Abstract

It has been recently shown that photodarkening can significantly reduce the mode instability threshold in high power Yb-doped fiber amplifiers, thus resulting in an even more severe limitation to the scaling of the output average power of these systems. Therefore, an efficient reduction of photodarkening in an Yb-doped active fiber will lead to very significant gains in the output average power delivered by such systems. In this context, it has been reported that photodarkening can be significantly mitigated when co-doping a fiber core with Al and P, which makes this approach potentially appealing to increase the TMI threshold. Unfortunately co-doping the fiber core with Al and P also alters the effective cross-sections of the fiber, which has repercussion in the amplification efficiency. Thus, a fiber with a higher P concentration will exhibit lower cross-sections, therefore requiring a higher Yb-ion concentration to reach a certain desired amplification efficiency. However, increasing the Yb-ion concentration leads to higher photodarkening losses, which might potentially counteract the benefits of using P co-doping. In this paper we present a comparative analysis of the expected performance of different fiber amplifiers for a given constant average heat-load and amplification efficiency as a function of the ratio of Al:P concentration in the fiber core. This study indicates which core compositions are more beneficial for increasing the mode instability threshold in Yb-doped high-power fiber amplifier systems.

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

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References

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    [Crossref] [PubMed]
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2016 (4)

2015 (3)

2014 (1)

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

2013 (8)

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjold, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).

H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Mitigation of mode instabilities by dynamic excitation of fiber modes,” Proc. SPIE 8601, 86010A (2013).

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express 21(3), 2606–2623 (2013).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Increasing mode instability thresholds of fiber amplifiers by gain saturation,” Opt. Express 21(13), 15168–15182 (2013).
[Crossref] [PubMed]

S. Naderi, I. Dajani, T. Madden, and C. Robin, “Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations,” Opt. Express 21(13), 16111–16129 (2013).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Passive mitigation strategies for mode instabilities in high-power fiber laser systems,” Opt. Express 21(16), 19375–19386 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (5)

2010 (1)

2008 (1)

2007 (2)

2006 (1)

1993 (1)

Alkeskjold, T. T.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjold, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013).
[Crossref] [PubMed]

Andersen, T. V.

Bello Doua, R.

Boullet, J.

Breitkopf, S.

Broeng, J.

Broer, M. M.

Cadier, B.

Cardinal, T.

Dajani, I.

S. Naderi, I. Dajani, J. Grosek, and T. Madden, “Theoretical treatment of modal instability in high-power cladding-pumped Raman amplifiers,” Proc. SPIE 9344, 93442X (2015).

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

S. Naderi, I. Dajani, T. Madden, and C. Robin, “Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations,” Opt. Express 21(13), 16111–16129 (2013).
[Crossref] [PubMed]

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407–11422 (2012).
[Crossref] [PubMed]

Desmoulins, S.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Digiovanni, D. J.

Dinh, T.-N.

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

Doerfel, F.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Durrant, T.

Eidam, T.

Ermeneux, S.

Fan, T. Y.

C. X. Yu, O. Shatrovoy, and T. Y. Fan, “All-glass fiber amplifier pumped by ultrahigh brightness pump,” Proc. SPIE 9728, 972806 (2016).

Flohrer, F.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Gabler, T.

Gebavi, H.

Ghiringhelli, F.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Grosek, J.

S. Naderi, I. Dajani, J. Grosek, and T. Madden, “Theoretical treatment of modal instability in high-power cladding-pumped Raman amplifiers,” Proc. SPIE 9344, 93442X (2015).

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

Guillen, F.

Hanf, S.

Hansen, K. R.

Hoffman, H. J.

Horley, R.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Jansen, F.

Jauregui, C.

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]

H.-J. Otto, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “Impact of photodarkening on the mode instability threshold,” Opt. Express 23(12), 15265–15277 (2015).
[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]

C. Jauregui, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Passive mitigation strategies for mode instabilities in high-power fiber laser systems,” Opt. Express 21(16), 19375–19386 (2013).
[Crossref] [PubMed]

H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Mitigation of mode instabilities by dynamic excitation of fiber modes,” Proc. SPIE 8601, 86010A (2013).

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light Sci. Appl. 1(4), e8 (2012).
[Crossref]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20(12), 12912–12925 (2012).
[Crossref] [PubMed]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011).
[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]

Jetschke, S.

Jørgensen, M. M.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjold, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).

Kirchhof, J.

Koponen, J. J.

Kozak, M.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Krol, D. M.

Lægsgaard, J.

Landais, D.

Laurila, M.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjold, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).

Le Goffic, O.

Leich, M.

Liem, A.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Limpert, J.

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]

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]

H.-J. Otto, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “Impact of photodarkening on the mode instability threshold,” Opt. Express 23(12), 15265–15277 (2015).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Passive mitigation strategies for mode instabilities in high-power fiber laser systems,” Opt. Express 21(16), 19375–19386 (2013).
[Crossref] [PubMed]

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Mitigation of mode instabilities by dynamic excitation of fiber modes,” Proc. SPIE 8601, 86010A (2013).

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light Sci. Appl. 1(4), e8 (2012).
[Crossref]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20(12), 12912–12925 (2012).
[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]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011).
[Crossref] [PubMed]

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010).
[Crossref] [PubMed]

Linke, S.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Madden, T.

S. Naderi, I. Dajani, J. Grosek, and T. Madden, “Theoretical treatment of modal instability in high-power cladding-pumped Raman amplifiers,” Proc. SPIE 9344, 93442X (2015).

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

S. Naderi, I. Dajani, T. Madden, and C. Robin, “Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations,” Opt. Express 21(13), 16111–16129 (2013).
[Crossref] [PubMed]

Manek-Hönninger, I.

Mechin, D.

Milanese, D.

Modsching, N.

Monteville, A.

Naderi, S.

S. Naderi, I. Dajani, J. Grosek, and T. Madden, “Theoretical treatment of modal instability in high-power cladding-pumped Raman amplifiers,” Proc. SPIE 9344, 93442X (2015).

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

S. Naderi, I. Dajani, T. Madden, and C. Robin, “Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations,” Opt. Express 21(13), 16111–16129 (2013).
[Crossref] [PubMed]

Noordegraaf, D.

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjold, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).

Otto, H. J.

Otto, H.-J.

Peschel, T.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Podgorski, M.

Riedel, P.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Robin, C.

Robin, T.

Röpke, U.

Salin, F.

Schmidt, O.

Schreiber, T.

Schwuchow, A.

Seise, E.

Shatrovoy, O.

C. X. Yu, O. Shatrovoy, and T. Y. Fan, “All-glass fiber amplifier pumped by ultrahigh brightness pump,” Proc. SPIE 9728, 972806 (2016).

Smith, A. V.

Smith, J. J.

Söderlund, M. J.

Stutzki, F.

Taccheo, S.

Tammela, S. K. T.

Tregoat, D.

Tünnermann, A.

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]

H.-J. Otto, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “Impact of photodarkening on the mode instability threshold,” Opt. Express 23(12), 15265–15277 (2015).
[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]

C. Jauregui, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Passive mitigation strategies for mode instabilities in high-power fiber laser systems,” Opt. Express 21(16), 19375–19386 (2013).
[Crossref] [PubMed]

H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Mitigation of mode instabilities by dynamic excitation of fiber modes,” Proc. SPIE 8601, 86010A (2013).

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light Sci. Appl. 1(4), e8 (2012).
[Crossref]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20(12), 12912–12925 (2012).
[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]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011).
[Crossref] [PubMed]

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010).
[Crossref] [PubMed]

Unger, S.

Ward, B.

Wirth, C.

Yu, C. X.

C. X. Yu, O. Shatrovoy, and T. Y. Fan, “All-glass fiber amplifier pumped by ultrahigh brightness pump,” Proc. SPIE 9728, 972806 (2016).

Zervas, M.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Zimer, H.

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

Appl. Opt. (1)

Light Sci. Appl. (1)

J. Limpert, F. Stutzki, F. Jansen, H.-J. Otto, T. Eidam, C. Jauregui, and A. Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light Sci. Appl. 1(4), e8 (2012).
[Crossref]

Nat. Photonics (1)

C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
[Crossref]

Opt. Express (19)

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011).
[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]

J. J. Koponen, M. J. Söderlund, H. J. Hoffman, and S. K. T. Tammela, “Measuring photodarkening from single-mode ytterbium doped silica fibers,” Opt. Express 14(24), 11539–11544 (2006).
[Crossref] [PubMed]

I. Manek-Hönninger, J. Boullet, T. Cardinal, F. Guillen, S. Ermeneux, M. Podgorski, R. Bello Doua, and F. Salin, “Photodarkening and photobleaching of an ytterbium-doped silica double-clad LMA fiber,” Opt. Express 15(4), 1606–1611 (2007).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express 21(3), 2606–2623 (2013).
[Crossref] [PubMed]

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407–11422 (2012).
[Crossref] [PubMed]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20(12), 12912–12925 (2012).
[Crossref] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013).
[Crossref] [PubMed]

S. Naderi, I. Dajani, T. Madden, and C. Robin, “Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations,” Opt. Express 21(13), 16111–16129 (2013).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Passive mitigation strategies for mode instabilities in high-power fiber laser systems,” Opt. Express 21(16), 19375–19386 (2013).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Increasing mode instability thresholds of fiber amplifiers by gain saturation,” Opt. Express 21(13), 15168–15182 (2013).
[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]

S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, “Efficient Yb laser fibers with low photodarkening by optimization of the core composition,” Opt. Express 16(20), 15540–15545 (2008).
[Crossref] [PubMed]

H.-J. Otto, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “Impact of photodarkening on the mode instability threshold,” Opt. Express 23(12), 15265–15277 (2015).
[Crossref] [PubMed]

B. Ward, “Theory and modeling of photodarkening-induced quasi static degradation in fiber amplifiers,” Opt. Express 24(4), 3488–3501 (2016).
[Crossref] [PubMed]

S. Taccheo, H. Gebavi, A. Monteville, O. Le Goffic, D. Landais, D. Mechin, D. Tregoat, B. Cadier, T. Robin, D. Milanese, and T. Durrant, “Concentration dependence and self-similarity of photodarkening losses induced in Yb-doped fibers by comparable excitation,” Opt. Express 19(20), 19340–19345 (2011).
[Crossref] [PubMed]

S. Jetschke, S. Unger, U. Röpke, and J. Kirchhof, “Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power,” Opt. Express 15(22), 14838–14843 (2007).
[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]

Opt. Lett. (2)

Proc. SPIE (6)

S. Naderi, I. Dajani, J. Grosek, T. Madden, and T.-N. Dinh, “Theoretical analysis of effect of pump and signal wavelengths on modal instabilities in Yb-doped fiber amplifiers,” Proc. SPIE 8964, 89641W (2014).

M. M. Jørgensen, M. Laurila, D. Noordegraaf, T. T. Alkeskjold, and J. Lægsgaard, “Thermal-recovery of modal instability in rod fiber amplifiers,” Proc. SPIE 8601, 86010U (2013).

H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Mitigation of mode instabilities by dynamic excitation of fiber modes,” Proc. SPIE 8601, 86010A (2013).

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Desmoulins, M. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiber-optic components for high-power fiber lasers,” Proc. SPIE 7914, 791414 (2011).

S. Naderi, I. Dajani, J. Grosek, and T. Madden, “Theoretical treatment of modal instability in high-power cladding-pumped Raman amplifiers,” Proc. SPIE 9344, 93442X (2015).

C. X. Yu, O. Shatrovoy, and T. Y. Fan, “All-glass fiber amplifier pumped by ultrahigh brightness pump,” Proc. SPIE 9728, 972806 (2016).

Other (1)

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Thermally Induced Index Gratings in Few-Mode High-Power Fiber Laser Systems,” in Lasers, Sources, and Related Photonic Devices (2012), p. AT4A.10.

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Figures (7)

Fig. 1
Fig. 1 Dependence of the PD losses at 633 nm on the ratio between the concentration of P2O5 (CP2O5) and Al2O3 (CAl2O3) in the fiber core (Cratio). These PD losses have been extracted from [26], normalized with Eq. (1) and linearly interpolated. The normalization has been done for a reference fiber with N ref =2 10 26 ions/m3 (comparable to the one used in the measurements presented in [26]) and a relative inversion of 0.46.
Fig. 2
Fig. 2 Absorption (dashed lines) and emission (solid lines) cross-sections of Yb-doped fiber with different core compositions characterized by Cratio (after [26,27]).
Fig. 3
Fig. 3 Dependence of the TMI threshold on the core composition (characterized by Cratio) and on the PD losses α PD 1μm at the signal wavelength (normalized for an AFF = 1 and a relative inversion level of 0.46) in a LPF. The dashed line corresponds to the PD losses given by Eq. (2) (with an Nbulk fulfilling the constant amplification efficiency requirement for each Cratio).
Fig. 4
Fig. 4 Expected dependence of the TMI threshold on the core composition (characterized by Cratio) in a LPF.
Fig. 5
Fig. 5 Dependence of the Nbulk on the core composition (characterized by Cratio) and on the PD losses α PD 1μm at the signal wavelength (normalized for an AFF = 1 and a relative inversion level of 0.46) in a LPF. The dashed line corresponds to the PD losses given by Eq. (2) (with an Nbulk fulfilling the constant amplification efficiency requirement for each Cratio).
Fig. 6
Fig. 6 Dependence of the TMI threshold on the core composition (characterized by Cratio) and on the PD losses α PD 1μm at the signal wavelength (normalized for an AFF = 1 and a relative inversion level of 0.46) in a 15m long 20/400µm SIF. The dashed line corresponds to the PD losses given by Eq. (2) (with an Nbulk fulfilling the constant amplification efficiency requirement for each Cratio).
Fig. 7
Fig. 7 Expected dependence of the TMI threshold on the core composition (characterized by Cratio) in a 15m long 20/400µm SIF.

Equations (4)

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α PD norm ( dB/m )= α PD meas N ref 2 0.46 AF F meas Γ PD meas N meas 2 ( N 2 N meas ) .
α PD 1µm ( dB/m )={ ( 472.91 C ratio +244.73 ) ( N bulk 1.95 10 26 ) 2 1 γ        if  C ratio <0.49 13 ( N bulk 1.95 10 26 ) 2 1 γ                                          if  C ratio 0.49 ,
α PD ( dB/m )= α PD 1µm N 2 /N 0.46 AFF.
η amp = P out P seed P pump ,

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