Abstract

Multiphonon relaxation rate saturation is observed for rare-earth-doped glasses for high excited-state densities. This behavior is analyzed in a statistical approach; a theoretical model for the microscopic process is proposed. A phonon bottleneck effect on radiationless relaxation related to an accepting-modes saturation is suggested. At high excited-state density, ions in a phonon diffusion volume simultaneously fill the accepting modes. The critical distance below which excited ions share a common phonon bath is related to the phonon diffusion length in the host and deduced from our model. The results are in good agreement with the phonon mean free path independently deduced from sound velocity, thermal conductivity, and heat capacity.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968).
    [CrossRef]
  2. C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977).
    [CrossRef]
  3. F. Auzel, “Multiphonon interaction of excited luminescent centers in the weak coupling limit: nonradiative decay and multiphonon side bands,” in Luminescence of Inorganic Solids, B. Di Bartolo, ed. (Plenum, New York, 1978), pp. 67–113.
  4. Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
    [CrossRef]
  5. Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
    [CrossRef]
  6. R. Reisfeld and Y. Eckstein, “Radiative and non-radiative transition probabilities and quantum yields for excited states of Er3+ in germanate and tellurite glasses,” J. Non-Cryst. Solids 15, 125–140 (1974).
    [CrossRef]
  7. A. M. Stoneham, “The phonon bottleneck in paramagnetic crystals,” Proc. Phys. Soc. London 86, 1163–1177 (1965).
    [CrossRef]
  8. J. I. Dijkhuis, A. C. Van der Pol, and H. W. de Wijn, “Spectral width of optically generated bottleneck 29 cm−1 phonons in ruby,” Phys. Rev. Lett. 37, 1554–1557 (1976).
    [CrossRef]
  9. L. Godfrey, J. E. Rives, and R. S. Meltzer, “Anomalous luminescence decay in LaF3:Pr3+ due to resonant trapping and bottlenecking of 23 cm−1 phonons,” J. Lumin. 18/19, 929–932 (1979).
    [CrossRef]
  10. S. G. Demos and R. R. Alfano, “Subpicosecond time-resolved Raman investigation of optical phonon modes in Cr-doped forsterite,” Phys. Rev. B 52, 987–996 (1995).
    [CrossRef]
  11. D. M. Calistru, S. G. Demos, and R. R. Alfano, “Dynamics of local modes during nonradiative relaxation,” Phys. Rev. Lett. 78, 374–377 (1997).
    [CrossRef]
  12. F. Auzel and F. Pellé, “Saturation of accepting modes in multiphonon radiative transitions,” C. R. Acad. Sci. IIb, 835–841 (1996).
  13. F. Auzel and F. Pellé, “Concentration and excitation effects in multiphonon nonradiative transitions of rare-earth ions,” J. Lumin. 69, 249–255 (1996).
    [CrossRef]
  14. F. Auzel and F. Pellé, “Bottleneck in multiphonon nonradiative transitions,” Phys. Rev. B 55, 11,006–11,009 (1997).
    [CrossRef]
  15. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
    [CrossRef]
  16. G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
    [CrossRef]
  17. F. Auzel, “Contribution à l’étude spectroscopique de verres dopés avec Er3+ pour obtenir l’effect laser,” Ph.D. dissertation (University of Paris, Paris, 1968).
  18. M. J. Weber, “Probabilities for radiative and nonradiative decay of Er3+ in LaF3,” Phys. Rev. B 157, 262–272 (1967).
    [CrossRef]
  19. W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, “Energy level structure and transition probabilities of the rare earth lanthanides in LaF3,” internal report (Johns Hopkins University, Baltimore, Md., 1997).
  20. N. Spector, R. Reisfeld, and L. Boehm, “Eigenstates and radiative transition probabilities for Tm3+(4f12) in phosphate and tellurite glasses,” Chem. Phys. Lett. 49, 49–53 (1977).
    [CrossRef]
  21. H. Takebe, S. Fujino, and K. Morinaga, “Refractive index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm,” J. Am. Ceram. Soc. 77, 2455–2457 (1994).
    [CrossRef]
  22. F. Pellé, N. Gardant, and F. Auzel, “Nonradiative processes in Yb3+-doped borate glasses,” to be submitted in J. Lumin.
  23. 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, 5317–5323 (1983).
    [CrossRef]
  24. A. Kiel, “Line broadening in the excited state of paramagnetic crystals,” in Paramagnetic Resonance, W. Low, ed. (Academic, New York, 1963), pp. 525–534.
  25. H. W. Moos, “Spectroscopic relaxation processes of rare-earth ions in crystals,” J. Lumin. 1/2, 106–121 (1970).
    [CrossRef]
  26. W. E. Hagston and J. E. Lowther, “Multiphonon processes in rare-earth ions,” Physica (Amsterdam) 70, 40–61 (1973).
    [CrossRef]
  27. L. A. Riseberg and M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, pp. 91–159.
  28. K. Huang and A. Rhys, “Theory of light absorption and non-radiative transition in F-centres,” Proc. R. Soc. London, Ser. A 204, 406–423 (1950).
    [CrossRef]
  29. S. Fisher, “Correlation function approach to radiationless transitions,” J. Chem. Phys. 53, 3195–3207 (1970).
    [CrossRef]
  30. M. Lax, “The Franck–Condon principle and its application to crystals,” J. Chem. Phys. 20, 1752–1760 (1952).
    [CrossRef]
  31. R. Kubo and Y. Toyozawa, “Application of the method of generating function to radiative and non-radiative transitions of a trapped electron in a crystal,” Prog. Theor. Phys. 13, 160–182 (1955).
    [CrossRef]
  32. F. K. Fong, ed., Theory of Molecular Relaxation: Applications in Chemistry and Biology (Wiley, New York, 1975).
  33. C. W. Struck and W. H. Fonger, “Unified model of the temperature quenching of narrow-line and broad-band emissions,” J. Lumin. 10, 1–30 (1975).
    [CrossRef]
  34. T. Miyakawa and D. L. Dexter, “Phonon sidebands, multiphonon relaxation of excited states and phonon assisted energy transfer between ions in solids,” Phys. Rev. B 1, 2961–2969 (1970).
    [CrossRef]
  35. E. Gutsche, “Non-Condon approximation and the static approach in the theory of nonradiative multiphonon transitions,” Phys. Status Solidi B 109, 583–597 (1982).
    [CrossRef]
  36. C. Kittel, ed., Introduction to Solid State Physics (Wiley, New York, 1971).
  37. E. H. Ratcliffe, “A survey of most probable values for the thermal conductivities of glasses between about −150 and 100 °C, including new data on twenty-two glasses and a working formula for the calculation of conductivity from composition,” Glass Technol. 4, 113–128 (1963).
  38. H. Scholze, ed., GLAS, Natur. Struktur und Eigenschaften (Springer-Verlag, Berlin, 1977).
  39. C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2363 (1993).
    [CrossRef]

1997

D. M. Calistru, S. G. Demos, and R. R. Alfano, “Dynamics of local modes during nonradiative relaxation,” Phys. Rev. Lett. 78, 374–377 (1997).
[CrossRef]

F. Auzel and F. Pellé, “Bottleneck in multiphonon nonradiative transitions,” Phys. Rev. B 55, 11,006–11,009 (1997).
[CrossRef]

1996

F. Auzel and F. Pellé, “Concentration and excitation effects in multiphonon nonradiative transitions of rare-earth ions,” J. Lumin. 69, 249–255 (1996).
[CrossRef]

1995

Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
[CrossRef]

S. G. Demos and R. R. Alfano, “Subpicosecond time-resolved Raman investigation of optical phonon modes in Cr-doped forsterite,” Phys. Rev. B 52, 987–996 (1995).
[CrossRef]

1994

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

H. Takebe, S. Fujino, and K. Morinaga, “Refractive index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm,” J. Am. Ceram. Soc. 77, 2455–2457 (1994).
[CrossRef]

1993

1983

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, 5317–5323 (1983).
[CrossRef]

1982

E. Gutsche, “Non-Condon approximation and the static approach in the theory of nonradiative multiphonon transitions,” Phys. Status Solidi B 109, 583–597 (1982).
[CrossRef]

1979

L. Godfrey, J. E. Rives, and R. S. Meltzer, “Anomalous luminescence decay in LaF3:Pr3+ due to resonant trapping and bottlenecking of 23 cm−1 phonons,” J. Lumin. 18/19, 929–932 (1979).
[CrossRef]

1977

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977).
[CrossRef]

N. Spector, R. Reisfeld, and L. Boehm, “Eigenstates and radiative transition probabilities for Tm3+(4f12) in phosphate and tellurite glasses,” Chem. Phys. Lett. 49, 49–53 (1977).
[CrossRef]

1976

J. I. Dijkhuis, A. C. Van der Pol, and H. W. de Wijn, “Spectral width of optically generated bottleneck 29 cm−1 phonons in ruby,” Phys. Rev. Lett. 37, 1554–1557 (1976).
[CrossRef]

1975

C. W. Struck and W. H. Fonger, “Unified model of the temperature quenching of narrow-line and broad-band emissions,” J. Lumin. 10, 1–30 (1975).
[CrossRef]

1974

R. Reisfeld and Y. Eckstein, “Radiative and non-radiative transition probabilities and quantum yields for excited states of Er3+ in germanate and tellurite glasses,” J. Non-Cryst. Solids 15, 125–140 (1974).
[CrossRef]

1973

W. E. Hagston and J. E. Lowther, “Multiphonon processes in rare-earth ions,” Physica (Amsterdam) 70, 40–61 (1973).
[CrossRef]

1970

S. Fisher, “Correlation function approach to radiationless transitions,” J. Chem. Phys. 53, 3195–3207 (1970).
[CrossRef]

T. Miyakawa and D. L. Dexter, “Phonon sidebands, multiphonon relaxation of excited states and phonon assisted energy transfer between ions in solids,” Phys. Rev. B 1, 2961–2969 (1970).
[CrossRef]

H. W. Moos, “Spectroscopic relaxation processes of rare-earth ions in crystals,” J. Lumin. 1/2, 106–121 (1970).
[CrossRef]

1968

L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968).
[CrossRef]

1967

M. J. Weber, “Probabilities for radiative and nonradiative decay of Er3+ in LaF3,” Phys. Rev. B 157, 262–272 (1967).
[CrossRef]

1965

A. M. Stoneham, “The phonon bottleneck in paramagnetic crystals,” Proc. Phys. Soc. London 86, 1163–1177 (1965).
[CrossRef]

1963

E. H. Ratcliffe, “A survey of most probable values for the thermal conductivities of glasses between about −150 and 100 °C, including new data on twenty-two glasses and a working formula for the calculation of conductivity from composition,” Glass Technol. 4, 113–128 (1963).

1962

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
[CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
[CrossRef]

1955

R. Kubo and Y. Toyozawa, “Application of the method of generating function to radiative and non-radiative transitions of a trapped electron in a crystal,” Prog. Theor. Phys. 13, 160–182 (1955).
[CrossRef]

1952

M. Lax, “The Franck–Condon principle and its application to crystals,” J. Chem. Phys. 20, 1752–1760 (1952).
[CrossRef]

1950

K. Huang and A. Rhys, “Theory of light absorption and non-radiative transition in F-centres,” Proc. R. Soc. London, Ser. A 204, 406–423 (1950).
[CrossRef]

Alfano, R. R.

D. M. Calistru, S. G. Demos, and R. R. Alfano, “Dynamics of local modes during nonradiative relaxation,” Phys. Rev. Lett. 78, 374–377 (1997).
[CrossRef]

S. G. Demos and R. R. Alfano, “Subpicosecond time-resolved Raman investigation of optical phonon modes in Cr-doped forsterite,” Phys. Rev. B 52, 987–996 (1995).
[CrossRef]

Auzel, F.

F. Auzel and F. Pellé, “Bottleneck in multiphonon nonradiative transitions,” Phys. Rev. B 55, 11,006–11,009 (1997).
[CrossRef]

F. Auzel and F. Pellé, “Concentration and excitation effects in multiphonon nonradiative transitions of rare-earth ions,” J. Lumin. 69, 249–255 (1996).
[CrossRef]

C. Gouedard, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2363 (1993).
[CrossRef]

Basiev, T. T.

Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
[CrossRef]

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

Boehm, L.

N. Spector, R. Reisfeld, and L. Boehm, “Eigenstates and radiative transition probabilities for Tm3+(4f12) in phosphate and tellurite glasses,” Chem. Phys. Lett. 49, 49–53 (1977).
[CrossRef]

Calistru, D. M.

D. M. Calistru, S. G. Demos, and R. R. Alfano, “Dynamics of local modes during nonradiative relaxation,” Phys. Rev. Lett. 78, 374–377 (1997).
[CrossRef]

de Wijn, H. W.

J. I. Dijkhuis, A. C. Van der Pol, and H. W. de Wijn, “Spectral width of optically generated bottleneck 29 cm−1 phonons in ruby,” Phys. Rev. Lett. 37, 1554–1557 (1976).
[CrossRef]

Demos, S. G.

D. M. Calistru, S. G. Demos, and R. R. Alfano, “Dynamics of local modes during nonradiative relaxation,” Phys. Rev. Lett. 78, 374–377 (1997).
[CrossRef]

S. G. Demos and R. R. Alfano, “Subpicosecond time-resolved Raman investigation of optical phonon modes in Cr-doped forsterite,” Phys. Rev. B 52, 987–996 (1995).
[CrossRef]

Dexter, D. L.

T. Miyakawa and D. L. Dexter, “Phonon sidebands, multiphonon relaxation of excited states and phonon assisted energy transfer between ions in solids,” Phys. Rev. B 1, 2961–2969 (1970).
[CrossRef]

Dijkhuis, J. I.

J. I. Dijkhuis, A. C. Van der Pol, and H. W. de Wijn, “Spectral width of optically generated bottleneck 29 cm−1 phonons in ruby,” Phys. Rev. Lett. 37, 1554–1557 (1976).
[CrossRef]

Eckstein, Y.

R. Reisfeld and Y. Eckstein, “Radiative and non-radiative transition probabilities and quantum yields for excited states of Er3+ in germanate and tellurite glasses,” J. Non-Cryst. Solids 15, 125–140 (1974).
[CrossRef]

Fisher, S.

S. Fisher, “Correlation function approach to radiationless transitions,” J. Chem. Phys. 53, 3195–3207 (1970).
[CrossRef]

Fonger, W. H.

C. W. Struck and W. H. Fonger, “Unified model of the temperature quenching of narrow-line and broad-band emissions,” J. Lumin. 10, 1–30 (1975).
[CrossRef]

Fujino, S.

H. Takebe, S. Fujino, and K. Morinaga, “Refractive index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm,” J. Am. Ceram. Soc. 77, 2455–2457 (1994).
[CrossRef]

Godfrey, L.

L. Godfrey, J. E. Rives, and R. S. Meltzer, “Anomalous luminescence decay in LaF3:Pr3+ due to resonant trapping and bottlenecking of 23 cm−1 phonons,” J. Lumin. 18/19, 929–932 (1979).
[CrossRef]

Gouedard, C.

Gutsche, E.

E. Gutsche, “Non-Condon approximation and the static approach in the theory of nonradiative multiphonon transitions,” Phys. Status Solidi B 109, 583–597 (1982).
[CrossRef]

Hagston, W. E.

W. E. Hagston and J. E. Lowther, “Multiphonon processes in rare-earth ions,” Physica (Amsterdam) 70, 40–61 (1973).
[CrossRef]

Huang, K.

K. Huang and A. Rhys, “Theory of light absorption and non-radiative transition in F-centres,” Proc. R. Soc. London, Ser. A 204, 406–423 (1950).
[CrossRef]

Husson, D.

Judd, B. R.

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
[CrossRef]

Kubo, R.

R. Kubo and Y. Toyozawa, “Application of the method of generating function to radiative and non-radiative transitions of a trapped electron in a crystal,” Prog. Theor. Phys. 13, 160–182 (1955).
[CrossRef]

Lax, M.

M. Lax, “The Franck–Condon principle and its application to crystals,” J. Chem. Phys. 20, 1752–1760 (1952).
[CrossRef]

Layne, C. B.

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977).
[CrossRef]

Lowdermilk, W. H.

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977).
[CrossRef]

Lowther, J. E.

W. E. Hagston and J. E. Lowther, “Multiphonon processes in rare-earth ions,” Physica (Amsterdam) 70, 40–61 (1973).
[CrossRef]

Meltzer, R. S.

L. Godfrey, J. E. Rives, and R. S. Meltzer, “Anomalous luminescence decay in LaF3:Pr3+ due to resonant trapping and bottlenecking of 23 cm−1 phonons,” J. Lumin. 18/19, 929–932 (1979).
[CrossRef]

Migus, A.

Miyakawa, T.

T. Miyakawa and D. L. Dexter, “Phonon sidebands, multiphonon relaxation of excited states and phonon assisted energy transfer between ions in solids,” Phys. Rev. B 1, 2961–2969 (1970).
[CrossRef]

Moos, H. W.

H. W. Moos, “Spectroscopic relaxation processes of rare-earth ions in crystals,” J. Lumin. 1/2, 106–121 (1970).
[CrossRef]

L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968).
[CrossRef]

Morinaga, K.

H. Takebe, S. Fujino, and K. Morinaga, “Refractive index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm,” J. Am. Ceram. Soc. 77, 2455–2457 (1994).
[CrossRef]

Ofelt, G. S.

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
[CrossRef]

Orlovskii, Y. V.

Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
[CrossRef]

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

Pellé, F.

F. Auzel and F. Pellé, “Bottleneck in multiphonon nonradiative transitions,” Phys. Rev. B 55, 11,006–11,009 (1997).
[CrossRef]

F. Auzel and F. Pellé, “Concentration and excitation effects in multiphonon nonradiative transitions of rare-earth ions,” J. Lumin. 69, 249–255 (1996).
[CrossRef]

Powell, R. C.

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

Pukhov, K. K.

Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
[CrossRef]

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

Ratcliffe, E. H.

E. H. Ratcliffe, “A survey of most probable values for the thermal conductivities of glasses between about −150 and 100 °C, including new data on twenty-two glasses and a working formula for the calculation of conductivity from composition,” Glass Technol. 4, 113–128 (1963).

Reeves, R. J.

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

Reisfeld, R.

N. Spector, R. Reisfeld, and L. Boehm, “Eigenstates and radiative transition probabilities for Tm3+(4f12) in phosphate and tellurite glasses,” Chem. Phys. Lett. 49, 49–53 (1977).
[CrossRef]

R. Reisfeld and Y. Eckstein, “Radiative and non-radiative transition probabilities and quantum yields for excited states of Er3+ in germanate and tellurite glasses,” J. Non-Cryst. Solids 15, 125–140 (1974).
[CrossRef]

Rhys, A.

K. Huang and A. Rhys, “Theory of light absorption and non-radiative transition in F-centres,” Proc. R. Soc. London, Ser. A 204, 406–423 (1950).
[CrossRef]

Riseberg, L. A.

L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968).
[CrossRef]

Rives, J. E.

L. Godfrey, J. E. Rives, and R. S. Meltzer, “Anomalous luminescence decay in LaF3:Pr3+ due to resonant trapping and bottlenecking of 23 cm−1 phonons,” J. Lumin. 18/19, 929–932 (1979).
[CrossRef]

Sauteret, C.

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, 5317–5323 (1983).
[CrossRef]

Spector, N.

N. Spector, R. Reisfeld, and L. Boehm, “Eigenstates and radiative transition probabilities for Tm3+(4f12) in phosphate and tellurite glasses,” Chem. Phys. Lett. 49, 49–53 (1977).
[CrossRef]

Stoneham, A. M.

A. M. Stoneham, “The phonon bottleneck in paramagnetic crystals,” Proc. Phys. Soc. London 86, 1163–1177 (1965).
[CrossRef]

Struck, C. W.

C. W. Struck and W. H. Fonger, “Unified model of the temperature quenching of narrow-line and broad-band emissions,” J. Lumin. 10, 1–30 (1975).
[CrossRef]

Takebe, H.

H. Takebe, S. Fujino, and K. Morinaga, “Refractive index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm,” J. Am. Ceram. Soc. 77, 2455–2457 (1994).
[CrossRef]

Toyozawa, Y.

R. Kubo and Y. Toyozawa, “Application of the method of generating function to radiative and non-radiative transitions of a trapped electron in a crystal,” Prog. Theor. Phys. 13, 160–182 (1955).
[CrossRef]

Tsuboi, T.

Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
[CrossRef]

Van der Pol, A. C.

J. I. Dijkhuis, A. C. Van der Pol, and H. W. de Wijn, “Spectral width of optically generated bottleneck 29 cm−1 phonons in ruby,” Phys. Rev. Lett. 37, 1554–1557 (1976).
[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, 5317–5323 (1983).
[CrossRef]

Weber, M. J.

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977).
[CrossRef]

M. J. Weber, “Probabilities for radiative and nonradiative decay of Er3+ in LaF3,” Phys. Rev. B 157, 262–272 (1967).
[CrossRef]

Chem. Phys. Lett.

N. Spector, R. Reisfeld, and L. Boehm, “Eigenstates and radiative transition probabilities for Tm3+(4f12) in phosphate and tellurite glasses,” Chem. Phys. Lett. 49, 49–53 (1977).
[CrossRef]

Glass Technol.

E. H. Ratcliffe, “A survey of most probable values for the thermal conductivities of glasses between about −150 and 100 °C, including new data on twenty-two glasses and a working formula for the calculation of conductivity from composition,” Glass Technol. 4, 113–128 (1963).

J. Am. Ceram. Soc.

H. Takebe, S. Fujino, and K. Morinaga, “Refractive index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm,” J. Am. Ceram. Soc. 77, 2455–2457 (1994).
[CrossRef]

J. Chem. Phys.

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, 5317–5323 (1983).
[CrossRef]

S. Fisher, “Correlation function approach to radiationless transitions,” J. Chem. Phys. 53, 3195–3207 (1970).
[CrossRef]

M. Lax, “The Franck–Condon principle and its application to crystals,” J. Chem. Phys. 20, 1752–1760 (1952).
[CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
[CrossRef]

J. Lumin.

F. Auzel and F. Pellé, “Concentration and excitation effects in multiphonon nonradiative transitions of rare-earth ions,” J. Lumin. 69, 249–255 (1996).
[CrossRef]

L. Godfrey, J. E. Rives, and R. S. Meltzer, “Anomalous luminescence decay in LaF3:Pr3+ due to resonant trapping and bottlenecking of 23 cm−1 phonons,” J. Lumin. 18/19, 929–932 (1979).
[CrossRef]

C. W. Struck and W. H. Fonger, “Unified model of the temperature quenching of narrow-line and broad-band emissions,” J. Lumin. 10, 1–30 (1975).
[CrossRef]

H. W. Moos, “Spectroscopic relaxation processes of rare-earth ions in crystals,” J. Lumin. 1/2, 106–121 (1970).
[CrossRef]

J. Non-Cryst. Solids

R. Reisfeld and Y. Eckstein, “Radiative and non-radiative transition probabilities and quantum yields for excited states of Er3+ in germanate and tellurite glasses,” J. Non-Cryst. Solids 15, 125–140 (1974).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Mater.

Y. V. Orlovskii, K. K. Pukhov, T. T. Basiev, and T. Tsuboi, “Nonlinear mechanism of multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions,” Opt. Mater. 4, 583–595 (1995).
[CrossRef]

Phys. Rev.

L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968).
[CrossRef]

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
[CrossRef]

Phys. Rev. B

F. Auzel and F. Pellé, “Bottleneck in multiphonon nonradiative transitions,” Phys. Rev. B 55, 11,006–11,009 (1997).
[CrossRef]

C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977).
[CrossRef]

Y. V. Orlovskii, R. J. Reeves, R. C. Powell, T. T. Basiev, and K. K. Pukhov, “Multiple-phonon nonradiative relaxation: experimental rates in fluoride crystals doped with Er3+ and Nd3+ ions and a theoretical model,” Phys. Rev. B 49, 3821–3830 (1994).
[CrossRef]

S. G. Demos and R. R. Alfano, “Subpicosecond time-resolved Raman investigation of optical phonon modes in Cr-doped forsterite,” Phys. Rev. B 52, 987–996 (1995).
[CrossRef]

M. J. Weber, “Probabilities for radiative and nonradiative decay of Er3+ in LaF3,” Phys. Rev. B 157, 262–272 (1967).
[CrossRef]

T. Miyakawa and D. L. Dexter, “Phonon sidebands, multiphonon relaxation of excited states and phonon assisted energy transfer between ions in solids,” Phys. Rev. B 1, 2961–2969 (1970).
[CrossRef]

Phys. Rev. Lett.

D. M. Calistru, S. G. Demos, and R. R. Alfano, “Dynamics of local modes during nonradiative relaxation,” Phys. Rev. Lett. 78, 374–377 (1997).
[CrossRef]

J. I. Dijkhuis, A. C. Van der Pol, and H. W. de Wijn, “Spectral width of optically generated bottleneck 29 cm−1 phonons in ruby,” Phys. Rev. Lett. 37, 1554–1557 (1976).
[CrossRef]

Phys. Status Solidi B

E. Gutsche, “Non-Condon approximation and the static approach in the theory of nonradiative multiphonon transitions,” Phys. Status Solidi B 109, 583–597 (1982).
[CrossRef]

Physica (Amsterdam)

W. E. Hagston and J. E. Lowther, “Multiphonon processes in rare-earth ions,” Physica (Amsterdam) 70, 40–61 (1973).
[CrossRef]

Proc. Phys. Soc. London

A. M. Stoneham, “The phonon bottleneck in paramagnetic crystals,” Proc. Phys. Soc. London 86, 1163–1177 (1965).
[CrossRef]

Proc. R. Soc. London, Ser. A

K. Huang and A. Rhys, “Theory of light absorption and non-radiative transition in F-centres,” Proc. R. Soc. London, Ser. A 204, 406–423 (1950).
[CrossRef]

Prog. Theor. Phys.

R. Kubo and Y. Toyozawa, “Application of the method of generating function to radiative and non-radiative transitions of a trapped electron in a crystal,” Prog. Theor. Phys. 13, 160–182 (1955).
[CrossRef]

Other

F. K. Fong, ed., Theory of Molecular Relaxation: Applications in Chemistry and Biology (Wiley, New York, 1975).

C. Kittel, ed., Introduction to Solid State Physics (Wiley, New York, 1971).

L. A. Riseberg and M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, pp. 91–159.

A. Kiel, “Line broadening in the excited state of paramagnetic crystals,” in Paramagnetic Resonance, W. Low, ed. (Academic, New York, 1963), pp. 525–534.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, “Energy level structure and transition probabilities of the rare earth lanthanides in LaF3,” internal report (Johns Hopkins University, Baltimore, Md., 1997).

F. Pellé, N. Gardant, and F. Auzel, “Nonradiative processes in Yb3+-doped borate glasses,” to be submitted in J. Lumin.

F. Auzel, “Contribution à l’étude spectroscopique de verres dopés avec Er3+ pour obtenir l’effect laser,” Ph.D. dissertation (University of Paris, Paris, 1968).

F. Auzel and F. Pellé, “Saturation of accepting modes in multiphonon radiative transitions,” C. R. Acad. Sci. IIb, 835–841 (1996).

F. Auzel, “Multiphonon interaction of excited luminescent centers in the weak coupling limit: nonradiative decay and multiphonon side bands,” in Luminescence of Inorganic Solids, B. Di Bartolo, ed. (Plenum, New York, 1978), pp. 67–113.

H. Scholze, ed., GLAS, Natur. Struktur und Eigenschaften (Springer-Verlag, Berlin, 1977).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Er3+(4S3/2) fluorescence decay time as a function of excitation power and excited-state population density in (a) germanate, (b) tellurite, (c) phosphate, (d) ZBLAN.

Fig. 2
Fig. 2

Fluorescence transients recorded at low and high excitation powers: (a) Er3+(4S3/2) in tellurite glass, (b) Tm3+(3H4) in germanate glass.

Fig. 3
Fig. 3

Multiphonon relaxation rates of RE-ion excited states in germanate glass versus excited-state population density. Theoretical fits of experimental data, plotted as solid lines, were obtained from Eq. (13) with phonon diffusion lengths of (b) 2.8 and (c), (d) 2.4 nm.

Fig. 4
Fig. 4

Multiphonon relaxation rates of RE-ion excited states in tellurite glass versus excited-state population density. Theoretical fits of experimental data, plotted as solid lines, were obtained from Eq. (13) with phonon diffusion lengths of (a) 2.2, (b), 1.5, and (c) 1.7 nm.  

Fig. 5
Fig. 5

Variation of the exponential gap law versus the multiphonon order for several excited-state densities. Theoretical fits (solid lines) were obtained through Eq. (13): (a) germanate glass (■, Nexc=1017 cm-3; ○, Nexc=4×1018 cm-3; △, Nexc=1019 cm-3) and (b) tellurite glass (■, Nexc=1018 cm-3; ○, Nexc=6×1018 cm-3; +, Nexc=8×1018 cm-3; ×, Nexc=1.5 ×1019 cm-3).

Fig. 6
Fig. 6

Comparison between phonon diffusion length lc and excited-state population density, derived from nonradiative relaxation rates fits through Eq. (13): (■, germanate; ○, tellurite) and phonon mean free path independently derived from Eq. (16): germanate glass lc=2.9 nm (dotted line) and tellurite glass lc=2.0 nm (solid line).

Fig. 7
Fig. 7

Exponential parameter (α) versus excited-state density. Solid lines result from the least-squares fit of data through Eq. (15). Best fits are obtained for lc=2.9 nm (■, germanate glass) and 2.2 nm (○, tellurite glass).

Tables (6)

Tables Icon

Table 1 Chemical Composition of Host Glasses

Tables Icon

Table 2 Observed and Calculated Oscillator Strengths of Er3+ Absorption Transitions in the Various Glasses a

Tables Icon

Table 3 Observed and Calculated Oscillator Strengths of Tm3+ Absorption Transitions in the Various Glasses a

Tables Icon

Table 4 Observed and Calculated Oscillator Strengths of Nd3+ Absorption Transitions in the Various Glasses

Tables Icon

Table 5 Calculated Radiative Decay Rates of the Levels Investigated

Tables Icon

Table 6 Physical Properties of Host Glasses

Equations (19)

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

I(z)=P1 erfc[P2(z-P3)],
erfc(r)=22π re-rdr,
fmd=1χ h6mc nσ(2J+1)×4fnα[SL]J(L+2S)4fnα[SL]J2
(χ=n).
Nexc=σCQ,
Wivjvnr=2π×v,vPv|Ψfv|HNA|Ψiv|2δ(Ejv-Eiv),
Wijnr=2πv,vPv×sN-2ϕfQsϕi2χfvsQsχivs2×ks|χfvk|χivk|2δ(Ejv-Eiv),
WNR=2π |i|Hint|j|2RNδ(Ej-Ei),
RN=exp[-(2n¯+1)S0]n¯+1n¯N/2IN[2S0n¯(n¯+1)],
WNR=2π |i|Hint|j|2×exp[-S0(2n¯+1)](n¯+1)N S0NN! (Np/S0)2,
WNR=W0 exp(-αΔE),
α=1ω 1-2NLnNS0(n¯+1)-1.
vl=4π3 lc3.
x¯=Nexcvl[1-exp(-Nexcvl)].
WNR=W0 exp[-S0(2n¯+1)](n¯+1)(1+x¯)N×S0(1+x¯)N[(1+x¯)N]! (Np/S0)2.
WNR=W0 exp-N(1+x¯)1-2N(1+x¯)×Ln(N/S0)+Ln(1+x¯)-1.
α=(1+x¯)ω 1-2N(1+x¯)×Ln(N/S0)+Ln(1+x¯)-1.
κ=1/3Cνlcνs.
κ(calcm-1s-1deg-1)=0.005ρ+0.0004,

Metrics