Abstract

The effect of repeated radiative energy transfer on the observed excited-state lifetime τobs of a luminescent species in a solid is studied by Monte Carlo simulations. Increasing the sample path length, the reabsorption coefficient, or the luminescence quantum yield significantly lengthens τobs relative to its intrinsic value τ0. This effect is additionally amplified by total internal reflection. Room-temperature lifetimes of  2F5/2 in YAG:1%Yb3+ and  4I11/2 in YLF:5%Er3+ were measured in a spherically refractive-index-matched geometry, yielding the low values of 0.9489±0.0006 and 3.75±0.01 ms, respectively. It is concluded that lifetimes obtained from non-refractive-index matched experiments are usually significantly overestimated. The technique presented is easily applicable to room-temperature excited-state lifetime measurements of many luminescent solids.

© 1997 Optical Society of America

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References

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  1. E. A. Milne, “The diffusion of imprisoned radiation through a gas,” J. London Math. Soc. 1, 40 (1926).
  2. T. Holstein, “Imprisonment of resonance radiation in gases,” Phys. Rev. 72, 1212 (1947); “Imprisonment of resonance radiation in gases. II,” Phys. Rev. 83, 1159 (1951).
    [CrossRef]
  3. P. J. Walsh, “Imprisonment of resonance radiation in a gaseous discharge,” Phys. Rev. 107, 338 (1957).
    [CrossRef]
  4. A. V. Phelps, “Role of molecular ions, metastable molecules, and resonance radiation in the breakdown of rare gases,” Phys. Rev. 117, 619 (1960).
    [CrossRef]
  5. A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1961).
  6. M. J. Boxall, C. J. Chapman, and R. P. Wayne, “Imprisonment and absorption of resonance radiation,” J. Photochem. 4, 281 (1975).
  7. W. P. Garver, M. R. Pierce, and J. J. Leventhal, “Measurement of atomic densities using radiation trapping,” J. Chem. Phys. 77, 1201 (1982).
    [CrossRef]
  8. J. Huennekens and A. Gallagher, “Radiation diffusion and saturation in optically thick Na vapor,” Phys. Rev. A 28, 238 (1983).
    [CrossRef]
  9. J. W. Mills and G. M. Hieftje, “A detailed consideration of resonance radiation trapping in the argon inductively coupled plasma,” Spectrochim. Acta 39B, 859 (1984).
  10. D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
    [CrossRef]
  11. C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
    [CrossRef]
  12. P. P. Yaney, D. M. Schaeffer, and J. L. Wolf, “Fluorescence and absorption studies of Sr0.999−xGd0.001CexF2.001+x,” Phys. Rev. B 11, 2460 (1975).
    [CrossRef]
  13. D. S. Sumida and T. Y. Fan, “Effect of radiation trapping on fluorescence lifetime and emission cross section measurements in solid-state laser media,” Opt. Lett. 19, 1343 (1994).
    [CrossRef] [PubMed]
  14. W. A. Shurcliff and R. C. Jones, “The trapping of fluorescent light produced within objects of high geometrical symmetry,” J. Opt. Soc. Am. 39, 912 (1949).
    [CrossRef]
  15. 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 (1993).
    [CrossRef]
  16. G. A. Bogomolova, D. N. Vylegzhanin, and A. A. Kaminskii, “Spectral and lasing investigations of garnets with Yb3+ ions,” Sov. Phys. JETP 42, 440 (1976).
  17. P. Lacovara, H. K. Choi, C. A. Wang, R. A. Aggarwal, and T. Y. Fan, “Room-temperature diode-pumped Yb:YAG laser,” Opt. Lett. 16, 1089 (1991).
    [CrossRef] [PubMed]
  18. W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1992).
  19. S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885 (1988).
    [CrossRef]
  20. H. Chou and H. P. Jenssen, in Tunable Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 167–174.
  21. E. P. Chicklis, L. Esterowitz, R. Allen, and M. Kruer, “Stimulated emission at 2.8 μm in Er3+:YLF,” in Proceedings of the International Conference on Lasers (STS, McLean, Va., 1979), pp. 172–178.
  22. S. A. Pollack, D. B. Chang, and M. Birnbaum, “Threefold upconversion laser at 0.83, 1.23, and 1.73 μm in Er:YLF pumped with a 1.53 μm Er glass laser,” Appl. Phys. Lett. 54, 869 (1989).
    [CrossRef]
  23. S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
    [CrossRef]
  24. J. M. F. van Dijk and M. F. H. Schuurmans, “On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions,” J. Chem. Phys. 78, 5317 (1983).
    [CrossRef]

1995 (2)

D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
[CrossRef]

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

1994 (1)

1993 (1)

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 (1993).
[CrossRef]

1991 (2)

P. Lacovara, H. K. Choi, C. A. Wang, R. A. Aggarwal, and T. Y. Fan, “Room-temperature diode-pumped Yb:YAG laser,” Opt. Lett. 16, 1089 (1991).
[CrossRef] [PubMed]

S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
[CrossRef]

1989 (1)

S. A. Pollack, D. B. Chang, and M. Birnbaum, “Threefold upconversion laser at 0.83, 1.23, and 1.73 μm in Er:YLF pumped with a 1.53 μm Er glass laser,” Appl. Phys. Lett. 54, 869 (1989).
[CrossRef]

1988 (1)

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885 (1988).
[CrossRef]

1983 (2)

J. M. F. van Dijk and M. F. H. Schuurmans, “On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions,” J. Chem. Phys. 78, 5317 (1983).
[CrossRef]

J. Huennekens and A. Gallagher, “Radiation diffusion and saturation in optically thick Na vapor,” Phys. Rev. A 28, 238 (1983).
[CrossRef]

1982 (1)

W. P. Garver, M. R. Pierce, and J. J. Leventhal, “Measurement of atomic densities using radiation trapping,” J. Chem. Phys. 77, 1201 (1982).
[CrossRef]

1976 (1)

G. A. Bogomolova, D. N. Vylegzhanin, and A. A. Kaminskii, “Spectral and lasing investigations of garnets with Yb3+ ions,” Sov. Phys. JETP 42, 440 (1976).

1975 (1)

P. P. Yaney, D. M. Schaeffer, and J. L. Wolf, “Fluorescence and absorption studies of Sr0.999−xGd0.001CexF2.001+x,” Phys. Rev. B 11, 2460 (1975).
[CrossRef]

1960 (1)

A. V. Phelps, “Role of molecular ions, metastable molecules, and resonance radiation in the breakdown of rare gases,” Phys. Rev. 117, 619 (1960).
[CrossRef]

1957 (1)

P. J. Walsh, “Imprisonment of resonance radiation in a gaseous discharge,” Phys. Rev. 107, 338 (1957).
[CrossRef]

1949 (1)

Aggarwal, R. A.

Auzel, F.

S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
[CrossRef]

Benredjem, D.

D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
[CrossRef]

Birnbaum, M.

S. A. Pollack, D. B. Chang, and M. Birnbaum, “Threefold upconversion laser at 0.83, 1.23, and 1.73 μm in Er:YLF pumped with a 1.53 μm Er glass laser,” Appl. Phys. Lett. 54, 869 (1989).
[CrossRef]

Bogomolova, G. A.

G. A. Bogomolova, D. N. Vylegzhanin, and A. A. Kaminskii, “Spectral and lasing investigations of garnets with Yb3+ ions,” Sov. Phys. JETP 42, 440 (1976).

Chai, B. H. T.

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

Chang, D. B.

S. A. Pollack, D. B. Chang, and M. Birnbaum, “Threefold upconversion laser at 0.83, 1.23, and 1.73 μm in Er:YLF pumped with a 1.53 μm Er glass laser,” Appl. Phys. Lett. 54, 869 (1989).
[CrossRef]

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885 (1988).
[CrossRef]

Chase, L. 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 (1993).
[CrossRef]

Choi, H. K.

DeLoach, L. D.

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 (1993).
[CrossRef]

Fan, T. Y.

Gallagher, A.

J. Huennekens and A. Gallagher, “Radiation diffusion and saturation in optically thick Na vapor,” Phys. Rev. A 28, 238 (1983).
[CrossRef]

Garver, W. P.

W. P. Garver, M. R. Pierce, and J. J. Leventhal, “Measurement of atomic densities using radiation trapping,” J. Chem. Phys. 77, 1201 (1982).
[CrossRef]

Guennou, H.

D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
[CrossRef]

Hubert, S.

S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
[CrossRef]

Huennekens, J.

J. Huennekens and A. Gallagher, “Radiation diffusion and saturation in optically thick Na vapor,” Phys. Rev. A 28, 238 (1983).
[CrossRef]

Jones, R. C.

Kaminskii, A. A.

G. A. Bogomolova, D. N. Vylegzhanin, and A. A. Kaminskii, “Spectral and lasing investigations of garnets with Yb3+ ions,” Sov. Phys. JETP 42, 440 (1976).

Krupke, W. F.

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

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 (1993).
[CrossRef]

Kway, W. 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 (1993).
[CrossRef]

Lacovara, P.

Leventhal, J. J.

W. P. Garver, M. R. Pierce, and J. J. Leventhal, “Measurement of atomic densities using radiation trapping,” J. Chem. Phys. 77, 1201 (1982).
[CrossRef]

Marshall, C. D.

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

Meichenin, D.

S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
[CrossRef]

Möller, C.

D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
[CrossRef]

Payne, S. A.

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

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 (1993).
[CrossRef]

Phelps, A. V.

A. V. Phelps, “Role of molecular ions, metastable molecules, and resonance radiation in the breakdown of rare gases,” Phys. Rev. 117, 619 (1960).
[CrossRef]

Pierce, M. R.

W. P. Garver, M. R. Pierce, and J. J. Leventhal, “Measurement of atomic densities using radiation trapping,” J. Chem. Phys. 77, 1201 (1982).
[CrossRef]

Pollack, S. A.

S. A. Pollack, D. B. Chang, and M. Birnbaum, “Threefold upconversion laser at 0.83, 1.23, and 1.73 μm in Er:YLF pumped with a 1.53 μm Er glass laser,” Appl. Phys. Lett. 54, 869 (1989).
[CrossRef]

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885 (1988).
[CrossRef]

Powell, H. T.

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

Schaeffer, D. M.

P. P. Yaney, D. M. Schaeffer, and J. L. Wolf, “Fluorescence and absorption studies of Sr0.999−xGd0.001CexF2.001+x,” Phys. Rev. B 11, 2460 (1975).
[CrossRef]

Schuurmans, M. F. H.

J. M. F. van Dijk and M. F. H. Schuurmans, “On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions,” J. Chem. Phys. 78, 5317 (1983).
[CrossRef]

Shurcliff, W. A.

Smith, L. K.

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

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 (1993).
[CrossRef]

Sumida, D. S.

Sureau, A.

D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
[CrossRef]

van Dijk, J. M. F.

J. M. F. van Dijk and M. F. H. Schuurmans, “On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions,” J. Chem. Phys. 78, 5317 (1983).
[CrossRef]

Vylegzhanin, D. N.

G. A. Bogomolova, D. N. Vylegzhanin, and A. A. Kaminskii, “Spectral and lasing investigations of garnets with Yb3+ ions,” Sov. Phys. JETP 42, 440 (1976).

Walsh, P. J.

P. J. Walsh, “Imprisonment of resonance radiation in a gaseous discharge,” Phys. Rev. 107, 338 (1957).
[CrossRef]

Wang, C. A.

Wolf, J. L.

P. P. Yaney, D. M. Schaeffer, and J. L. Wolf, “Fluorescence and absorption studies of Sr0.999−xGd0.001CexF2.001+x,” Phys. Rev. B 11, 2460 (1975).
[CrossRef]

Yaney, P. P.

P. P. Yaney, D. M. Schaeffer, and J. L. Wolf, “Fluorescence and absorption studies of Sr0.999−xGd0.001CexF2.001+x,” Phys. Rev. B 11, 2460 (1975).
[CrossRef]

Zhou, B. W.

S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

S. A. Pollack, D. B. Chang, and M. Birnbaum, “Threefold upconversion laser at 0.83, 1.23, and 1.73 μm in Er:YLF pumped with a 1.53 μm Er glass laser,” Appl. Phys. Lett. 54, 869 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

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 (1993).
[CrossRef]

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

C. D. Marshall, S. A. Payne, L. K. Smith, H. T. Powell, W. F. Krupke, and B. H. T. Chai, “1.047-μm Yb:Sr5(PO4)3F energy storage optical amplifier,” IEEE J. Sel. Topics Quantum Electron. 1, 67 (1995).
[CrossRef]

J. Appl. Phys. (1)

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2, and CaF2 crystals,” J. Appl. Phys. 64, 2885 (1988).
[CrossRef]

J. Chem. Phys. (2)

J. M. F. van Dijk and M. F. H. Schuurmans, “On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions,” J. Chem. Phys. 78, 5317 (1983).
[CrossRef]

W. P. Garver, M. R. Pierce, and J. J. Leventhal, “Measurement of atomic densities using radiation trapping,” J. Chem. Phys. 77, 1201 (1982).
[CrossRef]

J. Lumin. (1)

S. Hubert, D. Meichenin, B. W. Zhou, and F. Auzel, “Emission properties, oscillator strengths and laser parameters of Er3+ in LiYF4 at 2.7 μm,” J. Lumin. 50, 7 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Phys. Lett. A (1)

D. Benredjem, A. Sureau, H. Guennou, and C. Möller, “Radiation trapping and X-ray lasing in Al10+ in the recombination scheme,” Phys. Lett. A 203, 137 (1995).
[CrossRef]

Phys. Rev. (2)

P. J. Walsh, “Imprisonment of resonance radiation in a gaseous discharge,” Phys. Rev. 107, 338 (1957).
[CrossRef]

A. V. Phelps, “Role of molecular ions, metastable molecules, and resonance radiation in the breakdown of rare gases,” Phys. Rev. 117, 619 (1960).
[CrossRef]

Phys. Rev. A (1)

J. Huennekens and A. Gallagher, “Radiation diffusion and saturation in optically thick Na vapor,” Phys. Rev. A 28, 238 (1983).
[CrossRef]

Phys. Rev. B (1)

P. P. Yaney, D. M. Schaeffer, and J. L. Wolf, “Fluorescence and absorption studies of Sr0.999−xGd0.001CexF2.001+x,” Phys. Rev. B 11, 2460 (1975).
[CrossRef]

Sov. Phys. JETP (1)

G. A. Bogomolova, D. N. Vylegzhanin, and A. A. Kaminskii, “Spectral and lasing investigations of garnets with Yb3+ ions,” Sov. Phys. JETP 42, 440 (1976).

Other (8)

W. Koechner, Solid-State Laser Engineering (Springer-Verlag, Berlin, 1992).

J. W. Mills and G. M. Hieftje, “A detailed consideration of resonance radiation trapping in the argon inductively coupled plasma,” Spectrochim. Acta 39B, 859 (1984).

E. A. Milne, “The diffusion of imprisoned radiation through a gas,” J. London Math. Soc. 1, 40 (1926).

T. Holstein, “Imprisonment of resonance radiation in gases,” Phys. Rev. 72, 1212 (1947); “Imprisonment of resonance radiation in gases. II,” Phys. Rev. 83, 1159 (1951).
[CrossRef]

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. Press, Cambridge, 1961).

M. J. Boxall, C. J. Chapman, and R. P. Wayne, “Imprisonment and absorption of resonance radiation,” J. Photochem. 4, 281 (1975).

H. Chou and H. P. Jenssen, in Tunable Solid State Lasers, M. L. Shand and H. P. Jenssen, eds., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1989), pp. 167–174.

E. P. Chicklis, L. Esterowitz, R. Allen, and M. Kruer, “Stimulated emission at 2.8 μm in Er3+:YLF,” in Proceedings of the International Conference on Lasers (STS, McLean, Va., 1979), pp. 172–178.

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Figures (3)

Fig. 1
Fig. 1

Excited-state lifetime lengthening factors κ=τobs/τ0 calculated by a Monte Carlo simulation of the model described in Subsection 2.A for two average sample path lengths l¯ and various luminescence quantum yields η and reabsorption coefficients σrρ. The filled and open circles indicate the  4I11/2  4I15/2 (YLF:5%Er3+) and  2F5/2  2F7/2 (YAG:1%Yb3+) transitions, respectively (see Section 5).

Fig. 2
Fig. 2

(a) Defining the sphere radius r with respect to the sample size (a3) and the sample refractive index (ns) such that no angle φ at the sphere–air (n0=1) interface is greater than the critical angle (φcrit) for TIR. (b) Schematic of the actual design of the refractive-index-matched glass sphere (r=18 mm) used in the experiments.

Fig. 3
Fig. 3

Room-temperature luminescence transients (dashed curves) of (a)  2F5/2 (YAG:1%Yb3+) and (b)  4I11/2 (YLF:5%Er3+) measured for samples positioned in the experimental geometry shown in Fig. 2(b). u and m denote non-refractive-index-matched (surrounded by air) and refractive-index-matched (immersed in appropriate index-matching liquid; see Section 3) samples, respectively. The solid curves are least-squares fits to a single exponential, and the resulting excited-state lifetimes are summarized in Table 1.

Tables (1)

Tables Icon

Table 1 Room-Temperature Excited-State Lifetimes of  2F5/2 (YAG:1%Yb3+) and  4I11/2 (YLF:5%Er3+)a

Equations (2)

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

r>ans2n0.
m¯=Δl¯d¯TIRF

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