Abstract

The decay processes relating to the potential H613/2H615/2 laser transition for 2.9 μm emission in single Dy3+-doped tellurite (TZNF and TZN) glasses have been investigated in detail using time-resolved fluorescence spectroscopy. The selective laser excitation of the F65/2 and H69/2, F611/2 energy levels at 805 and 1300 nm, respectively, have established that the decay processes of the lowest excited level (i.e., H613/2) entirely favors multiphonon emission in a tellurite glass host. Detailed investigation of the H613/2 luminescence decay characteristic revealed that two decay constants are involved in the TZNF glass composition; approximately 90% of the decay has a time constant (τ1) of 19.6 μs. The remaining centers decay with a time constant τ2=112μs due to the Dy3+ fluorine bonds, which are possibly present in the TZNF glass matrix. Slight quenching of τ1 for Dy3+ concentration increases to 2 mol. % may indicate energy transfer to OH molecules in the TZNF glass despite the low OH content, [α(OH)0.04cm1]; further decrease of τ1 (to 9.7 μs) was measured in TZN glass matrix, which is commensurate with the higher OH density (α=0.15cm1).

© 2014 Optical Society of America

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  1. S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
    [CrossRef]
  2. M. C. Nostrand, R. H. Page, S. A. Payne, L. I. Isaenko, and A. P. Yelisseyev, “Optical properties of Dy3+- and Nd3+-doped KPb2Cl5,” J. Opt. Soc. Am. B 18, 264–276 (2001).
    [CrossRef]
  3. T. Schweizer, D. W. Hewak, B. N. Samson, and D. N. Payne, “Spectroscopic data of the 1.8-, 2,9-, and 4.3 μm transitions in dysprosium-doped gallium lanthanum,” Opt. Lett. 21, 1594–1596 (1996).
    [CrossRef]
  4. L. Gomes and S. D. Jackson, “Spectroscopic properties of ytterbium, praseodymium-codoped fluorozirconate glass for laser emission at 3.6  μm,” J. Opt. Soc. Am. 30, 1410–1419 (2013).
    [CrossRef]
  5. B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
    [CrossRef]
  6. M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).
  7. L. Nemec and J. Gotz, “Infrared absorption of OH− in E glass,” J. Am Ceram. Soc. 53, 526–533 (1970).
  8. J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
    [CrossRef]
  9. L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
    [CrossRef]
  10. M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
    [CrossRef]
  11. J. Hormadaly and R. Reisfeld, “Intensity parameters and laser analysis of Pr3+ and Dy3+ in oxide glasses,” J. Non-Cryst. Solids 30, 337–348 (1979).
    [CrossRef]
  12. W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
    [CrossRef]
  13. C. K. Jayasankar and E. Rukmini, “Spectroscopic investigations of Dy3+ ions in borosulphate glasses,” Physica B 240, 273–288 (1997).
    [CrossRef]

2014

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

2013

L. Gomes and S. D. Jackson, “Spectroscopic properties of ytterbium, praseodymium-codoped fluorozirconate glass for laser emission at 3.6  μm,” J. Opt. Soc. Am. 30, 1410–1419 (2013).
[CrossRef]

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

2012

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

2003

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

2001

1997

C. K. Jayasankar and E. Rukmini, “Spectroscopic investigations of Dy3+ ions in borosulphate glasses,” Physica B 240, 273–288 (1997).
[CrossRef]

1996

S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
[CrossRef]

T. Schweizer, D. W. Hewak, B. N. Samson, and D. N. Payne, “Spectroscopic data of the 1.8-, 2,9-, and 4.3 μm transitions in dysprosium-doped gallium lanthanum,” Opt. Lett. 21, 1594–1596 (1996).
[CrossRef]

1986

M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).

1979

J. Hormadaly and R. Reisfeld, “Intensity parameters and laser analysis of Pr3+ and Dy3+ in oxide glasses,” J. Non-Cryst. Solids 30, 337–348 (1979).
[CrossRef]

1970

L. Nemec and J. Gotz, “Infrared absorption of OH− in E glass,” J. Am Ceram. Soc. 53, 526–533 (1970).

1968

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Arnaudov, M.

M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).

Binks, D.

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

Bowman, S. R.

S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
[CrossRef]

Carnall, W. T.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Dimitriev, Y.

M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).

Dimitrov, V.

M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).

Dimitrovapankoval, M.

M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).

Feldman, B. J.

S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
[CrossRef]

Fields, P. R.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Furniss, D.

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

Ganem, J.

S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
[CrossRef]

Gomes, L.

L. Gomes and S. D. Jackson, “Spectroscopic properties of ytterbium, praseodymium-codoped fluorozirconate glass for laser emission at 3.6  μm,” J. Opt. Soc. Am. 30, 1410–1419 (2013).
[CrossRef]

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

Gotz, J.

L. Nemec and J. Gotz, “Infrared absorption of OH− in E glass,” J. Am Ceram. Soc. 53, 526–533 (1970).

He, J.

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

Hewak, D. W.

Hormadaly, J.

J. Hormadaly and R. Reisfeld, “Intensity parameters and laser analysis of Pr3+ and Dy3+ in oxide glasses,” J. Non-Cryst. Solids 30, 337–348 (1979).
[CrossRef]

Isaenko, L. I.

Jackson, S. D.

L. Gomes and S. D. Jackson, “Spectroscopic properties of ytterbium, praseodymium-codoped fluorozirconate glass for laser emission at 3.6  μm,” J. Opt. Soc. Am. 30, 1410–1419 (2013).
[CrossRef]

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

Jayasankar, C. K.

C. K. Jayasankar and E. Rukmini, “Spectroscopic investigations of Dy3+ ions in borosulphate glasses,” Physica B 240, 273–288 (1997).
[CrossRef]

Jha, A.

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

Jose, G.

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

Lin, A.

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

Lousteau, J.

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

Milanese, D.

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

Miller, C. A.

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

Nemec, L.

L. Nemec and J. Gotz, “Infrared absorption of OH− in E glass,” J. Am Ceram. Soc. 53, 526–533 (1970).

Nostrand, M. C.

O’Donnell, M. D.

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

Page, R. H.

Payne, D. N.

Payne, S. A.

Rajnak, K.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

Reisfeld, R.

J. Hormadaly and R. Reisfeld, “Intensity parameters and laser analysis of Pr3+ and Dy3+ in oxide glasses,” J. Non-Cryst. Solids 30, 337–348 (1979).
[CrossRef]

Richards, B. D. O.

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

Rukmini, E.

C. K. Jayasankar and E. Rukmini, “Spectroscopic investigations of Dy3+ ions in borosulphate glasses,” Physica B 240, 273–288 (1997).
[CrossRef]

Samson, B. N.

Scarpignato, G.

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

Schweizer, T.

Seddon, A. B.

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

Shaw, L. B.

S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
[CrossRef]

Teddy-Fernandez, T.

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

Tikhomirov, V. K.

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

Yelisseyev, A. P.

Zhan, H.

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

Zhang, A.

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

Zhou, Z.

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

IEEE J. Quantum Electron.

S. R. Bowman, L. B. Shaw, B. J. Feldman, and J. Ganem, “A 7-μm praseodymium-based solid-state laser,” IEEE J. Quantum Electron. 32, 646–649 (1996).
[CrossRef]

J. Am Ceram. Soc.

L. Nemec and J. Gotz, “Infrared absorption of OH− in E glass,” J. Am Ceram. Soc. 53, 526–533 (1970).

J. Appl. Phys.

L. Gomes, J. Lousteau, D. Milanese, G. Scarpignato, and S. D. Jackson, “Energy transfer and energy level decay processes in Tm3+-doped tellurite glass,” J. Appl. Phys. 111, 063105 (2012).
[CrossRef]

J. Chem. Phys.

W. T. Carnall, P. R. Fields, and K. Rajnak, “Electronic energy levels in the trivalent lanthanide aquo ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+,” J. Chem. Phys. 49, 4424–4442 (1968).
[CrossRef]

J. Lumin.

J. He, Z. Zhou, H. Zhan, A. Zhang, and A. Lin, “2.85  μm fluorescence of Ho-doped water-free fluorotellutite glasses,” J. Lumin. 145, 507–511 (2014).
[CrossRef]

J. Non-Cryst. Solids

J. Hormadaly and R. Reisfeld, “Intensity parameters and laser analysis of Pr3+ and Dy3+ in oxide glasses,” J. Non-Cryst. Solids 30, 337–348 (1979).
[CrossRef]

J. Non-Crystalline Solids

M. D. O’Donnell, C. A. Miller, D. Furniss, V. K. Tikhomirov, and A. B. Seddon, “Fluorotellurite glasses with improved mid-infrared transmission,” J. Non-Crystalline Solids 331, 48–57 (2003).
[CrossRef]

J. Opt. Soc. Am.

L. Gomes and S. D. Jackson, “Spectroscopic properties of ytterbium, praseodymium-codoped fluorozirconate glass for laser emission at 3.6  μm,” J. Opt. Soc. Am. 30, 1410–1419 (2013).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys. Lett.

B. D. O. Richards, T. Teddy-Fernandez, G. Jose, D. Binks, and A. Jha, “Mid-IR (3–4  μm) fluorescence and ASE studies in Dy3+ doped tellurite and germanate glasses and a fs laser inscribed waveguide,” Laser Phys. Lett. 10, 085802 (2013).
[CrossRef]

Opt. Lett.

Phys. Chem. Glasses

M. Arnaudov, Y. Dimitriev, V. Dimitrov, and M. Dimitrovapankoval, “Infrared spectral investigation of water in tellurite glasses,” Phys. Chem. Glasses 27, 48–50 (1986).

Physica B

C. K. Jayasankar and E. Rukmini, “Spectroscopic investigations of Dy3+ ions in borosulphate glasses,” Physica B 240, 273–288 (1997).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Measured absorption spectrum of the Dy3+ ions measured in Dy3+-doped TZNF (0.25, 0.5, 1, and 2 mol. %) and TZN (3 wt. %) tellurite glasses from (a) 700–1500 nm and (b) 1500–3300 nm.

Fig. 2.
Fig. 2.

Measured mid-infrared absorption coefficient of TZN and TZNF tellurite glasses measured using a Nicolet 6700 FTIR spectrophotometer.

Fig. 3.
Fig. 3.

Measured mid-infrared absorption spectrum of (a) Dy3+-doped TZN (3 wt. %) and (b) TZBiGe:Tm3+ (2%) and ZBLAN:Ho3+ (2%) glass. The broad absorption band at 3370 nm is due to the free OH radical impurities in TZN and TZNF and TZBiGe tellurites glasses. The OH absorption is located at 2920 nm in ZBLAN glass (red curve), and the double narrow peaks at 3427 and 3508 nm are attributed to CH molecules.

Fig. 4.
Fig. 4.

Measured luminescence spectrum of the H613/2H615/2 transition of Dy3+ doped in TZNF (1 mol. %) and TZN (3 wt. %) glass using pulsed laser excitation at 1300 nm.

Fig. 5.
Fig. 5.

Measured decay time of the luminescence intensity (normalized) of the H69/2 and H611/2 excited level of Dy3+ in TZNF (2 mol. %) sample at 1300 and 1700 nm, respectively, after pulsed laser excitation at 805 nm. The best fit to the luminescence transient using exponential functions provided the decay time constants τ equal to 1.04 μs for 1300 nm and 1.03 μs for 1700 nm emission and rise times of 0.253 and 0.246 μs, respectively.

Fig. 6.
Fig. 6.

Measured decay time of the H613/2 excited level of Dy3+ doped in TZNF (1 mol. %) and TZN (3 wt. %) glasses measured at 2850 nm after pulsed laser excitation at 805 nm. The best fit to the decay time using Eq. (2) provided two decay constants τ1=19.6μs (90%) and τ2=112μs (10%) for TZNF (1 mol. %), and a single exponential decay with τ1=9.7μs for the TZN (3 wt. %) sample. The luminescence risetimes were equal to 1.65 μs for TZNF and 1.25 μs for TZN, respectively.

Fig. 7.
Fig. 7.

Experimental decay time of the H613/2 level as a function of [Dy3+] or x (mol. %) in the TZNF glass samples.

Fig. 8.
Fig. 8.

Simplified energy-level diagram for Dy3+-doped tellurite (TZNF) glass used for the rate equation analysis showing how the H69/2 and F611/2 states are populated by optical excitation at 1300 nm, and the 2.9 μm laser transition and ET process to the OH radical.

Fig. 9.
Fig. 9.

(a) Decomposition of the mid-infrared fluorescence using a three Gaussian fit that suggests emission bands with peaks located at 2590, 2870, and at 3042 nm. (b) The calculated population inversion (in mol. %) as a function of the pump intensity for [Dy3+]=1mol% for pumping at 1300 nm for each laser emission exhibited in (a). The absorption cross section is equal to 2.06×1020cm2 at 1300 nm, and the relation between pumping rate, RP(s1), and the pumping intensity, IP(Wcm2), is given by IP(Wcm2)=7.38×RP(s1).

Tables (3)

Tables Icon

Table 1. Experimental Values of the Absorption Coefficient, α(OH)a

Tables Icon

Table 2. Experimental Values of the Intrinsic (τ1, τ2) Lifetimes, Luminescence Rise Time (τRise), and f Parametera

Tables Icon

Table 3. Experimental Values of the Intrinsic (τ1) and Radiative Lifetimes (τR), Luminescence Branching Ratios (βi,j), Multiphonon Decay Rates (WnR), and Wt as a Function of [Dy3+] in TZNFa

Equations (9)

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

I(t)=A[exp(t/τ)exp(t/τRise)],
I(t)=A[exp(t/τ1)+(1f)exp(t/τ2)exp(t/τRise)],
τ1=[1τi+Wt]1,
Aed(JJ)=64π4e2χ3(2J+1)hλ¯3Sed(JJ),
A(ed+md)meas(JJ)=8πn2cN(λ¯emis)2(λ¯abs)22J+12J+1k(λ)dλ,
dn1dt=RPn1+n2τR2+WnR(21)n2+B31τR3n3+B41τR4n4+Wtn2,
dn2dt=n2τR2WnR(21)n2+β32τR3n3+β42τR4n4+WnR(32)n3Wtn2,
dn3dt=WnR(43)n4n3τR3,
dn4dt=RPn1n4τR4,

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