Abstract

A novel and simple solution doping technique is used to explore the refractive index behavior of Al,P-doped SiO2 in the vicinity of the Al:P-ratio of 1:1 at low doping concentrations (0.4 up to 2.0 mol% Al2O3 and/or P2O5). It is found that even if Al:P = 1:1 is matched precisely, an index increase is observed. This is in contradiction to previous findings in the literature and the already sophisticated models need to be refined in this region. In the proposed model, an incomplete formation of AlPO4 is assumed and solves the contradiction. Furthermore, the presented model can be combined with previous literature models.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
    [Crossref]
  2. S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
    [Crossref]
  3. D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
    [Crossref]
  4. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011).
    [Crossref] [PubMed]
  5. C. Jauregui, H.-J. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015).
    [Crossref] [PubMed]
  6. C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).
  7. C. Jauregui, H.-J. Otto, S. Breitkopf, J. Limpert, and A. Tünnermann, “Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities,” Opt. Express 24(8), 7879–7892 (2016).
    [Crossref] [PubMed]
  8. F. Beier, C. Hupel, J. Nold, S. Kuhn, S. Hein, J. Ihring, B. Sattler, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Narrow linewidth, single mode 3 kW average power from a directly diode pumped ytterbium-doped low NA fiber amplifier,” Opt. Express 24(6), 6011–6020 (2016).
    [Crossref] [PubMed]
  9. F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017).
    [Crossref] [PubMed]
  10. F. Beier, F. Moeller, J. Nold, B. Sattler, S. Kuhn, C. Hupel, S. Hein, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “TMI Investigations of Very Low NA Yb-doped Fibers and Scaling to Extreme Stable 4.4 kW Single-mode Output,” in Advanced Solid State Lasers (Optical Society of America, 2017), ATu3A.2.
    [Crossref]
  11. J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
    [Crossref]
  12. S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
    [Crossref]
  13. M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
    [Crossref]
  14. J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
    [Crossref]
  15. S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).
  16. R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
    [Crossref]
  17. F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
    [Crossref]
  18. A. D. Yablon, M. F. Yan, D. J. DiGiovanni, M. E. Lines, S. L. Jones, D. N. Ridgway, G. A. Sandels, I. A. White, P. Wisk, F. V. DiMarcello, E. M. Monberg, and J. Jasapara, “Frozen-In Viscoelasticity for Novel Beam Expanders and High-Power Connectors,” J. Lightwave Technol. 22(1), 16–23 (2004).
    [Crossref]

2017 (2)

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (1)

2014 (1)

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

2011 (2)

2009 (1)

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

2007 (1)

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

2005 (1)

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

2004 (2)

1999 (1)

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

1990 (1)

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

1989 (1)

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

1988 (1)

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Aichele, C.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Beier, F.

Breitkopf, S.

Bubnov, M. M.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Dellith, J.

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

DiGiovanni, D. J.

DiMarcello, F. V.

Douglas, D. C.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Duncan, T. M.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Eberhardt, R.

Eidam, T.

Gur’yanov, A. N.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Haarlammert, N.

Handke, M.

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

Hein, S.

Hupel, C.

Ihring, J.

Jansen, F.

Jasapara, J.

Jauregui, C.

Jetschke, S.

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

Jones, S. L.

Kirchhof, J.

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

Knappe, B.

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

Kometani, T. Y.

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

Kosinski, S. G.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Krol, D. M.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Kuhn, S.

Leich, M.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Liem, A.

Likhachev, M. E.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Limpert, J.

Lindner, F.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Lines, M. E.

Lipatov, D. S.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

MacChesney, J. B.

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

McCollum, B. C.

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

Monberg, E. M.

Mozgawa, W.

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

Nold, J.

Otto, H.-J.

Proske, F.

Ridgway, D. N.

Rokita, M.

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

Sandels, G. A.

Sattler, B.

Scheffel, A.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

Schmidt, O.

Schreiber, T.

Schwuchow, A.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

Simpson, J. R.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Snitzer, E.

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

Stihler, C.

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

Stutzki, F.

Tumminelli, R. P.

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

Tünnermann, A.

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, S. Breitkopf, J. Limpert, and A. Tünnermann, “Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities,” Opt. Express 24(8), 7879–7892 (2016).
[Crossref] [PubMed]

F. Beier, C. Hupel, J. Nold, S. Kuhn, S. Hein, J. Ihring, B. Sattler, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Narrow linewidth, single mode 3 kW average power from a directly diode pumped ytterbium-doped low NA fiber amplifier,” Opt. Express 24(6), 6011–6020 (2016).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015).
[Crossref] [PubMed]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011).
[Crossref] [PubMed]

Unger, S.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

Vechkanov, V. N.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

White, I. A.

Wirth, C.

Wisk, P.

Yablon, A. D.

Yan, M. F.

Yashkov, M. V.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Zotov, K. V.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Inorg. Mater. (1)

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

J. Lightwave Technol. (2)

J. Mol. Struct. (1)

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

J. Non-Cryst. Solids (3)

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

Opt. Express (5)

Phys. Chem. Glasses B (1)

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

Proc. SPIE (4)

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Other (1)

F. Beier, F. Moeller, J. Nold, B. Sattler, S. Kuhn, C. Hupel, S. Hein, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “TMI Investigations of Very Low NA Yb-doped Fibers and Scaling to Extreme Stable 4.4 kW Single-mode Output,” in Advanced Solid State Lasers (Optical Society of America, 2017), ATu3A.2.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) concentration profile of an example preform prepared by means of all-solution doping; (b) measured refractive index and calculated refractive index according to Ref. [1] and [2].
Fig. 2
Fig. 2 measured refractive index as function of the Al/P (P excess) or P/Al (Al excess) for SiO2 concentrations ranging from 96 to 99 mol%; comparison to the calculated refractive indices from EPMA using models in Ref. [1] and [2].
Fig. 3
Fig. 3 Glass structure of Al,P-doped SiO2 with 100% formation of AlPO4 units.
Fig. 4
Fig. 4 proposed glass structure when an incomplete formation of AlPO4 units (AlPO4 marked in red) takes place.
Fig. 5
Fig. 5 measured refractive index (black curve), calculated refractive index using the models presented in Ref. [1] and [2] taking a fraction f = 0.8 into account.
Fig. 6
Fig. 6 (a) Assumed dependency of parameter f on the respective ratios of Al:P or P:Al according to Eq. (3) (fsigma = 0.32); (b) Assumed dependency of the fraction parameter f on the absolute concentration according to Eq. (4) (fmin = 0.52, fτ = 2.7 mol%).
Fig. 7
Fig. 7 dependency of the refractive index on the ratio of Al/P (P excess) and P/Al (Al excess); (black points) measure values; a) (green circles) best fit model; b) (blue circles) extended model of Ref. [1]; c) (red circles) extended model of Ref. [2].
Fig. 8
Fig. 8 Best fit model for the dependency of the refractive index on the respective ratios for different concentrations

Tables (1)

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Table 1 Molar refractivities of Al2O3 (∆nAl), P2O5 (∆nP) and AlPO4 (∆nAlP) and f parameter values resulting from the least-squares fitting method for the model equations (Eq. (5-6); comparison to and extension of the previously reported values in the literature (Refs. [1] and [2])

Equations (12)

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A l 2 O 3 + P 2 O 5 2AlP O 4
A l 2 O 3 + P 2 O 5 2fAlP O 4 +( 1f )( A l 2 O 3 + P 2 O 5 )
A l 2 O 3 + P 2 O 5 2AlP O 4
f=1( 1 f c ( c ) )exp( ( x1 ) 2 2 f sigma 2 )
x={ c Al c P ,   c Al < c P c P c Al , c Al c P
f c ( c )=1( 1 f min )exp( c f τ )
Δn= ( c P c Al )Δ n P excess P + f c Al Δ n AlP formed AlP O 4 + ( 1f ) c Al 0.5( Δ n P +Δ n Al ) not formed AlP O 4
f=1( 1 f c ( c ) )exp( ( c Al c P 1 ) 2 2 f sigma 2 )
f c ( c )=1( 1 f min )exp( c f τ )
Δn= ( c Al c P )Δ n Al excess Al + f c P Δ n AlP formed AlP O 4 + ( 1f ) c P 0.5( Δ n P +Δ n Al ) not formed AlP O 4
f=1( 1 f c ( c ) )exp( ( c P c Al 1 ) 2 2 f sigma 2 )
f c ( c )=1( 1 f min )exp( c f τ )

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