Abstract

A finite element steady periodic scalar beam propagation method suited to treating mode instability in amplifiers incorporating fibers with complicated design features is presented and demonstrated on test cases. These incorporate large pitch photonic crystal fibers with confined and down-doped cores in co-pumped and counter-pumped configurations. Seed power fluctuations and slight launch misalignment are proposed and implemented as a noise source to seed the instability. Down doping the confined core by −7.0E-5 was found to increase the instability threshold by 25% in the co-pumped case and 9% in the counter-pumped case. The increase in threshold is correlated with the suppression of higher frequency components of intensity gratings associated with the instability.

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References

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    [Crossref] [PubMed]
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2018 (1)

2017 (1)

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

2016 (1)

B. Ward, “Accurate modeling of rod-type photonic crystal fiber amplifiers,” Proc. SPIE 9728, 97280F (2016).

2015 (2)

2014 (6)

2013 (6)

2012 (4)

2011 (4)

2008 (1)

B. Ward, “Finite element analysis of photonic crystal rods with inhomogeneous anisotropic refractive index tensor,” IEEE J. Quantum Electron. 44(2), 150–156 (2008).
[Crossref]

2007 (1)

1997 (1)

R. Paschotta, J. Nilsson, A. Tropper, and D. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Alkeskjold, T. T.

Carstens, H.

Codemard, C.

M. Zervas and C. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
[Crossref]

Dajani, I.

Dong, L.

Eidam, T.

H. J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

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

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012).
[Crossref] [PubMed]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (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]

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011).
[Crossref] [PubMed]

Hädrich, S.

Hanna, D.

R. Paschotta, J. Nilsson, A. Tropper, and D. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Hansen, K. R.

Jansen, F.

F. Stutzki, F. Jansen, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233–242 (2014).
[Crossref]

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, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

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

F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26 mJ, 130 W Q-switched fiber-laser system with near-diffraction-limited beam quality,” Opt. Lett. 37(6), 1073–1075 (2012).
[Crossref] [PubMed]

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (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]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011).
[Crossref] [PubMed]

Jauregui, C.

C. Jauregui, F. Stutzki, A. Tünnermann, and J. Limpert, “Thermal analysis of Yb-doped high-power fiber amplifiers with Al:P co-doped cores,” Opt. Express 26(6), 7614–7624 (2018).
[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, F. Stutzki, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “2 kW average power from a pulsed Yb-doped rod-type fiber amplifier,” Opt. Lett. 39(22), 6446–6449 (2014).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233–242 (2014).
[Crossref]

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, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26 mJ, 130 W Q-switched fiber-laser system with near-diffraction-limited beam quality,” Opt. Lett. 37(6), 1073–1075 (2012).
[Crossref] [PubMed]

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012).
[Crossref] [PubMed]

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

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (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]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011).
[Crossref] [PubMed]

Jetschke, S.

Johansen, M. M.

Kirchhof, J.

Lægsgaard, J.

Laurila, M.

Liem, A.

Limpert, J.

C. Jauregui, F. Stutzki, A. Tünnermann, and J. Limpert, “Thermal analysis of Yb-doped high-power fiber amplifiers with Al:P co-doped cores,” Opt. Express 26(6), 7614–7624 (2018).
[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, F. Stutzki, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “2 kW average power from a pulsed Yb-doped rod-type fiber amplifier,” Opt. Lett. 39(22), 6446–6449 (2014).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233–242 (2014).
[Crossref]

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]

F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26 mJ, 130 W Q-switched fiber-laser system with near-diffraction-limited beam quality,” Opt. Lett. 37(6), 1073–1075 (2012).
[Crossref] [PubMed]

H. J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012).
[Crossref] [PubMed]

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

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (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]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011).
[Crossref] [PubMed]

Lu, Q.

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

Modsching, N.

Nilsson, J.

R. Paschotta, J. Nilsson, A. Tropper, and D. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Otto, H.

Otto, H. J.

Otto, H.-J.

Paschotta, R.

R. Paschotta, J. Nilsson, A. Tropper, and D. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Pulford, B.

Robin, C.

Röpke, U.

Rothhardt, J.

Schmidt, O.

Schreiber, T.

Shi, C.

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

Smith, A. V.

Smith, J. J.

Steinmetz, A.

Stutzki, F.

C. Jauregui, F. Stutzki, A. Tünnermann, and J. Limpert, “Thermal analysis of Yb-doped high-power fiber amplifiers with Al:P co-doped cores,” Opt. Express 26(6), 7614–7624 (2018).
[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, F. Stutzki, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “2 kW average power from a pulsed Yb-doped rod-type fiber amplifier,” Opt. Lett. 39(22), 6446–6449 (2014).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233–242 (2014).
[Crossref]

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, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

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

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26 mJ, 130 W Q-switched fiber-laser system with near-diffraction-limited beam quality,” Opt. Lett. 37(6), 1073–1075 (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]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011).
[Crossref] [PubMed]

Su, R.

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

Tropper, A.

R. Paschotta, J. Nilsson, A. Tropper, and D. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 33(7), 1049–1056 (1997).
[Crossref]

Tünnermann, A.

C. Jauregui, F. Stutzki, A. Tünnermann, and J. Limpert, “Thermal analysis of Yb-doped high-power fiber amplifiers with Al:P co-doped cores,” Opt. Express 26(6), 7614–7624 (2018).
[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, F. Stutzki, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann, “2 kW average power from a pulsed Yb-doped rod-type fiber amplifier,” Opt. Lett. 39(22), 6446–6449 (2014).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, H. Otto, C. Jauregui, J. Limpert, and A. Tünnermann, “Designing advanced very-large-mode-area fibers for power scaling of fiber-laser systems,” Optica 1(4), 233–242 (2014).
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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]

F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26 mJ, 130 W Q-switched fiber-laser system with near-diffraction-limited beam quality,” Opt. Lett. 37(6), 1073–1075 (2012).
[Crossref] [PubMed]

H. J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

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

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (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]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011).
[Crossref] [PubMed]

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011).
[Crossref] [PubMed]

Unger, S.

Wang, X.

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

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B. Ward, “Accurate modeling of rod-type photonic crystal fiber amplifiers,” Proc. SPIE 9728, 97280F (2016).

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C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

Yang, B.

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
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M. Zervas and C. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
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C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

Zhou, P.

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

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M. Zervas and C. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014).
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IEEE Photonics J. (1)

C. Shi, R. Su, H. Zhang, B. Yang, X. Wang, P. Zhou, X. Xu, and Q. Lu, “Experimental study of output characteristics of bi-directional pumping high power fiber amplifier in different pumping schemes,” IEEE Photonics J. 9(3), 1–10 (2017).
[Crossref]

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 singlemode operation based on higher-order mode delocalisation,” Light Sci. Appl. 1(4), e8 (2012).
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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, 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]

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C. Jauregui, F. Stutzki, A. Tünnermann, and J. Limpert, “Thermal analysis of Yb-doped high-power fiber amplifiers with Al:P co-doped cores,” Opt. Express 26(6), 7614–7624 (2018).
[Crossref] [PubMed]

T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19(9), 8656–8661 (2011).
[Crossref] [PubMed]

F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Express 20(4), 3997–4008 (2012).
[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, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high-power fiber lasers and amplifiers,” Opt. Express 20(14), 15710–15722 (2012).
[Crossref] [PubMed]

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Opt. Lett. (5)

Optica (1)

Proc. SPIE (1)

B. Ward, “Accurate modeling of rod-type photonic crystal fiber amplifiers,” Proc. SPIE 9728, 97280F (2016).

Supplementary Material (1)

NameDescription
» Visualization 1       Amplifier output visualization

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Figures (4)

Fig. 1
Fig. 1 The fiber cross-section (a), The LP01-like and LP11-like mode intensity profiles (b), and the frequency-dependent STRS gain spectrum for core down-doping levels from 0.0 (top curve) to −7.0E-5 (bottom curve) in increments of 1.0E-5. Note: The modes in (b) were calculated using the full region shown in (a) but are magnified to show more detail.
Fig. 2
Fig. 2 Simulated instability thresholds as determined by Eq. (5) for co and counter-pumped amplifiers described in the text (a) and output intensity profile for the counter-pumped case with −1.0E-5 down doping within the core. Visualization 1 shows the evolution of (b) over 73 time steps spanning a total time of 12.8 milliseconds.
Fig. 3
Fig. 3 Logarithmic-scale temporal intensity fluctuation spectra at one of the offset sampling points (x-direction) along the amplifier lengths for the co-pumped amplifier with zero down doping (a), the co-pumped amplifier with maximum (−7.0E-5) down doping (b), the counter-pumped amplifier with zero down doping (c) and the counter-pumped amplifier with maximum (−7.0E-5) down doping (d).
Fig. 4
Fig. 4 Intensity gratings over the last 11 cm of the amplifier and all 73 time steps for the co-pumped amplifier with uniform core index (a), the co-pumped amplifier with the core down-doped by −7.0E-5 (b), the counter-pumped amplifier with uniform core index (c), and the counter-pumped amplifier with the core down-doped by −7.0E-5 (d). The length of the propagation step was 545 µm, and the time step was 0.175 ms.

Tables (1)

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Table 1 Observed Intensity Grating Characteristics

Equations (5)

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[ t 2 2ik z k 2 +ε( x,y,z ) k 0 2 ]ψ( x,y,z )=0
Ψ m+1 j = ( M+ ikΔz 4 ( K+ Ε m+1 j ) ) 1 ( M ikΔz 4 ( K+ Ε m j ) ) Ψ m j ,
( iΩρC M th +κ K th ) T Ω = Q Ω .
v= Ω Δβ
d σ norm ( P out ) d P out | P Th 0.1%

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