Abstract

The ~2.0μm emission characteristics of Ho3+ both by direct excitation and through Yb3+ sensitization in barium-tellurite glass are reported. The radiative properties of active ions have been evaluated by applying Judd-Ofelt theory on the measured absorption spectrum. A significant enhancement of Ho3+ emission (2.0μm) observed with 12 fold decrease of Yb3+ emission (1008nm) in co-doped sample entrenched the efficient energy transfer from Yb3+:2F5/2→Ho3+:5I6. The host phonon assistance in the energy transfer process has been conferred by using Dexter model. Comparatively better emission properties (Arad, Δλeff, σem) reveal that, the present material could be promising for laser emission at ~2.0μm.

© 2011 OSA

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    [CrossRef] [PubMed]
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2010 (5)

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[CrossRef]

D. Tatar, G. Özen, F. B. Erim, and M. L. Övecoğlu, “Raman characterization and structural properties of the binary TeO2-WO3, TeO2-CdF2 and ternary TeO2-CdF2-WO3 glasses,” J. Raman. Spectrosc. 41, 797–807 (2010).

A. D. Sontakke, K. Biswas, A. K. Mandal, and K. Annapurna, “Concentration quenched luminescence and energy transfer analysis of Nd3+ doped Ba-Al-metaphosphate laser glasses,” Appl. Phys. B 101(1-2), 235–244 (2010).
[CrossRef]

M. Wang, G. Wang, L. Yi, S. Li, L. Hu, and J. Zhang, “2-µm emission performance of Tm3+-Ho3+ co-doped tellurite glass,” Chin. Opt. Lett. 8(1), 78–81 (2010).
[CrossRef]

2009 (4)

K. L. Nash, R. C. Dennis, N. J. Ray, J. B. Gruber, and D. K. Sardar, “Absorption intensities, emission cross sections and crystal field analysis of selected intermanifold transitions of Ho3+ in Ho3+:Y2O3 nanocrystals,” J. Appl. Phys. 106(063117), 1–8 (2009).

A. Ghosh and R. Debnath, “Judd-Ofelt analysis of Er3+ activated lead free fluoro-tellurite glass,” Opt. Mater. 31(4), 604–608 (2009).
[CrossRef]

R. Debnath, A. Ghosh, and S. Balaji, “Synthesis and luminescence properties of an (Er2Te4O11) nanocrystals dispersed highly efficient upconverting lead free tellurite glass,” Chem. Phys. Lett. 474(4-6), 331–335 (2009).
[CrossRef]

F. Cornacchia, A. Toncelli, and M. Tonelli, “2-μm2-μm lasers with fluoride crystals: Research and development,” Prog. Quantum Electron. 33(2-4), 61–109 (2009).
[CrossRef]

2008 (3)

Y. Dwivedi, A. Roy, and S. B. Rai, “Intense white upconversion emission in Pr/Er/Yb codoped tellurite glass,” J. Appl. Phys. 104(043509), 1–4 (2008).

P. R. Watekar, S. Ju, and W.-T. Han, “Optical properties of Ho-doped alumino-germano-silica glass optical fiber,” J. Non-Cryst. Solids 354(14), 1453–1459 (2008).
[CrossRef]

Y. Tsang, B. Richards, D. Binks, J. Lousteau, and A. Jha, “A Yb3+/Tm3+/Ho3+ triply-doped tellurite fibre laser,” Opt. Express 16(14), 10690–10695 (2008).
[CrossRef] [PubMed]

2007 (4)

G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+,” J. Fluoresc. 17(3), 301–307 (2007).
[CrossRef] [PubMed]

K. Annapurna, R. Chakrabarti, and S. Buddhudu,“Absorption and emission spectral analysis of Pr3+: tellurite glasses,” J. Mater. Sci. 42(16), 6755–6761 (2007).
[CrossRef]

A. Godard, “Infrared (2–12 μm) solid-state laser sources: a review,” C. R. Phys. 8(10), 1100–1128 (2007).
[CrossRef]

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

2004 (3)

Lihui Huang, Shaoxiong Shen, and Animesh Jha, “Near infrared spectroscopic investigation of Tm3+-Yb3+ co-doped tellurite glass”, J. Non-Cryst. Solids 345&346, 349–353 (2004).

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm[sup 3+] and Ho[sup 3+] in YLiF[sub 4] and LuLiF[sub 4],” J. Appl. Phys. 95(7), 3255–3271 (2004).
[CrossRef]

J. Lin, W. Huang, Z. Sun, C. S. Ray, and D. E. Day, “Structure and non-linear optical performance of TeO2-Nb2O5-ZnO glasses,” J. Non-Cryst. Solids 336(3), 189–194 (2004).
[CrossRef]

2003 (2)

G. A. Hebbink, L. Grave, L. A. Woldering, D. N. Reinhoudt, and F. C. M. J. Van Veggel, “Unexpected Sensitization Efficiency of the Near-Infrared Nd3+, Er3+ and Yb3+ Emission by Fluorescein Compared to Eosin and Erythrosin,” J. Phys. Chem. A 107(14), 2483–2491 (2003).
[CrossRef]

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

2001 (1)

2000 (1)

A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5-µm emission in Er3+-doped tellurite glasses,” Phys. Rev. B 62(10), 6215–6227 (2000).
[CrossRef]

1999 (1)

1998 (2)

Th. Rothacher, W. Lüthy, and H. P. Weber, “Spectral properties of a Tm:Ho:YAG laser in active mirror configuration,” Appl. Phys. B 66(5), 543–546 (1998).
[CrossRef]

Th. Rothacher, W. Lüthy, and H. P. Weber, “Diode pumping and laser properties of Yb:Ho:YAG,” Opt. Commun. 155(1-3), 68–72 (1998).
[CrossRef]

1996 (1)

Y. S. Kim, W. Y. Cho, Y. B. Shin, and J. Heo, “Emission characteristics of Ge-Ga-S glasses doped with Tm3+/Ho3+,” J. Non-Cryst. Solids 203, 176–181 (1996).
[CrossRef]

1995 (1)

B. Peng and T. Izumitani, “Optical properties, fluorescence mechanisms and energy transfer in Tm3+, Ho3+ and Tm3+ -Ho3+ doped near-infrared laser glasses, sensitized by Yb3+,” Opt. Mater. 4(6), 797–810 (1995).
[CrossRef]

1991 (1)

1989 (1)

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

1978 (1)

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14(8), 601–608 (1978).
[CrossRef]

1968 (1)

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(10), 4424–4442 (1968).
[CrossRef]

Adam, J.

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

Annapurna, K.

A. D. Sontakke, K. Biswas, A. K. Mandal, and K. Annapurna, “Concentration quenched luminescence and energy transfer analysis of Nd3+ doped Ba-Al-metaphosphate laser glasses,” Appl. Phys. B 101(1-2), 235–244 (2010).
[CrossRef]

K. Annapurna, R. Chakrabarti, and S. Buddhudu,“Absorption and emission spectral analysis of Pr3+: tellurite glasses,” J. Mater. Sci. 42(16), 6755–6761 (2007).
[CrossRef]

Balaji, S.

R. Debnath, A. Ghosh, and S. Balaji, “Synthesis and luminescence properties of an (Er2Te4O11) nanocrystals dispersed highly efficient upconverting lead free tellurite glass,” Chem. Phys. Lett. 474(4-6), 331–335 (2009).
[CrossRef]

Balsley, D

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Barnes, N. P.

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm[sup 3+] and Ho[sup 3+] in YLiF[sub 4] and LuLiF[sub 4],” J. Appl. Phys. 95(7), 3255–3271 (2004).
[CrossRef]

Bausà, L. E.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Bell, J

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Bettinelli, M.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Binks, D.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Y. Tsang, B. Richards, D. Binks, J. Lousteau, and A. Jha, “A Yb3+/Tm3+/Ho3+ triply-doped tellurite fibre laser,” Opt. Express 16(14), 10690–10695 (2008).
[CrossRef] [PubMed]

Biswas, K.

A. D. Sontakke, K. Biswas, A. K. Mandal, and K. Annapurna, “Concentration quenched luminescence and energy transfer analysis of Nd3+ doped Ba-Al-metaphosphate laser glasses,” Appl. Phys. B 101(1-2), 235–244 (2010).
[CrossRef]

Boling, N. L.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14(8), 601–608 (1978).
[CrossRef]

Bougher, M

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Brocklesby, W. S.

Brown, C.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Buddhudu, S.

K. Annapurna, R. Chakrabarti, and S. Buddhudu,“Absorption and emission spectral analysis of Pr3+: tellurite glasses,” J. Mater. Sci. 42(16), 6755–6761 (2007).
[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(10), 4424–4442 (1968).
[CrossRef]

Cavalli, E.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Chakrabarti, R.

K. Annapurna, R. Chakrabarti, and S. Buddhudu,“Absorption and emission spectral analysis of Pr3+: tellurite glasses,” J. Mater. Sci. 42(16), 6755–6761 (2007).
[CrossRef]

Chen, G. X.

G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+,” J. Fluoresc. 17(3), 301–307 (2007).
[CrossRef] [PubMed]

Cho, W. Y.

Y. S. Kim, W. Y. Cho, Y. B. Shin, and J. Heo, “Emission characteristics of Ge-Ga-S glasses doped with Tm3+/Ho3+,” J. Non-Cryst. Solids 203, 176–181 (1996).
[CrossRef]

Cornacchia, F.

F. Cornacchia, A. Toncelli, and M. Tonelli, “2-μm2-μm lasers with fluoride crystals: Research and development,” Prog. Quantum Electron. 33(2-4), 61–109 (2009).
[CrossRef]

Crump, P.

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Das, S

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Day, D. E.

J. Lin, W. Huang, Z. Sun, C. S. Ray, and D. E. Day, “Structure and non-linear optical performance of TeO2-Nb2O5-ZnO glasses,” J. Non-Cryst. Solids 336(3), 189–194 (2004).
[CrossRef]

Debnath, R.

R. Debnath, A. Ghosh, and S. Balaji, “Synthesis and luminescence properties of an (Er2Te4O11) nanocrystals dispersed highly efficient upconverting lead free tellurite glass,” Chem. Phys. Lett. 474(4-6), 331–335 (2009).
[CrossRef]

A. Ghosh and R. Debnath, “Judd-Ofelt analysis of Er3+ activated lead free fluoro-tellurite glass,” Opt. Mater. 31(4), 604–608 (2009).
[CrossRef]

Dennis, R. C.

K. L. Nash, R. C. Dennis, N. J. Ray, J. B. Gruber, and D. K. Sardar, “Absorption intensities, emission cross sections and crystal field analysis of selected intermanifold transitions of Ho3+ in Ho3+:Y2O3 nanocrystals,” J. Appl. Phys. 106(063117), 1–8 (2009).

DeVito, M

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Dong, W

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Dwivedi, Y.

Y. Dwivedi, A. Roy, and S. B. Rai, “Intense white upconversion emission in Pr/Er/Yb codoped tellurite glass,” J. Appl. Phys. 104(043509), 1–4 (2008).

Elim, S

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Erim, F. B.

D. Tatar, G. Özen, F. B. Erim, and M. L. Övecoğlu, “Raman characterization and structural properties of the binary TeO2-WO3, TeO2-CdF2 and ternary TeO2-CdF2-WO3 glasses,” J. Raman. Spectrosc. 41, 797–807 (2010).

Fan, S.

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[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(10), 4424–4442 (1968).
[CrossRef]

Fusari, F.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

García Solé, J.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Ghosh, A.

R. Debnath, A. Ghosh, and S. Balaji, “Synthesis and luminescence properties of an (Er2Te4O11) nanocrystals dispersed highly efficient upconverting lead free tellurite glass,” Chem. Phys. Lett. 474(4-6), 331–335 (2009).
[CrossRef]

A. Ghosh and R. Debnath, “Judd-Ofelt analysis of Er3+ activated lead free fluoro-tellurite glass,” Opt. Mater. 31(4), 604–608 (2009).
[CrossRef]

Glass, A. J.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14(8), 601–608 (1978).
[CrossRef]

Godard, A.

A. Godard, “Infrared (2–12 μm) solid-state laser sources: a review,” C. R. Phys. 8(10), 1100–1128 (2007).
[CrossRef]

Grave, L.

G. A. Hebbink, L. Grave, L. A. Woldering, D. N. Reinhoudt, and F. C. M. J. Van Veggel, “Unexpected Sensitization Efficiency of the Near-Infrared Nd3+, Er3+ and Yb3+ Emission by Fluorescein Compared to Eosin and Erythrosin,” J. Phys. Chem. A 107(14), 2483–2491 (2003).
[CrossRef]

Grimshaw, M

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Gruber, J. B.

K. L. Nash, R. C. Dennis, N. J. Ray, J. B. Gruber, and D. K. Sardar, “Absorption intensities, emission cross sections and crystal field analysis of selected intermanifold transitions of Ho3+ in Ho3+:Y2O3 nanocrystals,” J. Appl. Phys. 106(063117), 1–8 (2009).

Hale, C. P.

Han, W.-T.

P. R. Watekar, S. Ju, and W.-T. Han, “Optical properties of Ho-doped alumino-germano-silica glass optical fiber,” J. Non-Cryst. Solids 354(14), 1453–1459 (2008).
[CrossRef]

Hebbink, G. A.

G. A. Hebbink, L. Grave, L. A. Woldering, D. N. Reinhoudt, and F. C. M. J. Van Veggel, “Unexpected Sensitization Efficiency of the Near-Infrared Nd3+, Er3+ and Yb3+ Emission by Fluorescein Compared to Eosin and Erythrosin,” J. Phys. Chem. A 107(14), 2483–2491 (2003).
[CrossRef]

Hector, J. R.

Henderson, S. W.

Heo, J.

Y. S. Kim, W. Y. Cho, Y. B. Shin, and J. Heo, “Emission characteristics of Ge-Ga-S glasses doped with Tm3+/Ho3+,” J. Non-Cryst. Solids 203, 176–181 (1996).
[CrossRef]

Hewak, D. W.

Hu, L.

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[CrossRef]

M. Wang, G. Wang, L. Yi, S. Li, L. Hu, and J. Zhang, “2-µm emission performance of Tm3+-Ho3+ co-doped tellurite glass,” Chin. Opt. Lett. 8(1), 78–81 (2010).
[CrossRef]

Huang, Lihui

Lihui Huang, Shaoxiong Shen, and Animesh Jha, “Near infrared spectroscopic investigation of Tm3+-Yb3+ co-doped tellurite glass”, J. Non-Cryst. Solids 345&346, 349–353 (2004).

Huang, W.

J. Lin, W. Huang, Z. Sun, C. S. Ray, and D. E. Day, “Structure and non-linear optical performance of TeO2-Nb2O5-ZnO glasses,” J. Non-Cryst. Solids 336(3), 189–194 (2004).
[CrossRef]

Huffaker, A. V.

Isaenko, L. I.

Izumitani, T.

B. Peng and T. Izumitani, “Optical properties, fluorescence mechanisms and energy transfer in Tm3+, Ho3+ and Tm3+ -Ho3+ doped near-infrared laser glasses, sensitized by Yb3+,” Opt. Mater. 4(6), 797–810 (1995).
[CrossRef]

Jaque, D.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Jha, A.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Y. Tsang, B. Richards, D. Binks, J. Lousteau, and A. Jha, “A Yb3+/Tm3+/Ho3+ triply-doped tellurite fibre laser,” Opt. Express 16(14), 10690–10695 (2008).
[CrossRef] [PubMed]

A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5-µm emission in Er3+-doped tellurite glasses,” Phys. Rev. B 62(10), 6215–6227 (2000).
[CrossRef]

Jha, Animesh

Lihui Huang, Shaoxiong Shen, and Animesh Jha, “Near infrared spectroscopic investigation of Tm3+-Yb3+ co-doped tellurite glass”, J. Non-Cryst. Solids 345&346, 349–353 (2004).

Jiang, Z. H.

G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+,” J. Fluoresc. 17(3), 301–307 (2007).
[CrossRef] [PubMed]

Ju, S.

P. R. Watekar, S. Ju, and W.-T. Han, “Optical properties of Ho-doped alumino-germano-silica glass optical fiber,” J. Non-Cryst. Solids 354(14), 1453–1459 (2008).
[CrossRef]

Kavaya, M. J.

Kim, Y. S.

Y. S. Kim, W. Y. Cho, Y. B. Shin, and J. Heo, “Emission characteristics of Ge-Ga-S glasses doped with Tm3+/Ho3+,” J. Non-Cryst. Solids 203, 176–181 (1996).
[CrossRef]

Lagatsky, A.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Li, K.

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[CrossRef]

Li, S.

Lin, J.

J. Lin, W. Huang, Z. Sun, C. S. Ray, and D. E. Day, “Structure and non-linear optical performance of TeO2-Nb2O5-ZnO glasses,” J. Non-Cryst. Solids 336(3), 189–194 (2004).
[CrossRef]

Lousteau, J.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Y. Tsang, B. Richards, D. Binks, J. Lousteau, and A. Jha, “A Yb3+/Tm3+/Ho3+ triply-doped tellurite fibre laser,” Opt. Express 16(14), 10690–10695 (2008).
[CrossRef] [PubMed]

Lüthy, W.

Th. Rothacher, W. Lüthy, and H. P. Weber, “Spectral properties of a Tm:Ho:YAG laser in active mirror configuration,” Appl. Phys. B 66(5), 543–546 (1998).
[CrossRef]

Th. Rothacher, W. Lüthy, and H. P. Weber, “Diode pumping and laser properties of Yb:Ho:YAG,” Opt. Commun. 155(1-3), 68–72 (1998).
[CrossRef]

Madigou, V.

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

Magee, J. R.

Mandal, A. K.

A. D. Sontakke, K. Biswas, A. K. Mandal, and K. Annapurna, “Concentration quenched luminescence and energy transfer analysis of Nd3+ doped Ba-Al-metaphosphate laser glasses,” Appl. Phys. B 101(1-2), 235–244 (2010).
[CrossRef]

Martinsen, R

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Matson, T

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Naftaly, M.

A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5-µm emission in Er3+-doped tellurite glasses,” Phys. Rev. B 62(10), 6215–6227 (2000).
[CrossRef]

Nash, K. L.

K. L. Nash, R. C. Dennis, N. J. Ray, J. B. Gruber, and D. K. Sardar, “Absorption intensities, emission cross sections and crystal field analysis of selected intermanifold transitions of Ho3+ in Ho3+:Y2O3 nanocrystals,” J. Appl. Phys. 106(063117), 1–8 (2009).

Nostrand, M. C.

Övecoglu, M. L.

D. Tatar, G. Özen, F. B. Erim, and M. L. Övecoğlu, “Raman characterization and structural properties of the binary TeO2-WO3, TeO2-CdF2 and ternary TeO2-CdF2-WO3 glasses,” J. Raman. Spectrosc. 41, 797–807 (2010).

Owyoung, A.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationship for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. 14(8), 601–608 (1978).
[CrossRef]

Özen, G.

D. Tatar, G. Özen, F. B. Erim, and M. L. Övecoğlu, “Raman characterization and structural properties of the binary TeO2-WO3, TeO2-CdF2 and ternary TeO2-CdF2-WO3 glasses,” J. Raman. Spectrosc. 41, 797–807 (2010).

Page, R. H.

Patterson, J.

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Patterson, S

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Payne, D. N.

Payne, S. A.

Peng, B.

B. Peng and T. Izumitani, “Optical properties, fluorescence mechanisms and energy transfer in Tm3+, Ho3+ and Tm3+ -Ho3+ doped near-infrared laser glasses, sensitized by Yb3+,” Opt. Mater. 4(6), 797–810 (1995).
[CrossRef]

Petrin, R.

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

Petros, M.

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm[sup 3+] and Ho[sup 3+] in YLiF[sub 4] and LuLiF[sub 4],” J. Appl. Phys. 95(7), 3255–3271 (2004).
[CrossRef]

Rai, S. B.

Y. Dwivedi, A. Roy, and S. B. Rai, “Intense white upconversion emission in Pr/Er/Yb codoped tellurite glass,” J. Appl. Phys. 104(043509), 1–4 (2008).

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(10), 4424–4442 (1968).
[CrossRef]

Ramirez, M. O.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Ray, C. S.

J. Lin, W. Huang, Z. Sun, C. S. Ray, and D. E. Day, “Structure and non-linear optical performance of TeO2-Nb2O5-ZnO glasses,” J. Non-Cryst. Solids 336(3), 189–194 (2004).
[CrossRef]

Ray, N. J.

K. L. Nash, R. C. Dennis, N. J. Ray, J. B. Gruber, and D. K. Sardar, “Absorption intensities, emission cross sections and crystal field analysis of selected intermanifold transitions of Ho3+ in Ho3+:Y2O3 nanocrystals,” J. Appl. Phys. 106(063117), 1–8 (2009).

Reinhoudt, D. N.

G. A. Hebbink, L. Grave, L. A. Woldering, D. N. Reinhoudt, and F. C. M. J. Van Veggel, “Unexpected Sensitization Efficiency of the Near-Infrared Nd3+, Er3+ and Yb3+ Emission by Fluorescein Compared to Eosin and Erythrosin,” J. Phys. Chem. A 107(14), 2483–2491 (2003).
[CrossRef]

Richards, B.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Y. Tsang, B. Richards, D. Binks, J. Lousteau, and A. Jha, “A Yb3+/Tm3+/Ho3+ triply-doped tellurite fibre laser,” Opt. Express 16(14), 10690–10695 (2008).
[CrossRef] [PubMed]

Rothacher, Th.

Th. Rothacher, W. Lüthy, and H. P. Weber, “Spectral properties of a Tm:Ho:YAG laser in active mirror configuration,” Appl. Phys. B 66(5), 543–546 (1998).
[CrossRef]

Th. Rothacher, W. Lüthy, and H. P. Weber, “Diode pumping and laser properties of Yb:Ho:YAG,” Opt. Commun. 155(1-3), 68–72 (1998).
[CrossRef]

Roy, A.

Y. Dwivedi, A. Roy, and S. B. Rai, “Intense white upconversion emission in Pr/Er/Yb codoped tellurite glass,” J. Appl. Phys. 104(043509), 1–4 (2008).

Samson, B. N.

Sardar, D. K.

K. L. Nash, R. C. Dennis, N. J. Ray, J. B. Gruber, and D. K. Sardar, “Absorption intensities, emission cross sections and crystal field analysis of selected intermanifold transitions of Ho3+ in Ho3+:Y2O3 nanocrystals,” J. Appl. Phys. 106(063117), 1–8 (2009).

Schweizer, T.

Shen, S.

A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5-µm emission in Er3+-doped tellurite glasses,” Phys. Rev. B 62(10), 6215–6227 (2000).
[CrossRef]

Shen, Shaoxiong

Lihui Huang, Shaoxiong Shen, and Animesh Jha, “Near infrared spectroscopic investigation of Tm3+-Yb3+ co-doped tellurite glass”, J. Non-Cryst. Solids 345&346, 349–353 (2004).

Shin, Y. B.

Y. S. Kim, W. Y. Cho, Y. B. Shin, and J. Heo, “Emission characteristics of Ge-Ga-S glasses doped with Tm3+/Ho3+,” J. Non-Cryst. Solids 203, 176–181 (1996).
[CrossRef]

Sibbett, W.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Sibley, W.

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

Singh, U. N.

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm[sup 3+] and Ho[sup 3+] in YLiF[sub 4] and LuLiF[sub 4],” J. Appl. Phys. 95(7), 3255–3271 (2004).
[CrossRef]

Sontakke, A. D.

A. D. Sontakke, K. Biswas, A. K. Mandal, and K. Annapurna, “Concentration quenched luminescence and energy transfer analysis of Nd3+ doped Ba-Al-metaphosphate laser glasses,” Appl. Phys. B 101(1-2), 235–244 (2010).
[CrossRef]

Speghini, A.

D. Jaque, M. O. Ramirez, L. E. Bausà, J. García Solé, E. Cavalli, A. Speghini, and M. Bettinelli, “Nd3+ → Yb3+ energy transfer in YAl3(BO3)4 nonlinear laser crystal,” Phys. Rev. B 68,035118 (2003).

Sun, Z.

J. Lin, W. Huang, Z. Sun, C. S. Ray, and D. E. Day, “Structure and non-linear optical performance of TeO2-Nb2O5-ZnO glasses,” J. Non-Cryst. Solids 336(3), 189–194 (2004).
[CrossRef]

Suscavage, M.

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

Tatar, D.

D. Tatar, G. Özen, F. B. Erim, and M. L. Övecoğlu, “Raman characterization and structural properties of the binary TeO2-WO3, TeO2-CdF2 and ternary TeO2-CdF2-WO3 glasses,” J. Raman. Spectrosc. 41, 797–807 (2010).

Toncelli, A.

F. Cornacchia, A. Toncelli, and M. Tonelli, “2-μm2-μm lasers with fluoride crystals: Research and development,” Prog. Quantum Electron. 33(2-4), 61–109 (2009).
[CrossRef]

Tonelli, M.

F. Cornacchia, A. Toncelli, and M. Tonelli, “2-μm2-μm lasers with fluoride crystals: Research and development,” Prog. Quantum Electron. 33(2-4), 61–109 (2009).
[CrossRef]

Tsang, Y.

B. Richards, A. Jha, Y. Tsang, D. Binks, J. Lousteau, F. Fusari, A. Lagatsky, C. Brown, and W. Sibbett, “Tellurite glass lasers operating close to 2 µm,” Laser Phys. Lett. 7(3), 177–193 (2010).
[CrossRef]

Y. Tsang, B. Richards, D. Binks, J. Lousteau, and A. Jha, “A Yb3+/Tm3+/Ho3+ triply-doped tellurite fibre laser,” Opt. Express 16(14), 10690–10695 (2008).
[CrossRef] [PubMed]

Van Veggel, F. C. M. J.

G. A. Hebbink, L. Grave, L. A. Woldering, D. N. Reinhoudt, and F. C. M. J. Van Veggel, “Unexpected Sensitization Efficiency of the Near-Infrared Nd3+, Er3+ and Yb3+ Emission by Fluorescein Compared to Eosin and Erythrosin,” J. Phys. Chem. A 107(14), 2483–2491 (2003).
[CrossRef]

Walsh, B. M.

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm[sup 3+] and Ho[sup 3+] in YLiF[sub 4] and LuLiF[sub 4],” J. Appl. Phys. 95(7), 3255–3271 (2004).
[CrossRef]

Wang, G.

Wang, J

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Wang, M.

Watekar, P. R.

P. R. Watekar, S. Ju, and W.-T. Han, “Optical properties of Ho-doped alumino-germano-silica glass optical fiber,” J. Non-Cryst. Solids 354(14), 1453–1459 (2008).
[CrossRef]

Weber, H. P.

Th. Rothacher, W. Lüthy, and H. P. Weber, “Spectral properties of a Tm:Ho:YAG laser in active mirror configuration,” Appl. Phys. B 66(5), 543–546 (1998).
[CrossRef]

Th. Rothacher, W. Lüthy, and H. P. Weber, “Diode pumping and laser properties of Yb:Ho:YAG,” Opt. Commun. 155(1-3), 68–72 (1998).
[CrossRef]

Wise, D

P. Crump, S Patterson, W Dong, M Grimshaw, J Wang, S Zhang, S Elim, M Bougher, J. Patterson, S Das, D Wise, T Matson, D Balsley, J Bell, M DeVito, and R Martinsen, “Room temperature high power mid-IR diode laser bars for atmospheric sensing applications,” Proc. SPIE 6552(655214), 1–6 (2007).

Woldering, L. A.

G. A. Hebbink, L. Grave, L. A. Woldering, D. N. Reinhoudt, and F. C. M. J. Van Veggel, “Unexpected Sensitization Efficiency of the Near-Infrared Nd3+, Er3+ and Yb3+ Emission by Fluorescein Compared to Eosin and Erythrosin,” J. Phys. Chem. A 107(14), 2483–2491 (2003).
[CrossRef]

Yang, G. F.

G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+,” J. Fluoresc. 17(3), 301–307 (2007).
[CrossRef] [PubMed]

Yeh, D.

D. Yeh, R. Petrin, W. Sibley, V. Madigou, J. Adam, and M. Suscavage, “Energy transfer between Er3+ and Tm3+ ions in barium fluoride – thorium fluoride glass,” Phys. Rev. B 39(1), 80–90 (1989).
[CrossRef]

Yelisseyev, A. P.

Yi, L.

Yu, J.

B. M. Walsh, N. P. Barnes, M. Petros, J. Yu, and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: Application to trivalent Tm[sup 3+] and Ho[sup 3+] in YLiF[sub 4] and LuLiF[sub 4],” J. Appl. Phys. 95(7), 3255–3271 (2004).
[CrossRef]

Zhang, J.

M. Wang, G. Wang, L. Yi, S. Li, L. Hu, and J. Zhang, “2-µm emission performance of Tm3+-Ho3+ co-doped tellurite glass,” Chin. Opt. Lett. 8(1), 78–81 (2010).
[CrossRef]

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[CrossRef]

Zhang, L.

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[CrossRef]

Zhang, Q.

K. Li, Q. Zhang, S. Fan, L. Zhang, J. Zhang, and L. Hu, “Midinfrared luminescence and energy transfer characteristics of Ho3+/Yb3+ codoped lanthanum-tungsten-tellurite glasses,” Opt. Mater. 33(1), 31–35 (2010).
[CrossRef]

Zhang, Q. Y.

G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+,” J. Fluoresc. 17(3), 301–307 (2007).
[CrossRef] [PubMed]

Zhang, S

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Figures (7)

Fig. 1
Fig. 1

FTIR reflectance spectra of tellurite glasses.

Fig. 2
Fig. 2

Absorption spectra of base glass corrected and not corrected Yb3+/Ho3+ co-doped tellurite glass along with base glass.

Fig. 3
Fig. 3

Fluorescence spectra of Yb3+/Ho3+ co-doped tellurite glass (Inset: Excitation spectra for λemi = 2050nm.)

Fig. 4
Fig. 4

Emission spectra of Sensitizer, Yb3+ ions in absence (black) and in the presence (red) of activator, Ho3+ ions, (Inset: Decay profiles for the same.)

Fig. 5
Fig. 5

Partial energy level diagram of Yb3+/Ho3+ co-doped tellurite glass showing the energy transfer mechanism under 980nm (red) and direct 1191nm, 658nm excitations (black)

Fig. 6
Fig. 6

Energy transfer probability (Vs) Phonon energy in the co-doped glass.

Fig. 7
Fig. 7

Emission and absorption cross-section spectra of Yb3+ and Ho3+ ions with corresponding phonon sidebands

Tables (5)

Tables Icon

Table 1 Physical and Optical properties of Yb3+/Ho3+ co-doped and Yb3+ singly doped tellurite glass: Density (ρ), Rare earth ion concentration (NRE ), linear refractive indices (nD, nF, nC ), Abbe number (ν), Non-linear refractive index (n2 ), Third-order nonlinear susceptibility (χ3 ).

Tables Icon

Table 2 Electric dipole line strengths (measured: Sed mea, calculated: Sed cal), magnetic dipole strength (Smd), Total Oscillator strengths (measured: Pmea, calculated: Pcal), refractive index (n) of different absorption transitions and (Ωt = 2,4,6) J-O intensity parameters of Ho3+ions in the co-doped glass.

Tables Icon

Table 3 Comparative chart of J-O intensity parameters of Ho3+ ion in various hosts.

Tables Icon

Table 4 Electric dipole line strength (Sed), Refractive index (n), Spontaneous emission probability (Ar), Radiative rate (ΣAr), Radiative lifetime (τr), Branching ratio (βR), for fluorescent levels of Ho3+ ions in the present tellurite glass.

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Table 5 Comparative chart of peak wavelength (λP), concentration of Ho2O3 (in wt%), radiative transition probability (Ar), effective bandwidth (Δλp) and stimulated emission cross section (σe) for ~2.0µm emission of Ho3+ ions in various glass hosts.

Equations (8)

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σ e ( λ ) = λ p 4 8 π c n 2 Δ λ e f f A r
W E T = 1 τ 1 τ 0 ,
η E T = 1 τ τ 0 ,
P E T f D ( E ) f A ( E ) E 2 d E ,
P E T I ( E p h ) = e E p h k B T e E p h k B T 1 f D ( E E p h ) f A ( E ) E 2 d E ,
C D A = 3 c 8 π 4 n 2 σ e m D ( λ ) σ a b s A ( λ ) d λ .
σ S t o k e s = σ e l e c t exp ( α S Δ E ) ,
α S = ( h ν ) 1 ( ln { ( N ¯ / S 0 ) [ 1 exp ( h ν max / k T ) } 1 ) ,

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