Abstract

A phase shift between the modal interference pattern and the thermally-induced refractive index grating is most likely the ultimate trigger for the damaging effect of transverse mode instabilities (TMI) in high-power fiber laser systems. By using comprehensive simulations, the creation and evolution of a thermally-induced phase shift is explained and illustrated in detail. It is shown that such a phase shift can be induced by a variation of the pump power. The gained knowledge about the generation and evolution of the phase shift will allow for the development of new mitigation strategies for TMI.

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

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  1. C. Jauregui, J. Limpert, and A. Tünnermann, “High-power fibre lasers,” Nat. Photonics 7(11), 861–867 (2013).
    [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. 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]
  4. 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]
  5. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011).
    [Crossref] [PubMed]
  6. 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]
  7. 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]
  8. K. R. Hansen and J. Lægsgaard, “Impact of gain saturation on the mode instability threshold in high-power fiber amplifiers,” Opt. Express 22(9), 11267–11278 (2014).
    [Crossref] [PubMed]
  9. A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express 20(22), 24545–24558 (2012).
    [Crossref] [PubMed]
  10. 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]
  11. B. G. Ward, “Modeling of transient modal instability in fiber amplifiers,” Opt. Express 21(10), 12053–12067 (2013).
    [Crossref] [PubMed]
  12. 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]
  13. L. Dong, “Stimulated thermal Rayleigh scattering in optical fibers,” Opt. Express 21(3), 2642–2656 (2013).
    [Crossref] [PubMed]
  14. 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]
  15. C. Jauregui, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691–10704 (2018).
    [Crossref] [PubMed]
  16. C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Modal energy transfer by thermally-induced refractive index gratings in Yb-doped fibers,” Light Sci. Appl.submitted.
  17. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
    [Crossref]
  18. C. Jauregui, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE 10512, 1051207 (2018).

2018 (2)

C. Jauregui, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE 10512, 1051207 (2018).

C. Jauregui, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691–10704 (2018).
[Crossref] [PubMed]

2014 (1)

2013 (5)

2012 (3)

2011 (3)

2010 (2)

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

Andermahr, N.

Andersen, T. V.

Dajani, I.

Dong, L.

Eidam, T.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

Fallnich, C.

Gabler, T.

Hanf, S.

Hansen, K. R.

Jansen, F.

Jauregui, C.

Lægsgaard, J.

Limpert, J.

C. Jauregui, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE 10512, 1051207 (2018).

C. Jauregui, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691–10704 (2018).
[Crossref] [PubMed]

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

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]

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]

C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Modal energy transfer by thermally-induced refractive index gratings in Yb-doped fibers,” Light Sci. Appl.submitted.

Madden, T.

Naderi, S.

Otto, H. J.

Otto, H.-J.

Robin, C.

Schmidt, O.

Schreiber, T.

Seise, E.

Smith, A. V.

Smith, J. J.

Stihler, C.

C. Jauregui, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691–10704 (2018).
[Crossref] [PubMed]

C. Jauregui, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE 10512, 1051207 (2018).

C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Modal energy transfer by thermally-induced refractive index gratings in Yb-doped fibers,” Light Sci. Appl.submitted.

Stutzki, F.

Tünnermann, A.

C. Jauregui, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691–10704 (2018).
[Crossref] [PubMed]

C. Jauregui, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE 10512, 1051207 (2018).

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

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]

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]

C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Modal energy transfer by thermally-induced refractive index gratings in Yb-doped fibers,” Light Sci. Appl.submitted.

Ward, B.

Ward, B. G.

Wirth, C.

J. Lightwave Technol. (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[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 (13)

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]

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]

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]

K. R. Hansen and J. Lægsgaard, “Impact of gain saturation on the mode instability threshold in high-power fiber amplifiers,” Opt. Express 22(9), 11267–11278 (2014).
[Crossref] [PubMed]

A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express 20(22), 24545–24558 (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]

B. G. Ward, “Modeling of transient modal instability in fiber amplifiers,” Opt. Express 21(10), 12053–12067 (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]

L. Dong, “Stimulated thermal Rayleigh scattering in optical fibers,” Opt. Express 21(3), 2642–2656 (2013).
[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, C. Stihler, A. Tünnermann, and J. Limpert, “Pump-modulation-induced beam stabilization in high-power fiber laser systems above the mode instability threshold,” Opt. Express 26(8), 10691–10704 (2018).
[Crossref] [PubMed]

Opt. Lett. (1)

Proc. SPIE (1)

C. Jauregui, C. Stihler, J. Limpert, and A. Tünnermann, “Transverse mode instabilities in burst operation of high-power fiber laser systems,” Proc. SPIE 10512, 1051207 (2018).

Other (1)

C. Stihler, C. Jauregui, A. Tünnermann, and J. Limpert, “Modal energy transfer by thermally-induced refractive index gratings in Yb-doped fibers,” Light Sci. Appl.submitted.

Supplementary Material (1)

NameDescription
» Visualization 1       Temporal evolution of a phase-shift between the modal interference pattern (MIP, top graph) and the thermally-induced refractive index grating (RIG, bottom graph) caused by a pump power jump from 100 W to 200 W. The white line indicates the position

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Figures (7)

Fig. 1
Fig. 1 Energy transfer induced by a pump power modulation - comparison between experiment and simulations (average signal power 150 W, modulation frequency 50 Hz, modulation depth ± 50 W). a) Experiment: temporal evolution of the normalized signal output power. b) Experiment: temporal evolution of the relative modal content (FM - blue, HOMs - red). c) Simulations: temporal evolution of the normalized signal output power. d) Simulations: temporal evolution of the relative modal content (FM - blue, HOMs - red).
Fig. 2
Fig. 2 Phase-shift evolution caused by a pump power jump from 100 W to 200 W. The last 50 mm of the fiber are depicted. a) Modal interference pattern right before the pump power jump (t = 0 µs) with the white line indicating the position of the intensity maximum of the MIP that will be tracked. b) Refractive index grating right before the pump power jump (t = 0 µs) with the black line indicating the position of the maximum of the RIG that is aligned with the tracked MIP maximum. c) MIP after the pump power jump (t = 250 µs) with the white line indicating the new position of the tracked MIP maximum. d) RIG after the pump power jump (t = 250 µs) with the black line indicating the new position of the tracked RIG maximum.
Fig. 3
Fig. 3 Temporal evolution of the local beat length of a modal-interference-pattern period at the end of the fiber (at the position of the marked MIP maximum) after a pump power jump from 100 W to 200 W.
Fig. 4
Fig. 4 Phase-shift evolution between the modal interference pattern and the refractive index grating at the end of the fiber after a pump power jump from 100 W to 200 W. a) Temporal evolution of the shifts in position of the marked MIP maximum (blue) and of the corresponding RIG maximum (red). b) Temporal evolution of the phase shift, e.g. the relative difference in position normalized to the local beat length, between these two maxima.
Fig. 5
Fig. 5 Accumulation of the shift in position of the modal-interference-pattern maxima along the fiber (blue dots), 250 µs after the pump power jump from 100 W to 200 W. Low numbers correspond to MIP maxima at the seed side of the fiber and high numbers to the ones at the pump side of the fiber. The corresponding phase shift (normalized to the local beat length) is illustrated by the red dots.
Fig. 6
Fig. 6 Temporal evolution of the refractive index grating at the initial position of the marked RIG maximum (see black dot in Fig. 2(b)).
Fig. 7
Fig. 7 Phase-shift evolution between the modal interference pattern and the refractive index grating at the end of the fiber after a slow pump power increase from 100 W to 200 W (within 10 s). a) Temporal evolution of the shifts in position of the marked MIP maximum (blue) and of the corresponding RIG maximum (dashed red). b) Temporal evolution of the phase shift (relative difference in position) between these two maxima.

Equations (1)

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L b ( z )= λ ( n eff,  FM ( z ) n eff, HOM (z) )

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