Abstract

State-of-the-art high power Yb-doped large mode area fibers have been developed to a performance level able to reach the so-called mode instability threshold. In this contribution we will discuss the experimental results regarding the temporal evolution (build up and decay) of this effect to come closer to a comprehensive understanding of its driving mechanisms. Our investigations prove that the relevant time scale for build up and decay of mode instability is in the millisecond range and thus deliver experimental evidence of underlying thermal effects. To the best of our knowledge these are the first systematic, time resolved investigations on that topic.

© 2012 OSA

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  1. J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
    [CrossRef]
  2. 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]
  3. C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36(16), 3118–3120 (2011).
    [CrossRef] [PubMed]
  4. 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]
  5. G. D. Goodno, L. D. Book, and J. E. Rothenberg, “Single-frequency, single-mode emission at 2040 nm from a 600-W Thulium-doped fiber amplifier chain,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper MF2.
  6. 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]
  7. 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]
  8. N. Andermahr and C. Fallnich, “Optically induced long-period fiber gratings for guided mode conversion in few-mode fibers,” Opt. Express 18(5), 4411–4416 (2010).
    [CrossRef] [PubMed]
  9. 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]
  10. C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (2012).
    [CrossRef] [PubMed]
  11. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011).
    [CrossRef] [PubMed]
  12. 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]
  13. F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
    [CrossRef] [PubMed]
  14. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, Friedrich-Schiller-University Jena, Institute of Applied Physics, Max-Wien-Platz 1, 07743 Jena, Germany, are preparing a manuscript to be called “Temporal dynamics of mode-instabilities in high-power fiber lasers and amplifiers.”
  15. S. Hädrich, T. Schreiber, T. Pertsch, J. Limpert, T. Peschel, R. Eberhardt, and A. Tünnermann, “Thermo-optical behavior of rare-earth-doped low-NA fibers in high power operation,” Opt. Express 14(13), 6091–6097 (2006).
    [CrossRef] [PubMed]
  16. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermo-optical effects in high-power ytterbium-doped fiber amplifiers,” Opt. Express 19(24), 23965–23980 (2011).
    [CrossRef] [PubMed]

2012 (2)

2011 (8)

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]

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, 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]

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]

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36(16), 3118–3120 (2011).
[CrossRef] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermo-optical effects in high-power ytterbium-doped fiber amplifiers,” Opt. Express 19(24), 23965–23980 (2011).
[CrossRef] [PubMed]

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[CrossRef] [PubMed]

2010 (2)

2007 (1)

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

2006 (1)

Alkeskjold, T. T.

Andermahr, N.

Andersen, T. V.

Broeng, J.

Carstens, H.

Dajani, I.

Eberhardt, R.

Eidam, T.

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (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, 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]

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. 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]

Fallnich, C.

Gabler, T.

Gaida, C.

Gowin, M.

Hädrich, S.

Hanf, S.

Hansen, K. R.

Jansen, F.

Jauregui, C.

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (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]

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, 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, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (2011).
[CrossRef] [PubMed]

Jung, M.

Klingebiel, S.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Lægsgaard, J.

Limpert, J.

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (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, 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]

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. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36(16), 3118–3120 (2011).
[CrossRef] [PubMed]

F. Stutzki, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (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]

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

S. Hädrich, T. Schreiber, T. Pertsch, J. Limpert, T. Peschel, R. Eberhardt, and A. Tünnermann, “Thermo-optical behavior of rare-earth-doped low-NA fibers in high power operation,” Opt. Express 14(13), 6091–6097 (2006).
[CrossRef] [PubMed]

Ludewigt, K.

Otto, H.-J.

Pertsch, T.

Peschel, T.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

S. Hädrich, T. Schreiber, T. Pertsch, J. Limpert, T. Peschel, R. Eberhardt, and A. Tünnermann, “Thermo-optical behavior of rare-earth-doped low-NA fibers in high power operation,” Opt. Express 14(13), 6091–6097 (2006).
[CrossRef] [PubMed]

Robin, C.

Röser, F.

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Rothhardt, J.

Schmidt, O.

Schreiber, T.

Seise, E.

Smith, A. V.

Smith, J. J.

Steinmetz, A.

Stutzki, F.

ten Have, E.

Tsybin, I.

Tünnermann, A.

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (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, 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]

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36(16), 3118–3120 (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, H.-J. Otto, F. Jansen, C. Gaida, C. Jauregui, J. Limpert, and A. Tünnermann, “High-speed modal decomposition of mode instabilities in high-power fiber lasers,” Opt. Lett. 36(23), 4572–4574 (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]

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

S. Hädrich, T. Schreiber, T. Pertsch, J. Limpert, T. Peschel, R. Eberhardt, and A. Tünnermann, “Thermo-optical behavior of rare-earth-doped low-NA fibers in high power operation,” Opt. Express 14(13), 6091–6097 (2006).
[CrossRef] [PubMed]

Ward, B.

Wirth, C.

IEEE J. Sel. Top. Quantum Electron. (1)

J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[CrossRef]

Opt. Express (9)

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]

N. Andermahr and C. Fallnich, “Optically induced long-period fiber gratings for guided mode conversion in few-mode fibers,” Opt. Express 18(5), 4411–4416 (2010).
[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]

C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Temperature-induced index gratings and their impact on mode instabilities in high-power fiber laser systems,” Opt. Express 20(1), 440–451 (2012).
[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]

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]

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]

S. Hädrich, T. Schreiber, T. Pertsch, J. Limpert, T. Peschel, R. Eberhardt, and A. Tünnermann, “Thermo-optical behavior of rare-earth-doped low-NA fibers in high power operation,” Opt. Express 14(13), 6091–6097 (2006).
[CrossRef] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermo-optical effects in high-power ytterbium-doped fiber amplifiers,” Opt. Express 19(24), 23965–23980 (2011).
[CrossRef] [PubMed]

Opt. Lett. (4)

Other (2)

G. D. Goodno, L. D. Book, and J. E. Rothenberg, “Single-frequency, single-mode emission at 2040 nm from a 600-W Thulium-doped fiber amplifier chain,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2009), paper MF2.

H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, Friedrich-Schiller-University Jena, Institute of Applied Physics, Max-Wien-Platz 1, 07743 Jena, Germany, are preparing a manuscript to be called “Temporal dynamics of mode-instabilities in high-power fiber lasers and amplifiers.”

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Figures (7)

Fig. 1
Fig. 1

Experimental setup: Fiber amplifier in counter-propagating geometry; PCF: photonic crystal fiber, MFD: mode field diameter, HR: highly reflective mirror, DM: dichroitic mirror. The amplifier was driven in pulsed-pump and cw-seed operation.

Fig. 2
Fig. 2

Examples to illustrate the pump pulse scheme and the detected signal for stable and unstable operation: pulsed pumping scheme for a pump power below (a) and above (b) the threshold for MI (red dotted line), according signals below (c) and above (d) the threshold. The inset in (b) shows the rise time (1 ms) of the pump pulses. The insets in (c) and (d) illustrate the beam profile for stable and unstable mode operation. Above the MI threshold (d), temporally, the amplifier showed stable fundamental-mode operation (light gray shaded areas), but switched to unstable mode operation with a delay of some milliseconds (dark gray shaded areas). This delay we refer to as MI build-up time.

Fig. 3
Fig. 3

MI build-up time in dependence on the absorbed pump power on a millisecond time scale. The build-up time followed an exponential decay, which converged to a minimum build-up time of 1.6 ms (indicated by the horizontal gray shaded area). For comparison: cw-pump operation MI was observed for Pabsorbed Pump > 750 W (indicated by the vertical gray shaded area).

Fig. 4
Fig. 4

MI build-up time in dependence on the duty cycle's off time: (a) Build-up time for steady-state operation, (b) Build-up times of following pulses in the transition time directly after starting the duty cycle after one second pause (for 120 ms off times, gray dots and for 20 ms off times, black squares).

Fig. 5
Fig. 5

MI build-up time in dependence on the pre-pulse power P1 in a two-step pump scheme: (a) pump scheme, (b) measured build-up time for different pre-pulse powers (P1). The pre-pulse power was varied but stayed below the threshold power for MI (Pth) for all measurements. The main-pulse power (P2) was kept constant slightly above the threshold power (P2 = 1.05·Pth).

Fig. 6
Fig. 6

MI decay time in dependencye on the post-pulse power P2 in a two-step pumping scheme: (a) pumping scheme, (b) measured decay time for different post-pulse powers (P2). The post-pulse was varied but stayed below the threshold power for MI (Pth) for all measurements. The main-pulse power (P1) was kept constant above the threshold (P1 = 1.2·Pth). The decay time refers to the delay from reducing the power below the threshold to vanishing MI.

Fig. 7
Fig. 7

Reinterpretation of the data in Fig. 3. MI threshold pump power as a function of the pulse duration for the case of long off times (> 90 ms). The threshold power is increased for short pulse duration. For a pulse duration of 1.7 ms the threshold power was increased by a factor of 1.6 compared to the cw-threshold. The gray shaded area indicates the parameter region of stable mode operation.

Equations (1)

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P output =-3.8W+0.79· P absorbed pump

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