Abstract

We present low-loss tungstate-tellurite fibers doped with Er3+ for laser operation near 2.7 μm. Two “ultra-dry” preforms with cores of TeO2-WO3-La2O3-Bi2O3 glasses doped with 0.4 and 4 mol% of Er2O3 and undoped TeO2-WO3-La2O3 claddings were produced. High-quality multimode fibers were fabricated and characterized. Photoluminescence spectra of about 2.7 μm (4I11/24I13/2 transition) and about 1.6 μm (4I13/24I15/2 transition) were measured under excitation by diode pumping at 975 nm (4I15/24I11/2 transition). The production test and the theoretical investigation of gain-switched laser generation showed potential applicability of the designed samples in the spectral range of interest. Prospective application of single-mode fibers based on the developed glass preforms was also simulated. A feasibility of pulse train generation was demonstrated even for a rough choice of parameters, which is very encouraging for experimental implementation.

© 2017 Optical Society of America

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2017 (4)

2016 (8)

L.-R. Robichaud, V. Fortin, J.-C. Gauthier, S. Châtigny, J.-F. Couillard, J.-L. Delarosbil, R. Vallée, and M. Bernier, “Compact 3-8 μm supercontinuum generation in a low-loss As2Se3 step-index fiber,” Opt. Lett. 41(20), 4605–4608 (2016).
[PubMed]

V. Fortin, F. Maes, M. Bernier, S. T. Bah, M. D’Auteuil, and R. Vallée, “Watt-level erbium-doped all-fiber laser at 3.44 μm,” Opt. Lett. 41(3), 559–562 (2016).
[PubMed]

M. R. Majewski and S. D. Jackson, “Highly efficient mid-infrared dysprosium fiber laser,” Opt. Lett. 41(10), 2173–2176 (2016).
[PubMed]

S. Antipov, D. D. Hudson, A. Fuerbach, and S. D. Jackson, “High-power mid-infrared femtosecond fiber laser in the water vapor transmission window,” Optica 3(12), 1373–1376 (2016).

K. Yin, B. Zhang, J. Yao, L. Yang, G. Liu, and J. Hou, “1.9-3.6 μm supercontinuum generation in a very short highly nonlinear germania fiber with a high mid-infrared power ratio,” Opt. Lett. 41(21), 5067–5070 (2016).
[PubMed]

Y. Tian, X. Jing, B. Li, P. Li, Y. Li, R. Lei, J. Zhang, and S. Xu, “Synthesis, theoretical analysis, and characterization of highly Er3+ doped fluoroaluminate–tellurite glass with 2.7 μm emission,” Opt. Mater. Express 6(10), 3274–3285 (2016).

E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, and A. V. Kim, “Toward a mid-infrared femtosecond laser system with suspended-core tungstate-tellurite glass fibers,” Appl. Opt. 55(17), 4522–4530 (2016).
[PubMed]

A. M. Kut’in, A. D. Plekhovich, and V. V. Dorofeev, “A mathematical model for analysis of sequentially coupled crystallization–melting differential scanning calorimetry peaks and the use of the model for assessing the crystallization resistance of tellurite glasses,” Inorg. Mater. 52(6), 604–610 (2016).

2015 (4)

M. Y. Koptev, E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. F. Kosolapov, S. V. Muravyev, and A. V. Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015).
[PubMed]

W. C. Wang, J. Yuan, L. X. Li, D. D. Chen, Q. Qian, and Q. Y. Zhang, “Broadband 2.7 μm amplified spontaneous emission of Er3+ doped tellurite fibers for mid-infrared laser applications,” Opt. Mater. Express 5(12), 2964–2977 (2015).

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

2014 (4)

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

I. T. Sorokina, V. V. Dvoyrin, N. Tolstik, and E. Sorokin, “Mid-IR ultrashort pulsed fiber-based lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 99–110 (2014).

E. A. Anashkina, A. V. Andrianov, M. Y. Koptev, S. V. Muravyev, and A. V. Kim, “Towards mid-infrared supercontinuum generation with germano-silicate fibers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 643–650 (2014).

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

2013 (1)

2012 (1)

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).

2011 (7)

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

S. Tokita, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “12 W Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Lett. 36(15), 2812–2814 (2011).
[PubMed]

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

D. Manzani, Y. Ledemi, I. Skripachev, Y. Messaddeq, S. J. L. Ribeiro, R. E. P. de Oliveira, and C. J. S. de Matos, “Yb3+, Tm3+ and Ho3+ triply-doped tellurite core-cladding optical fiber for white light generation,” Opt. Mater. Express 1(8), 1515–1526 (2011).

M. Gorjan, R. Petkovšek, M. Marinček, and M. Čopič, “High-power pulsed diode-pumped Er:ZBLAN fiber laser,” Opt. Lett. 36(10), 1923–1925 (2011).
[PubMed]

2009 (1)

2008 (1)

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

2007 (1)

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

1999 (1)

X. Feng, Ch. Qi, F. Lin, and H. Hu, “Tungsten-tellurite glass: a new candidate medium for Yb3+ - doping,” J. Non-Cryst. Solids 256–257(2), 372–377 (1999).

1997 (1)

A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33(10), 863–864 (1997).

1975 (1)

B. V. Tatarintsev and A. K. Yakhkind, “The water content in tellurite glasses and its effect on infrared transmission,” Optikomekhanicheskaya promyshlennost, 3, 40– 43 (1975).

Abdel-Moneim, N.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Abouraddy, A. F.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Anashkina, E. A.

Andrianov, A. V.

Antipov, S.

Aydin, Y. O.

Badding, J. V.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Bah, S. T.

Ballato, J.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Bang, O.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Benson, T.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Bernier, M.

Châtigny, S.

Chen, D. D.

Chen, F.

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

Chilyasov, A. V.

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Churbanov, M. F.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Copic, M.

Couillard, J.-F.

D’Auteuil, M.

Danto, S.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

de Matos, C. J. S.

de Oliveira, R. E. P.

Delarosbil, J.-L.

Désévédavy, F.

Dianov, E. M.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Dorofeev, V. V.

A. M. Kut’in, A. D. Plekhovich, and V. V. Dorofeev, “A mathematical model for analysis of sequentially coupled crystallization–melting differential scanning calorimetry peaks and the use of the model for assessing the crystallization resistance of tellurite glasses,” Inorg. Mater. 52(6), 604–610 (2016).

E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, and A. V. Kim, “Toward a mid-infrared femtosecond laser system with suspended-core tungstate-tellurite glass fibers,” Appl. Opt. 55(17), 4522–4530 (2016).
[PubMed]

M. Y. Koptev, E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. F. Kosolapov, S. V. Muravyev, and A. V. Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015).
[PubMed]

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Dupont, S.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Dvoyrin, V. V.

I. T. Sorokina, V. V. Dvoyrin, N. Tolstik, and E. Sorokin, “Mid-IR ultrashort pulsed fiber-based lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 99–110 (2014).

Ebendorff-Heidepriem, H.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

M. R. Oermann, H. Ebendorff-Heidepriem, Y. Li, T. C. Foo, and T. M. Monro, “Index matching between passive and active tellurite glasses for use in microstructured fiber lasers: erbium doped lanthanum-tellurite glass,” Opt. Express 17(18), 15578–15584 (2009).
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Feng, X.

X. Feng, Ch. Qi, F. Lin, and H. Hu, “Tungsten-tellurite glass: a new candidate medium for Yb3+ - doping,” J. Non-Cryst. Solids 256–257(2), 372–377 (1999).

Feng, Y.

Fink, Y.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Foo, T. C.

Fortin, V.

Froidevaux, P.

Fuerbach, A.

Furniss, D.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Gadret, G.

Gauthier, J.-C.

Gerasimenko, V. V.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

Giessen, H.

Gomes, L.

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

Gorjan, M.

Guo, Y.

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

Hashida, M.

Hou, J.

Hu, H.

X. Feng, Ch. Qi, F. Lin, and H. Hu, “Tungsten-tellurite glass: a new candidate medium for Yb3+ - doping,” J. Non-Cryst. Solids 256–257(2), 372–377 (1999).

Hu, L.

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

Huang, F.

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

Hudson, D. D.

Jackson, S. D.

Y. O. Aydın, V. Fortin, F. Maes, F. Jobin, S. D. Jackson, R. Vallée, and M. Bernier, “Diode-pumped mid-infrared fiber laser with 50% slope efficiency,” Optica 4(2), 235–238 (2017).

S. Antipov, D. D. Hudson, A. Fuerbach, and S. D. Jackson, “High-power mid-infrared femtosecond fiber laser in the water vapor transmission window,” Optica 3(12), 1373–1376 (2016).

M. R. Majewski and S. D. Jackson, “Highly efficient mid-infrared dysprosium fiber laser,” Opt. Lett. 41(10), 2173–2176 (2016).
[PubMed]

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

Jing, X.

Y. Tian, X. Jing, B. Li, P. Li, Y. Li, R. Lei, J. Zhang, and S. Xu, “Synthesis, theoretical analysis, and characterization of highly Er3+ doped fluoroaluminate–tellurite glass with 2.7 μm emission,” Opt. Mater. Express 6(10), 3274–3285 (2016).

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

Jobin, F.

Jules, J.-C.

Kedenburg, S.

Ketkova, L. A.

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

Kibler, B.

Kim, A. V.

Koltashev, V. V.

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

Koptev, M. Y.

M. Y. Koptev, E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. F. Kosolapov, S. V. Muravyev, and A. V. Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015).
[PubMed]

E. A. Anashkina, A. V. Andrianov, M. Y. Koptev, S. V. Muravyev, and A. V. Kim, “Towards mid-infrared supercontinuum generation with germano-silicate fibers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 643–650 (2014).

Kosolapov, A. F.

M. Y. Koptev, E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. F. Kosolapov, S. V. Muravyev, and A. V. Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015).
[PubMed]

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

Kotereva, T. V.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Kotov, L. V.

Kraev, I. A.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Kryukova, E. B.

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Kubat, I.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Kut’in, A. M.

A. M. Kut’in, A. D. Plekhovich, and V. V. Dorofeev, “A mathematical model for analysis of sequentially coupled crystallization–melting differential scanning calorimetry peaks and the use of the model for assessing the crystallization resistance of tellurite glasses,” Inorg. Mater. 52(6), 604–610 (2016).

Ledemi, Y.

Lei, R.

Li, B.

Li, L. X.

Li, P.

Li, Y.

Librantz, A. F. H.

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

Lin, F.

X. Feng, Ch. Qi, F. Lin, and H. Hu, “Tungsten-tellurite glass: a new candidate medium for Yb3+ - doping,” J. Non-Cryst. Solids 256–257(2), 372–377 (1999).

Lipatova, M. M.

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Liu, G.

Lobanov, A. S.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

Ma, Y.

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

Maes, F.

Majewski, M. R.

Manzani, D.

Marincek, M.

Meng, X.

Messaddeq, Y.

Moiseev, A. N.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Moller, U.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Monro, T.

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

Monro, T. M.

Mori, A.

A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33(10), 863–864 (1997).

Mörz, F.

Murakami, M.

Muravyev, S. V.

M. Y. Koptev, E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. F. Kosolapov, S. V. Muravyev, and A. V. Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015).
[PubMed]

E. A. Anashkina, A. V. Andrianov, M. Y. Koptev, S. V. Muravyev, and A. V. Kim, “Towards mid-infrared supercontinuum generation with germano-silicate fibers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 643–650 (2014).

Norwood, R. A.

Oermann, M.

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

Oermann, M. R.

Ohishi, Y.

A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33(10), 863–864 (1997).

Ottaway, D.

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

Petersen, C. R.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Petkovšek, R.

Peyghambarian, N.

Pimenov, V. G.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

Plekhovich, A. D.

A. M. Kut’in, A. D. Plekhovich, and V. V. Dorofeev, “A mathematical model for analysis of sequentially coupled crystallization–melting differential scanning calorimetry peaks and the use of the model for assessing the crystallization resistance of tellurite glasses,” Inorg. Mater. 52(6), 604–610 (2016).

Plotnichenko, V. G.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Pushkin, A. A.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

Pyrkov, Yu. N.

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

Qi, Ch.

X. Feng, Ch. Qi, F. Lin, and H. Hu, “Tungsten-tellurite glass: a new candidate medium for Yb3+ - doping,” J. Non-Cryst. Solids 256–257(2), 372–377 (1999).

Qian, Q.

Qin, G.

Qin, W.

Ramsay, J.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Ribeiro, S. J. L.

Robichaud, L.-R.

Sakabe, S.

Seddon, A.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Shimizu, S.

Skripachev, I.

Smektala, F.

Snopatin, G. E.

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

Sorokin, E.

I. T. Sorokina, V. V. Dvoyrin, N. Tolstik, and E. Sorokin, “Mid-IR ultrashort pulsed fiber-based lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 99–110 (2014).

Sorokina, I. T.

I. T. Sorokina, V. V. Dvoyrin, N. Tolstik, and E. Sorokin, “Mid-IR ultrashort pulsed fiber-based lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 99–110 (2014).

Steinle, T.

Steinmann, A.

Stolyarov, A. M.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Strutynski, C.

Sudo, S.

A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33(10), 863–864 (1997).

Sujecki, S.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Tang, Z.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Tao, G.

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Tatarintsev, B. V.

B. V. Tatarintsev and A. K. Yakhkind, “The water content in tellurite glasses and its effect on infrared transmission,” Optikomekhanicheskaya promyshlennost, 3, 40– 43 (1975).

Tian, Y.

Y. Tian, X. Jing, B. Li, P. Li, Y. Li, R. Lei, J. Zhang, and S. Xu, “Synthesis, theoretical analysis, and characterization of highly Er3+ doped fluoroaluminate–tellurite glass with 2.7 μm emission,” Opt. Mater. Express 6(10), 3274–3285 (2016).

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

Tokita, S.

Tolstik, N.

I. T. Sorokina, V. V. Dvoyrin, N. Tolstik, and E. Sorokin, “Mid-IR ultrashort pulsed fiber-based lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 99–110 (2014).

Tong, M.

Vallée, R.

Wang, J.

Wang, R.

Wang, W. C.

Wei, C.

Wei, T.

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

Xu, S.

Y. Tian, X. Jing, B. Li, P. Li, Y. Li, R. Lei, J. Zhang, and S. Xu, “Synthesis, theoretical analysis, and characterization of highly Er3+ doped fluoroaluminate–tellurite glass with 2.7 μm emission,” Opt. Mater. Express 6(10), 3274–3285 (2016).

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

Yakhkind, A. K.

B. V. Tatarintsev and A. K. Yakhkind, “The water content in tellurite glasses and its effect on infrared transmission,” Optikomekhanicheskaya promyshlennost, 3, 40– 43 (1975).

Yang, L.

Yao, J.

Yin, F.

Yin, K.

Yuan, J.

Zhang, B.

Zhang, J.

Y. Tian, X. Jing, B. Li, P. Li, Y. Li, R. Lei, J. Zhang, and S. Xu, “Synthesis, theoretical analysis, and characterization of highly Er3+ doped fluoroaluminate–tellurite glass with 2.7 μm emission,” Opt. Mater. Express 6(10), 3274–3285 (2016).

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
[PubMed]

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

Zhang, Q. Y.

Zhou, B.

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

Zhu, G.

Zhu, X.

Adv. Opt. Photonics (1)

G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015).

Appl. Opt. (1)

Electron. Lett. (1)

A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33(10), 863–864 (1997).

IEEE J. Sel. Top. Quantum Electron. (2)

I. T. Sorokina, V. V. Dvoyrin, N. Tolstik, and E. Sorokin, “Mid-IR ultrashort pulsed fiber-based lasers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 99–110 (2014).

E. A. Anashkina, A. V. Andrianov, M. Y. Koptev, S. V. Muravyev, and A. V. Kim, “Towards mid-infrared supercontinuum generation with germano-silicate fibers,” IEEE J. Sel. Top. Quantum Electron. 20(5), 643–650 (2014).

Inorg. Mater. (2)

A. M. Kut’in, A. D. Plekhovich, and V. V. Dorofeev, “A mathematical model for analysis of sequentially coupled crystallization–melting differential scanning calorimetry peaks and the use of the model for assessing the crystallization resistance of tellurite glasses,” Inorg. Mater. 52(6), 604–610 (2016).

A. N. Moiseev, V. V. Dorofeev, A. V. Chilyasov, V. G. Pimenov, T. V. Kotereva, I. A. Kraev, L. A. Ketkova, A. F. Kosolapov, V. G. Plotnichenko, and V. V. Koltashev, “Low-loss, high-purity (TeO2)0.75(WO3)0.25 glass,” Inorg. Mater. 47(6), 665–669 (2011).

J. Appl. Phys. (1)

L. Gomes, M. Oermann, H. Ebendorff-Heidepriem, D. Ottaway, T. Monro, A. F. H. Librantz, and S. D. Jackson, “Energy level decay and excited state absorption processes in erbium-doped tellurite glass,” J. Appl. Phys. 110(8), 083111 (2011).

J. Lumin. (1)

Y. Ma, Y. Guo, F. Huang, L. Hu, and J. Zhang, “Spectroscopic properties in Er 3+ doped zinc-and tungsten-modified tellurite glasses for 2.7 μm laser materials,” J. Lumin. 147, 372–377 (2014).

J. Non-Cryst. Solids (2)

X. Feng, Ch. Qi, F. Lin, and H. Hu, “Tungsten-tellurite glass: a new candidate medium for Yb3+ - doping,” J. Non-Cryst. Solids 256–257(2), 372–377 (1999).

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, T. V. Kotereva, A. V. Chilyasov, I. A. Kraev, V. G. Pimenov, L. A. Ketkova, E. M. Dianov, V. G. Plotnichenko, A. F. Kosolapov, and V. V. Koltashev, “Production and properties of high purity TeO2−WO3−(La2O3, Bi2O3) and TeO2−ZnO−Na2O−Bi2O3 glasses,” J. Non-Cryst. Solids 357(11), 2366–2370 (2011).

J. Opt. Soc. Am. B (2)

J. Optoelectron. Adv. Mater. (1)

M. F. Churbanov, A. N. Moiseev, A. V. Chilyasov, V. V. Dorofeev, I. A. Kraev, M. M. Lipatova, T. V. Kotereva, E. M. Dianov, V. G. Plotnichenko, and E. B. Kryukova, “Production of high-purity TeO2-ZnO and TeO2-WO3 glasses with the reduced content of OH-groups,” J. Optoelectron. Adv. Mater. 9(10), 3229–3234 (2007).

Nat. Photonics (2)

C. R. Petersen, U. Moller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4-13.3 μm molecular fingerprint region using ultra-high NA chalcogenide stepindex fibre,” Nat. Photonics 8(11), 830–834 (2014).

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).

Opt. Express (1)

Opt. Lett. (8)

V. Fortin, F. Maes, M. Bernier, S. T. Bah, M. D’Auteuil, and R. Vallée, “Watt-level erbium-doped all-fiber laser at 3.44 μm,” Opt. Lett. 41(3), 559–562 (2016).
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M. R. Majewski and S. D. Jackson, “Highly efficient mid-infrared dysprosium fiber laser,” Opt. Lett. 41(10), 2173–2176 (2016).
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L.-R. Robichaud, V. Fortin, J.-C. Gauthier, S. Châtigny, J.-F. Couillard, J.-L. Delarosbil, R. Vallée, and M. Bernier, “Compact 3-8 μm supercontinuum generation in a low-loss As2Se3 step-index fiber,” Opt. Lett. 41(20), 4605–4608 (2016).
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K. Yin, B. Zhang, L. Yang, and J. Hou, “15.2 W spectrally flat all-fiber supercontinuum laser source with >1 W power beyond 3.8 μm,” Opt. Lett. 42(12), 2334–2337 (2017).
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K. Yin, B. Zhang, J. Yao, L. Yang, G. Liu, and J. Hou, “1.9-3.6 μm supercontinuum generation in a very short highly nonlinear germania fiber with a high mid-infrared power ratio,” Opt. Lett. 41(21), 5067–5070 (2016).
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M. Y. Koptev, E. A. Anashkina, A. V. Andrianov, V. V. Dorofeev, A. F. Kosolapov, S. V. Muravyev, and A. V. Kim, “Widely tunable mid-infrared fiber laser source based on soliton self-frequency shift in microstructured tellurite fiber,” Opt. Lett. 40(17), 4094–4097 (2015).
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S. Tokita, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “12 W Q-switched Er:ZBLAN fiber laser at 2.8 μm,” Opt. Lett. 36(15), 2812–2814 (2011).
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Opt. Mater. (1)

V. V. Dorofeev, A. N. Moiseev, M. F. Churbanov, G. E. Snopatin, A. V. Chilyasov, I. A. Kraev, A. S. Lobanov, T. V. Kotereva, L. A. Ketkova, A. A. Pushkin, V. V. Gerasimenko, V. G. Plotnichenko, A. F. Kosolapov, and E. M. Dianov, “High purity TeO2-WO3-(La2O3, Bi2O3) glasses for fiber-optics,” Opt. Mater. 33(12), 1911–1915 (2011).

Opt. Mater. Express (4)

Optica (2)

Optikomekhanicheskaya promyshlennost, (1)

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Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B (1)

M. F. Churbanov, A. N. Moiseev, G. E. Snopatin, V. V. Dorofeev, V. G. Pimenov, A. V. Chilyasov, A. S. Lobanov, T. V. Kotereva, V. G. Plotnichenko, V. V. Koltashev, and Yu. N. Pyrkov, “Production and properties of high purity glasses of TeO2–WO3, TeO2–ZnO systems,” Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49(6), 297–300 (2008).

Sci. Rep. (1)

F. Chen, T. Wei, X. Jing, Y. Tian, J. Zhang, and S. Xu, “Investigation of mid-infrared emission characteristics and energy transfer dynamics in Er3+ doped oxyfluoride tellurite glass,” Sci. Rep. 5, 10676 (2015).
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I.A. Grishin, G.G. Devyatykh, E.M. Dianov, N.I. Kiselev, O.N. Lapshin, L.K. Olonov, V.G. Plotnichenko, A.M. Prokhorov, M.F. Churbanov, “Method of obtaining double-layer cylindrical preforms for optical fibers and the device for its implementation,” USSR certificate of authorship for invention Nº 1284181, Application No. 3906975, Priority of the invention of April 18, 1985, Registered in the State Inventory of USSR inventions on September 15, 1986.

A. M. Kut’in, A. D. Plekhovich, K. V. Balueva, and V. V. Dorofeev, “Effects of Er2O3 content on heat capacity, thermodynamic functions and vitrification characteristics of Er3+-doped tellurite glass,” J. Non-Cryst. Sol., In Press, Corrected Proof, Available online 24 June 2017, https://doi.org/10.1016/j.jnoncrysol.2017.06.020 .

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Figures (12)

Fig. 1
Fig. 1 (a) Scheme of preforms for producing tellurite fibers. (b) Photo of Preform-0.4 with diameter of 16 mm and length of 51 mm. (c) Photo of Preform-4 with diameter of 16 mm and length of 60 mm
Fig. 2
Fig. 2 Thermograms of differential scanning calorimetry of TWLBE-0.4 and TWLBE-4 glasses.
Fig. 3
Fig. 3 (a) Visible and near IR transmission spectra of TWL, TWLBE-0.4, TWLBE-4 glass samples 0.2 cm thick. (b) IR transmission spectra of pieces of Preform 0.4 (TWL, TWLBE-0.4 glasses) and Preform 4 (TWL, TWLBE-4 glasses)
Fig. 4
Fig. 4 Absorption spectra within hydroxyl groups band of Preform-0.4 (TWL, TWLBE-0.4 glasses, 0.4 cm thick) and Preform-4 (TWL, TWLBE-4 glasses, 0.6 cm thick)
Fig. 5
Fig. 5 Total optical loss of multimode fiber made of Preform-4. Core doped with Er3+/undoped cladding diameters are 50/130 μm.
Fig. 6
Fig. 6 (a) Luminescence spectra of TWLBE-0.4 and TWLBE-4 glasses for 4I11/24I13/2 transition under excitation at 975 nm with 0.5W power. (b) Measured luminescence decay at 0.98 μm after 5-ns pump pulse.
Fig. 7
Fig. 7 Photoluminescence spectra of multimode fiber with 50/130 μm core/cladding diameters made of Preform-4 under excitation at 975 nm: for pump power of 88 mW for different gain fiber lengths (a); for different pump powers for fiber length of 10 cm (b).
Fig. 8
Fig. 8 Simplified scheme of Er energy levels (a). Variant of experimental laser scheme (b). Pump pulses at the input end (blue) and generated output pulses (black) (c). Temporal evolution of output signal power in periodic regime (d). Averaged population defined by Eq. (10) for different time scales (e, f). RL = 0.85, αs = 2 dB/m, Ppump = 10 W.
Fig. 9
Fig. 9 Laser signal energy as a function of reflection coefficient at the multimode fiber output for different pump peak powers Ppump and fiber losses.
Fig. 10
Fig. 10 Laser signal energy at 2.7 µm as a function of reflection coefficient at single-mode fiber output for different pump peak powers Ppump and fiber loss.
Fig. 11
Fig. 11 (Upper row) Temporal evolution of output signal power for different reflection coefficients. Green curves correspond to the time profile of the leading edge of the pump (right axes). (Lower row) Temporal evolution of output signal energy. Each subplot is calculated for the indicated thereon pump peak power and fiber loss of 2 dB/m.
Fig. 12
Fig. 12 Energy of the first spike (a), spike duration (b), and optimal pump pulse duration for generating only one spike (c) as functions of reflection coefficients for different pump peak powers Ppump. The inset demonstrates typical temporal structure of pump and signal pulses. Fiber loss is 2 dB/m for (a), (b), (c). Energy of the first spike (d), its duration (e), and optimal pump pulse duration for generating only one spike (f) as functions of fiber loss (for RL = 0.1). t1 = 100 ns for all subplots.

Tables (2)

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Table 1 Physical properties of the produced preforms

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Table 2 Parameters for fiber laser modeling

Equations (10)

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n 3 t = W pa n 1 W pe n 3 W se n 3 + W sa n 2 n 3 τ 3 ,
n 2 t = W se n 3 W sa n 2 + n 3 τ 32 n 2 τ 2 ,
n 1 + n 2 + n 3 =1,
W pa = Γ p λ p σ pa hc A eff P p , W pe = Γ p λ p σ pe hc A eff P p , W sa = Γ s λ s σ sa hc A eff ( P s + + P s ), W se = Γ s λ s σ se hc A eff ( P s + + P s ),
P p z + P p V gr t = Γ p N Er ( σ pa n 1 σ pe n 3 ) P p α p P p ,
± P s ± z + P s ± V gr t = Γ s N Er ( σ se n 3 σ sa n 2 ) P s ± α s P s ± ,
P s + (0,t)= R 0 P s (0,t), P s (L,t)= R L P s + (L,t),
P p (0,t)= P pump { 1exp(t/ t 1 ),t< T p exp[ (t T p )/ t 1 ],t> T p ,
P out (t)= P s + (L,t) P s (L,t).
n ¯ 2,3 (t)= 1 L 0 L n 2,3 (z,t)dz .

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