Abstract

A simple and highly accurate model is presented for the decay of the excited state density of randomly distributed luminescent centers (e.g., rare-earth ions or fluorescent dyes) affected by migration-assisted nonlinear quenching (e.g., upconversion or singlet–singlet annihilation). The model relates quenching efficiency, interpreted in terms of the time-dependent quenching coefficient, to parameters of underlying Förster energy transfer phenomena and to center concentration. The accuracy of the model is verified by comparison with Monte Carlo simulations. The model sets up a rigorous basis for the characterization of nonlinear quenching in Er-doped glasses and disordered organic optoelectronic materials.

© 2007 Optical Society of America

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  1. D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
    [CrossRef]
  2. A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).
  3. E. N. Bodunov, "Approximate methods in the theory of nonradiative energy transfer of localized excitations in disordered media: a review," Opt. Spektrosk. 74, 518-551 (1993).
  4. G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
    [CrossRef]
  5. D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady-state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005).
    [CrossRef]
  6. S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer induced upconversion in Er-doped glasses," Phys. Rev. B 62, 15628 (2000).
    [CrossRef]
  7. S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silicawaveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104 (2002).
    [CrossRef]
  8. D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Upconversion assisted decay of the population inversion in Er-doped silica after delta-pulse excitation," IEEE J. Quantum Electron. 41, 205-212 (2005).
    [CrossRef]
  9. J. L. Philipsen and A. Bjarklev, "Monte Carlo simulation of homogeneous upconversion in erbium-doped silica glasses," IEEE J. Quantum Electron. 33, 845-854 (1997).
    [CrossRef]
  10. J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
    [CrossRef]
  11. N. V. Nikonorov, A. K. Przhevuskii, and A. V. Chukharev, "Characterization of non-linear upconversion quenching in Er-doped glasses: modeling and experiment," J. Non-Cryst. Solids 324, 92-108 (2003).
    [CrossRef]
  12. A. K. Przhevuskii and N. V. Nikonorov, "Monte Carlo simulation of upconversion processes in erbium-doped materials," Opt. Mater. 21, 729-741 (2003).
    [CrossRef]
  13. V. P. Gaponsev and N. S. Platonov, "Migration accelerated quenching of luminescence in glasses activated by rareearth ions," in Dynamical Process in Disordered Systems, W.M.Yen, ed., Vol. 50 of Material Science Forum, 1st ed. (Trans. Tech Publications, 1989), pp. 165-222.
  14. S. F. Kilin, M. S. Mikhelashvili, and I. M. Rozman, "Kinetics of nonlinear luminescence quenching," Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 42, 155-158 (1978).
  15. U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
    [CrossRef]
  16. L. D. Zusman, "Quenching of luminescence when migration of excitations in solid solution is present," Opt. Spectrosc. 36, 287-289 (1974).
  17. L. D. Zusman, "Kinetics of luminescence decay in the case of the jump mechanism," Sov. Phys. JETP 73, 662-670 (1977).
  18. S. Jang, K. J. Shin, and S. Lee, "Effects of excitation migration and translational diffusion in the luminescence quanching dynamics," J. Chem. Phys. 102, 815-827 (1995).
    [CrossRef]
  19. C. R. Gochanour, H. C. Anderson, and M. D. Fayer, "Electronic excited state transport in solution," J. Chem. Phys. 70, 4254-4271 (1979).
    [CrossRef]

2005

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady-state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005).
[CrossRef]

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Upconversion assisted decay of the population inversion in Er-doped silica after delta-pulse excitation," IEEE J. Quantum Electron. 41, 205-212 (2005).
[CrossRef]

2003

N. V. Nikonorov, A. K. Przhevuskii, and A. V. Chukharev, "Characterization of non-linear upconversion quenching in Er-doped glasses: modeling and experiment," J. Non-Cryst. Solids 324, 92-108 (2003).
[CrossRef]

A. K. Przhevuskii and N. V. Nikonorov, "Monte Carlo simulation of upconversion processes in erbium-doped materials," Opt. Mater. 21, 729-741 (2003).
[CrossRef]

2002

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silicawaveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104 (2002).
[CrossRef]

2000

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer induced upconversion in Er-doped glasses," Phys. Rev. B 62, 15628 (2000).
[CrossRef]

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

1999

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

1997

D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
[CrossRef]

J. L. Philipsen and A. Bjarklev, "Monte Carlo simulation of homogeneous upconversion in erbium-doped silica glasses," IEEE J. Quantum Electron. 33, 845-854 (1997).
[CrossRef]

1995

S. Jang, K. J. Shin, and S. Lee, "Effects of excitation migration and translational diffusion in the luminescence quanching dynamics," J. Chem. Phys. 102, 815-827 (1995).
[CrossRef]

1993

E. N. Bodunov, "Approximate methods in the theory of nonradiative energy transfer of localized excitations in disordered media: a review," Opt. Spektrosk. 74, 518-551 (1993).

1984

A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).

1979

C. R. Gochanour, H. C. Anderson, and M. D. Fayer, "Electronic excited state transport in solution," J. Chem. Phys. 70, 4254-4271 (1979).
[CrossRef]

1978

S. F. Kilin, M. S. Mikhelashvili, and I. M. Rozman, "Kinetics of nonlinear luminescence quenching," Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 42, 155-158 (1978).

1977

L. D. Zusman, "Kinetics of luminescence decay in the case of the jump mechanism," Sov. Phys. JETP 73, 662-670 (1977).

1975

U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
[CrossRef]

1974

L. D. Zusman, "Quenching of luminescence when migration of excitations in solid solution is present," Opt. Spectrosc. 36, 287-289 (1974).

Anderson, H. C.

C. R. Gochanour, H. C. Anderson, and M. D. Fayer, "Electronic excited state transport in solution," J. Chem. Phys. 70, 4254-4271 (1979).
[CrossRef]

Bjarklev, A.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

J. L. Philipsen and A. Bjarklev, "Monte Carlo simulation of homogeneous upconversion in erbium-doped silica glasses," IEEE J. Quantum Electron. 33, 845-854 (1997).
[CrossRef]

Bodunov, E. N.

E. N. Bodunov, "Approximate methods in the theory of nonradiative energy transfer of localized excitations in disordered media: a review," Opt. Spektrosk. 74, 518-551 (1993).

Bremberg, D.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

Broeng, J.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

Burstein, A. I.

A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).

Cerullo, G.

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

Chukharev, A. V.

N. V. Nikonorov, A. K. Przhevuskii, and A. V. Chukharev, "Characterization of non-linear upconversion quenching in Er-doped glasses: modeling and experiment," J. Non-Cryst. Solids 324, 92-108 (2003).
[CrossRef]

De Silvestri, S.

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

Egelhaaf, H.-J.

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

Fayer, M. D.

C. R. Gochanour, H. C. Anderson, and M. D. Fayer, "Electronic excited state transport in solution," J. Chem. Phys. 70, 4254-4271 (1979).
[CrossRef]

Frey, R.

U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
[CrossRef]

Gaponsev, V. P.

V. P. Gaponsev and N. S. Platonov, "Migration accelerated quenching of luminescence in glasses activated by rareearth ions," in Dynamical Process in Disordered Systems, W.M.Yen, ed., Vol. 50 of Material Science Forum, 1st ed. (Trans. Tech Publications, 1989), pp. 165-222.

Gochanour, C. R.

C. R. Gochanour, H. C. Anderson, and M. D. Fayer, "Electronic excited state transport in solution," J. Chem. Phys. 70, 4254-4271 (1979).
[CrossRef]

Gösele, U.

U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
[CrossRef]

Hauser, M.

U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
[CrossRef]

Helmfrid, S.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

Jang, S.

S. Jang, K. J. Shin, and S. Lee, "Effects of excitation migration and translational diffusion in the luminescence quanching dynamics," J. Chem. Phys. 102, 815-827 (1995).
[CrossRef]

Jaskorzynska, B.

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Upconversion assisted decay of the population inversion in Er-doped silica after delta-pulse excitation," IEEE J. Quantum Electron. 41, 205-212 (2005).
[CrossRef]

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady-state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005).
[CrossRef]

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silicawaveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104 (2002).
[CrossRef]

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer induced upconversion in Er-doped glasses," Phys. Rev. B 62, 15628 (2000).
[CrossRef]

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

Khoptyar, D.

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Upconversion assisted decay of the population inversion in Er-doped silica after delta-pulse excitation," IEEE J. Quantum Electron. 41, 205-212 (2005).
[CrossRef]

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady-state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005).
[CrossRef]

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silicawaveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104 (2002).
[CrossRef]

Kilin, S. F.

S. F. Kilin, M. S. Mikhelashvili, and I. M. Rozman, "Kinetics of nonlinear luminescence quenching," Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 42, 155-158 (1978).

Klein, U. K. A.

U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
[CrossRef]

Lanzani, G.

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

Lee, S.

S. Jang, K. J. Shin, and S. Lee, "Effects of excitation migration and translational diffusion in the luminescence quanching dynamics," J. Chem. Phys. 102, 815-827 (1995).
[CrossRef]

Luer, L.

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

Mikhelashvili, M. S.

S. F. Kilin, M. S. Mikhelashvili, and I. M. Rozman, "Kinetics of nonlinear luminescence quenching," Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 42, 155-158 (1978).

Nikonorov, N. V.

A. K. Przhevuskii and N. V. Nikonorov, "Monte Carlo simulation of upconversion processes in erbium-doped materials," Opt. Mater. 21, 729-741 (2003).
[CrossRef]

N. V. Nikonorov, A. K. Przhevuskii, and A. V. Chukharev, "Characterization of non-linear upconversion quenching in Er-doped glasses: modeling and experiment," J. Non-Cryst. Solids 324, 92-108 (2003).
[CrossRef]

Noginov, M. A.

D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
[CrossRef]

Oelkrug, D.

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

Palsdonir, B.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

Philipsen, J. L.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

J. L. Philipsen and A. Bjarklev, "Monte Carlo simulation of homogeneous upconversion in erbium-doped silica glasses," IEEE J. Quantum Electron. 33, 845-854 (1997).
[CrossRef]

Platonov, N. S.

V. P. Gaponsev and N. S. Platonov, "Migration accelerated quenching of luminescence in glasses activated by rareearth ions," in Dynamical Process in Disordered Systems, W.M.Yen, ed., Vol. 50 of Material Science Forum, 1st ed. (Trans. Tech Publications, 1989), pp. 165-222.

Przhevuskii, A. K.

N. V. Nikonorov, A. K. Przhevuskii, and A. V. Chukharev, "Characterization of non-linear upconversion quenching in Er-doped glasses: modeling and experiment," J. Non-Cryst. Solids 324, 92-108 (2003).
[CrossRef]

A. K. Przhevuskii and N. V. Nikonorov, "Monte Carlo simulation of upconversion processes in erbium-doped materials," Opt. Mater. 21, 729-741 (2003).
[CrossRef]

Rozman, I. M.

S. F. Kilin, M. S. Mikhelashvili, and I. M. Rozman, "Kinetics of nonlinear luminescence quenching," Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 42, 155-158 (1978).

Sergeyev, S.

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Upconversion assisted decay of the population inversion in Er-doped silica after delta-pulse excitation," IEEE J. Quantum Electron. 41, 205-212 (2005).
[CrossRef]

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady-state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005).
[CrossRef]

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silicawaveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104 (2002).
[CrossRef]

Sergeyev, S. V.

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer induced upconversion in Er-doped glasses," Phys. Rev. B 62, 15628 (2000).
[CrossRef]

Shcherbakov, I. A.

D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
[CrossRef]

Shin, K. J.

S. Jang, K. J. Shin, and S. Lee, "Effects of excitation migration and translational diffusion in the luminescence quanching dynamics," J. Chem. Phys. 102, 815-827 (1995).
[CrossRef]

Smirnov, V. A.

D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
[CrossRef]

Zubenko, D. A.

D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
[CrossRef]

Zusman, L. D.

L. D. Zusman, "Kinetics of luminescence decay in the case of the jump mechanism," Sov. Phys. JETP 73, 662-670 (1977).

L. D. Zusman, "Quenching of luminescence when migration of excitations in solid solution is present," Opt. Spectrosc. 36, 287-289 (1974).

Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.)

S. F. Kilin, M. S. Mikhelashvili, and I. M. Rozman, "Kinetics of nonlinear luminescence quenching," Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 42, 155-158 (1978).

Chem. Phys. Lett.

U. Gösele, M. Hauser, U. K. A. Klein, and R. Frey, "Diffusion and long-range energy transfer," Chem. Phys. Lett. 34, 519-522 (1975).
[CrossRef]

IEEE J. Quantum Electron.

D. Khoptyar, S. Sergeyev, and B. Jaskorzynska, "Upconversion assisted decay of the population inversion in Er-doped silica after delta-pulse excitation," IEEE J. Quantum Electron. 41, 205-212 (2005).
[CrossRef]

J. L. Philipsen and A. Bjarklev, "Monte Carlo simulation of homogeneous upconversion in erbium-doped silica glasses," IEEE J. Quantum Electron. 33, 845-854 (1997).
[CrossRef]

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

J. Chem. Phys.

S. Jang, K. J. Shin, and S. Lee, "Effects of excitation migration and translational diffusion in the luminescence quanching dynamics," J. Chem. Phys. 102, 815-827 (1995).
[CrossRef]

C. R. Gochanour, H. C. Anderson, and M. D. Fayer, "Electronic excited state transport in solution," J. Chem. Phys. 70, 4254-4271 (1979).
[CrossRef]

J. Non-Cryst. Solids

N. V. Nikonorov, A. K. Przhevuskii, and A. V. Chukharev, "Characterization of non-linear upconversion quenching in Er-doped glasses: modeling and experiment," J. Non-Cryst. Solids 324, 92-108 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Mater.

A. K. Przhevuskii and N. V. Nikonorov, "Monte Carlo simulation of upconversion processes in erbium-doped materials," Opt. Mater. 21, 729-741 (2003).
[CrossRef]

Opt. Spectrosc.

L. D. Zusman, "Quenching of luminescence when migration of excitations in solid solution is present," Opt. Spectrosc. 36, 287-289 (1974).

Opt. Spektrosk.

E. N. Bodunov, "Approximate methods in the theory of nonradiative energy transfer of localized excitations in disordered media: a review," Opt. Spektrosk. 74, 518-551 (1993).

Phys. Rev. B

G. Cerullo, G. Lanzani, S. De Silvestri, H.-J. Egelhaaf, L. Luer, and D. Oelkrug, "Primary photoexcitations in oligophenylenevinylene thin films probed by femtosecond spectroscopy," Phys. Rev. B 62, 2429-2436 (2000).
[CrossRef]

D. A. Zubenko, M. A. Noginov, V. A. Smirnov, and I. A. Shcherbakov, "Different mechanisms of nonlinear quenching of luminescence," Phys. Rev. B 55, 8881-8886 (1997).
[CrossRef]

S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer induced upconversion in Er-doped glasses," Phys. Rev. B 62, 15628 (2000).
[CrossRef]

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silicawaveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104 (2002).
[CrossRef]

Sov. Phys. JETP

L. D. Zusman, "Kinetics of luminescence decay in the case of the jump mechanism," Sov. Phys. JETP 73, 662-670 (1977).

Sov. Phys. Usp.

A. I. Burstein, "Concentration quenching of noncoherent excitation in solutions," Sov. Phys. Usp. 143, 553-600 (1984).

Other

V. P. Gaponsev and N. S. Platonov, "Migration accelerated quenching of luminescence in glasses activated by rareearth ions," in Dynamical Process in Disordered Systems, W.M.Yen, ed., Vol. 50 of Material Science Forum, 1st ed. (Trans. Tech Publications, 1989), pp. 165-222.

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Figures (5)

Fig. 1
Fig. 1

Comparison of the contribution of migration, k ST (normalized to the center lifetime, τ) to the nonlinear quenching coefficient k NL ( t ) , following from different models. Solid line: k ST versus R m in the present model, calculated using Eq. (17), asymptotically approaches the kinetic limit (12) (dotted line) for large R m . Line with triangles: k ST calculated according to [1]. There the kinetic limit is given as upper bound for k ST without smooth transition as in the present model. Line with squares: k ST computed according to [6] in the limit of high center concentrations. Curve with circles: k ST G following from the diffusion model, calculated according to Eqs. (C1, C2, C3, C4). Parameters for all computations: c = 5 × 10 25 m 3 , R 0 = 0.35 nm , R u = 1 nm . Approximate boundaries for diffusion regime, hopping regime, and the kinetic limit are depicted by thin vertical dashed lines.

Fig. 2
Fig. 2

Nonlinear quenching coefficient k NL ( t ) (normalized to center lifetime, τ) versus time, calculated according to Eq. (13) and using Eqs. (8, 10, 11, 12, 17, 18) (solid curves). Model predictions are compared to Monte Carlo simulations (dots). The parameters for computations and simulations are c = 5 × 10 25 m 3 , R 0 = 0.35 nm , R u = 1 nm . The maximum value of k NL ( t ) for these parameters, corresponding to R m , is given by the kinetic limit (dotted line). Note that all curves start in the kinetic limit. The curve for R m = 0 gives Q ( t ) .

Fig. 3
Fig. 3

Nonlinear quenching coefficient k NL ( t ) (normalized to center lifetime, τ) versus time, calculated as in Fig. 2 for different center concentrations, c (solid curves). The model predictions correspond well to Monte Carlo simulations (dots). Parameters for calculations and simulations: R m = 2 nm , R u = 1 nm , R 0 = 0.35 nm . The static quenching rate, Q ( t ) , given by Eq. (10), is plotted for the smallest ( c = 5 × 10 25 m 3 , dashed curve) and the largest center concentrations ( c = 5 × 10 26 m 3 , dashed–dotted curve).

Fig. 4
Fig. 4

Quenching efficiency calculated according to Eq. (21) as a function of R u and R m for different initial excitation levels, n 0 (given in the figures). Center concentration c = 10 26 m 3 .

Fig. 5
Fig. 5

Illustration of transitions inside a pair of two centers susceptible to ETU. In the pair either (a) none, (b) one, or (c) both centers can be excited. Each of the centers can be excited or de-excited independently with the transition rates W ex and W de , respectively; the rates account for spontaneous relaxation, migration, and MANLQ with surrounding centers; additionally, when both centers are excited (c), each of them can be de-excited owing to ETU inside the pair with the probability P u ( r ) 2 .

Equations (50)

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D * + D * ETU D + D * * nonradiatve relaxation D + D * .
P u ( r ) = 1 τ R u 6 r 6 ,
P m ( r ) = 1 τ R m 6 r 6 ,
d d t n ( t ) = n ( t ) τ n 2 ( t ) k NL ( t ) ,
n ( 0 ) = n 0 ,
n ( t ) = n 0 exp ( t τ ) 1 + n 0 0 t k NL ( t ) exp ( t τ ) d t .
k NL ( t ) = 1 2 4 π c n 2 ( t ) 0 P u ( r ) f * * ( r , t ) r 2 d r ,
f * * ( r , t ) = c 2 n 2 ( t ) H ( r R 0 ) { R 2 ( t ) exp ( P u ( r ) t ) + 0 t exp ( P u c ( r ) t ) R 2 ( t ) d t 0 R 2 ( t ) d t } .
R 2 ( t ) = exp ( 2 t τ M ) ,
τ M = 2 τ γ D D 2 ,
γ D D = 4 π π 3 c R m 6 2 R m 6 + 4 R m 3 R u 3 .
k NL ( t ) = R 2 ( t ) Q ( t ) + 0 t Q ( t ) R 2 ( t ) d t 0 R 2 ( t ) d t ,
Q ( t ) = γ D A 4 t τ erf ( 2 π γ KL γ D A t τ ) .
γ D A = ( 4 3 ) π π R u 3 c ,
γ KL = 2 3 π R u 6 R 0 3 c .
k NL ( t ) = ( γ KL τ k ST γ KL τ ) Q ( t ) + k ST ,
k ST = 0 Q ( t ) R 2 ( t ) d t 0 R 2 ( t ) d t .
k ST = γ D A 2 π τ τ M arctan ( 2 π γ KL τ M γ D A τ ) .
exp ( 2 0 t k M p ( t ) d t ) .
k ST = γ KL τ ( 1 F ( γ D A γ D D 2 π γ KL ) ) ,
F ( x ) = 1 π x exp ( x 2 ) erfc ( x ) .
k ST γ D A γ D D 2 τ ,
k ST 8 π 3 R u 3 R m 6 c 2 τ 1 9 2 R m 6 + 4 R m 3 R u 3 { 19.5 τ 1 c 2 R u 3 R m 3 , R m > R u 13.8 τ 1 c 2 R u 3 2 R m 9 2 , R m < R u . }
QE = 1 1 n 0 τ 0 n ( t ) d t .
f 00 ( r , t ) t = 2 W ex f 00 ( r , t ) + 2 W de f 0 * ( r , t ) ,
f 0 * ( r , t ) t = W ex f 00 ( r , t ) ( W ex + W de ) f 0 * ( r , t ) + ( W de + ( 1 2 ) P u ( r ) ) f * * ( r , t ) ,
f * * ( r , t ) t = 2 W ex f 0 * ( r , t ) ( 2 W de + P u ( r ) ) f * * ( r , t ) ,
f * * ( r , t ) + 2 f * 0 ( r , t ) + f 00 ( r , t ) = c 2 f D 2 ( r ) .
W ex = n ( t ) τ M ,
W dex = 1 τ + ( 1 n ( t ) ) τ M + k NL ,
lim t 0 f * * ( r , t ) = c 2 n 0 2 H ( r R 0 ) ,
lim t 0 f * 0 ( r , t ) = c 2 n 0 ( 1 n 0 ) H ( r R 0 ) ,
lim t 0 f 00 ( r , t ) = c 2 ( 1 n 0 ) 2 H ( r R 0 ) .
lim r f * * ( r , t ) = c 2 n 2 ( t ) ,
lim r f * 0 ( r , t ) = c 2 n ( t ) ( 1 n ( t ) ) ,
lim r f 00 ( r , t ) = c 2 ( 1 n ( t ) ) 2 .
f * * ( r , t ) = c 2 n 2 ( t ) g * * ( r , t ) H ( r R 0 ) ,
f * 0 ( r , t ) = c 2 n ( t ) ( 1 n ( t ) ) g * 0 ( r , t ) H ( r R 0 ) .
t g * * ( r , t ) = ( 2 τ M + P u ( r ) ) g * * ( r , t ) + ( 2 τ M ) g * 0 ( r , t ) ,
t g * 0 ( r , t ) = ( 1 τ M ) g * 0 ( r , t ) + 1 τ M .
g * * ( r , t ) = 2 τ M + P u ( r ) exp ( ( 2 τ M + P u ( r ) ) t ) 2 τ M + P u ( r ) ,
g * 0 ( r , t ) = 1 .
k M s ( t ) = 4 π c 0 P m ( r ) exp ( P m ( r ) t ) r 2 d r .
τ M = [ 0 exp ( 0 t k M s ( t ) d t ) d t ] 1 .
k M p ( t ) = 4 π c 0 P m ( r ) exp ( ( 2 P m ( r ) + 4 P u ( r ) P m ( r ) ) t ) r 2 d r ,
k M p ( t ) = 1 2 γ D D t τ .
k ST G = 4 π c D σ F ,
D = 0.43 ( 4 π 3 R D D 3 c ) 4 3 R D D 2 τ ,
σ F = R D A 2 2 4 Γ ( 3 4 ) Γ ( 5 4 ) ( R D A 2 D τ ) 1 4 I 3 4 ( z 0 ) I 3 4 ( , z 0 ) ,
z 0 = 1 2 2 ( R D A R 0 ) 2 ( R D A 2 D τ ) 1 2 .

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