Abstract

The temporal behavior of mode instabilities in active large mode area fibers is experimentally investigated in detail. Thus, apart from the onset threshold of mode instabilities, the output beam is characterized using both high-speed camera measurements with 20,000 frames per second and photodiode traces. Based on these measurements, an empiric definition of the power threshold of mode instabilities is introduced. Additionally, it is shown that the temporal dynamics show a transition zone between the stable and the unstable regimes where well-defined periodic temporal fluctuations on ms-timescale can be observed. Finally, it is experimentally shown that the larger the mode-field area, the slower the mode-instability fluctuation is. The observations support the thermal origin of mode instabilities.

© 2012 OSA

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References

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
    [CrossRef]
  2. 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]
  3. J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006).
    [CrossRef] [PubMed]
  4. C.-H. Liu, G. Chang, N. Litchinitser, D. Guertin, N. Jacobsen, K. Tankala, and A. Galvanauskas, “Chirally coupled core fibers at 1550-nm and 1064-nm for effectively single-mode core size scaling,” CLEO, paper CTuBB3 (2007).
  5. 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]
  6. J. Limpert, F. Stutzki, F. Jansen, H-J. Otto, T. Eidam, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).
  7. 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]
  8. 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]
  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. A. A. Fotiadi, O. L. Antipov, and P. Megret, “Resonantly induced refractive index changes in Yb-Doped fibers: the origin, properties and application for all-fiber coherent beam combining,” Frontiers in Guided Wave Optics And Optoelectronics, 209–234 (2010).
  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. 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]
  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. M. Laurila, M. M. Jørgensen, K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability,” Opt. Express 20(5), 5742–5753 (2012).
    [CrossRef] [PubMed]
  15. H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” (Oxford University Press, London, 1948), 191.

2012 (4)

2011 (5)

2010 (2)

2006 (1)

Alkeskjold, T. T.

Andersen, T. V.

Broeng, J.

Carstens, H.

Clarkson, W. A.

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]

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, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

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]

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]

Ermeneux, S.

Gabler, T.

Gaida, C.

Hädrich, S.

Hanf, S.

Hansen, K. R.

Jansen, F.

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]

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, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

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. 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]

Jauregui, C.

J. Limpert, F. Stutzki, F. Jansen, H-J. Otto, T. Eidam, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

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, 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]

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, 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. 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]

Jørgensen, M. M.

Lægsgaard, J.

Laurila, M.

Liem, A.

Limpert, J.

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, 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]

J. Limpert, F. Stutzki, F. Jansen, H-J. Otto, T. Eidam, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

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. 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]

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]

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, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006).
[CrossRef] [PubMed]

Nilsson, J.

Otto, H. J.

Otto, H.-J.

Otto, H-J.

J. Limpert, F. Stutzki, F. Jansen, H-J. Otto, T. Eidam, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

Richardson, D. J.

Röser, F.

Rothhardt, J.

Salin, F.

Schmidt, O.

Schreiber, T.

Seise, E.

Smith, A. V.

Smith, J. J.

Stutzki, F.

J. Limpert, F. Stutzki, F. Jansen, H-J. Otto, T. Eidam, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

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]

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, 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. 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]

Tünnermann, A.

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, 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]

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, 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. 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, 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, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006).
[CrossRef] [PubMed]

Wirth, C.

Yvernault, P.

J. Opt. Soc. Am. B (1)

Opt. Express (8)

J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006).
[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. 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, 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]

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

M. Laurila, M. M. Jørgensen, K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability,” Opt. Express 20(5), 5742–5753 (2012).
[CrossRef] [PubMed]

Opt. Lett. (2)

Other (4)

C.-H. Liu, G. Chang, N. Litchinitser, D. Guertin, N. Jacobsen, K. Tankala, and A. Galvanauskas, “Chirally coupled core fibers at 1550-nm and 1064-nm for effectively single-mode core size scaling,” CLEO, paper CTuBB3 (2007).

A. A. Fotiadi, O. L. Antipov, and P. Megret, “Resonantly induced refractive index changes in Yb-Doped fibers: the origin, properties and application for all-fiber coherent beam combining,” Frontiers in Guided Wave Optics And Optoelectronics, 209–234 (2010).

J. Limpert, F. Stutzki, F. Jansen, H-J. Otto, T. Eidam, and C. Jauregui, and Andreas Tünnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalization,” Light: Science & Applications 1, (2012).

H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” (Oxford University Press, London, 1948), 191.

Supplementary Material (2)

» Media 1: MOV (1314 KB)     
» Media 2: MOV (1446 KB)     

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Figures (7)

Fig. 1
Fig. 1

Single-frame excerpt from a high-speed video recording of mode instability occurring in a rod-type large pitch photonic crystal fiber (LPF) with a hole-to-hole distance of 30 µm (LPF30) (Media 1).

Fig. 2
Fig. 2

(a) Fourier spectra of the temporal power evolution within an artificial aperture at three different positions of the beam. The corresponding high-speed video shows mode instabilities in a LPF45 within a time period of 350 ms. The diameter of the apertures is 5% of the MFD corresponding to the incoherent superposition of all high-speed video frames. (b) Fourier spectra corresponding to three centered apertures with three different diameters: 5%, 15% and 40% relative to the MFD.

Fig. 3
Fig. 3

(a) Two examples of time traces measured by a photodiode following the method described in section 2 at two different power levels. The fiber used is a commercially available DC-285/100-PM-Yb-ROD. The lower power trace (red line) was measured at 80 W and corresponds to the upper limit of the stable operation regime; the high power trace (blue line) was measured at 160 W and corresponds to mode instabilities. Both traces have been normalized to have a mean-value of one. (b) Normalized RMS-deviation σnorm of the time-traces vs. output power. The measured data (blue dots) is fitted by an exponential function (red line) and its first derivative is calculated (black line). The power-value corresponding to a derivative of 0.1 ‰/W is defined as the mode-instability threshold.

Fig. 4
Fig. 4

(a) Evolution of the normalized standard deviation of the photodiode time-traces vs. output power for the DC-285/100-PM-Yb-ROD fiber. There are three distinguishable regions: stable (I), transition (II) and chaotic (III). (b) Characteristic Fourier spectra calculated from the time-traces recorded in the three different regions. The Fourier spectra have been normalized to the same maximum amplitude (the DC peak has the highest amplitude but is not shown).

Fig. 5
Fig. 5

(a) Spectrogram calculated from a time trace at 158 W of the DC-285/100-PM-Yb-ROD fiber. The frequency and time resolutions are 10 Hz and 10 ms, respectively. The output power corresponds to the transition region (region II) depicted in Fig. 4(a). There are five equally spaced discrete frequency peaks. The frequency separation between the peaks is ~210 Hz. For illustration purposes frequencies below 50 Hz are cut to allow for a proper scaling. (b) Spectrogram calculated from a time trace acquired at 342 W that corresponds to the chaotic region (region III). The energy is spread over a wide frequency range instead of being concentrated around discrete peaks.

Fig. 6
Fig. 6

: Single frame excerpts from a high-speed video recording of mode instabilities occurring in DC-170/40-PZ-YB-03 (170/40), LPF30, LPF45 and LPF60. (Media 2)

Fig. 7
Fig. 7

(a) Retrieved photodiode-like time traces from the high-speed videos of mode instabilities occurring in the 170/40, LPF30 and LPF45 fibers in the chaotic regime over a time period of 10 ms. The time traces are normalized to a mean value of one. (b) Corresponding Fourier spectra normalized to the same maximum amplitude.

Tables (1)

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Table 1 Active Fibers Under Test

Equations (2)

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d σ norm ( P out ) d P out | P th 0.1 W
ν lim  = 4κ/( CρMF D 2 )

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