Abstract

The cooperative upconversion processes of erbium ions in silver film ion-exchanged waveguides in a phosphate glass were studied from the pump intensity dependence of luminescence decay curves. Cooperative upconversion coefficients of the  4I13/2 level, 7.7±0.7×10-19 and 9.3±0.7×10-19cm3/s, were obtained for an Er3+ concentration of 1×1020cm-3 in bulk and waveguide samples, respectively. These values are 1 order of magnitude smaller than the ones reported for silica glass. The increase in the cooperative upconversion coefficient with the increase in Er3+ concentration was found to be small. The effects of cooperative upconversion on the gain performance were analyzed for different Er3+ concentrations by a theoretical model based on experimentally measured gain with a 1.48-µm pump wavelength. Given the small cooperative upconversion coefficients in this glass, Er3+ concentrations potentially as high as 3.7×1020cm-3 were shown to be feasible. Such high concentrations would result in a 12-dB gain at 150-mW pump power with a 4-cm-long waveguide.

© 1997 Optical Society of America

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1996

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

1995

T. Ohtsuki, N. Peyghambarian, S. Honkanen, and S. I. Najafi, “Gain characteristics of a high concentration Er3+ doped phosphate glass waveguide,” J. Appl. Phys. 78, 3617 (1995).
[CrossRef]

E. Snokes, G. N. van den Hoven, A. Polman, B. Hendriksen, M. B. J. Diemeer, and F. Priolo, “Cooperative upconversion in erbium-implanted soda-lime silicate glass optical waveguides,” J. Opt. Soc. Am. B 12, 1468 (1995).
[CrossRef]

O. Lumholt, A. Bjarklev, T. Ramussen, and C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275 (1995).
[CrossRef]

F. D. Pasquale and M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858 (1995).
[CrossRef]

1993

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

O. Lumholt, T. Rasmussen, and A. Bjarklev, “Modeling of extremely high Er concentration,” Electron. Lett. 5, 495 (1993).
[CrossRef]

M. Federighi, I. Massarek, and P. F. Trwoga, “Optical amplification in thin optical waveguides with high Er concentration,” IEEE Photonics Technol. Lett. 5, 227 (1993).
[CrossRef]

G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
[CrossRef]

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73 (1993).
[CrossRef]

1992

H. Masuda, A. Takada, and K. Aida, “Modeling the gain degradation of high concentration erbium-doped fiber amplifiers by introducing inhomogeneous cooperative up-conversion,” J. Lightwave Technol. 10, 1789 (1992).
[CrossRef]

M. Haruna, Y. Segawa, and H. Nishihara, “Nondestructive and simple method of optical-waveguide loss measurement with optimization of end-fire coupling,” Electron. Lett. 28, 1612 (1992).
[CrossRef]

P. Poyhonen, “Low loss photoresist masked silver film ion-exchange glass optical waveguides,” Acta Polytech. Scand. 184, 1 (1992).

1991

D. C. Yeh, W. A. Sibley, I. Schneider, R. S. Afzal, and I. Aggarwal, “Intensity-dependent upconversion efficiencies of Er3+ ions in heavy-metal fluoride glass,” J. Appl. Phys. 69, 1648 (1991).
[CrossRef]

P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration-dependent upconversion in Er3+-doped fiber amplifiers: experiments and modeling,” IEEE Photonics Technol. Lett. 3, 996 (1991).
[CrossRef]

1990

1986

1982

P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189 (1982).
[CrossRef]

1975

M. Tomozawa, C. H. Kim, and R. H. Doremus, “Glass surface characterization by electrical measurements,” J. Non-Cryst. Solids 19, 115 (1975).
[CrossRef]

1972

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Electrode ‘polarization’ in alkali-containing glasses,” J. Am. Ceram. Soc. 55, 337 (1972).
[CrossRef]

1962

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

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 3, 750 (1962).

Afzal, R. S.

D. C. Yeh, W. A. Sibley, I. Schneider, R. S. Afzal, and I. Aggarwal, “Intensity-dependent upconversion efficiencies of Er3+ ions in heavy-metal fluoride glass,” J. Appl. Phys. 69, 1648 (1991).
[CrossRef]

Aggarwal, I.

D. C. Yeh, W. A. Sibley, I. Schneider, R. S. Afzal, and I. Aggarwal, “Intensity-dependent upconversion efficiencies of Er3+ ions in heavy-metal fluoride glass,” J. Appl. Phys. 69, 1648 (1991).
[CrossRef]

Aida, K.

H. Masuda, A. Takada, and K. Aida, “Modeling the gain degradation of high concentration erbium-doped fiber amplifiers by introducing inhomogeneous cooperative up-conversion,” J. Lightwave Technol. 10, 1789 (1992).
[CrossRef]

Bass, M.

Bayon, J.-F.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73 (1993).
[CrossRef]

Becker, P. C.

G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
[CrossRef]

Beguin, A.

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

Birnhaum, M.

Bjarklev, A.

O. Lumholt, A. Bjarklev, T. Ramussen, and C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275 (1995).
[CrossRef]

O. Lumholt, T. Rasmussen, and A. Bjarklev, “Modeling of extremely high Er concentration,” Electron. Lett. 5, 495 (1993).
[CrossRef]

Blixt, P.

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration-dependent upconversion in Er3+-doped fiber amplifiers: experiments and modeling,” IEEE Photonics Technol. Lett. 3, 996 (1991).
[CrossRef]

Brannon, P. J.

Bruce, A. J.

G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
[CrossRef]

Camy, P.

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

Carlnas, T.

P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration-dependent upconversion in Er3+-doped fiber amplifiers: experiments and modeling,” IEEE Photonics Technol. Lett. 3, 996 (1991).
[CrossRef]

Carlson, D. E.

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Electrode ‘polarization’ in alkali-containing glasses,” J. Am. Ceram. Soc. 55, 337 (1972).
[CrossRef]

Delevaque, E.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73 (1993).
[CrossRef]

Diemeer, M. B. J.

DiGiovanni, D. J.

G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
[CrossRef]

Doremus, R. H.

M. Tomozawa, C. H. Kim, and R. H. Doremus, “Glass surface characterization by electrical measurements,” J. Non-Cryst. Solids 19, 115 (1975).
[CrossRef]

Federighi, M.

F. D. Pasquale and M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858 (1995).
[CrossRef]

M. Federighi, I. Massarek, and P. F. Trwoga, “Optical amplification in thin optical waveguides with high Er concentration,” IEEE Photonics Technol. Lett. 5, 227 (1993).
[CrossRef]

Gapontsev, P.

P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189 (1982).
[CrossRef]

Georges, T.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73 (1993).
[CrossRef]

Hang, K. W.

D. E. Carlson, K. W. Hang, and G. F. Stockdale, “Electrode ‘polarization’ in alkali-containing glasses,” J. Am. Ceram. Soc. 55, 337 (1972).
[CrossRef]

Haruna, M.

M. Haruna, Y. Segawa, and H. Nishihara, “Nondestructive and simple method of optical-waveguide loss measurement with optimization of end-fire coupling,” Electron. Lett. 28, 1612 (1992).
[CrossRef]

Hempstead, M.

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

Hendriksen, B.

Honkanen, S.

T. Ohtsuki, N. Peyghambarian, S. Honkanen, and S. I. Najafi, “Gain characteristics of a high concentration Er3+ doped phosphate glass waveguide,” J. Appl. Phys. 78, 3617 (1995).
[CrossRef]

Isineev, A. A.

P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189 (1982).
[CrossRef]

Jaskorzynska, B.

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration-dependent upconversion in Er3+-doped fiber amplifiers: experiments and modeling,” IEEE Photonics Technol. Lett. 3, 996 (1991).
[CrossRef]

Judd, B. R.

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

Kim, C. H.

M. Tomozawa, C. H. Kim, and R. H. Doremus, “Glass surface characterization by electrical measurements,” J. Non-Cryst. Solids 19, 115 (1975).
[CrossRef]

Koonen, A. M. J.

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

Kravchenko, V. B.

P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189 (1982).
[CrossRef]

Lamouler, P.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73 (1993).
[CrossRef]

Lerminiaux, C.

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

Lester, C.

O. Lumholt, A. Bjarklev, T. Ramussen, and C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275 (1995).
[CrossRef]

Lumholt, O.

O. Lumholt, A. Bjarklev, T. Ramussen, and C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275 (1995).
[CrossRef]

O. Lumholt, T. Rasmussen, and A. Bjarklev, “Modeling of extremely high Er concentration,” Electron. Lett. 5, 495 (1993).
[CrossRef]

Massarek, I.

M. Federighi, I. Massarek, and P. F. Trwoga, “Optical amplification in thin optical waveguides with high Er concentration,” IEEE Photonics Technol. Lett. 5, 227 (1993).
[CrossRef]

Masuda, H.

H. Masuda, A. Takada, and K. Aida, “Modeling the gain degradation of high concentration erbium-doped fiber amplifiers by introducing inhomogeneous cooperative up-conversion,” J. Lightwave Technol. 10, 1789 (1992).
[CrossRef]

Matitsin, S. M.

P. Gapontsev, S. M. Matitsin, A. A. Isineev, and V. B. Kravchenko, “Erbium glass lasers and their applications,” Opt. Laser Technol. 14, 189 (1982).
[CrossRef]

Monerie, M.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, and J.-F. Bayon, “Modeling of pair-induced quenching in erbium-doped silicate fibers,” IEEE Photonics Technol. Lett. 5, 73 (1993).
[CrossRef]

Najafi, S. I.

T. Ohtsuki, N. Peyghambarian, S. Honkanen, and S. I. Najafi, “Gain characteristics of a high concentration Er3+ doped phosphate glass waveguide,” J. Appl. Phys. 78, 3617 (1995).
[CrossRef]

Nilsson, J.

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration-dependent upconversion in Er3+-doped fiber amplifiers: experiments and modeling,” IEEE Photonics Technol. Lett. 3, 996 (1991).
[CrossRef]

Nishihara, H.

M. Haruna, Y. Segawa, and H. Nishihara, “Nondestructive and simple method of optical-waveguide loss measurement with optimization of end-fire coupling,” Electron. Lett. 28, 1612 (1992).
[CrossRef]

Nykolak, G.

G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
[CrossRef]

Ofelt, G. S.

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 3, 750 (1962).

Ohtsuki, T.

T. Ohtsuki, N. Peyghambarian, S. Honkanen, and S. I. Najafi, “Gain characteristics of a high concentration Er3+ doped phosphate glass waveguide,” J. Appl. Phys. 78, 3617 (1995).
[CrossRef]

Pasquale, F. D.

F. D. Pasquale and M. Federighi, “Modeling of uniform and pair-induced upconversion mechanisms in high-concentration erbium-doped silica waveguides,” J. Lightwave Technol. 13, 1858 (1995).
[CrossRef]

Peyghambarian, N.

T. Ohtsuki, N. Peyghambarian, S. Honkanen, and S. I. Najafi, “Gain characteristics of a high concentration Er3+ doped phosphate glass waveguide,” J. Appl. Phys. 78, 3617 (1995).
[CrossRef]

Polman, A.

Poyhonen, P.

P. Poyhonen, “Low loss photoresist masked silver film ion-exchange glass optical waveguides,” Acta Polytech. Scand. 184, 1 (1992).

Prel, C.

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

Priolo, F.

Ramussen, T.

O. Lumholt, A. Bjarklev, T. Ramussen, and C. Lester, “Rare earth-doped integrated glass components: modeling and optimization,” J. Lightwave Technol. 13, 275 (1995).
[CrossRef]

Rasmussen, T.

O. Lumholt, T. Rasmussen, and A. Bjarklev, “Modeling of extremely high Er concentration,” Electron. Lett. 5, 495 (1993).
[CrossRef]

Roman, J. E.

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P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

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P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

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P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

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G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
[CrossRef]

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D. C. Yeh, W. A. Sibley, I. Schneider, R. S. Afzal, and I. Aggarwal, “Intensity-dependent upconversion efficiencies of Er3+ ions in heavy-metal fluoride glass,” J. Appl. Phys. 69, 1648 (1991).
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[CrossRef]

P. Camy, J. E. Roman, F. W. Willems, M. Hempstead, J. C. van der Plaats, C. Prel, A. Beguin, A. M. J. Koonen, J. S. Wilkinson, and C. Lerminiaux, “Ion-exchanged planar lossless splitter at 1.5 μm,” Electron. Lett. 32, 321 (1996).
[CrossRef]

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P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska, “Concentration-dependent upconversion in Er3+-doped fiber amplifiers: experiments and modeling,” IEEE Photonics Technol. Lett. 3, 996 (1991).
[CrossRef]

G. Nykolak, P. C. Becker, J. Shmulovich, Y. H. Wong, D. J. DiGiovanni, and A. J. Bruce, “Concentration-dependent 4I13/2 lifetimes in Er3+-doped fibers and Er3+-doped planar waveguides,” IEEE Photonics Technol. Lett. 5, 1014 (1993).
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[CrossRef]

J. Nilsson, B. Jaskorzynska, and P. Blixt, “Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching,” IEEE Photonics Technol. Lett. 5, 1427 (1993).
[CrossRef]

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[CrossRef]

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D. C. Yeh, W. A. Sibley, I. Schneider, R. S. Afzal, and I. Aggarwal, “Intensity-dependent upconversion efficiencies of Er3+ ions in heavy-metal fluoride glass,” J. Appl. Phys. 69, 1648 (1991).
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Figures (8)

Fig. 1
Fig. 1

Cooperative upconversion processes (dashed arrows) and radiative (solid arrows) and nonradiative (dotted arrows) transitions relevant to amplifier operation.

Fig. 2
Fig. 2

Contour plots of the normalized intensity distribution taken by an infrared camera for (a) pump and (b) signal beams.

Fig. 3
Fig. 3

Luminescence decay curves at different pump intensities for (a) bulk and (b) waveguide samples. The average population inversion rates are (a) 0.23, 0.13, 0.068, 0.028, 0.012, and 0.007 and (b) 0.84, 0.61, 0.29, 0.15, and 0.098. Dashed curves show single exponential decays with lifetimes of (a) 7.15 and (b) 5.75 ms. Solid curves are results calculated with cooperative upconversion coefficients of (a) 7.7×10-19 and (b) 9.3×10-19 cm3/s.

Fig. 4
Fig. 4

Small-signal gain at 1.534 µm versus 1.48-µm pump power launched into a 1.8-cm-long Er3+-doped phosphate glass waveguide. The polarization state of the pump is TE, and the signal is TE (filled circles) and TM (open circles). The three curves are results calculated with the experimentally obtained cooperative upconversion coefficient C=9.3×10-19 cm3/s (solid curve), with 10-times larger values of C (dashed curve), and without cooperative upconversion processes (dotted curve).

Fig. 5
Fig. 5

Luminescence decay curves at different pump intensities for bulk samples with Er3+ concentrations of (a) 1.9, (b) 2.8, and (c) 3.7×1020 cm-3. The average population inversion rates are (a) 0.23, 0.13, 0.070, 0.027, 0.011, and 0.0062, (b) 0.24, 0.14, 0.068, 0.030, 0.013, and 0.0057, and (c) 0.22, 0.13, 0.072, 0.029, 0.011, and 0.0069. Dashed curves show single exponential decays with lifetimes of (a) 8.2, (b) 8.1, and (c) 7.9 ms. Solid curves are results calculated with cooperative upconversion coefficients of (a) 6.0×10-19, (b) 7.4×10-19, and (c) 8.4×10-19 cm3/s.

Fig. 6
Fig. 6

Cooperative upconversion coefficients (filled squares) and the transition probabilities A21=1/τ (filled circles) as functions of Er3+ concentrations.

Fig. 7
Fig. 7

Calculated small-signal gain at 1.534 µm versus 1.48-µm pump over for a 4-cm-long waveguide with an Er3+ concentration of 3.7×1020 cm-3 and a propagation loss of 0.15 dB/cm. The solid curve shows the result with the experimentally obtained cooperative upconversion coefficient C=8.4×10-19 cm3/s, and the dashed curve shows the result without the cooperative upconversion processes.

Fig. 8
Fig. 8

Calculated gain versus Er3+ concentration at pump powers of 90 mW (dashed curves) and 150 mW (solid curves), with (filled circles) and without (filled squares) cooperative upconversion effects.

Equations (17)

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dN1dt=-R13N1+R31N3-W12N1+W21N2+A21RN2+CN22,
dN2dt=W12N1-W21N2-A21RN2+A32NRN3-2CN22,
dN3dt=R13N1-R31N3+A32NRN3+A43NRN4,
dN4dt=-A43NRN4+CN22,
ANR=B exp[-a(ΔE-2Ω)],
dN2dt=W12N1-W21N2-A21RN2+R13N1-CN22.
N2(t)=1τ1τN2(0)+Cexptτ-C-1,
dpdz=p[ρ0σa(νs)Γp(q)-α],
Γp[q(z)]=ξp[x, y,q(z)]dxdy,
ξp[x, y,q(z)]=ψs(x, y)Ssηs-ηp1+ηpq(z)ψp(x, y)-1-τCρ0(1+ηp)11+ηpq(z)ψp(x, y)2[1+q(z)ψp(x, y)]21+q(z)ψp(x, y);
dqdz=-q[ρ0σa(νp)Γq(q)-α],
Γq[q(z)]=ξq[x, y, q(z)]dxdy,
ξq[x,y,q(z)]=ψp(x, y)Sp1+τCρ0(1+ηs)11+ηpq(z)ψp(x, y)2[1+q(z)ψp(x, y)]21+q(z)ψp(x, y),
p(z)=Ps(z)Psat(νs),q(z)=Pp(z)Psat(νp),
Psat(νs)=hνsSsσa(νs)(1+ηs)τ,
Psat(νp)=hνpSpσa(νp)(1+ηp)τ,ηp=σe(νs)σa(νs),
ηq=σe(νp)σa(νp),

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