Abstract

In this study, the spectroscopic properties of Tm3+/Ho3+ co-doped silicate glasses under an 808 nm diode laser excitation are reported to discover their potential laser performance. To confirm the best candidates for glass fiber drawing, the optimal ratio of Tm3+ and Ho3+ is 1: 0.3. We calculate and discuss the J-O parameters (Ωt), the transition probability (A) of the transition from 5I7 to 5I8 is 129.89s−1 and the calculated lifetime (τrad) is 7.70 ms, respectively. The maximum emission cross section of the transition from Ho: 5I75I8 is 7.59 × 10−21 cm2 at 2065 nm as well as the gain coefficient of the STH glasses is discussed. The energy transfer between Tm3+ and Ho3+ plays an important role in the luminescence process. The sample doped with 1 mol% Tm2O3 and 0.3 mol% Ho2O3 presents a broad band spectrum with a full width at half-maximum of 189 nm, the transfer efficiency from Tm3+ to Ho3+ is 0.6702. Energy transfer constant is 63.2 × 10−40 cm6 /s and the measured fluorescence lifetimes of the sample is 0.637 ms, and the ΔT is 167 °C.These values indicate that the Tm3+/Ho3+ co-doped silicate is a promising way to achieve 2 μm laser emissions.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  31. H. Gebavi, D. Milanese, R. Balda, S. Taccheo, J. Fernandez, J. Lousteau, and M. Ferraris, “Spectroscopy of thulium and holmium heavily doped tellurite glasses,” J. Lumin. 132(2), 270–276 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
  38. T. Wei, F. Chen, X. Jing, F. Wang, Y. Tian, and S. Xu, “Structure and spectroscopic properties of Er3+ doped germanate glass for mid-infrared application,” Solid State Sci. 31, 54–61 (2014).
    [Crossref]
  39. Y. Guo, M. Li, L. Hu, and J. Zhang, “Intense 2.7 μm emission and structural origin in Er3+ doped bismuthate glass,” Opt. Lett. 37(2), 268–270 (2012).
    [Crossref] [PubMed]
  40. Y. P. Peng, X. Yuan, J. Zhang, and L. Zhang, “The effect of La₂O₃ in Tm³⁺-doped germanate-tellurite glasses for ~2 μm emission,” Sci. Rep. 4, 5256 (2014).
    [Crossref] [PubMed]

2016 (7)

L. Wang, Y. Zhao, S. Xu, and M. Peng, “Thermal degradation of ultrabroad bismuth NIR luminescence in bismuth-doped tantalum germanate laser glasses,” Opt. Lett. 41(7), 1340–1343 (2016).
[Crossref] [PubMed]

S. Stanek, P. Nekvindova, B. Svecova, S. Vytykacova, M. Mika, J. Oswald, A. Mackova, P. Malinsky, and J. Spirkova, “The influence of silver-ion doping using ion implantation on the luminescence properties of Er-Yb silicate glasses,” Nucl. Instrum. Methods Phys. Res. B 371, 350–354 (2016).
[Crossref]

T. Togashi, T. Honma, K. Shinozaki, and T. Komatsu, “Electrochemical performance as cathode of lithium iron silicate, borate and phosphate glasses with different Fe2+ fractions,” J. Non-Cryst. Solids 436, 51–57 (2016).
[Crossref]

B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
[Crossref]

R. Cao, M. Cai, Y. Lu, Y. Tian, F. Huang, S. Xu, and J. Zhang,“Ho3+/Yb3+ co-doped silicate glasses for 2 μm emission performances,” Appl. Opt. 55, 2065–2070 (2016).
[Crossref] [PubMed]

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

2015 (1)

Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
[Crossref]

2014 (4)

X. Wang, X. K. Fan, S. Gao, K. F. Li, and L. L. Hu, “Spectroscopic properties of Tm3+/Ho3+ co-doped SiO2-Al2O3-CaO-SrO glasses,” Ceram. Int. 40(7), 9751–9756 (2014).
[Crossref]

F. Huang, Y. Guo, Y. Ma, L. Hu, and J. Zhang, “2.7 μm Emission Properties of Er3+ Doped Fluorozirconate Glass,” Glass Phys. Chem. 40(3), 277–282 (2014).
[Crossref]

T. Wei, F. Chen, X. Jing, F. Wang, Y. Tian, and S. Xu, “Structure and spectroscopic properties of Er3+ doped germanate glass for mid-infrared application,” Solid State Sci. 31, 54–61 (2014).
[Crossref]

Y. P. Peng, X. Yuan, J. Zhang, and L. Zhang, “The effect of La₂O₃ in Tm³⁺-doped germanate-tellurite glasses for ~2 μm emission,” Sci. Rep. 4, 5256 (2014).
[Crossref] [PubMed]

2013 (4)

L. L. Yang, J. F. Tang, J. H. Huang, X. H. Gong, Y. J. Chen, Y. F. Lin, Z. D. Luo, and Y. D. Huang, “Spectral properties of Ho3+/Tm3+ co-doped β′-Gd2(MoO4)3 crystal as laser gain medium around 2.0 μm,” Opt. Mater. 35(12), 2188–2193 (2013).
[Crossref]

M. Li, Y. Guo, G. Bai, Y. Tian, L. Hu, and J. Zhang, “2 μm luminescence and energy transfer characteristics in Tm3+/Ho3+ co-doped silicate glass,” J. Quant. Spectrosc. Radiat 127, 70–77 (2013).
[Crossref]

D. Dorosz, J. Zmojda, and M. Kochanowicz, “Investigation on broadband near-infrared emission in Yb3+/Ho3+ co-doped antimony-silicate glass and optical fiber,” Opt. Mater. 35(12), 2577–2580 (2013).
[Crossref]

Y. Tian, X. F. Jing, and S. Q. Xu, “Spectroscopic analysis and efficient diode-pumped 2.0 μm emission in Ho3+/Tm3+ co-doped fluoride glass,” Spectro chemic Acta Part A: Molecular and Bimolecular Spectroscopy 115, 33–38 (2013).
[Crossref]

2012 (6)

H. Gebavi, D. Milanese, R. Balda, S. Taccheo, J. Fernandez, J. Lousteau, and M. Ferraris, “Spectroscopy of thulium and holmium heavily doped tellurite glasses,” J. Lumin. 132(2), 270–276 (2012).
[Crossref]

E. M. Dianov, “Bismuth-doped optical fibers: a challenging active medium for near-IR lasers and optical amplifiers,” Light Sci. Appl. 1(5), e12 (2012).
[Crossref]

T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
[Crossref]

C. Guo, D. Shen, J. Long, and F. Wang, “High-power and widely tunable Tm doped fiber laser at 2 μm,” Chin. Opt. Lett. 10(9), 091406 (2012).
[Crossref]

B. Yao, W. Wang, K. Yu, G. Li, and Y. Wang, “Passively mode-locked Tm, Ho: YVO4 laser based on a semiconductor saturable absorber mirror, Chin,” Opt. Lett. 10(7), 071402 (2012).
[Crossref]

Y. Guo, M. Li, L. Hu, and J. Zhang, “Intense 2.7 μm emission and structural origin in Er3+ doped bismuthate glass,” Opt. Lett. 37(2), 268–270 (2012).
[Crossref] [PubMed]

2010 (3)

2009 (1)

B. M. Walsh, “Review of Tm and Ho materials spectroscopy and lasers,” Laser Phys. 19(4), 855–866 (2009).
[Crossref]

2008 (1)

A. Jouini, A. Brenier, Y. Guyot, G. Boulon, H. Sato, A. Yoshikawa, K. Fukuda, and T. Fukudat, “Spectroscopic and laser properties of the near-infrared tunable laser material Yb3+ doped CaF2 crystal,” Cryst. Growth Des. 8(3), 808–811 (2008).
[Crossref]

2007 (2)

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]

I. Razdobreev, L. Bigot, V. Pureur, A. Favre, G. Bouwmans, and M. Douay, “Efficient all-fiber bismuth-doped laser,” Appl. Phys. Lett. 90(3), 031103 (2007).
[Crossref]

2006 (1)

2005 (1)

B. Jacquier, L. Bigot, S. Guy, and A. M. Jurdyc, “Rare earth doped confined structures for lasers and amplifiers,” The Series Springer Series in Materials Science 83, 430–461 (2005).
[Crossref]

2001 (3)

G. Ozen and B. DiBartolo, “The microscopic interaction parameter for Tm-to-Ho resonant energy transfer in LiYF4,” J. Phys. Condens. Matter 13(1), 195–202 (2001).
[Crossref]

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

L. Zhang, H. Hu, C. Qi, and F. Lin, “Spectroscopic properties and energy transfer in Yb3+/Er3+ doped phosphate glasses,” Opt. Mater. 17(3), 371–377 (2001).
[Crossref]

1996 (1)

X. Zou and H. Toratani, “Spectroscopic properties and energy transfers in Tm3+ singly and Tm3+/Ho3+ doubly doped glasses,” J. Non-Cryst. Solids 195(1-2), 113–124 (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]

1988 (1)

F. Auzel, D. Meichenin, and H. Poignant, “Laser cross section and quantum yield of Er3+ at 2.7 μm in a ZrF4 based fluoride glass,” Electron. Lett. 24(15), 909–910 (1988).
[Crossref]

1962 (2)

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[Crossref]

G. S. Ofelt, “Intensities of crystal spectra of rare earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[Crossref]

1953 (1)

D. L. A. Dexter, “Theory of sensitized luminescence in solids,” J. Chem. Phys. 21(5), 836–850 (1953).
[Crossref]

Ashok, J.

B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
[Crossref]

Auzel, F.

F. Auzel, D. Meichenin, and H. Poignant, “Laser cross section and quantum yield of Er3+ at 2.7 μm in a ZrF4 based fluoride glass,” Electron. Lett. 24(15), 909–910 (1988).
[Crossref]

Bai, G.

M. Li, Y. Guo, G. Bai, Y. Tian, L. Hu, and J. Zhang, “2 μm luminescence and energy transfer characteristics in Tm3+/Ho3+ co-doped silicate glass,” J. Quant. Spectrosc. Radiat 127, 70–77 (2013).
[Crossref]

Balda, R.

H. Gebavi, D. Milanese, R. Balda, S. Taccheo, J. Fernandez, J. Lousteau, and M. Ferraris, “Spectroscopy of thulium and holmium heavily doped tellurite glasses,” J. Lumin. 132(2), 270–276 (2012).
[Crossref]

Bigot, L.

I. Razdobreev, L. Bigot, V. Pureur, A. Favre, G. Bouwmans, and M. Douay, “Efficient all-fiber bismuth-doped laser,” Appl. Phys. Lett. 90(3), 031103 (2007).
[Crossref]

B. Jacquier, L. Bigot, S. Guy, and A. M. Jurdyc, “Rare earth doped confined structures for lasers and amplifiers,” The Series Springer Series in Materials Science 83, 430–461 (2005).
[Crossref]

Boulon, G.

A. Jouini, A. Brenier, Y. Guyot, G. Boulon, H. Sato, A. Yoshikawa, K. Fukuda, and T. Fukudat, “Spectroscopic and laser properties of the near-infrared tunable laser material Yb3+ doped CaF2 crystal,” Cryst. Growth Des. 8(3), 808–811 (2008).
[Crossref]

Bouwmans, G.

I. Razdobreev, L. Bigot, V. Pureur, A. Favre, G. Bouwmans, and M. Douay, “Efficient all-fiber bismuth-doped laser,” Appl. Phys. Lett. 90(3), 031103 (2007).
[Crossref]

Brenier, A.

A. Jouini, A. Brenier, Y. Guyot, G. Boulon, H. Sato, A. Yoshikawa, K. Fukuda, and T. Fukudat, “Spectroscopic and laser properties of the near-infrared tunable laser material Yb3+ doped CaF2 crystal,” Cryst. Growth Des. 8(3), 808–811 (2008).
[Crossref]

Brown, C. T. A.

Bufetov, I. A.

Bulatov, L. I.

Cai, M.

Calvez, S.

Cao, R.

Chen, B.

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

Chen, D.

Chen, F.

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

T. Wei, F. Chen, X. Jing, F. Wang, Y. Tian, and S. Xu, “Structure and spectroscopic properties of Er3+ doped germanate glass for mid-infrared application,” Solid State Sci. 31, 54–61 (2014).
[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]

Chen, Y. J.

L. L. Yang, J. F. Tang, J. H. Huang, X. H. Gong, Y. J. Chen, Y. F. Lin, Z. D. Luo, and Y. D. Huang, “Spectral properties of Ho3+/Tm3+ co-doped β′-Gd2(MoO4)3 crystal as laser gain medium around 2.0 μm,” Opt. Mater. 35(12), 2188–2193 (2013).
[Crossref]

Chiasera, A.

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Dai, S.

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B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
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Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
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T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
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I. Razdobreev, L. Bigot, V. Pureur, A. Favre, G. Bouwmans, and M. Douay, “Efficient all-fiber bismuth-doped laser,” Appl. Phys. Lett. 90(3), 031103 (2007).
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L. Zhang, H. Hu, C. Qi, and F. Lin, “Spectroscopic properties and energy transfer in Yb3+/Er3+ doped phosphate glasses,” Opt. Mater. 17(3), 371–377 (2001).
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I. Razdobreev, L. Bigot, V. Pureur, A. Favre, G. Bouwmans, and M. Douay, “Efficient all-fiber bismuth-doped laser,” Appl. Phys. Lett. 90(3), 031103 (2007).
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R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Rolli, R.

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Ronchin, S.

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Sato, H.

A. Jouini, A. Brenier, Y. Guyot, G. Boulon, H. Sato, A. Yoshikawa, K. Fukuda, and T. Fukudat, “Spectroscopic and laser properties of the near-infrared tunable laser material Yb3+ doped CaF2 crystal,” Cryst. Growth Des. 8(3), 808–811 (2008).
[Crossref]

Shen, D.

Shen, Y.

Shinozaki, K.

T. Togashi, T. Honma, K. Shinozaki, and T. Komatsu, “Electrochemical performance as cathode of lithium iron silicate, borate and phosphate glasses with different Fe2+ fractions,” J. Non-Cryst. Solids 436, 51–57 (2016).
[Crossref]

Shubin, A. V.

Sibbett, W.

Spirkova, J.

S. Stanek, P. Nekvindova, B. Svecova, S. Vytykacova, M. Mika, J. Oswald, A. Mackova, P. Malinsky, and J. Spirkova, “The influence of silver-ion doping using ion implantation on the luminescence properties of Er-Yb silicate glasses,” Nucl. Instrum. Methods Phys. Res. B 371, 350–354 (2016).
[Crossref]

Srinivasa Reddy, M.

B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
[Crossref]

Stanek, S.

S. Stanek, P. Nekvindova, B. Svecova, S. Vytykacova, M. Mika, J. Oswald, A. Mackova, P. Malinsky, and J. Spirkova, “The influence of silver-ion doping using ion implantation on the luminescence properties of Er-Yb silicate glasses,” Nucl. Instrum. Methods Phys. Res. B 371, 350–354 (2016).
[Crossref]

Suresh, B.

B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
[Crossref]

Svecova, B.

S. Stanek, P. Nekvindova, B. Svecova, S. Vytykacova, M. Mika, J. Oswald, A. Mackova, P. Malinsky, and J. Spirkova, “The influence of silver-ion doping using ion implantation on the luminescence properties of Er-Yb silicate glasses,” Nucl. Instrum. Methods Phys. Res. B 371, 350–354 (2016).
[Crossref]

Taccheo, S.

H. Gebavi, D. Milanese, R. Balda, S. Taccheo, J. Fernandez, J. Lousteau, and M. Ferraris, “Spectroscopy of thulium and holmium heavily doped tellurite glasses,” J. Lumin. 132(2), 270–276 (2012).
[Crossref]

Tan, S. Y.

T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
[Crossref]

Tang, J.

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

Tang, J. F.

L. L. Yang, J. F. Tang, J. H. Huang, X. H. Gong, Y. J. Chen, Y. F. Lin, Z. D. Luo, and Y. D. Huang, “Spectral properties of Ho3+/Tm3+ co-doped β′-Gd2(MoO4)3 crystal as laser gain medium around 2.0 μm,” Opt. Mater. 35(12), 2188–2193 (2013).
[Crossref]

Tian, Y.

R. Cao, M. Cai, Y. Lu, Y. Tian, F. Huang, S. Xu, and J. Zhang,“Ho3+/Yb3+ co-doped silicate glasses for 2 μm emission performances,” Appl. Opt. 55, 2065–2070 (2016).
[Crossref] [PubMed]

T. Wei, F. Chen, X. Jing, F. Wang, Y. Tian, and S. Xu, “Structure and spectroscopic properties of Er3+ doped germanate glass for mid-infrared application,” Solid State Sci. 31, 54–61 (2014).
[Crossref]

Y. Tian, X. F. Jing, and S. Q. Xu, “Spectroscopic analysis and efficient diode-pumped 2.0 μm emission in Ho3+/Tm3+ co-doped fluoride glass,” Spectro chemic Acta Part A: Molecular and Bimolecular Spectroscopy 115, 33–38 (2013).
[Crossref]

M. Li, Y. Guo, G. Bai, Y. Tian, L. Hu, and J. Zhang, “2 μm luminescence and energy transfer characteristics in Tm3+/Ho3+ co-doped silicate glass,” J. Quant. Spectrosc. Radiat 127, 70–77 (2013).
[Crossref]

Tikhomirov, V. K.

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Tikhomirova, S. A.

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Togashi, T.

T. Togashi, T. Honma, K. Shinozaki, and T. Komatsu, “Electrochemical performance as cathode of lithium iron silicate, borate and phosphate glasses with different Fe2+ fractions,” J. Non-Cryst. Solids 436, 51–57 (2016).
[Crossref]

Toratani, H.

X. Zou and H. Toratani, “Spectroscopic properties and energy transfers in Tm3+ singly and Tm3+/Ho3+ doubly doped glasses,” J. Non-Cryst. Solids 195(1-2), 113–124 (1996).
[Crossref]

Umnikov, A. A.

Veeraiah, N.

B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
[Crossref]

Vytykacova, S.

S. Stanek, P. Nekvindova, B. Svecova, S. Vytykacova, M. Mika, J. Oswald, A. Mackova, P. Malinsky, and J. Spirkova, “The influence of silver-ion doping using ion implantation on the luminescence properties of Er-Yb silicate glasses,” Nucl. Instrum. Methods Phys. Res. B 371, 350–354 (2016).
[Crossref]

Walsh, B. M.

B. M. Walsh, “Review of Tm and Ho materials spectroscopy and lasers,” Laser Phys. 19(4), 855–866 (2009).
[Crossref]

Wang, C.

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

Wang, F.

T. Wei, F. Chen, X. Jing, F. Wang, Y. Tian, and S. Xu, “Structure and spectroscopic properties of Er3+ doped germanate glass for mid-infrared application,” Solid State Sci. 31, 54–61 (2014).
[Crossref]

C. Guo, D. Shen, J. Long, and F. Wang, “High-power and widely tunable Tm doped fiber laser at 2 μm,” Chin. Opt. Lett. 10(9), 091406 (2012).
[Crossref]

Wang, G.

K. Li, G. Wang, J. Zhang, and L. Hu, “Broadband 2 μm emission in Tm3+/Ho3+ co-doped TeO2-WO3-La2O3 glass,” Solid State Commun. 150, 1915–1918 (2010).
[Crossref]

Wang, J.

T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
[Crossref]

Wang, L.

Wang, W.

B. Yao, W. Wang, K. Yu, G. Li, and Y. Wang, “Passively mode-locked Tm, Ho: YVO4 laser based on a semiconductor saturable absorber mirror, Chin,” Opt. Lett. 10(7), 071402 (2012).
[Crossref]

Wang, X.

X. Wang, X. K. Fan, S. Gao, K. F. Li, and L. L. Hu, “Spectroscopic properties of Tm3+/Ho3+ co-doped SiO2-Al2O3-CaO-SrO glasses,” Ceram. Int. 40(7), 9751–9756 (2014).
[Crossref]

Wang, Y.

B. Yao, W. Wang, K. Yu, G. Li, and Y. Wang, “Passively mode-locked Tm, Ho: YVO4 laser based on a semiconductor saturable absorber mirror, Chin,” Opt. Lett. 10(7), 071402 (2012).
[Crossref]

Wei, T.

T. Wei, F. Chen, X. Jing, F. Wang, Y. Tian, and S. Xu, “Structure and spectroscopic properties of Er3+ doped germanate glass for mid-infrared application,” Solid State Sci. 31, 54–61 (2014).
[Crossref]

Wen, X. D.

T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
[Crossref]

Wu, L.

Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
[Crossref]

Xia, H.

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

Xu, S.

Xu, S. Q.

Y. Tian, X. F. Jing, and S. Q. Xu, “Spectroscopic analysis and efficient diode-pumped 2.0 μm emission in Ho3+/Tm3+ co-doped fluoride glass,” Spectro chemic Acta Part A: Molecular and Bimolecular Spectroscopy 115, 33–38 (2013).
[Crossref]

Xu, Y.

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

Yan, F. P.

T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
[Crossref]

Yang, F.

Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
[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]

Yang, L. L.

L. L. Yang, J. F. Tang, J. H. Huang, X. H. Gong, Y. J. Chen, Y. F. Lin, Z. D. Luo, and Y. D. Huang, “Spectral properties of Ho3+/Tm3+ co-doped β′-Gd2(MoO4)3 crystal as laser gain medium around 2.0 μm,” Opt. Mater. 35(12), 2188–2193 (2013).
[Crossref]

Yang, S.

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

Yao, B.

B. Yao, W. Wang, K. Yu, G. Li, and Y. Wang, “Passively mode-locked Tm, Ho: YVO4 laser based on a semiconductor saturable absorber mirror, Chin,” Opt. Lett. 10(7), 071402 (2012).
[Crossref]

Yashkov, M. V.

Yin, D.

Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
[Crossref]

Yoshikawa, A.

A. Jouini, A. Brenier, Y. Guyot, G. Boulon, H. Sato, A. Yoshikawa, K. Fukuda, and T. Fukudat, “Spectroscopic and laser properties of the near-infrared tunable laser material Yb3+ doped CaF2 crystal,” Cryst. Growth Des. 8(3), 808–811 (2008).
[Crossref]

Yu, K.

B. Yao, W. Wang, K. Yu, G. Li, and Y. Wang, “Passively mode-locked Tm, Ho: YVO4 laser based on a semiconductor saturable absorber mirror, Chin,” Opt. Lett. 10(7), 071402 (2012).
[Crossref]

Yuan, X.

Y. P. Peng, X. Yuan, J. Zhang, and L. Zhang, “The effect of La₂O₃ in Tm³⁺-doped germanate-tellurite glasses for ~2 μm emission,” Sci. Rep. 4, 5256 (2014).
[Crossref] [PubMed]

Zhang, G.

Zhang, J.

R. Cao, M. Cai, Y. Lu, Y. Tian, F. Huang, S. Xu, and J. Zhang,“Ho3+/Yb3+ co-doped silicate glasses for 2 μm emission performances,” Appl. Opt. 55, 2065–2070 (2016).
[Crossref] [PubMed]

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

F. Huang, Y. Guo, Y. Ma, L. Hu, and J. Zhang, “2.7 μm Emission Properties of Er3+ Doped Fluorozirconate Glass,” Glass Phys. Chem. 40(3), 277–282 (2014).
[Crossref]

Y. P. Peng, X. Yuan, J. Zhang, and L. Zhang, “The effect of La₂O₃ in Tm³⁺-doped germanate-tellurite glasses for ~2 μm emission,” Sci. Rep. 4, 5256 (2014).
[Crossref] [PubMed]

M. Li, Y. Guo, G. Bai, Y. Tian, L. Hu, and J. Zhang, “2 μm luminescence and energy transfer characteristics in Tm3+/Ho3+ co-doped silicate glass,” J. Quant. Spectrosc. Radiat 127, 70–77 (2013).
[Crossref]

Y. Guo, M. Li, L. Hu, and J. Zhang, “Intense 2.7 μm emission and structural origin in Er3+ doped bismuthate glass,” Opt. Lett. 37(2), 268–270 (2012).
[Crossref] [PubMed]

K. Li, G. Wang, J. Zhang, and L. Hu, “Broadband 2 μm emission in Tm3+/Ho3+ co-doped TeO2-WO3-La2O3 glass,” Solid State Commun. 150, 1915–1918 (2010).
[Crossref]

Zhang, L.

Y. P. Peng, X. Yuan, J. Zhang, and L. Zhang, “The effect of La₂O₃ in Tm³⁺-doped germanate-tellurite glasses for ~2 μm emission,” Sci. Rep. 4, 5256 (2014).
[Crossref] [PubMed]

L. Zhang, H. Hu, C. Qi, and F. Lin, “Spectroscopic properties and energy transfer in Yb3+/Er3+ doped phosphate glasses,” Opt. Mater. 17(3), 371–377 (2001).
[Crossref]

Zhang, P.

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

Zhang, Q.

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.

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

Zhang, Y.

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
[Crossref]

Zhao, Y.

Zhou, Y.

Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
[Crossref]

Zmojda, J.

D. Dorosz, J. Zmojda, and M. Kochanowicz, “Investigation on broadband near-infrared emission in Yb3+/Ho3+ co-doped antimony-silicate glass and optical fiber,” Opt. Mater. 35(12), 2577–2580 (2013).
[Crossref]

Zou, X.

X. Zou and H. Toratani, “Spectroscopic properties and energy transfers in Tm3+ singly and Tm3+/Ho3+ doubly doped glasses,” J. Non-Cryst. Solids 195(1-2), 113–124 (1996).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

I. Razdobreev, L. Bigot, V. Pureur, A. Favre, G. Bouwmans, and M. Douay, “Efficient all-fiber bismuth-doped laser,” Appl. Phys. Lett. 90(3), 031103 (2007).
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Ceram. Int. (1)

X. Wang, X. K. Fan, S. Gao, K. F. Li, and L. L. Hu, “Spectroscopic properties of Tm3+/Ho3+ co-doped SiO2-Al2O3-CaO-SrO glasses,” Ceram. Int. 40(7), 9751–9756 (2014).
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Chin. Opt. Lett. (1)

Cryst. Growth Des. (1)

A. Jouini, A. Brenier, Y. Guyot, G. Boulon, H. Sato, A. Yoshikawa, K. Fukuda, and T. Fukudat, “Spectroscopic and laser properties of the near-infrared tunable laser material Yb3+ doped CaF2 crystal,” Cryst. Growth Des. 8(3), 808–811 (2008).
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Electron. Lett. (1)

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Glass Phys. Chem. (1)

F. Huang, Y. Guo, Y. Ma, L. Hu, and J. Zhang, “2.7 μm Emission Properties of Er3+ Doped Fluorozirconate Glass,” Glass Phys. Chem. 40(3), 277–282 (2014).
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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]

J. Lumin. (2)

H. Gebavi, D. Milanese, R. Balda, S. Taccheo, J. Fernandez, J. Lousteau, and M. Ferraris, “Spectroscopy of thulium and holmium heavily doped tellurite glasses,” J. Lumin. 132(2), 270–276 (2012).
[Crossref]

B. Suresh, M. Srinivasa Reddy, J. Ashok, A. S. S. Reddy, P. V. Rao, V. R. Kumar, and N. Veeraiah, “Enhancement of orange emission of Co2+ ions with Bi3+ ions in lead silicate glasses,” J. Lumin. 172, 47–52 (2016).
[Crossref]

J. Non-Cryst. Solids (2)

T. Togashi, T. Honma, K. Shinozaki, and T. Komatsu, “Electrochemical performance as cathode of lithium iron silicate, borate and phosphate glasses with different Fe2+ fractions,” J. Non-Cryst. Solids 436, 51–57 (2016).
[Crossref]

X. Zou and H. Toratani, “Spectroscopic properties and energy transfers in Tm3+ singly and Tm3+/Ho3+ doubly doped glasses,” J. Non-Cryst. Solids 195(1-2), 113–124 (1996).
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J. Opt. Soc. Am. B (1)

J. Phys. Condens. Matter (1)

G. Ozen and B. DiBartolo, “The microscopic interaction parameter for Tm-to-Ho resonant energy transfer in LiYF4,” J. Phys. Condens. Matter 13(1), 195–202 (2001).
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M. Li, Y. Guo, G. Bai, Y. Tian, L. Hu, and J. Zhang, “2 μm luminescence and energy transfer characteristics in Tm3+/Ho3+ co-doped silicate glass,” J. Quant. Spectrosc. Radiat 127, 70–77 (2013).
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Laser Phys. (1)

B. M. Walsh, “Review of Tm and Ho materials spectroscopy and lasers,” Laser Phys. 19(4), 855–866 (2009).
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Mater. Lett. (1)

Y. Zhou, L. Wu, B. Huang, F. Yang, S. Peng, Y. Qi, and D. Yin, “Enhanced 2 μm fluorescence and thermal stability in Ho3+/Tm3+ co-doped WO3 modified tellurite glasses,” Mater. Lett. 142, 277–279 (2015).
[Crossref]

Mater. Res. Bull. (1)

Z. Feng, S. Yang, H. Xia, C. Wang, D. Jiang, J. Zhang, X. Gu, Y. Zhang, B. Chen, and H. Jiang, “Energy transfer and 2.0 μm emission in Tm3+/Ho3+ co-doped α-NaYF4 single crystals,” Mater. Res. Bull. 76, 279–283 (2016).
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Nucl. Instrum. Methods Phys. Res. B (1)

S. Stanek, P. Nekvindova, B. Svecova, S. Vytykacova, M. Mika, J. Oswald, A. Mackova, P. Malinsky, and J. Spirkova, “The influence of silver-ion doping using ion implantation on the luminescence properties of Er-Yb silicate glasses,” Nucl. Instrum. Methods Phys. Res. B 371, 350–354 (2016).
[Crossref]

Opt. Express (1)

Opt. Fiber Technol. (1)

T. Feng, F. P. Yan, W. J. Peng, Q. Li, S. Y. Tan, J. Wang, and X. D. Wen, “Theoretical analysis of characteristics for 2 μm Tm3+: Ho3+ co-doped silica fiber laser pumped by a 1550 nm fiber laser,” Opt. Fiber Technol. 18(4), 204–208 (2012).
[Crossref]

Opt. Lett. (4)

Opt. Mater. (5)

L. L. Yang, J. F. Tang, J. H. Huang, X. H. Gong, Y. J. Chen, Y. F. Lin, Z. D. Luo, and Y. D. Huang, “Spectral properties of Ho3+/Tm3+ co-doped β′-Gd2(MoO4)3 crystal as laser gain medium around 2.0 μm,” Opt. Mater. 35(12), 2188–2193 (2013).
[Crossref]

J. Tang, K. Lu, S. Zhang, P. Zhang, F. Chen, S. Dai, and Y. Xu, “Surface Plasmon resonance-enhanced 2 μm emission of bismuth germanate glasses doped with Ho3+/Tm3+ ions,” Opt. Mater. 54, 160–164 (2016).
[Crossref]

D. Dorosz, J. Zmojda, and M. Kochanowicz, “Investigation on broadband near-infrared emission in Yb3+/Ho3+ co-doped antimony-silicate glass and optical fiber,” Opt. Mater. 35(12), 2577–2580 (2013).
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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).
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L. Zhang, H. Hu, C. Qi, and F. Lin, “Spectroscopic properties and energy transfer in Yb3+/Er3+ doped phosphate glasses,” Opt. Mater. 17(3), 371–377 (2001).
[Crossref]

Phys. Rev. (1)

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[Crossref]

Proc. SPIE (1)

R. Rolli, A. Chiasera, M. Montagna, E. Moser, S. Ronchin, S. Pelli, G. C. Righini, A. Jha, V. K. Tikhomirov, S. A. Tikhomirova, C. Duverger, P. Galinetto, and M. Ferrari, “Rare-earth-activated fluoride and tellurite glasses: optical and spectroscopic properties,” Proc. SPIE 4282, 10 (2001).
[Crossref]

Sci. Rep. (1)

Y. P. Peng, X. Yuan, J. Zhang, and L. Zhang, “The effect of La₂O₃ in Tm³⁺-doped germanate-tellurite glasses for ~2 μm emission,” Sci. Rep. 4, 5256 (2014).
[Crossref] [PubMed]

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K. Li, G. Wang, J. Zhang, and L. Hu, “Broadband 2 μm emission in Tm3+/Ho3+ co-doped TeO2-WO3-La2O3 glass,” Solid State Commun. 150, 1915–1918 (2010).
[Crossref]

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[Crossref]

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[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Absorption spectrum of silicate glass doped Tm3+, Ho3+ singly and Tm3+/Ho3+ co-doped.
Fig. 2
Fig. 2 the fluorescence spectra of STH glass.
Fig. 3
Fig. 3 The transmittance spectrum of silicate glass samples with different fluoride content.
Fig. 4
Fig. 4 Calculated absorption cross sections and emission cross sections corresponding to the 5I75I8 transition of the Ho3+ doped and to the 3F43H6 transition of the Tm3+ doped glasses.
Fig. 5
Fig. 5 Gain coefficient with various population inversion values P ranging from 0 to1 for Ho3+ 5I75I8 transition.
Fig. 6
Fig. 6 Energy level diagram of Tm3+ and Ho3+ in silicate glass samples.
Fig. 7
Fig. 7 The decay curves of 5I7 level in the STH glass samples.
Fig. 8
Fig. 8 The Raman spectra of silicate glass.
Fig. 9
Fig. 9 DSC curve of silicate glass (STH-3).

Tables (2)

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Table 1 Judd-Ofelt parameters Ωt of Ho3+ in various glasses

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Table 2 energy transfer constant and critical radius of each energy transfer process

Equations (11)

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A= 1 τ rad = 64 π 4 e 2 3h( 2J+1 ) λ 3 [ n ( n 2 +1 ) 2 9 S ED + n 2 S MD ]
S ED = λ=2,4,6 Ω λ | <S, L, J U (λ) S ' , L ' , J ' > | 2
S MD =( ħ 2mc )| <S, L, J L+2S S ' , L ' , J ' > | 2
OH + F = O 2 +HF
σ em ( λ )= λ 4 A rad 8 πcn 2 λI(λ) λI(λ)
σ a = 2.303log( I 0 I ) Nl
G( λ )=N[ P σ e ( λ )( 1P ) σ a ( λ ) ]
η =1 τ Tm τ Tm 0
W da = C da / R 6
 C DA = 6 cg low D ( 2π ) 4 n 2 g up D m=0 e ( 2 n ¯ +1 ) S 0 S 0 m m! ( n+1 ) m σ ems D λ m + σ abs A ( λ )
R c 6 = C DA τ D

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