Abstract

Using numerical simulations of thermally induced mode coupling we show how the instability threshold can be substantially reduced if the pump or injected signal is modulated in the kHz range. We also show how the mode coupling gain varies with the frequency offset of the parasitic mode. We model thresholds when the source of detuned light is quantum background, amplitude modulation of the pump power, and amplitude modulation of the signal seed. We suggest several key experimental and modeling tests of our model.

© 2012 OSA

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  1. 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, 13218–13224 (2011).
    [CrossRef] [PubMed]
  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, 94–96 (2010).
    [CrossRef] [PubMed]
  3. C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “Impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19, 3258–3271 (2011).
    [CrossRef] [PubMed]
  4. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20, 11407–11422 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. 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, 4572–4574 (2011).
    [CrossRef] [PubMed]
  20. N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tüunnermann, “Build up and decay of mode instability in a high power fiber amplifier,” Opt. Express 20, 13274–13283 (2012).
    [CrossRef] [PubMed]
  21. 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, 15710–15722 (2012).
    [CrossRef] [PubMed]
  22. M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

2012 (7)

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20, 11407–11422 (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, 440–451 (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, 12912–12925 (2012).
[CrossRef] [PubMed]

O. Okusaga, J. Cahill, A. Docherty, W. Zhou, and C. R. Menyuk, “Guided entropy mode Rayleigh scattering in optical fibers,” Opt. Lett. 37, 683–685 (2012).
[CrossRef] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Laegsgaard, “Thermally induced mode coupling in rare-earth doped fiber amplifiers,” Opt. Lett. 37, 2382–2384 (2012).
[CrossRef] [PubMed]

N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tüunnermann, “Build up and decay of mode instability in a high power fiber amplifier,” Opt. Express 20, 13274–13283 (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, 15710–15722 (2012).
[CrossRef] [PubMed]

2011 (6)

2010 (1)

2007 (1)

T. C. Newell, P. Peterson, A. Gavrielides, and M. P. Sharma, “Temperature effects on the emission properties of Yb-doped optical fibers,” Opt. Commun. 273, 256–259 (2007).
[CrossRef]

1996 (1)

P. C. Wait and T. P. Newson, “Landau-Placzek ratio applied to distributed fiber sensing,” Opt. Commun. 122, 141–146 (1996).
[CrossRef]

1995 (1)

1980 (1)

Alkeskjold, T. T.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Laegsgaard, “Thermally induced mode coupling in rare-earth doped fiber amplifiers,” Opt. Lett. 37, 2382–2384 (2012).
[CrossRef] [PubMed]

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

Andersen, T. V.

Barnett, T.

S. W. Moore, T. Barnett, T. A. Reichardt, and R. L. Farrow, “Optical properties of Yb3+-doped fibers and fiber lasers at high temperature,” Opt. Commun. 284, 5774–5780 (2011).
[CrossRef]

Bowers, M. S.

Boyd, R.W.

R.W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003).

Broeng, J.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Laegsgaard, “Thermally induced mode coupling in rare-earth doped fiber amplifiers,” Opt. Lett. 37, 2382–2384 (2012).
[CrossRef] [PubMed]

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

Cahill, J.

Dajani, I.

de Vries, O.

Docherty, A.

Eberhardt, R.

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, 15710–15722 (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, 440–451 (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, 12912–12925 (2012).
[CrossRef] [PubMed]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “Impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19, 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, 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, 689–691 (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, 94–96 (2010).
[CrossRef] [PubMed]

Farrow, R. L.

S. W. Moore, T. Barnett, T. A. Reichardt, and R. L. Farrow, “Optical properties of Yb3+-doped fibers and fiber lasers at high temperature,” Opt. Commun. 284, 5774–5780 (2011).
[CrossRef]

Feit, M. D.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1992).

Fleck, J. A.

Gabler, T.

Gaida, C.

Gavrielides, A.

T. C. Newell, P. Peterson, A. Gavrielides, and M. P. Sharma, “Temperature effects on the emission properties of Yb-doped optical fibers,” Opt. Commun. 273, 256–259 (2007).
[CrossRef]

Haarlammert, N.

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, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Express 20, 12912–12925 (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, 440–451 (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, 15710–15722 (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, 4572–4574 (2011).
[CrossRef] [PubMed]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “Impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19, 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, 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, 689–691 (2011).
[CrossRef] [PubMed]

Jørgensen, M. M.

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

Kliner, A.

Laegsgaard, J.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Laegsgaard, “Thermally induced mode coupling in rare-earth doped fiber amplifiers,” Opt. Lett. 37, 2382–2384 (2012).
[CrossRef] [PubMed]

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

Laurila, M.

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

Liem, A.

Limpert, J.

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, 15710–15722 (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, 12912–12925 (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, 440–451 (2012).
[CrossRef] [PubMed]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “Impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19, 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, 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, 689–691 (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, 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, 94–96 (2010).
[CrossRef] [PubMed]

Menyuk, C. R.

Moore, S. W.

S. W. Moore, T. Barnett, T. A. Reichardt, and R. L. Farrow, “Optical properties of Yb3+-doped fibers and fiber lasers at high temperature,” Opt. Commun. 284, 5774–5780 (2011).
[CrossRef]

Newell, T. C.

T. C. Newell, P. Peterson, A. Gavrielides, and M. P. Sharma, “Temperature effects on the emission properties of Yb-doped optical fibers,” Opt. Commun. 273, 256–259 (2007).
[CrossRef]

Newson, T. P.

P. C. Wait and T. P. Newson, “Landau-Placzek ratio applied to distributed fiber sensing,” Opt. Commun. 122, 141–146 (1996).
[CrossRef]

Okusaga, O.

Otto, H.-J.

Peschel, T.

Petersen, S. R.

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

Peterson, P.

T. C. Newell, P. Peterson, A. Gavrielides, and M. P. Sharma, “Temperature effects on the emission properties of Yb-doped optical fibers,” Opt. Commun. 273, 256–259 (2007).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1992).

Reichardt, T. A.

S. W. Moore, T. Barnett, T. A. Reichardt, and R. L. Farrow, “Optical properties of Yb3+-doped fibers and fiber lasers at high temperature,” Opt. Commun. 284, 5774–5780 (2011).
[CrossRef]

Robin, C.

Schmidt, O.

Schreiber, T.

Seise, E.

Sharma, M. P.

T. C. Newell, P. Peterson, A. Gavrielides, and M. P. Sharma, “Temperature effects on the emission properties of Yb-doped optical fibers,” Opt. Commun. 273, 256–259 (2007).
[CrossRef]

Smith, A. V.

Smith, J. J.

Steinmetz, A.

Stutzki, F.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1992).

Tünnermann, A.

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, 12912–12925 (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, 440–451 (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, 15710–15722 (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, 4572–4574 (2011).
[CrossRef] [PubMed]

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “Impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19, 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, 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, 689–691 (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, 94–96 (2010).
[CrossRef] [PubMed]

Tüunnermann, A.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1992).

Wait, P. C.

P. C. Wait and T. P. Newson, “Landau-Placzek ratio applied to distributed fiber sensing,” Opt. Commun. 122, 141–146 (1996).
[CrossRef]

Ward, B.

Wirth, C.

Zhou, W.

Appl. Opt. (1)

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

Opt. Commun. (3)

S. W. Moore, T. Barnett, T. A. Reichardt, and R. L. Farrow, “Optical properties of Yb3+-doped fibers and fiber lasers at high temperature,” Opt. Commun. 284, 5774–5780 (2011).
[CrossRef]

T. C. Newell, P. Peterson, A. Gavrielides, and M. P. Sharma, “Temperature effects on the emission properties of Yb-doped optical fibers,” Opt. Commun. 273, 256–259 (2007).
[CrossRef]

P. C. Wait and T. P. Newson, “Landau-Placzek ratio applied to distributed fiber sensing,” Opt. Commun. 122, 141–146 (1996).
[CrossRef]

Opt. Express (8)

N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tüunnermann, “Build up and decay of mode instability in a high power fiber amplifier,” Opt. Express 20, 13274–13283 (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, 15710–15722 (2012).
[CrossRef] [PubMed]

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

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20, 11407–11422 (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, 440–451 (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, 12912–12925 (2012).
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19, 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, 13218–13224 (2011).
[CrossRef] [PubMed]

Opt. Lett. (5)

Other (4)

M. Laurila, T. T. Alkeskjold, M. M. Jørgensen, S. R. Petersen, J. Broeng, and J. Laegsgaard, “Highly efficient high power single-mode fiber amplifier utilizing the distributed mode filtering bandgap rod fiber,” in Fiber Lasers IX: Technology, Systems, and Applications, E.C. Honea and S.T. Hendow eds., Proc. SPIE 8237, 8237–8265 (2012).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge Univ. Press, 1992).

K. D. Cole, “Steady-periodic Green’s functions and thermal-measurement applications in rectangular coordinates,” Mech. Eng. Faculty Pubs., Univ. Nebraska, Lincoln, Paper 49, http://digitalcommons.unl.edu/mechengfacpub/49 .

R.W. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, 2003).

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Figures (4)

Fig. 1
Fig. 1

Total modal gains (laser gain plus mode coupling gain) computed for LP′11 and LP′02 for the amplifier design studied in [7]. The detuning Δν is the frequency shift of the mode of interest relative to the strong driving mode LP01.

Fig. 2
Fig. 2

Results for quantum noise seeding. Power in the pump, and two signal modes for Δν = −525 Hz. The brackets around Power indicate powers are time averaged over a beat cycle.

Fig. 3
Fig. 3

Results for 300 ppm pump modulation at 525 Hz. The pump power in is 288 W; the signal output power is 302 W in all modes with 12 W in LP′11.

Fig. 4
Fig. 4

Results for 30 ppm signal modulation. Power in the pump, and three signal modes for Δν = −525 Hz. The pump power is 257 W in and 1.4 W out; the total output signal power is 275 W with 5.1 W in LP′11.

Tables (1)

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Table 1 Parameters of test amplifier.

Equations (19)

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n u = σ p a I p / h ν p + σ s a I s / h ν s ( σ p a + σ p e ) I p / h ν p + ( σ s a + σ s e ) I s / h ν s + 1 / τ
Q = [ σ p a ( σ p a + σ p e ) n u ] N Y b I p [ 1 ν s ν p ] .
ρ C d T d t = Q + K ( 2 T x 2 + 2 T y 2 )
T x , y t + Δ t / 2 T x , y t = ( T x + Δ x , y t + Δ t / 2 2 T x , y t + Δ t / 2 + T x Δ x , y t + Δ t / 2 ) λ x 2 + ( T x , y + Δ y t 2 T x , y t + T x , y Δ y t ) λ y 2
+ Δ t 2 ρ C Q t + Δ t / 4
T t + Δ t / 2 A x + B y T t + Δ t 2 ρ C Q t + Δ t / 4
T t + Δ t / 2 = B y T t A x 1 + Δ t 2 ρ C Q t + Δ t / 4 A x 1
λ x = K Δ t ρ C Δ x 2
λ y = K Δ t ρ C Δ y 2 .
T x , y t + Δ t T x , y t + Δ t / 2 = ( T x + Δ x , y t + Δ t / 2 2 T x , y t + Δ t / 2 + T x Δ x , y t + Δ t / 2 ) λ x 2 + ( T x , y + Δ y t + Δ t 2 T x , y t + Δ t + T x , y Δ y t + Δ t ) λ y 2
+ Δ t 2 ρ C Q t + 3 Δ t / 4
A y T t + Δ t = T t + Δ t / 2 B x + Δ t 2 ρ C Q t + 3 Δ t / 4
T t + Δ t = A y 1 T t + Δ t / 2 B x + Δ t 2 ρ C A y 1 Q t + 3 Δ t / 4
T t + Δ t = A y 1 B y T t A x 1 B x + Δ t 2 ρ C A y 1 ( Q t + Δ t / 4 A x 1 B x + Q t + 3 Δ t / 4 ) .
G ( x , y , ω | x , y ) = n = 0 F n ( y , y ) P n ( x , x , ω )
F n ( y , y ) = 1 W K sin ( n π W y ) sin ( n π W y )
P n ( x , x , ω ) = { exp [ σ n ( 2 L | x x | ) ] exp [ σ n ( 2 L x x ) ] + exp [ σ n | x x | ] exp [ σ n ( x + x ) } / σ n ( 1 exp [ 2 σ n L ] ) ,
σ n 2 = ( n π W ) 2 + i ω ρ C K .
T ( x , y , t ) = Real [ m = 0 max x , y q ( x , y , ω m ) G ( x , y , ω m | x , y ) exp ( i ω m t ) ]

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