Abstract

We present a dynamic model of thermal modal instability in large mode area fiber amplifiers. This model allows the pump and signal optical intensity distributions to apply a time-varying heat load distribution within the fiber. This influences the temperature distribution that modifies the optical distributions through the thermo-optic effect thus creating a feedback loop that gives rise to time-dependent modal instability. We describe different regimes of operation for a representative fiber design. We find qualitative agreement between simulation results and experimental results obtained with a different fiber including the time-dependent behavior of the instability and the effects of different cooling configurations on the threshold. We describe the physical processes responsible for the onset of the instability and suggest possible mitigation approaches.

© 2012 OSA

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  1. C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .
  2. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
    [CrossRef] [PubMed]
  3. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5742 .
    [CrossRef] [PubMed]
  4. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
    [CrossRef] [PubMed]
  5. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
    [CrossRef] [PubMed]
  6. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180 .
    [CrossRef] [PubMed]
  7. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
    [CrossRef] [PubMed]
  8. 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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-24-23965 .
    [CrossRef] [PubMed]
  9. A. A. Fotiadi, O. L. Antipov, and P. M’egret, “Resonantly induced refractive index changes in Yb-doped fibers: the origin, properties and application for all-fiber coherent beam combining,” in Frontiers in Guided Wave Optics and Optoelectronics, B. Pal, ed. (Intec, 2010), 209–234.
  10. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
    [CrossRef] [PubMed]
  11. C. Robin and I. Dajani, “Acoustically segmented photonic crystal fiber for single-frequency high-power laser applications,” Opt. Lett. 36(14), 2641–2643 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-14-2641 .
    [CrossRef] [PubMed]
  12. 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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
    [CrossRef] [PubMed]

2012

2011

C. Robin and I. Dajani, “Acoustically segmented photonic crystal fiber for single-frequency high-power laser applications,” Opt. Lett. 36(14), 2641–2643 (2011), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-14-2641 .
[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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-24-23965 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[CrossRef] [PubMed]

Alkeskjold, T. T.

Broeng, J.

Carstens, H.

Dajani, I.

Eberhardt, R.

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

Eidam, T.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

Gaida, C.

Hädrich, S.

Hansen, K. R.

Jansen, F.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[CrossRef] [PubMed]

Jauregui, C.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

Jørgensen, M. M.

Lægsgaard, J.

Laurila, M.

Liem, A.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
[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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[CrossRef] [PubMed]

Otto, H.-J.

Peschel, T.

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

Rekas, M.

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

Robin, C.

Rothhardt, J.

Schmidt, O.

Schreiber, T.

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

Smith, A. V.

Smith, J. J.

Stutzki, 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
[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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

Tsybin, I.

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[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), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-23-4572 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

Wirth, C.

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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[CrossRef] [PubMed]

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

Opt. Express

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5742 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-14-13218 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 .
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10180 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-440 .
[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), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-24-23965 .
[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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3997 .
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Opt. Lett.

Other

C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tünnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE7580, 75801H, 75801H-6 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13240 .

A. A. Fotiadi, O. L. Antipov, and P. M’egret, “Resonantly induced refractive index changes in Yb-doped fibers: the origin, properties and application for all-fiber coherent beam combining,” in Frontiers in Guided Wave Optics and Optoelectronics, B. Pal, ed. (Intec, 2010), 209–234.

Supplementary Material (6)

» Media 1: MOV (1834 KB)     
» Media 2: MOV (2585 KB)     
» Media 3: MOV (2942 KB)     
» Media 4: MOV (1922 KB)     
» Media 5: MOV (2746 KB)     
» Media 6: MOV (2889 KB)     

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Figures (11)

Fig. 1
Fig. 1

Photonic crystal fiber design (a), LP01 mode field profile (b) and LP11 field profile (c).

Fig. 2
Fig. 2

Propagation distance dependence of the powers of the LP01 and LP11 modes after a time of 60 ms (a, c, e) and the output power in each mode as a function of time (b, d, f) for pump powers of 380, 636, and 952 Watts for a convectively-cooled amplifier. The media show the evolution over time from 0 to 60 ms (a [Media 1], c [Media 2], e [Media3]).

Fig. 4
Fig. 4

Propagation distance dependence of the powers of the LP01 and LP11 modes after a time of 60 ms (a, c, e) and the output power in each mode as a function of time (b, d, f) for pump powers of 500, 1060, and 1750 Watts for a conductively-cooled amplifier. The media show the evolution over time from 0 to 60 ms (a [Media 4], c [Media 5], e [Media6]).

Fig. 3
Fig. 3

Temperature profiles at the end of the 60 ms simulation for the convectively-cooled amplifier with 952 Watts pump within planes passing through the center of the fiber core. Temperature is in °C with respect to the temperature of the cooling medium.

Fig. 5
Fig. 5

Logarithmic spectral intensity of the time variations in the simulated output power of the LP01 mode for pump powers of 500 Watts (a), 1060 Watts (b), and 1750 Watts (c) obtained via the Fourier transform of the time series shown in Fig. 4(b), 4(d), and 4(f).

Fig. 6
Fig. 6

Temperature profiles at the end of the 60 ms simulation for the conductively-cooled amplifier with 1750 Watts pump within planes passing through the center of the fiber core. Temperature is in °C with respect to the temperature of the heat sink.

Fig. 7
Fig. 7

Experimental setup of counter-pumped PCF amplifier. A three stage amplifier system was utilized to provide approximately 30 Watts of seed power. An image of the beam was captured using a commercial M2 beam analyzer. The phase modulator was not utilized in the single-frequency experiments.

Fig. 8
Fig. 8

Conductively cooled fiber amplifier setup. The seed laser is input from the left, where the fiber is held in a water-cooled chuck. The output end of the fiber departs the aluminum ring on the right and is held in a water-cooled chuck.

Fig. 9
Fig. 9

Beam quality as a function of output power for the PCF amplifier seeded with a single-frequency source which is (blue) conductively cooled and (red) convectively cooled (suspended in air).

Fig. 10
Fig. 10

Near field image of SAT PCF amplifier operating at 300 Watts output power (a). Near field image of SAT PCF amplifier operating at ~530 Watts showing evidence of multi-mode behavior (b).

Fig. 11
Fig. 11

Time series output (a) and frequency spectrum (b) of the fiber-coupled fast photodetector measuring the output of the PCF amplifier showing periodic oscillatory behavior. The output power was 500 Watts.

Equations (17)

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i ψ z = 1 2k [ t 2 k 2 +n ( x,y ) 2 k 0 2 ]ψ
[ t 2 β 0 2 +n ( x,y ) 2 k 0 2 ] ϕ 0 ( x,y )=0
Ω | ϕ 0 | 2 dxdy ϕ 0 | ϕ 0 =1
1 2 β 0 [ t 2 β 0 2 +n ( x,y ) 2 k 0 2 ] ϕ 1 ( x,y )=Δβ ϕ 1 .
ψ( x,y,z )= c 1 ϕ 1 (x,y)exp[ iΔβz ]
ψ( x,y,z )= c 0 (z) ϕ 0 (x,y)+ c 1 (z) ϕ 1 (x,y)exp[ iΔβz ]
i ψ z [ n 0 ( x,y,z )T(x,y,z) k 0 2 β 0 dn dT +i g(x,y,z) 2 ]ψ c 1 Δβ ϕ 1 exp( iΔβz )
i c 0 z ϕ 0 +i c 1 z ϕ 1 exp[ iΔβz ][ k 0 T dn dT +i g 2 ][ c 0 ϕ 0 + c 1 ϕ 1 exp( iΔβz ) ]
i c 0 z = ϕ 0 |δH| ϕ 0 c 0 + ϕ 0 |δH| ϕ 1 exp( iΔβz ) c 1
i c 1 z = ϕ 1 |δH| ϕ 1 c 1 + ϕ 1 |δH| ϕ 0 exp( iΔβz ) c 0
δH k 0 T(x,y,z) dn dT +i g(x,y,z) 2
c i (z)= c ˜ i (z)exp[ i 0 z κ( z )d z ]
i c ˜ 0 z =[ ϕ 0 |δH| ϕ 0 κ(z) ] c ˜ 0 + ϕ 0 |δH| ϕ 1 exp( iΔβz ) c ˜ 1
i c ˜ 1 z =[ ϕ 1 |δH| ϕ 1 κ(z) ] c ˜ 1 + ϕ 1 |δH| ϕ 0 exp( iΔβz ) c ˜ 0
T t = K Cρ 2 T+ Q Cρ
g= N 2 σ es N 1 σ as
Q= N 2 σ es ( ν p ν s 1 ) I s .

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