Abstract

Applying a nonlinear spectroscopic technique, we accurately monitor the dynamics of the homogeneous upconversion (HUC) in Er-doped fibers. We provide the first experimental confirmation, to our knowledge, of the earlier theoretical predictions that, for low erbium concentrations, a decay of HUC-influenced excitation probability of Er ions can be well approximated by the formula describing the static HUC. By correlating the experimentally obtained HUC dynamics with the results of our analytical model in a wide range of Er concentrations, we accurately estimate energy-transfer parameters for Er-doped silica glass and experimentally assess the validity of the model.

© 2005 Optical Society of America

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  1. S. V. Sergeyev and B. Jaskorzynska, "Statistical model for energy-transfer-induced upconversion in Er-doped glasses," Phys. Rev. B 62, 15628 (2000).
    [CrossRef]
  2. S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silica waveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104-1-233104-4 (2002).
    [CrossRef]
  3. 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]
  4. N. V. Nikonorov, A. K. Przhevuskii, M. Prassas, and D. Jacob, "Experimental determination of the upconversion rate in erbium-doped silicate glasses," Appl. Opt. 38, 6284-6291 (1999).
    [CrossRef]
  5. 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]
  6. A. K. Przhevuskii and N. V. Nikonorov, "Monte-Carlo simulation of upconversion processes in erbium-doped materials," Opt. Mater. 21, 729-741 (2003).
    [CrossRef]
  7. S. E. Sverchkov and Yu. E. Sverchkov, "Effect of host matrix structure on quenching of impurity-center luminescence in hopping migration theory," Opt. Spektrosk. 73, 484-492 (1992).
  8. J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
    [CrossRef]
  9. 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]
  10. 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]
  11. B. Di Bartolo, Energy Transfer Processes in Condensed Matter, NATO ASI Series B: Physics (Plenum, 1984), Vol. 114.
    [CrossRef]
  12. 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]
  13. M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.
  14. S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.
  15. J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
    [CrossRef]

2005

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]

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 silica waveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104-1-233104-4 (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]

1999

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

N. V. Nikonorov, A. K. Przhevuskii, M. Prassas, and D. Jacob, "Experimental determination of the upconversion rate in erbium-doped silicate glasses," Appl. Opt. 38, 6284-6291 (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

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[CrossRef]

1992

S. E. Sverchkov and Yu. E. Sverchkov, "Effect of host matrix structure on quenching of impurity-center luminescence in hopping migration theory," Opt. Spektrosk. 73, 484-492 (1992).

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 Er3+-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]

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 Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.

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 Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

Camy, P.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[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]

Di Bartolo, B.

B. Di Bartolo, Energy Transfer Processes in Condensed Matter, NATO ASI Series B: Physics (Plenum, 1984), Vol. 114.
[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 Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.

Hempstead, M.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[CrossRef]

Hotoleanu, M.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Jacob, D.

Janka, K.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Jaskorzynska, B.

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]

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silica waveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104-1-233104-4 (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 Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[CrossRef]

M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.

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 silica waveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104-1-233104-4 (2002).
[CrossRef]

Kiiveri, P.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Kurki, J.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Laborde, P.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[CrossRef]

Lerminiaux, C.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[CrossRef]

Nikonorov, N. 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]

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, M. Prassas, and D. Jacob, "Experimental determination of the upconversion rate in erbium-doped silicate glasses," Appl. Opt. 38, 6284-6291 (1999).
[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]

Nouh, S.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[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 Er3+-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 Er3+-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]

M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.

Prassas, M.

Przhevuskii, A. K.

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]

N. V. Nikonorov, A. K. Przhevuskii, M. Prassas, and D. Jacob, "Experimental determination of the upconversion rate in erbium-doped silicate glasses," Appl. Opt. 38, 6284-6291 (1999).
[CrossRef]

Rajala, M.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Roman, J. E.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[CrossRef]

Sarkilahti, S.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Sergeyev, S.

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]

S. Sergeyev, D. Khoptyar, and B. Jaskorzynska, "Upconversion and migration in erbium-doped silica waveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104-1-233104-4 (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]

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]

Sverchkov, S. E.

S. E. Sverchkov and Yu. E. Sverchkov, "Effect of host matrix structure on quenching of impurity-center luminescence in hopping migration theory," Opt. Spektrosk. 73, 484-492 (1992).

Sverchkov, Yu. E.

S. E. Sverchkov and Yu. E. Sverchkov, "Effect of host matrix structure on quenching of impurity-center luminescence in hopping migration theory," Opt. Spektrosk. 73, 484-492 (1992).

Swillo, M.

M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.

Tammela, S.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Valkonen, H.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

Ye, C.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[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]

Appl. Opt.

Appl. Phys. Lett.

J. E. Roman, M. Hempstead, C. Ye, S. Nouh, P. Camy, P. Laborde, and C. Lerminiaux, "1.7 µm excited state absorption measurement in erbium-doped glasses," Appl. Phys. Lett. 67, 470-472 (1995).
[CrossRef]

IEEE J. Quantum Electron.

J. L. Philipsen, J. Broeng, A. Bjarklev, S. Helmfrid, D. Bremberg, B. Jaskorzynska, and B. Palsdonir, "Observation of strongly nonquadratic homogeneous upconversion in Er3+-doped silica fibers and reevaluation of the degree of clustering," IEEE J. Quantum Electron. 35, 1741-1749 (1999).
[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]

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. 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. Spektrosk.

S. E. Sverchkov and Yu. E. Sverchkov, "Effect of host matrix structure on quenching of impurity-center luminescence in hopping migration theory," Opt. Spektrosk. 73, 484-492 (1992).

Phys. Rev. B

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 silica waveguides in the continuous-wave excitation switch-off regime," Phys. Rev. B 65, 233104-1-233104-4 (2002).
[CrossRef]

Other

B. Di Bartolo, Energy Transfer Processes in Condensed Matter, NATO ASI Series B: Physics (Plenum, 1984), Vol. 114.
[CrossRef]

M. Swillo, D. Bremberg, B. Jaskorzynska, S. Helmfrid, and J. L. Philipsen, "Method for characterization of clustering and homogeneous upconversion in Er-doped waveguides," in Integrated Photonic Research, OSA Technical Digest (Optical Society of America, 1999), pp. 73-75.

S. Tammela, P. Kiiveri, S. Sarkilahti, M. Hotoleanu, H. Valkonen, M. Rajala, J. Kurki, and K. Janka, "Direct nanoparticle deposition process for manufacturing very short high gain Er-doped silica glass fibers," in Proceedings of the European Conference on Optical Communication 2002, P.Danielson, ed. (COM Center, Technical University of Denmark, 2002), p. 9.4.2.

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Figures (7)

Fig. 1
Fig. 1

Energy-transfer diagram illustrating the radiative transitions [double-line arrows in (b) and (c)] and the losses caused by ETU between the ions excited to the metastable ( I 13 2 4 ) level: (a) ETU causes energy transfer (curved down arrow) from the donor ion to the acceptor; as a result the donor is deactivated whereas the acceptor is promoted to the ( I 9 2 4 ) level (dotted arrows); (b) from the ( I 9 2 4 ) level the acceptor immediately nonradiatively relaxes (wavy arrow) to the second excited ( I 11 2 4 ) level and then it most probably further nonradiatively relaxes back to the metastable level (wavy arrow); 0.01% of the ions, however, radiatively decay to the ground state; (c) the net process thus results in dissipation of the excitation energy that originated at the donor. Excitation probabilities ( n 1 , n 2 , n 3 ) for the three lowest Er levels are shown on the right-hand side.

Fig. 2
Fig. 2

(a) Migration (curved down arrow) is the energy transfer between the excited and the unexcited Er ions. (b) The migration enables excitations to move from one ion to another. Therefore it intensifies the overall upconversion by bringing two excitations into proximity with each other.

Fig. 3
Fig. 3

Experimental setup. Personal computer, PC; pump ( 1480 nm ) and signal ( 1535 nm ) laser diodes, LDs; 1, isolator; 2 and 8, narrow-bandpass filters ( 1 nm ) ; 3 and 6, 1480 and 1550 pump signal combiners; 4, EDF sample; 5, 980 and 1550 band combiner (transparent for 1480 nm pump); 7, 980 nm bandpass filter; PD, photodiode.

Fig. 4
Fig. 4

Illustration of the normalization of the experimental signals P 2 ( t ) and P 3 ( t ) . Left axis (arbitrary units): time evolution of I 2 ( t ) and ( X 2 X 3 ) I 3 ( t ) , computed from the experimental data according to Eqs. (12, 13); both curves coincide as expected from Eq. (11). Right axis: γ ( t ) = I 2 ( t ) I 3 ( t ) is plotted as a function of the decay time. Since the proportionality coefficients between P 2 ( t ) and P 3 ( t ) and the corresponding populations are unchanged during the experiment, γ ( t ) fluctuates around an average value that defines X 2 X 3 (dashed line) and the fluctuations are well inside ± 10 % limits (dotted lines).

Fig. 5
Fig. 5

Experimentally determined (scatter) upconversion coefficient at low Er concentration ( 1.1 × 10 25 m 3 ) and model predictions (lines) for upconversion of different multipolarity ( s ) according to Eq. (2) that shows the dominant role of the dipole–dipole upconversion mechanism. Both axes are normalized to metastable level lifetime.

Fig. 6
Fig. 6

Experimentally determined (scatter) upconversion coefficient for EDF samples with different Er concentrations ( 1.1 × 10 25 , 2.9 × 10 25 , 8.7 × 10 25 m 3 ) and the modeling predictions according to Eqs. (4, 5, 6) for dipole–dipole upconversion with migration (solid curves), R u = 13 Å , R m = 15.5 Å . To highlight the migration effect, static upconversion is also plotted (dashed curve) according to Eq. (2) for R u = 13 Å , which gives an accurate fit to the experimental data at low concentrations. Both axes are normalized to metastable level lifetime.

Fig. 7
Fig. 7

Steady-state upconversion coefficient at the low pumping powers as a function for Er concentration. Squares, data computed using the modeling and effective critical radii estimated in Ref. [8]. Curves, the trend predicted using the present estimation of the ETU, the migration critical radii, and the modeling of Ref. [3]: solid curve, the steady-state upconversion coefficient for the migration-assisted upconversion; dotted curve, the static upconversion; dashed curve, asymptote for high Er concentrations. Circles, direct observation of the steady-state upconversion coefficient data from Refs. [4, 5].

Equations (24)

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P = 1 τ 2 s [ R ( s ) x ] s , s = { 6 , 8 , 10 } ,
d n 3 ( t ) d t = n 3 ( t ) τ 3 + C up ( t ) n 2 2 ( t ) d n 2 ( t ) d t = n 2 ( t ) τ 2 + n 3 ( t ) τ 3 2 C up ( t ) n 2 2 ( t ) .
C up ( t , S ) = 4 π s Γ ( 1 3 s ) 2 1 3 s R ( s ) UC 3 c Er τ 3 s t 3 s 1 ,
C up ( t ) = 4 π π 6 2 R UC 3 c Er 1 τ t .
C up ( t ) = 1 ξ ( t ) d d t ξ ( t ) ,
ξ ( t ) = Q ( t ) R ( t ) + 0 t ξ ( x ) Q ( t x ) x R ( t x ) d x ,
Q ( t ) = exp ( k t 2 ) , R ( t ) = exp [ h M ( k ) k D t ] .
k = 4 3 π π R u 3 c Er ,
k D = 4 3 π π R m 3 c Er ,
h M ( k ) = 1.26 0.31 × log ( k ) .
C up ( t ) = 1 n 2 2 ( t ) [ d d t n 3 ( t ) + n 3 ( t ) τ 3 ] .
C up ( t ) 1 n 2 2 ( t ) [ d d t n 2 ( t ) + n 2 ( t ) τ ] .
P 2 ( t ) = X 2 n 2 ( t ) ,
P 3 ( t ) = X 3 n 3 ( t ) .
2 d n 3 ( t ) d t + n 3 ( t ) τ 3 = d n 2 ( t ) d t n 2 ( t ) τ .
X 2 X 3 = d P 2 ( t ) d t + P 2 ( t ) τ 2 d P 3 ( t ) d t + P 3 ( t ) τ 3 ,
X 2 X 3 = γ ( t ) ,
γ ( t ) = I 2 ( t ) I 3 ( t ) ,
I 3 ( t ) = 2 [ P 3 ( t + Δ ) P 3 ( t ) ] + 1 τ 3 t t + Δ P 3 ( t ) d t ,
I 2 ( t ) = [ P 2 ( t + Δ ) P 2 ( t ) ] + 1 τ t t + Δ P 2 ( t ) d t ,
( n 2 B n 2 max n 2 max ) 2 ,
P 2 ( t ) = ln [ G ( t ) G ( ) ] ln [ G ( 0 ) G ( ) ] ,
P 3 ( t ) = Q 3 ( t ) ( 1 exp { A L [ 1 n 2 ( t ) ] } 1 n 2 ( t ) ) 1 ,
C up ( t ) = 1 n 2 ( t ) X 2 X 3 P 2 ( t ) [ d d t P 3 ( t ) + P 3 ( t ) τ 3 ] .

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