusion on energy transfer by resonance," J. Phys. Soc. Jpn. 22, 779-784 (1967).
[CrossRef]

Weber, M. J.

M. J. Weber, "Luminescence decay by energy migration and transfer: observation of diffusion-limited relaxation," Phys. Rev. B 4, 2932-2939 (1971).
[CrossRef]

Yokota, M.

M. Yokota and O. Tanimoto, "Effects of diffusion on energy transfer by resonance," J. Phys. Soc. Jpn. 22, 779-784 (1967).
[CrossRef]

Zhang, L.

L. Zhang and H. Hu, "The effect of OH− on IR emission of Nd3+, Yb3+ and Er3+ doped tetraphosphate glasses," J. Phys. Chem. Solids 63, 575-579 (2002).
[CrossRef]

Appl. Opt.

Commun. ACM

H. Stehfest, "Numerical inversion of Laplace transforms," Commun. ACM 13, 47-49 (1970).
[CrossRef]

IEEE J. Quantum Electron.

D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, "Evaluation of absorption and emission properties of Yb3+ doped crystals for laser applications," IEEE J. Quantum Electron. 29, 1179-1191 (1993).
[CrossRef]

F. D. Patel, E. C. Honea, J. Speth, S. A. Payne, R. Hutcheson, and R. Equall, "Laser demonstration of Yb3Al5O12 (YbAG) and materials properties of highly doped Yb:YAG," IEEE J. Quantum Electron. 37, 135-144 (2001).
[CrossRef]

T. Y. Fan, "Heat generation in Nd:YAG and Yb:YAG," IEEE J. Quantum Electron. 29, 1457-1459 (1993).
[CrossRef]

J. Chem. Phys.

D. L. Dexter, "A theory of sensitized luminescence in solids," J. Chem. Phys. 21, 836-850 (1953).
[CrossRef]

M. Inokuti and F. Hirayama, "Influence of energy transfer by the exchange mechanism on donor luminescence," J. Chem. Phys. 43, 1978-1989 (1965).
[CrossRef]

J. Lond. Math. Soc.

E. A. Milne, "The diffusion of imprisoned radiation through a gas," J. Lond. Math. Soc. 1, 40-51 (1926).
[CrossRef]

J. Lumin.

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]

A. Brenier, G. Boulon, C. Madej, C. Pédrini, and L. Lou, "Kinetics of transfer and back-transfer in thulium-holmium-doped Gd3Ga5O12(Ca,Zr) garnet," J. Lumin. 54, 271-277 (1993).
[CrossRef]

K. Petermann, G. Huber, L. Fornasiero, S. Kuch, E. Mix, V. Peters, and S. A. Basun, "Rare-earth-doped sesquioxides," J. Lumin. 87-89, 973-975 (2000).
[CrossRef]

A. Brenier, "A new evaluation of Yb3+-doped crystals for laser applications," J. Lumin. 92, 199-204 (2001).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem. Solids

L. Zhang and H. Hu, "The effect of OH− on IR emission of Nd3+, Yb3+ and Er3+ doped tetraphosphate glasses," J. Phys. Chem. Solids 63, 575-579 (2002).
[CrossRef]

J. Phys. Soc. Jpn.

M. Yokota and O. Tanimoto, "Effects of diffusion on energy transfer by resonance," J. Phys. Soc. Jpn. 22, 779-784 (1967).
[CrossRef]

Laser Focus World

D. S. Sumida, A. A. Betin, H. Bruesselbach, R. Bryen, S. Matthews, R. Reeder, and M. S. Mangir, "Diode-pumped Yb:YAG catches up with Nd:YAG," Laser Focus World 35, 63-70 (1999).

Opt. Mater.

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, "Radiation trapping and self-quenching analysis in Yb3+, Er3+ and Ho3+ doped Y2O3," Opt. Mater. 24, 103-109 (2003).
[CrossRef]

Phys. Rev.

D. E. McCumber, "Einstein relations connecting broadband emission and absorption spectra," Phys. Rev. 136, A954-A957 (1964).
[CrossRef]

Phys. Rev. B

M. J. Weber, "Luminescence decay by energy migration and transfer: observation of diffusion-limited relaxation," Phys. Rev. B 4, 2932-2939 (1971).
[CrossRef]

Sov. Phys. JETP

A. I. Burshtein, "Hopping mechanism of energy transfer," Sov. Phys. JETP 35, 882-885 (1972).

Z. Naturforsch. A

T. Forster, "Experimentelle und theoretische untersuchung des zsischenmolekularen ubergangs von elektronenanregungsenergie," Z. Naturforsch. A 4, 321-327 (1949).

Other

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

R. C. Powell, Physics of Solid-State Laser Materials (AIP Press, 1998).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Three steps of the excited-state dynamics model.

Fig. 2
Fig. 2

Absorption and emission cross sections of low concentrated Yb:YAG.

Fig. 3
Fig. 3

Yb 3 + : YAG extrinsic ( τ ) and intrinsic ( τ ) excited-state lifetimes and extrinsic thermal loading ξ . The symbols are experimental data from Ref. [10] and the solid curves are from the model (three fitting parameters).

Fig. 4
Fig. 4

Yb 3 + : YAG extrinsic ( τ ) and intrinsic ( τ ) excited-state lifetimes and extrinsic thermal loading ξ . The symbols are experimental data from Ref. [10] and the solid curves are from the model (four fitting parameters).

Fig. 5
Fig. 5

Yb 3 + : YAG extrinsic ( τ ) and intrinsic ( τ ) excited-state lifetimes and extrinsic thermal loading ξ . The symbols are experimental data from Ref. [10] and the solid curves are from the model (five fitting parameters).

Fig. 6
Fig. 6

Laplace transform of the Yb 3 + excited-state time evolution for the 5% content sample.

Fig. 7
Fig. 7

Outlined representation of the sample used in Appendix A.

Tables (4)

Tables Icon

Table 1 Theoretical Expressions of the Physical Parameters

Tables Icon

Table 2 Physical Parameters Extracted from Spectroscopy

Tables Icon

Table 3 Numerical Values of the Parameters Extracted from Spectroscopy

Tables Icon

Table 4 Intrinsic and Extrinsic Quantum Efficiencies and Number of Imprisoned Photons Calculated with the Model

Equations (27)

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d P i ( t ) d t = e ( t ) N D P i ( t ) τ rad + [ i i N D W i i P i ( t ) + i i N D W i i P i ( t ) ] + i i N D D i i P i ( t ) j N A X i j P i ( t ) ,
N ( t ) = i N D P i ( t ) .
N ( t ) = 0 t N 0 ( t τ ) e ( τ ) d τ .
N ̂ ( s ) = N ̂ 0 ( s ) e ̂ ( s ) .
1 τ 0 = ( 2 π 3 ) 3 d C D 2 ,
N ̂ ( s ) = { e ̂ ( s ) + [ 1 τ 0 + k R ( l ) ] N ̂ ( s ) } N ̂ 0 ( s + 1 τ 0 ) .
N ̂ ( s ) = e ̂ ( s ) N ̂ 0 ( s + 1 τ 0 ) 1 [ 1 τ 0 + k R ( l ) ] N ̂ 0 ( s + 1 τ 0 ) .
X ¯ ( t ) = i , j N D N A X i j P i ( t ) i N D P i ( t ) .
i i N D D i i P i ( t ) = i N ( i N D D i i ) P i ( t ) = i N D k R ( l ) P i ( t ) = k R ( l ) i N D P i ( t ) = k R N ( t ) ,
d N d t = e ( t ) ( 1 τ rad k R ) N ( t ) X ¯ ( t ) N ( t ) .
e DA ( t ) X ¯ ( t ) N ( t ) = e ( t ) ( 1 τ rad k R ) N ( t ) X ¯ ( t ) N ( t ) d N d t
e ̂ DA ( s ) = e ̂ ( s ) [ s + 1 τ rad k R ( l ) ] N ̂ ( s ) .
η = 0 e DA ( t ) d t = e ̂ DA ( 0 ) .
η F = 1 η ,
ξ = η λ P + ( 1 η ) ( 1 λ P 1 λ F ) 1 λ P ,
η imp = 0 k R ( l ) N ( t ) d t = k R ( l ) N ̂ ( 0 ) = k R ( l ) τ .
N 0 ( t ) = exp ( t rad b t 1 2 ) ,
b = 4 3 π 3 2 a 1 2 C A ,
N ̂ 0 ( s ) = 1 s + 1 τ rad π 1 2 b 2 ( s + 1 τ rad ) 3 2 exp ( b 2 4 s + 1 τ rad ) erfc [ b 2 ( s + 1 τ rad ) 1 2 ] ,
d = R c 6 τ rad = 3 c 8 π 4 n 2 σ e ( λ ) σ a ( λ ) d λ .
d I λ ( r ) = I λ ( r ) σ a 4 π r 2 ( 4 π r 2 C D d r ) ,
I λ ( 0 ) I λ ( l ) = I λ ( 0 ) [ 1 exp ( σ a C D l ) ] .
I λ ( 0 ) = 8 π c n 2 σ e ( λ ) λ 4 d λ ,
k R ( l ) = 8 π c n 2 { 1 exp [ σ a ( λ ) C D l ] } σ e ( λ ) λ 4 d λ .
sin ( r c ) = 1 n .
F = 3 cos ( r c ) 2 ,
k R ( l ) = 8 π c n 2 ( F + ( 1 F ) { 1 exp [ σ a ( λ ) C D l ] } ) σ e ( λ ) λ 4 d λ .

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