Abstract

A spectroscopic study of the population mechanisms in erbium-doped amorphous aluminum oxide up to the H11/22/S3/24 levels is performed. Via luminescence decay measurements, absorption and emission spectra, and a Judd–Ofelt analysis, we determine luminescence lifetimes, radiative and nonradiative decay-rate constants, and branching ratios of the Er3+ intermanifold transitions. With a continuous-wave pump-probe technique, the excited-state absorption (ESA) spectrum is recorded between 900 and 1800 nm and the cross sections of the ESA transitions I13/24I9/24, I13/24F9/24, and I11/24F7/24 are determined. The microparameters and efficiencies of resonant and phonon-assisted energy-migration and energy-transfer upconversion (ETU) processes among Er3+ ions occurring from the first and second excited states are evaluated. From the ratio of the S3/24 and F9/24 luminescence intensities as a function of Er3+ concentration, we prove the existence and quantify the macroscopic ETU coefficient of the two-phonon-assisted ETU process (I13/24,I11/24)(I15/24,F9/24).

© 2013 Optical Society of America

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    [CrossRef]
  5. F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
    [CrossRef]
  6. P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
    [CrossRef]
  7. L. Fornasiero, K. Petermann, E. Heumann, and G. Huber, “Spectroscopic properties and laser emission of Er3+ in scandium silicates near 1.5 μm,” Opt. Mater. 10, 9–17 (1998).
    [CrossRef]
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  9. M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
    [CrossRef]
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    [CrossRef]
  14. C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
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  18. K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
    [CrossRef]
  19. J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
    [CrossRef]
  20. J. Rubin, A. Brenier, R. Moncorgé, and C. Pedrini, “Excited-state absorption and energy-transfer in Er3+ doped LiYF4,” J. Lumin. 36, 39–47 (1986).
    [CrossRef]
  21. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962).
    [CrossRef]
  22. G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962).
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  25. N. Yamada, S. Shionoya, and T. Kushida, “Phonon-assisted energy transfer between trivalent rare earth ions,” J. Phys. Soc. Jpn. 32, 1577–1586 (1972).
    [CrossRef]
  26. H. Schober, D. Strauch, and B. Dorner, “Lattice dynamics of sapphire (Al2O3),” Z. Phys. B 92, 273–283 (1993).
    [CrossRef]
  27. J. Koetke and G. Huber, “Infrared excited-state absorption and stimulated-emission cross sections of Er3+-doped crystals,” Appl. Phys. B 61, 151–158 (1995).
    [CrossRef]
  28. J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
    [CrossRef]
  29. R. S. Quimby, W. J. Miniscalco, and B. Thompson, “Excited state absorption at 980 nm in erbium doped glass,” Proc. SPIE 1581, 72–79 (1991).
    [CrossRef]
  30. T. Förster, “Zwischenmolekulare energiewanderung und fluoreszenz,” Ann. Phys. 437, 55–75 (1948).
    [CrossRef]
  31. D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21, 836–850 (1953).
    [CrossRef]
  32. F. Auzel, “Multiphonon-assisted anti-Stokes and Stokes fluorescence of triply ionized rare-earth ions,” Phys. Rev. B 13, 2809–2817 (1976).
    [CrossRef]
  33. D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
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  34. P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy-transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
    [CrossRef]
  35. X. Zou and T. Izumitani, “Spectroscopic properties and mechanisms of excited state absorption and energy transfer upconversion for Er3+-doped glasses,” J. Non-Cryst. Solids 162, 68–80 (1993).
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    [CrossRef]
  37. I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
    [CrossRef]
  38. G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
    [CrossRef]
  39. M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
    [CrossRef]
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2011 (1)

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

2010 (1)

2009 (1)

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

2007 (1)

J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
[CrossRef]

2004 (3)

F. Auzel, “Upconversion and anti-Stokes processes with f and d ions in solids,” Chem. Rev. 104, 139–174 (2004).
[CrossRef]

G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
[CrossRef]

R. Balda, A. J. Garcia-Adeva, J. Fernández, and J. M. Fdez-Navarro, “Infrared-to-visible upconversion of Er3+ ions in GeO2-PbO-Nb2O5 glasses,” J. Opt. Soc. Am. B 21, 744–752 (2004).
[CrossRef]

2002 (1)

C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
[CrossRef]

2000 (2)

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy-transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
[CrossRef]

1999 (3)

P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
[CrossRef]

S. R. Lüthi, M. Pollnau, H. U. Güdel, and M. P. Hehlen, “Near-infrared to visible upconversion in Er3+ doped Cs3Lu2Cl9, Cs3Lu2Br9, and Cs3Y2I9 excited at 1.54 μm,” Phys. Rev. B 60, 162–178 (1999).
[CrossRef]

I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
[CrossRef]

1998 (4)

M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
[CrossRef]

P. E. A. Mobert, A. Diening, E. Heumann, G. Huber, and B. H. T. Chai, “Room-temperature continuous-wave upconversion-pumped laser emission in Ho, Yb:KYF4 at 756, 1070, and 1390 nm,” Laser Phys. 8, 210–213 (1998).

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

L. Fornasiero, K. Petermann, E. Heumann, and G. Huber, “Spectroscopic properties and laser emission of Er3+ in scandium silicates near 1.5 μm,” Opt. Mater. 10, 9–17 (1998).
[CrossRef]

1996 (1)

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

1995 (1)

J. Koetke and G. Huber, “Infrared excited-state absorption and stimulated-emission cross sections of Er3+-doped crystals,” Appl. Phys. B 61, 151–158 (1995).
[CrossRef]

1994 (1)

M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, and H. P. Weber, “Explanation of the cw operation of the Er3+ 3 μm crystal laser,” Phys. Rev. A 49, 3990–3996 (1994).
[CrossRef]

1993 (2)

X. Zou and T. Izumitani, “Spectroscopic properties and mechanisms of excited state absorption and energy transfer upconversion for Er3+-doped glasses,” J. Non-Cryst. Solids 162, 68–80 (1993).
[CrossRef]

H. Schober, D. Strauch, and B. Dorner, “Lattice dynamics of sapphire (Al2O3),” Z. Phys. B 92, 273–283 (1993).
[CrossRef]

1992 (1)

M. Pollnau, E. Heumann, and G. Huber, “Time-resolved spectra of excited-state absorption in Er3+ doped YAlO3,” Appl. Phys. A 54, 404–410 (1992).
[CrossRef]

1991 (2)

R. S. Quimby, W. J. Miniscalco, and B. Thompson, “Excited state absorption at 980 nm in erbium doped glass,” Proc. SPIE 1581, 72–79 (1991).
[CrossRef]

J. A. Caird, A. J. Ramponi, and P. R. Staver, “Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses,” J. Opt. Soc. Am. B 8, 1391–1403(1991).
[CrossRef]

1990 (1)

1988 (1)

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2 and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[CrossRef]

1986 (2)

S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986).
[CrossRef]

J. Rubin, A. Brenier, R. Moncorgé, and C. Pedrini, “Excited-state absorption and energy-transfer in Er3+ doped LiYF4,” J. Lumin. 36, 39–47 (1986).
[CrossRef]

1976 (1)

F. Auzel, “Multiphonon-assisted anti-Stokes and Stokes fluorescence of triply ionized rare-earth ions,” Phys. Rev. B 13, 2809–2817 (1976).
[CrossRef]

1972 (1)

N. Yamada, S. Shionoya, and T. Kushida, “Phonon-assisted energy transfer between trivalent rare earth ions,” J. Phys. Soc. Jpn. 32, 1577–1586 (1972).
[CrossRef]

1968 (1)

W. T. Carnall, P. R. Fields, and R. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

1964 (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[CrossRef]

1962 (2)

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]

1953 (1)

D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21, 836–850 (1953).
[CrossRef]

1948 (1)

T. Förster, “Zwischenmolekulare energiewanderung und fluoreszenz,” Ann. Phys. 437, 55–75 (1948).
[CrossRef]

Agazzi, L.

J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
[CrossRef]

L. Agazzi, K. Wörhoff, and M. Pollnau, “Energy-transfer-upconversion models, their applicability and breakdown in the presence of spectroscopically distinct ion classes: investigations on the example of amorphous Al2O3:Er3+,” submitted to J. Phys. Chem. C.

Amorim, H. T.

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

Auzel, F.

F. Auzel, “Upconversion and anti-Stokes processes with f and d ions in solids,” Chem. Rev. 104, 139–174 (2004).
[CrossRef]

F. Auzel, “Multiphonon-assisted anti-Stokes and Stokes fluorescence of triply ionized rare-earth ions,” Phys. Rev. B 13, 2809–2817 (1976).
[CrossRef]

Ay, F.

J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
[CrossRef]

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
[CrossRef]

Balda, R.

Balmer, J. E.

M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, and H. P. Weber, “Explanation of the cw operation of the Er3+ 3 μm crystal laser,” Phys. Rev. A 49, 3990–3996 (1994).
[CrossRef]

Bisson, J. F.

G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
[CrossRef]

Blauwendraat, T. P.

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

Boyraz, O.

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

Bradley, J. D. B.

J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
[CrossRef]

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
[CrossRef]

Brenier, A.

J. Rubin, A. Brenier, R. Moncorgé, and C. Pedrini, “Excited-state absorption and energy-transfer in Er3+ doped LiYF4,” J. Lumin. 36, 39–47 (1986).
[CrossRef]

Caird, J. A.

Camy, P.

C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
[CrossRef]

Carnall, W. T.

W. T. Carnall, P. R. Fields, and R. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Chai, B. H. T.

P. E. A. Mobert, A. Diening, E. Heumann, G. Huber, and B. H. T. Chai, “Room-temperature continuous-wave upconversion-pumped laser emission in Ho, Yb:KYF4 at 756, 1070, and 1390 nm,” Laser Phys. 8, 210–213 (1998).

Chang, D. B.

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2 and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[CrossRef]

S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986).
[CrossRef]

de Araujo, M. T.

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

Dexter, D. L.

D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21, 836–850 (1953).
[CrossRef]

Diening, A.

P. E. A. Mobert, A. Diening, E. Heumann, G. Huber, and B. H. T. Chai, “Room-temperature continuous-wave upconversion-pumped laser emission in Ho, Yb:KYF4 at 756, 1070, and 1390 nm,” Laser Phys. 8, 210–213 (1998).

Dorner, B.

H. Schober, D. Strauch, and B. Dorner, “Lattice dynamics of sapphire (Al2O3),” Z. Phys. B 92, 273–283 (1993).
[CrossRef]

Doualan, J.-L.

C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
[CrossRef]

P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
[CrossRef]

Fdez-Navarro, J. M.

Feng, Y.

G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
[CrossRef]

Fernández, J.

Fields, P. R.

W. T. Carnall, P. R. Fields, and R. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Fornasiero, L.

L. Fornasiero, K. Petermann, E. Heumann, and G. Huber, “Spectroscopic properties and laser emission of Er3+ in scandium silicates near 1.5 μm,” Opt. Mater. 10, 9–17 (1998).
[CrossRef]

Förster, T.

T. Förster, “Zwischenmolekulare energiewanderung und fluoreszenz,” Ann. Phys. 437, 55–75 (1948).
[CrossRef]

Gamelin, D. R.

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
[CrossRef]

Garcia-Adeva, A. J.

Geskus, D.

J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
[CrossRef]

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

Ghisler, C.

M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
[CrossRef]

Girard, S.

P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
[CrossRef]

Golding, P. S.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy-transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

Gouveia, E. A.

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

Gouveia-Neto, A. S.

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

Graf, T.

M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, and H. P. Weber, “Explanation of the cw operation of the Er3+ 3 μm crystal laser,” Phys. Rev. A 49, 3990–3996 (1994).
[CrossRef]

Gudel, H. U.

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
[CrossRef]

Güdel, H. U.

S. R. Lüthi, M. Pollnau, H. U. Güdel, and M. P. Hehlen, “Near-infrared to visible upconversion in Er3+ doped Cs3Lu2Cl9, Cs3Lu2Br9, and Cs3Y2I9 excited at 1.54 μm,” Phys. Rev. B 60, 162–178 (1999).
[CrossRef]

Hehlen, M. P.

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
[CrossRef]

S. R. Lüthi, M. Pollnau, H. U. Güdel, and M. P. Hehlen, “Near-infrared to visible upconversion in Er3+ doped Cs3Lu2Cl9, Cs3Lu2Br9, and Cs3Y2I9 excited at 1.54 μm,” Phys. Rev. B 60, 162–178 (1999).
[CrossRef]

Heumann, E.

P. E. A. Mobert, A. Diening, E. Heumann, G. Huber, and B. H. T. Chai, “Room-temperature continuous-wave upconversion-pumped laser emission in Ho, Yb:KYF4 at 756, 1070, and 1390 nm,” Laser Phys. 8, 210–213 (1998).

L. Fornasiero, K. Petermann, E. Heumann, and G. Huber, “Spectroscopic properties and laser emission of Er3+ in scandium silicates near 1.5 μm,” Opt. Mater. 10, 9–17 (1998).
[CrossRef]

M. Pollnau, E. Heumann, and G. Huber, “Time-resolved spectra of excited-state absorption in Er3+ doped YAlO3,” Appl. Phys. A 54, 404–410 (1992).
[CrossRef]

Huang, Y.

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

Huber, G.

P. E. A. Mobert, A. Diening, E. Heumann, G. Huber, and B. H. T. Chai, “Room-temperature continuous-wave upconversion-pumped laser emission in Ho, Yb:KYF4 at 756, 1070, and 1390 nm,” Laser Phys. 8, 210–213 (1998).

L. Fornasiero, K. Petermann, E. Heumann, and G. Huber, “Spectroscopic properties and laser emission of Er3+ in scandium silicates near 1.5 μm,” Opt. Mater. 10, 9–17 (1998).
[CrossRef]

J. Koetke and G. Huber, “Infrared excited-state absorption and stimulated-emission cross sections of Er3+-doped crystals,” Appl. Phys. B 61, 151–158 (1995).
[CrossRef]

M. Pollnau, E. Heumann, and G. Huber, “Time-resolved spectra of excited-state absorption in Er3+ doped YAlO3,” Appl. Phys. A 54, 404–410 (1992).
[CrossRef]

Izumitani, T.

X. Zou and T. Izumitani, “Spectroscopic properties and mechanisms of excited state absorption and energy transfer upconversion for Er3+-doped glasses,” J. Non-Cryst. Solids 162, 68–80 (1993).
[CrossRef]

Jackson, S. D.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy-transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

Judd, B. R.

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

Kalyoncu, S. K.

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, Crystalline Lasers: Physical Processes and Operating Schemes (CRC, 1996).

King, T. A.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy-transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

Koetke, J.

J. Koetke and G. Huber, “Infrared excited-state absorption and stimulated-emission cross sections of Er3+-doped crystals,” Appl. Phys. B 61, 151–158 (1995).
[CrossRef]

Kushida, T.

N. Yamada, S. Shionoya, and T. Kushida, “Phonon-assisted energy transfer between trivalent rare earth ions,” J. Phys. Soc. Jpn. 32, 1577–1586 (1972).
[CrossRef]

Labbe, C.

C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
[CrossRef]

Lavin, V.

I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
[CrossRef]

Le Boulanger, P.

P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
[CrossRef]

Lu, J.

G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
[CrossRef]

Lüthi, S. R.

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
[CrossRef]

S. R. Lüthi, M. Pollnau, H. U. Güdel, and M. P. Hehlen, “Near-infrared to visible upconversion in Er3+ doped Cs3Lu2Cl9, Cs3Lu2Br9, and Cs3Y2I9 excited at 1.54 μm,” Phys. Rev. B 60, 162–178 (1999).
[CrossRef]

Lüthy, W.

M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
[CrossRef]

M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, and H. P. Weber, “Explanation of the cw operation of the Er3+ 3 μm crystal laser,” Phys. Rev. A 49, 3990–3996 (1994).
[CrossRef]

Margerie, J.

P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
[CrossRef]

Martin, I. R.

I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
[CrossRef]

McCumber, D. E.

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[CrossRef]

Medeiros Neto, J. A.

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

Miniscalco, W. J.

R. S. Quimby, W. J. Miniscalco, and B. Thompson, “Excited state absorption at 980 nm in erbium doped glass,” Proc. SPIE 1581, 72–79 (1991).
[CrossRef]

Mobert, P. E. A.

P. E. A. Mobert, A. Diening, E. Heumann, G. Huber, and B. H. T. Chai, “Room-temperature continuous-wave upconversion-pumped laser emission in Ho, Yb:KYF4 at 756, 1070, and 1390 nm,” Laser Phys. 8, 210–213 (1998).

Moise, N. L.

S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986).
[CrossRef]

Moncorgé, R.

C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
[CrossRef]

P. Le Boulanger, J.-L. Doualan, S. Girard, J. Margerie, and R. Moncorgé, “Excited-state absorption spectroscopy of Er3+-doped Y3Al5O12, YVO4, and phosphate glass,” Phys. Rev. B 60, 11380–11390 (1999).
[CrossRef]

J. Rubin, A. Brenier, R. Moncorgé, and C. Pedrini, “Excited-state absorption and energy-transfer in Er3+ doped LiYF4,” J. Lumin. 36, 39–47 (1986).
[CrossRef]

Ofelt, G. S.

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

Pedrini, C.

J. Rubin, A. Brenier, R. Moncorgé, and C. Pedrini, “Excited-state absorption and energy-transfer in Er3+ doped LiYF4,” J. Lumin. 36, 39–47 (1986).
[CrossRef]

Petermann, K.

L. Fornasiero, K. Petermann, E. Heumann, and G. Huber, “Spectroscopic properties and laser emission of Er3+ in scandium silicates near 1.5 μm,” Opt. Mater. 10, 9–17 (1998).
[CrossRef]

Pollack, S. A.

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2 and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[CrossRef]

S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986).
[CrossRef]

Pollnau, M.

J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
[CrossRef]

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
[CrossRef]

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, “Energy-transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses,” Phys. Rev. B 62, 856–864 (2000).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Gudel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).
[CrossRef]

S. R. Lüthi, M. Pollnau, H. U. Güdel, and M. P. Hehlen, “Near-infrared to visible upconversion in Er3+ doped Cs3Lu2Cl9, Cs3Lu2Br9, and Cs3Y2I9 excited at 1.54 μm,” Phys. Rev. B 60, 162–178 (1999).
[CrossRef]

M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
[CrossRef]

M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, and H. P. Weber, “Explanation of the cw operation of the Er3+ 3 μm crystal laser,” Phys. Rev. A 49, 3990–3996 (1994).
[CrossRef]

M. Pollnau, E. Heumann, and G. Huber, “Time-resolved spectra of excited-state absorption in Er3+ doped YAlO3,” Appl. Phys. A 54, 404–410 (1992).
[CrossRef]

L. Agazzi, K. Wörhoff, and M. Pollnau, “Energy-transfer-upconversion models, their applicability and breakdown in the presence of spectroscopically distinct ion classes: investigations on the example of amorphous Al2O3:Er3+,” submitted to J. Phys. Chem. C.

Polman, A.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

Qian, F.

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

Qin, G.

G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
[CrossRef]

Quimby, R. S.

R. S. Quimby, W. J. Miniscalco, and B. Thompson, “Excited state absorption at 980 nm in erbium doped glass,” Proc. SPIE 1581, 72–79 (1991).
[CrossRef]

Rajnak, R.

W. T. Carnall, P. R. Fields, and R. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Ramponi, A. J.

Rand, S. C.

Rodriguez, V. D.

I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
[CrossRef]

Rodriguez-Mendoza, U. R.

I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
[CrossRef]

Rubin, J.

J. Rubin, A. Brenier, R. Moncorgé, and C. Pedrini, “Excited-state absorption and energy-transfer in Er3+ doped LiYF4,” J. Lumin. 36, 39–47 (1986).
[CrossRef]

Schober, H.

H. Schober, D. Strauch, and B. Dorner, “Lattice dynamics of sapphire (Al2O3),” Z. Phys. B 92, 273–283 (1993).
[CrossRef]

Shionoya, S.

N. Yamada, S. Shionoya, and T. Kushida, “Phonon-assisted energy transfer between trivalent rare earth ions,” J. Phys. Soc. Jpn. 32, 1577–1586 (1972).
[CrossRef]

Smit, M. K.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

Snoeks, E.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

Sombra, A. S. B.

H. T. Amorim, M. T. de Araujo, E. A. Gouveia, A. S. Gouveia-Neto, J. A. Medeiros Neto, and A. S. B. Sombra, “Infrared to visible frequency up-conversion fluorescence spectroscopy in Er3+-doped chalcogenide glass,” J. Lumin. 78, 271–277 (1998).
[CrossRef]

Song, Q.

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

Staver, P. R.

Strauch, D.

H. Schober, D. Strauch, and B. Dorner, “Lattice dynamics of sapphire (Al2O3),” Z. Phys. B 92, 273–283 (1993).
[CrossRef]

Thompson, B.

R. S. Quimby, W. J. Miniscalco, and B. Thompson, “Excited state absorption at 980 nm in erbium doped glass,” Proc. SPIE 1581, 72–79 (1991).
[CrossRef]

Thuau, M.

C. Labbe, J.-L. Doualan, P. Camy, R. Moncorgé, and M. Thuau, “The 2.8 μm laser properties of Er3+ doped CaF2 crystals,” Opt. Commun. 209, 193–199 (2002).
[CrossRef]

Tien, E.-K.

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

Ueda, K.

G. Qin, J. Lu, J. F. Bisson, Y. Feng, and K. Ueda, “Upconversion luminescence of Er3+ in highly transparent YAG ceramics,” Solid State Commun. 132, 103–106 (2004).
[CrossRef]

van Dam, C.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

van den Hoven, G. N.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

van Uffelen, J. W. M.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79, 1258–1266 (1996).
[CrossRef]

Velez, P.

I. R. Martın, P. Velez, V. D. Rodrıguez, U. R. Rodrıguez-Mendoza, and V. Lavin, “Upconversion dynamics in Er3+-doped fluoroindate glasses,” Spectrochim. Acta 55, 935–940 (1999).
[CrossRef]

Weber, H. P.

M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
[CrossRef]

M. Pollnau, T. Graf, J. E. Balmer, W. Lüthy, and H. P. Weber, “Explanation of the cw operation of the Er3+ 3 μm crystal laser,” Phys. Rev. A 49, 3990–3996 (1994).
[CrossRef]

Wörhoff, K.

J. D. B. Bradley, L. Agazzi, D. Geskus, F. Ay, K. Wörhoff, and M. Pollnau, “Gain bandwidth of 80 nm and 2  dB/cm peak gain in Al2O3:Er3+ optical amplifiers on silicon,” J. Opt. Soc. Am. B 27, 187–196 (2010).
[CrossRef]

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
[CrossRef]

L. Agazzi, K. Wörhoff, and M. Pollnau, “Energy-transfer-upconversion models, their applicability and breakdown in the presence of spectroscopically distinct ion classes: investigations on the example of amorphous Al2O3:Er3+,” submitted to J. Phys. Chem. C.

Xie, P.

Yamada, N.

N. Yamada, S. Shionoya, and T. Kushida, “Phonon-assisted energy transfer between trivalent rare earth ions,” J. Phys. Soc. Jpn. 32, 1577–1586 (1972).
[CrossRef]

Zou, X.

X. Zou and T. Izumitani, “Spectroscopic properties and mechanisms of excited state absorption and energy transfer upconversion for Er3+-doped glasses,” J. Non-Cryst. Solids 162, 68–80 (1993).
[CrossRef]

Ann. Phys. (1)

T. Förster, “Zwischenmolekulare energiewanderung und fluoreszenz,” Ann. Phys. 437, 55–75 (1948).
[CrossRef]

Appl. Phys. A (1)

M. Pollnau, E. Heumann, and G. Huber, “Time-resolved spectra of excited-state absorption in Er3+ doped YAlO3,” Appl. Phys. A 54, 404–410 (1992).
[CrossRef]

Appl. Phys. B (3)

J. D. B. Bradley, F. Ay, K. Wörhoff, and M. Pollnau, “Fabrication of low-loss channel waveguides in Al2O3 and Y2O3 layers by inductively coupled plasma reactive ion etching,” Appl. Phys. B 89, 311–318 (2007).
[CrossRef]

J. Koetke and G. Huber, “Infrared excited-state absorption and stimulated-emission cross sections of Er3+-doped crystals,” Appl. Phys. B 61, 151–158 (1995).
[CrossRef]

M. Pollnau, C. Ghisler, W. Lüthy, and H. P. Weber, “Cross sections of excited-state absorption at 800 nm in erbium-doped ZBLAN fiber,” Appl. Phys. B 67, 23–28 (1998).
[CrossRef]

Chem. Rev. (1)

F. Auzel, “Upconversion and anti-Stokes processes with f and d ions in solids,” Chem. Rev. 104, 139–174 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

F. Qian, Q. Song, E.-K. Tien, S. K. Kalyoncu, Y. Huang, and O. Boyraz, “Effects of design geometries and nonlinear losses on gain in silicon waveguides with erbium-doped regions,” IEEE J. Quantum Electron. 47, 327–334 (2011).
[CrossRef]

K. Wörhoff, J. D. B. Bradley, F. Ay, D. Geskus, T. P. Blauwendraat, and M. Pollnau, “Reliable low-cost fabrication of low-loss Al2O3:Er3+ waveguides with 5.4 dB optical gain,” IEEE J. Quantum Electron. 45, 454–461 (2009).
[CrossRef]

J. Appl. Phys. (3)

S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986).
[CrossRef]

S. A. Pollack and D. B. Chang, “Ion-pair upconversion pumped laser emission in Er3+ ions in YAG, YLF, SrF2 and CaF2 crystals,” J. Appl. Phys. 64, 2885–2893 (1988).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Partial energy-level diagram of Er3+, indicating the GSA, ESA, ETU, CR, multiphonon-relaxation, and luminescence decay processes relevant to this work, together with the measured or estimated luminescence lifetimes of the considered levels. Only the lifetimes of the F7/24 and F5/24/F3/24 levels are unknown and have been set to the approximate value of 1 μs.

Fig. 2.
Fig. 2.

Normalized luminescence decay curve from (a) the I11/24 level at a wavelength of 980 nm and (b) the S3/24 level at a wavelength of 550 nm, for an Er3+ concentration of 1.17×1020cm3. The solid curves are numerical fits to the data using Eqs. (1) and (2). (c) Concentration dependence of the I11/24 (squares) and S3/24 (dots) lifetime.

Fig. 3.
Fig. 3.

Measured absorption cross sections of Al2O3:Er3+ over the wavelength range from 500 to 1700 nm.

Fig. 4.
Fig. 4.

Energy-gap dependence of the nonradiative decay-rate constants in Al2O3:Er3+ in semi-logarithmic scale. Solid squares are the nonradiative decay-rate constants determined from Eq. (11) with the measured luminescence lifetimes and the calculated radiative decay-rate constants. The line is the fit through these data with Eq. (12). The open dots are estimated nonradiative decay-rate constants based on this fit.

Fig. 5.
Fig. 5.

Experimental setup of the ESA measurement based on the pump-and-probe technique described in [27].

Fig. 6.
Fig. 6.

Spectra representing (a) σGSA+iNieff/Neeff(σESA,iσSE,i), (b) iNieff/Neeff(σESA,iσSE,i), and (c) iσESA,i. The black solid curves in the graphs are spectra obtained from Eq. (16), whereas the red dashed curves derive from Eq. (17).

Fig. 7.
Fig. 7.

I15/24I13/24 absorption (solid blue curve) and emission (solid black curve) cross sections, taken from [28]; I13/24I9/24 ESA cross section (solid red curve) derived in Section 4 and then shifted by 195cm1 (dashed red curve), as explained in Section 5.A.

Fig. 8.
Fig. 8.

I15/24I11/24 absorption (blue curve) and emission (black curve) cross sections; the former is taken from [28], and the latter is calculated with the McCumber relation [33]. I11/24F7/24 ESA cross section (red curve) derived in Section 4.

Fig. 9.
Fig. 9.

Values of the macroscopic ETU coefficients WETU1 taken from [3] (squares) for the four Er3+ concentrations considered in this study, along with the calculations of WETU1 and WETU2 with Eq. (22) (solid and dashed lines, respectively), and WETU3 derived from the analysis of the Igreen/Ired ratio under 1480 nm pumping (triangles), as a function of Er3+ concentration.

Fig. 10.
Fig. 10.

(a) Upconversion emission spectra in the 500–750 nm spectral region, after excitation with 1480 nm pump light (solid blue curve) and 976 nm pump light (dashed magenta curve). Both spectra are normalized with respect to the S3/24 peak. (b) Ratio of 525–550 nm versus 660 nm intensity (Igreen/Ired) as a function of Er3+ concentration for the two pump wavelengths.

Fig. 11.
Fig. 11.

Population densities N1a and N2a under 1480 nm pumping calculated with the rate-equation system of [3].

Fig. 12.
Fig. 12.

I11/24I15/24 emission cross section and I13/24F9/24 ESA cross section derived in Section 4 and then shifted by 870cm1, as explained in Section 6.

Tables (7)

Tables Icon

Table 1. Mean Wavelengths, Values of Reduced Matrix Elements [23,24], Refractive Indices, Integrated Absorption Cross Sections, and Measured and Calculated Absorption Line Strengths for the Absorption Transitions of Er3+ in Al2O3

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Table 2. Reduced Matrix Elements [23,24], Predicted Fluorescence Line Strengths, Radiative Decay-Rate Constants, and Radiative Branching Ratios of Er3+ in Al2O3

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Table 3. Energy Gaps to the Next Lower Levels, Total Radiative Decay-Rate Constants, Radiative and Luminescence Lifetimes, and Nonradiative Decay-Rate Constants of the Lowest Five Excited States of Er3+ in Al2O3. The S3/24 and H11/22 Levels are Treated as a Single, Thermally Coupled Levela

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Table 4. ESA Transitions, Corresponding Peak Wavelengths, Peak Cross Sections, and Comparison between the Measured Integrated ESA Cross Sections and Those Calculated by the J–O Formalism

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Table 5. Microparameters of Energy Migration within, and ETU from, the First and Second Excited States, Calculated with Eq. (21) and the Measured Donor Emission and either Donor GSA or Acceptor ESA Spectraa

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Table 6. Values of the Macroscopic ETU Coefficients WETU1 Taken from [3], Along with the Calculations of WETU1 and WETU2 with Eq. (22), and WETU3 Derived from the Analysis of the Igreen/Ired Ratio under 1480 nm Pumping, for the Four Er3+ Concentrations Considered in this Study

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Table 7. Effective Population Densities and Relative Excited Population Densities under the Experimental Conditions of the ESA Measurements of Section 4, for the Example of λS=980nm

Equations (49)

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dNidt=Niτi+WETUjNj2,
dNjdt=Njτj2WETUjNj2+Niτi.
Ni(t)exp(2t/τj),
Nj(t)exp(t/τj),
Smeas(JJ)=3ch(2J+1)8π3λ¯e2[9n(n2+2)2]Γ(JJ),
Scalc(JJ)=t˜=2,4,6Ωt˜|(S,L)JU(t˜)(S,L)J|2=Ω2[U(2)]2+Ω4[U(4)]2+Ω6[U(6)]2.
ΔSrms=[(qp)1(SmeasScalc)2]1/2,
A(JJ)=64π4e23h(2J+1)λ3n(n2+2)29Scalc(JJ),
1τrad(J)=A(J)=JA(JJ),
β(JJ)=A(JJ)A(J).
1τ(J)=A(J)+Anon-rad(JJ1).
Anon-rad=CeαΔE,
Iu=I0exp[αLossL+0LdzArdxdy(σGSANdψS)],
Ip=I0exp[αLossL+0LdzArdxdy(σGSA(NdNe)ψSi(σESA,iσSE,i)NiψS)],
ln(IpIu)=0LdzArdxdy(σGSANeψSi(σESA,iσSE,i)NiψS).
ΔI=IpIu=Iuexp[0LdzArdxdy(σGSANeψS+i(σSE,iσESA,i)NiψS)]Iu.
ln(IpIu)=ln(1+IpIuIu)=ln(1+ΔIIu)ΔIIu,
ΔIIu=A*{exp[0LdzArdxdy(σGSANeψS+i(σSE,iσESA,i)NiψS)]1},
ΔIIu=A*0LdzArdxdy(σGSANeψS+i(σSE,iσESA,i)NiψS).
σGSA+i(σESA,iσSE,i)NieffNeeff,
Nieff=1L0LdzArdxdyNiψS,
Neeff=1L0LdzArdxdyNeψS=1L0LdzArdxdyiNiψS=iNieff.
i(σESA,iσSE,i)NieffNeeff.
CDD/DA=6c(2π)4n2σemD(λ)σGSA/ESAD/A(λ)dλ.
WETU=π23CDACDDNd.
dN4a/qdt=1τ5N5a/q1τ4N4a/q=0,
N4a/q=τ4τ5N5a/q,
IgreenIred(N5a+N5qN4a+N4q)=τ5τ4.
dN5a/qdt=φPσESA2(λP)N2a/q+WETU2N2a/q21τ5N5a/q=0,
dN4a/qdt=1τ5N5a/q1τ4N4a/q+WETU3N1a/qN2a/q=0,
IgreenIred(N5a+N5qN4a+N4q)=(φPσESA2(λP)(N2,a+N2,q)+WETU2N2a2φPσESA2(λP)(N2,a+N2,q)+WETU2N2a2+WETU3N1aN2a)τ5τ4.
dN5a/qdt=WETU2N2a/q21τ5N5a/q=0,
dN4a/qdt=1τ5N5a/q1τ4N4a/q+WETU3N1a/qN2a/q=0,
IgreenIred(N5a+N5qN4a+N4q)=(WETU2N2a2WETU2N2a2+WETU3N1aN2a)τ5τ4.
dN5a/qdt=RESA3a/q+RESA4a/q1τ5N5a/q,
dN2a/qdt=RGSA3a/qRESA4a/q+1τ5N5a/q1τ2N2a/q+WETU1N1a/q2,
dN1a/qdt=RESA3a/q+1τ2N2a/q1τ1/1qN1a/q2WETU1N1a/q2.
RGSA3,a/q=λPhcIPσGSA3(λP)N0a/q=φPσGSA3(λP)N0a/q,
RESA3,a/q=λPhcIPσESA3(λP)N1a/q=φPσESA3(λP)N1a/q,
RESA4,a/q=λPhcIPσESA4(λP)N2a/q=φPσESA4(λP)N2a/q.
N5a/q=τ5φP(σESA3(λP)N1a/q+σESA4(λP)N2a/q),
N2a/q=τ2[N1a/q(φPσESA3(λP)+1τ1/1q)+2WETU1N1a/q2],
N1a/q=Ba/q+Ba/q24ACa/q2A,
A=WETU1[2φPτ2(σGSA3(λP)+φPσGSA3(λP)σESA4(λP)τ5)+1],
Ba/q=φPσGSA3(λP)[1+(1τ1/1q+φPσESA3(λP))τ2]+φP2σGSA3(λP)τ5(σESA3(λP)+σESA4(λP)τ2τ1/1q+φPσESA3(λP)σESA4(λP)τ2)+1τ1/1q,
Ca/q=fa/qNdφPσGSA3(λP).
dPP(z)dz=PP(z)ArψP[σGSA3(λP)(N0a+N0q)]dxdyPP(z)ArψP[σESA3(λP)(N1a+N1q)+σESA4(λP)(N2a+N2q)]dxdyPP(z)αLoss(λP),
Nieff=1L0LdzArdxdyNiψS=1L0LdzArdxdy(Nia+Niq)ψS=1L0LdzArdxdyNiaψS+1L0LdzArdxdyNiqψS=Niaeff+Niqeff,
Neeff=iNieff=iNiaeff+Niqeff,

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