Abstract

We present a semi-analytic numerical model to estimate the transverse modal instability (TMI) threshold for photonic crystal rod amplifiers. The model includes thermally induced waveguide perturbations in the fiber cross section modeled with finite element simulations, and the relative intensity noise (RIN) of the seed laser, which seeds mode coupling between the fundamental and higher order mode. The TMI threshold is predicted to ~370 W – 440 W depending on RIN for the distributed modal filtering rod fiber.

© 2013 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 [Invited],” J. Opt. Soc. Am. B27(11), B63–B92 (2010).
    [CrossRef]
  2. T. T. Alkeskjold, M. Laurila, L. Scolari, and J. Broeng, “Single-mode ytterbium-doped large-mode-area photonic bandgap rod fiber amplifier,” Opt. Express19(8), 7398–7409 (2011).
    [CrossRef] [PubMed]
  3. F. Jansen, F. Stutzki, H.-J. Otto, M. Baumgartl, C. Jauregui, J. Limpert, and A. Tünnermann, “The influence of index-depressions in core-pumped Yb-doped large pitch fibers,” Opt. Express18(26), 26834–26842 (2010).
    [CrossRef] [PubMed]
  4. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express19(11), 10180–10192 (2011).
    [CrossRef] [PubMed]
  5. 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. Express19(14), 13218–13224 (2011).
    [CrossRef] [PubMed]
  6. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express20(10), 11407–11422 (2012).
    [CrossRef] [PubMed]
  7. C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express19(4), 3258–3271 (2011).
    [CrossRef] [PubMed]
  8. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermally induced mode coupling in rare-earth doped fiber amplifiers,” Opt. Lett.37(12), 2382–2384 (2012).
    [CrossRef] [PubMed]
  9. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 1944–1971 (2013).
    [CrossRef] [PubMed]
  10. E. Coscelli, F. Poli, T. T. Alkeskjold, M. M. Jørgensen, L. Leick, J. Broeng, A. Cucinotta, and S. Selleri, “Thermal Effects on the Single-Mode Regime of Distributed Modal Filtering Rod Fiber,” J. Lightwave Technol.30(22), 3494–3499 (2012).
    [CrossRef]
  11. D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” J. Quant. Electron.37(2), 207–217 (2001).
    [CrossRef]
  12. M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
    [CrossRef]
  13. J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express11(22), 2982–2990 (2003).
    [CrossRef] [PubMed]
  14. Comsol, “Products,” < http://www.comsol.com/products/multiphysics/ > (2 January 2013).
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    [CrossRef] [PubMed]
  16. 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. Express20(5), 5742–5753 (2012).
    [CrossRef] [PubMed]
  17. 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]
  18. 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. Express20(14), 15710–15722 (2012).
    [CrossRef] [PubMed]
  19. A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express20(22), 24545–24558 (2012).
    [CrossRef] [PubMed]

2013 (1)

2012 (7)

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. Express20(5), 5742–5753 (2012).
[CrossRef] [PubMed]

M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express20(7), 7263–7273 (2012).
[CrossRef] [PubMed]

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express20(10), 11407–11422 (2012).
[CrossRef] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Thermally induced mode coupling in rare-earth doped fiber amplifiers,” Opt. Lett.37(12), 2382–2384 (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. Express20(14), 15710–15722 (2012).
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express20(22), 24545–24558 (2012).
[CrossRef] [PubMed]

E. Coscelli, F. Poli, T. T. Alkeskjold, M. M. Jørgensen, L. Leick, J. Broeng, A. Cucinotta, and S. Selleri, “Thermal Effects on the Single-Mode Regime of Distributed Modal Filtering Rod Fiber,” J. Lightwave Technol.30(22), 3494–3499 (2012).
[CrossRef]

2011 (5)

2010 (2)

2009 (1)

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

2003 (1)

2001 (1)

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” J. Quant. Electron.37(2), 207–217 (2001).
[CrossRef]

Alkeskjold, T. T.

Baumgartl, M.

Broeng, J.

Brown, D. C.

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” J. Quant. Electron.37(2), 207–217 (2001).
[CrossRef]

Cain-Skaff, M.

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

Chatigny, S.

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

Clarkson, W. A.

Coscelli, E.

Cucinotta, A.

Dajani, I.

Eidam, T.

Gaida, C.

Guyenot, V.

Hansen, K. R.

Hoffman, H. J.

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” J. Quant. Electron.37(2), 207–217 (2001).
[CrossRef]

Jansen, F.

Jauregui, C.

Jørgensen, M. M.

Lægsgaard, J.

Lapointe, M.-A.

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

Laurila, M.

Leick, L.

Liem, A.

Limpert, J.

Maran, J.-N.

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

Nilsson, J.

Nolte, S.

Otto, H.-J.

Peschel, T.

Petersen, S. R.

Piché, M.

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

Poli, F.

Richardson, D. J.

Robin, C.

Schmidt, O.

Schreiber, T.

Scolari, L.

Selleri, S.

Smith, A. V.

Smith, J. J.

Stutzki, F.

Tünnermann, A.

Ward, B.

Wirth, C.

Zellmer, H.

J. Lightwave Technol. (1)

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

J. Quant. Electron. (1)

D. C. Brown and H. J. Hoffman, “Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers,” J. Quant. Electron.37(2), 207–217 (2001).
[CrossRef]

Opt. Express (12)

J. Limpert, T. Schreiber, A. Liem, S. Nolte, H. Zellmer, T. Peschel, V. Guyenot, and A. Tünnermann, “Thermo-optical properties of air-clad photonic crystal fiber lasers in high power operation,” Opt. Express11(22), 2982–2990 (2003).
[CrossRef] [PubMed]

M. M. Jørgensen, S. R. Petersen, M. Laurila, J. Lægsgaard, and T. T. Alkeskjold, “Optimizing single mode robustness of the distributed modal filtering rod fiber amplifier,” Opt. Express20(7), 7263–7273 (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. Express20(5), 5742–5753 (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. Express20(14), 15710–15722 (2012).
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express20(22), 24545–24558 (2012).
[CrossRef] [PubMed]

T. T. Alkeskjold, M. Laurila, L. Scolari, and J. Broeng, “Single-mode ytterbium-doped large-mode-area photonic bandgap rod fiber amplifier,” Opt. Express19(8), 7398–7409 (2011).
[CrossRef] [PubMed]

F. Jansen, F. Stutzki, H.-J. Otto, M. Baumgartl, C. Jauregui, J. Limpert, and A. Tünnermann, “The influence of index-depressions in core-pumped Yb-doped large pitch fibers,” Opt. Express18(26), 26834–26842 (2010).
[CrossRef] [PubMed]

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express19(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. Express19(14), 13218–13224 (2011).
[CrossRef] [PubMed]

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express20(10), 11407–11422 (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. Express19(4), 3258–3271 (2011).
[CrossRef] [PubMed]

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21(2), 1944–1971 (2013).
[CrossRef] [PubMed]

Opt. Lett. (2)

Proc. SPIE (1)

M.-A. Lapointe, S. Chatigny, M. Piché, M. Cain-Skaff, and J.-N. Maran, “Thermal effects in high power cw fiber lasers,” Proc. SPIE7195, 71951U, 71951U-11 (2009).
[CrossRef]

Other (1)

Comsol, “Products,” < http://www.comsol.com/products/multiphysics/ > (2 January 2013).

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Figures (6)

Fig. 1
Fig. 1

The rod fiber cross section (right) is approximated by four concentric circles representing core, inner cladding, air cladding, and outer fiber (left). The heat load Q0 is assumed uniform across the core.

Fig. 2
Fig. 2

Core overlap as a function of wavelength calculated for a cold DMF rod fiber and at a heat load corresponding to 125 W of extracted output power. The SM region is shaded and the signal wavelength at 1040 nm is marked by the red line. The increased heat load slightly blueshifts the curves indicated with the arrows.

Fig. 3
Fig. 3

Core overlap as a function of thermal load at signal wavelength of 1040 nm showing decreasing differential mode overlap with increasing thermal load. (a) Comparing DMF85 rod fiber with a 19 cell core PCF having the same structure as the DMF85 rod fiber without the resonators. (b) Comparing DMF85 rod fiber with a single mode SIF having V = 2.40.

Fig. 4
Fig. 4

Mode field diameter as a function of thermal load.

Fig. 5
Fig. 5

Calculated mode distributions of the FM (top) and first HOM (bottom) for the DMF85 rod fiber for selected signal powers. Larger thermal load causes larger core confinement.

Fig. 6
Fig. 6

Calculated TMI threshold as a function of thermal load using two values of RIN −120 dBc/Hz (solid) and −100 dBc/Hz (dashed) representing a seed laser with low and high RIN. The crossing of signal power vs. thermal load indicates the estimated TMI threshold for the DMF85 rod fiber.

Tables (1)

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Table 1 Parameters Used in This Work

Equations (10)

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1 r r ( r T(r) r )= q k i ,
Q 0 = 1 10 αdL / 10 dL ( 1 λ p λ s ) P pump 1 10 αdL / 10 dL ( 1 λ p λ s ) P signal S ,
T(r)= T core + Q 0 4 A core k i ( r core 2 r 2 ),
T(r)= T i + Q 0 2π k i ln( r i r )
T fiberedge = T 0 + Q 0 2π r fiber h
Δε=η( T(r) T 0 )
χ(Ω)= η ω 2 k fiber β c 2 Im[ A(Ω) ]( 1 λ s λ p )
A(Ω)= ψ FM ( r ) ψ HOM ( r ) core G( r , r ,Ω) ψ FM ( r ) ψ HOM ( r ) d 2 r d 2 r
G( r r ,Ω)= 1 2π K 0 [ iρC k Ω ( r r ) ],
ξ out = ξ in ( P seed P signal ) 1 Γ HOM Γ FM ( 1+ 1 4 R N 2π Γ FM | χ ( Ω p ) | P signal exp[ χ( Ω p ) Γ FM ( P signal P seed ) ] )

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