Abstract

We show by numerical modeling that saturation of the population inversion reduces the stimulated thermal Rayleigh gain relative to the laser gain in large mode area fiber amplifiers. We show how to exploit this effect to raise mode instability thresholds by a substantial factor. We also demonstrate that when suppression of stimulated Brillouin scattering and the population saturation effect are both taken into account, counter-pumped amplifiers have higher mode instability thresholds than co-pumped amplifiers for fully Yb3+ doped cores, and confined doping can further raise the thresholds.

© 2013 OSA

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References

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  1. A.V. Smith and J.J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express19, 10180–10192 (2011).
    [CrossRef] [PubMed]
  2. A.V. Smith and J.J. Smith, “A steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express21, 2606–2623 (2013).
    [CrossRef] [PubMed]
  3. A.V. Smith and J.J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express20, 24545–24558 (2012).
    [CrossRef] [PubMed]
  4. A.V. Smith and J.J. Smith, “Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering,” arXiv:1301.4277 [physics.optics](January18, 2013).
  5. A.V. Smith and J.J. Smith, “Maximizing the mode instability threshold of a fiber amplifier,” arXiv:1301.3489 [physics.optics](January16, 2013).
  6. 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]
  7. K.R. Hansen, T.T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express21, 1944–1971 (2013).
    [CrossRef] [PubMed]
  8. L. Dong, “Stimulated thermal rayleigh scattering in optical fibers,” Opt. Express21, 2642–2656 (2013).
    [CrossRef] [PubMed]
  9. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express20, 11407–11422 (2012).
    [CrossRef] [PubMed]
  10. 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. Express20, 440–451 (2012).
    [CrossRef] [PubMed]
  11. G.P. Agrawal, Nonlinear Fiber Optics(Academic, 1995).
  12. M. Hildebrandt, S. Büsche, P. Wessels, M. Frede, and D. Kracht, “Brillouin scattering spectra in high-power single-frequency ytterbium doped fiber amplifiers,” Opt. Express16, 15970–15979 (2008).
    [CrossRef] [PubMed]
  13. T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fiber,” IEEE Phot. Tech. Lett.1, 107–108 (1989).
    [CrossRef]
  14. J.E. Rothenberg, “Suppression of stimulated Brillouin scattering in single-frequency multi-kilowatt fiber amplifiers,” Proc. SPIE6873,68730O (2008).
    [CrossRef]
  15. M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J.A. Demeritt, A.B. Ruffin, A.M. Crowley, D.T. Walton, and L.A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express15, 8290–8299 (2007).
    [CrossRef] [PubMed]
  16. C. Robin and I. Dajani, “Acoustically segmented photonic crystal fiber for single-frequency high-power laser applications,” Opt. Lett.36, 2641–2643 (2011).
    [CrossRef] [PubMed]
  17. A.V. Smith and J.J. Smith, “Spontaneous Rayleigh seeding of stimulated Rayleigh scattering in high power fiber amplifiers,” Opt. Express. (submitted).
  18. M.J. Söderlund, J.J. Montiel i Ponsoda, S.K.T. Tammela, K. Ylä-Jarkko, A. Salokatve, and S. Honkanen, “Mode-induced transverse photodarkening loss variations in large-mode-area ytterbium doped silica fibers,” Opt. Express16, 10633–10640 (2008).
    [CrossRef] [PubMed]

2013 (5)

A.V. Smith and J.J. Smith, “Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering,” arXiv:1301.4277 [physics.optics](January18, 2013).

A.V. Smith and J.J. Smith, “Maximizing the mode instability threshold of a fiber amplifier,” arXiv:1301.3489 [physics.optics](January16, 2013).

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

A.V. Smith and J.J. Smith, “A steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express21, 2606–2623 (2013).
[CrossRef] [PubMed]

L. Dong, “Stimulated thermal rayleigh scattering in optical fibers,” Opt. Express21, 2642–2656 (2013).
[CrossRef] [PubMed]

2012 (4)

2011 (2)

2008 (3)

2007 (1)

1989 (1)

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fiber,” IEEE Phot. Tech. Lett.1, 107–108 (1989).
[CrossRef]

Agrawal, G.P.

G.P. Agrawal, Nonlinear Fiber Optics(Academic, 1995).

Alkeskjold, T.T.

Broeng, J.

Büsche, S.

Chen, X.

Crowley, A.M.

Dajani, I.

Demeritt, J.A.

Dong, L.

Eidam, T.

Frede, M.

Gray, S.

Hansen, K.R.

Hildebrandt, M.

Honkanen, S.

Horiguchi, T.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fiber,” IEEE Phot. Tech. Lett.1, 107–108 (1989).
[CrossRef]

Jansen, F.

Jauregui, C.

Kracht, D.

Kurashima, T.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fiber,” IEEE Phot. Tech. Lett.1, 107–108 (1989).
[CrossRef]

Lægsgaard, J.

Laegsgaard, J.

Li, M.-J.

Limpert, J.

Liu, A.

Montiel i Ponsoda, J.J.

Otto, H.-J.

Robin, C.

Rothenberg, J.E.

J.E. Rothenberg, “Suppression of stimulated Brillouin scattering in single-frequency multi-kilowatt fiber amplifiers,” Proc. SPIE6873,68730O (2008).
[CrossRef]

Ruffin, A.B.

Salokatve, A.

Smith, A.V.

A.V. Smith and J.J. Smith, “Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering,” arXiv:1301.4277 [physics.optics](January18, 2013).

A.V. Smith and J.J. Smith, “Maximizing the mode instability threshold of a fiber amplifier,” arXiv:1301.3489 [physics.optics](January16, 2013).

A.V. Smith and J.J. Smith, “A steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express21, 2606–2623 (2013).
[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, 24545–24558 (2012).
[CrossRef] [PubMed]

A.V. Smith and J.J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express19, 10180–10192 (2011).
[CrossRef] [PubMed]

A.V. Smith and J.J. Smith, “Spontaneous Rayleigh seeding of stimulated Rayleigh scattering in high power fiber amplifiers,” Opt. Express. (submitted).

Smith, J.J.

A.V. Smith and J.J. Smith, “Maximizing the mode instability threshold of a fiber amplifier,” arXiv:1301.3489 [physics.optics](January16, 2013).

A.V. Smith and J.J. Smith, “Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering,” arXiv:1301.4277 [physics.optics](January18, 2013).

A.V. Smith and J.J. Smith, “A steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express21, 2606–2623 (2013).
[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, 24545–24558 (2012).
[CrossRef] [PubMed]

A.V. Smith and J.J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express19, 10180–10192 (2011).
[CrossRef] [PubMed]

A.V. Smith and J.J. Smith, “Spontaneous Rayleigh seeding of stimulated Rayleigh scattering in high power fiber amplifiers,” Opt. Express. (submitted).

Söderlund, M.J.

Stutzki, F.

Tammela, S.K.T.

Tateda, M.

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fiber,” IEEE Phot. Tech. Lett.1, 107–108 (1989).
[CrossRef]

Tünnermann, A.

Walton, D.T.

Wang, J.

Ward, B.

Wessels, P.

Ylä-Jarkko, K.

Zenteno, L.A.

IEEE Phot. Tech. Lett. (1)

T. Horiguchi, T. Kurashima, and M. Tateda, “Tensile strain dependence of Brillouin frequency shift in silica optical fiber,” IEEE Phot. Tech. Lett.1, 107–108 (1989).
[CrossRef]

Opt. Express (10)

M.-J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J.A. Demeritt, A.B. Ruffin, A.M. Crowley, D.T. Walton, and L.A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express15, 8290–8299 (2007).
[CrossRef] [PubMed]

M.J. Söderlund, J.J. Montiel i Ponsoda, S.K.T. Tammela, K. Ylä-Jarkko, A. Salokatve, and S. Honkanen, “Mode-induced transverse photodarkening loss variations in large-mode-area ytterbium doped silica fibers,” Opt. Express16, 10633–10640 (2008).
[CrossRef] [PubMed]

M. Hildebrandt, S. Büsche, P. Wessels, M. Frede, and D. Kracht, “Brillouin scattering spectra in high-power single-frequency ytterbium doped fiber amplifiers,” Opt. Express16, 15970–15979 (2008).
[CrossRef] [PubMed]

A.V. Smith and J.J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express19, 10180–10192 (2011).
[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, 24545–24558 (2012).
[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, 1944–1971 (2013).
[CrossRef] [PubMed]

A.V. Smith and J.J. Smith, “A steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express21, 2606–2623 (2013).
[CrossRef] [PubMed]

L. Dong, “Stimulated thermal rayleigh scattering in optical fibers,” Opt. Express21, 2642–2656 (2013).
[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. Express20, 440–451 (2012).
[CrossRef] [PubMed]

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

Opt. Express. (1)

A.V. Smith and J.J. Smith, “Spontaneous Rayleigh seeding of stimulated Rayleigh scattering in high power fiber amplifiers,” Opt. Express. (submitted).

Opt. Lett. (2)

Proc. SPIE (1)

J.E. Rothenberg, “Suppression of stimulated Brillouin scattering in single-frequency multi-kilowatt fiber amplifiers,” Proc. SPIE6873,68730O (2008).
[CrossRef]

Other (3)

G.P. Agrawal, Nonlinear Fiber Optics(Academic, 1995).

A.V. Smith and J.J. Smith, “Frequency dependence of mode coupling gain in Yb doped fiber amplifiers due to stimulated thermal Rayleigh scattering,” arXiv:1301.4277 [physics.optics](January18, 2013).

A.V. Smith and J.J. Smith, “Maximizing the mode instability threshold of a fiber amplifier,” arXiv:1301.3489 [physics.optics](January16, 2013).

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Figures (8)

Fig. 1
Fig. 1

Signal and pump powers versus z for co-pumped fiber with dcore = ddope = 50 μm, dclad = 400 μm, operating at the mode instability threshold. The inset figures show the upper state fraction nu profiles at z = 0.1, 1.4, and 4.0 m. The range of the nu axis is 0–0.5. The circles on the bottom faces of the frames indicate the edge of the core.

Fig. 2
Fig. 2

Same fiber and z locations as in Fig. 1 except the amplifier is counter-pumped instead of co-pumped. The threshold powers are slightly different for co- and counter-pumped cases.

Fig. 3
Fig. 3

Normalized symmetric part of the heat profile (upper plot) and antisymmetric oscillatory portion of the heat profile (lower plot) for same co-pumped fiber at the same three z locations indicated in Fig. 1. Near the input end the symmetric heat profile closely resembles the LP01 irradiance profile, while the oscillatory part resembles the product of the fields of LP01 and LP11. Farther along the fiber the symmetric part of the heat profile becomes nearly flat topped while the antisymmetric part is strongly suppressed near the center (x = 0).

Fig. 4
Fig. 4

Normalized symmetric part of the heat profile (upper plot) and antisymmetric oscillatory portion of the heat profile (lower plot) for the same counter-pumped fiber at the same three z locations indicated in Fig. 2. The oscillatory anti symmetric heat profile never closely matches the product of the fields of LP01 and LP11.

Fig. 5
Fig. 5

Plots of χ′ versus z for co-pumped (dashed green curve) and counter-pumped (solid blue curve) fibers operating near the mode instability threshold. The fiber parameters: 50 μm diameter core and doping, 100 μm diameter pump cladding (upper plot) and 400 μm diameter pump cladding (lower plot), 1100 Hz red detuning of LP11, λs = 1032 nm, λp = 976 nm, NA=0.054 (ncore = 1.451, nclad = 1.45). In the upper plot the pump powers are 525 W co-pumped, and 493 W counter-pumped. In the lower plot the pump powers are 1200 W co-pumped, and 1350 W counter-pumped. The dotted black line is for zero saturation.

Fig. 6
Fig. 6

Plots of laser gain gs, total gain gcomp and total heat versus z for the same copumped fibers and the same operating conditions as in Fig. 5. The upper plot is for a 100 μm diameter cladding; the lower plot is for a 400 μm diameter cladding. In both plots it is clear that the gain and heat profiles are not closely matched.

Fig. 7
Fig. 7

Output signal powers at the instability threshold for different pump cladding diameters (100, 200, 300, 400, 500 μm). The parameters: dcore = 50 μm, λp = 976 nm, λs = 1032 nm, signal seed powers are 10 W in LP01 and 10−16 W in LP11. The lengths of the fibers are adjusted the minimum value necessary to achieve high efficiency, defined as pump absorption > 0.95. The solid curve at 345 W indicates the threshold computed in the limit of no population saturation for ddope = 50 μm. Details are given in Tables 2 and 5.

Fig. 8
Fig. 8

Plot of signal threshold output power versus PthresLeff for the 50 μm core fiber. The curves are spline fits to the computed data points. For PthresLeff = 2400 W·m (γ = 6) the threshold powers are 1050 W for co-pumped and fully doped; 1205 W for co-pumped and ddope = 40 μm; 1347 W for co-pumped and ddope = 30 μm; 1572 W for counter-pumped and fully doped.

Tables (5)

Tables Icon

Table 1 Amplifier parameters

Tables Icon

Table 2 Thresholds: co-pumped, dcore = 50 μm, ddope = 50 μm

Tables Icon

Table 3 Thresholds: counter-pumped, dcore = 50 μm, ddope = 50 μm

Tables Icon

Table 4 Thresholds: co-pumped, dcore = 50 μm, ddope = 40 μm

Tables Icon

Table 5 Thresholds: co-pumped, dcore = 50 μm, ddope = 30 μm

Equations (9)

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n u ( x , y ) = I p σ p a / h ν p + I s ( x , y ) σ s a / h ν s I p ( σ p a + σ p e ) / h ν p + I s ( x , y ) ( σ s a + σ s e ) / h ν s + 1 / τ .
Q ( x , y ) = N Y b ( x , y ) [ ν p ν s ν p ] [ σ p a ( σ p a + σ p e ) n u ( x , y ) ] I p ,
P 11 ( z ) z = [ g 11 + g 01 χ P 01 ( z ) ] P 11 ( z ) = g net P 11 ( z ) .
χ = g comp g s g s P s = g strs g s P s
P thres L eff = 0 L P s ( z ) d z .
g B γ P thres L eff A eff > 17 ,
γ > g B P thres L eff 17 A eff .
γ = P thres L eff 400 W m .
P thres = P ref log ( P start / 10 ) log ( 10 16 / 10 )

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