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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 15168–15182
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Increasing mode instability thresholds of fiber amplifiers by gain saturation

Arlee V. Smith and Jesse J. Smith  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 15168-15182 (2013)
http://dx.doi.org/10.1364/OE.21.015168


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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

1. Introduction

The essence of the STRS process responsible for mode instability is that laser gain necessarily deposits quantum defect heat in the core of the amplifier fiber, and the asymmetric heating produced by the asymmetric signal irradiance profile due to interference between modes LP01 and LP11 leads to an asymmetric thermal lens that couples light between those two modes. An additional requirement is that there be a phase shift between the temperature grating and the signal irradiance grating which, in our STRS model, is created by the time lag between an irradiance grating traveling along the fiber and the temperature grating that it creates.

Our model imposes a steady-periodic condition on the gain grating because we assume the frequency offset between modes has a narrow linewidth. Alternative STRS models have been presented by Hansen et al.[6

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

7. K.R. Hansen, T.T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21, 1944–1971 (2013) [CrossRef] [PubMed] .

] and by Dong [8

8. L. Dong, “Stimulated thermal rayleigh scattering in optical fibers,” Opt. Express 21, 2642–2656 (2013) [CrossRef] [PubMed] .

]. They used similar approximations, including the steady-periodic assumption. Another model by Ward et al.[9

9. 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] .

] is based on STRS, but without the steady-periodic assumption. Jauregui et al.[10

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. Express 20, 440–451 (2012) [CrossRef] [PubMed] .

] also model temperature gratings in fiber amplifiers.

The primary difference in the physics of the various models is that the models of Hansen et al. and Dong assume the profile of the quantum defect heating matches the profile of the signal light, while our model and those of Ward et al. and Jauregui et al. compute the heat profile based on the local population inversion plus either the local pump or signal irradiance. In the model of Ward et al. the increase of signal power in a mode due to laser gain is found from the overlap of the local gain g(x,y,z) with the field of that mode. In our BPM model laser gain increases the total signal field locally and is then apportioned among the modes automatically by diffraction in the presence of the core index step. Either the local signal field growth or the local pump irradiance loss is used to compute the quantum defect heating.

Both our model and that of Hansen et al. use the same steady-periodic assumption. Using this treatment they can both include multiple frequencies for the beat note between the coupled modes to address bandwidth issues. However, we find that in computing thresholds using a single frequency at the gain peak produces nearly identical thresholds to using multiple frequencies contained in the gain band. Since added frequencies slow the computation we use a single frequency in all the computations presented in this paper. The seed power is 10−16 W to approximate quantum noise. Only step index fibers will be discussed.

2. Transverse hole burning

In computing the upper state population fraction nu we use the steady state expression
nu(x,y)=Ipσpa/hνp+Is(x,y)σsa/hνsIp(σpa+σpe)/hνp+Is(x,y)(σsa+σse)/hνs+1/τ.
(1)
Here the σ’s are the absorption and emission cross sections for the pump and the signal, the ν’s are the optical frequencies, and Ip and Is are the pump and signal irradiances. The amplifier parameters used throughout this report are listed in Table 1. We model a fiber with a 50 μm diameter step index core with a typical numerical aperture of 0.054. The Yb3+ doping density is also typical of high power amplifiers.

Table 1. Amplifier parameters

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Figures 1 and 2 show upper state population profiles, nu(x, y) computed at three points along co-pumped and counter-pumped fiber amplifiers with a cladding diameter of 400 μm. The signal light is all in LP01 here. Near the input end of the co-pumped fiber the pump is strong and the signal is weak so the upper state population is weakly depleted. The shape of the population depletion closely matches the signal irradiance profile here. The undepleted population in the region with Is = 0 is nu=σpa/(σpa+σpe)0.5. Further along this fiber, near the crossing of the signal and pump powers, the saturation is strong at the mode center but moderate near the core boundary, while near the output end saturation is strong across the entire core. If the same fiber is counter-pumped the signal and pump powers are approximately equal along the full length of the fiber, so the saturation resembles that of the middle diagram of the co-pumped fiber where the signal and pump powers are equal. The degree of saturation would be reduced in a fiber with a smaller cladding, and increased in one with a larger cladding.

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 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.

The quantum defect heating is proportional to the pump absorption, which is determined from the value of nu(x, y) and the pump irradiance. The latter is assumed uniform across the pump cladding. We compute the heat deposition rate Q using
Q(x,y)=NYb(x,y)[νpνsνp][σpa(σpa+σpe)nu(x,y)]Ip,
(2)
where the first term in brackets is the quantum defect. The heat profile can be visualized by inverting the depletion profiles in Figs. 1 and 2 and multiplying them by the doping profile NYb(x, y).

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 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.

3. Mode coupling gain

3.1. Without hole burning

Both Dong and Hansen et al. showed that if the heat profile matches the signal irradiance profile over the portion of the core that is (uniformly) doped, the gain of mode LP11 satisfies
P11(z)z=[g11+g01χP01(z)]P11(z)=gnetP11(z).
(3)
Here we have simplified Dong’s expression by assuming there is no depletion of mode LP01 due to STRS, and no linear loss for either mode. The total gain gnet for LP11 is its laser gain, indicated by g11, plus the STRS gain, indicated by (g01χP01), where g01 is the laser gain for LP01. The quantum defect heat deposited by laser amplification of LP01 is (g01P01) so χ is a real valued coefficient that relates quantum defect heating to STRS gain. For each fiber design χ has a constant value determined by the frequency offset between LP01 and LP11 and the quantum defect, plus the thermal, geometrical, and optical properties of the fiber.

We used our model to verify the value of χ for one case analyzed by Hansen et al. (Fig. 4 of Ref. [7

7. K.R. Hansen, T.T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21, 1944–1971 (2013) [CrossRef] [PubMed] .

]). In order to avoid population saturation we used a pump power of 20 kW, dcore = 40 μm, dclad = 250 μm, and an LP01 seed power of 50 W. Otherwise the fiber parameters were those from Table 1. Our frequency of maximum gain was equal to that of Hansen et al., and our computed a value for χ was within 5% of that of Hansen et al. Of course, our fiber was extremely inefficient, using 20 kW to produce approximately 400 W of signal, and depleting the pump by only 2.5%. However, this exercise does demonstrate good agreement between our model and those of Hansen et al. and Dong in the limit of low saturation.

3.2. With hole burning

The model comparison just described illustrates the lack of realism of the assumption of equal shapes for the heat and irradiance profiles. For the heat profile to match the light profile the pump irradiance must be much stronger than the signal irradiance. However, amplifiers that efficiently convert pump power necessarily experience strong population saturation. To emphasize this contrast between our model and one that assumes matching heat and irradiance profiles and thus constant χ values, we define a new shape factor χ′ as
χ=gcompgsgsPs=gstrsgsPs
(4)
where gcomp is the total gain of LP11 computed with our model, replacing the gnet of Eq. (3), gs is the computed signal laser gain, and gstrs is the STRS gain. We do not distinguish between the nearly equal laser gains for the two modes in this high V fiber with fully doped core. Variables Ps, gs, and gstrs are all z dependent computed values. The denominator is proportional to the total deposited heat. Figure 5 shows plots of χ′ for co-pumped and counter-pumped amplifiers.

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.

The upper plot is for a 100 μm diameter cladding; the lower plot is for a 400 μm diameter cladding. Saturation effects are stronger with the larger cladding because of the reduced pump irradiances. In both fibers the value of χ′ near z = 0 for the co-pumped case is nearly equal to the χ we compute in the limit of zero saturation, as expected because of the low degree population saturation there. As z increases the population saturation strengthens so the value of χ′ falls, implying the mode coupling gain is reduced relative to the laser gain. This gain reduction raises the STRS threshold relative to that of Hansen et al. and Dong. In the small cladding fiber the reduction does not occur until half way along the fiber while in the large cladding fiber it occurs much sooner.

As expected from the nearly constant ratio of pump to signal for the counter-pumped fibers, the value of χ′ is nearly constant along the fiber. However, its value is still reduced to a level seen in the co-pumped fiber near the crossing point near z = 0.5 m for the small clad fiber and near z = 1.4 m for the large clad fiber. It is clear from a comparison of the values of χ′ that the STRS threshold should be higher for larger cladding sizes, and the threshold for an efficient amplifier should exceed the Hansen et al. and Dong threshold.

Another way to view the same information is to plot gcomp, gs, and the total heat rather than χ′. This is done in Fig. 6 for the same pair of fibers, co-pumped, with dclad = 100 μm (upper plot) and 400 μm (lower plot).

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.

The expected trend of higher thresholds for larger cladding sizes is illustrated in Fig. 7. The computed thresholds, defined as 1% of the signal power in LP11, are seen to rise with increasing cladding diameters and the resulting increasing degree of population saturation. Co-and counter-pumped fibers are found to have similar thresholds in this study, a finding that appears to be quite general based on our experience modeling many different designs. In the fiber design used in Fig. 7, saturation appears to raise thresholds more significantly for confined doping than for full doping, probably because saturation is strong across the entire doped zone. For comparison, we also show in the figure the threshold predicted without saturation. More details for the model runs included in Fig. 7 are listed in Tables 2 and 5.

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.

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

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

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

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

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4. Tables

In the following tables Δν is the frequency of LP01 minus the frequency of LP11.

5. Stimulated Brillouin scattering (SBS) suppression

Designing a narrow bandwidth fiber amplifier suitable for beam combining applications requires balancing SBS and STRS. Here we present a simplified version of this balancing act. We define an effective SBS gain length at the STRS threshold by
PthresLeff=0LPs(z)dz.
(5)
The SBS threshold power [11

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

] is exceeded if
gBγPthresLeffAeff>17,
(6)
where the 17 comes from the usual SBS threshold gain value of 21 minus the laser gain for the Stokes wave [11

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

]. The γ parameter is an SBS gain reduction factor that reduces the effective SBS gain from its nominal value of gB = 5 × 10−11 m/W for silica. The linewidth for silica is approximately 50 MHz and the Stokes shift is approximately 16 GHz for λ = 1032 nm. The value of γ can be increased by broadening the signal linewidth by phase modulation [11

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

] above 50 MHz, for example, or by introducing a temperature gradient [12

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. Express 16, 15970–15979 (2008) [CrossRef] [PubMed] .

] or a strain gradient [13

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

14. J.E. Rothenberg, “Suppression of stimulated Brillouin scattering in single-frequency multi-kilowatt fiber amplifiers,” Proc. SPIE 6873,68730O (2008) [CrossRef] .

] along the fiber length to vary the Stokes shift. Another approach is to vary the acoustic velocity, and thus the Brillouin shift, across the core region [15

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. Express 15, 8290–8299 (2007) [CrossRef] [PubMed] .

, 16

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] .

]. Temperature and strain shift the SBS frequency by known amounts, so from the signal linewidth and the temperature and strain gradient one can estimate γ using an SBS model. To avoid SBS the value of γ must satisfy
γ>gBPthresLeff17Aeff.
(7)
For our 50 μm diameter core, Aeff = 1175 μm2, so the SBS threshold condition is
γ=PthresLeff400Wm.
(8)
If PthresLeff > 400 W·m, this expression gives the minimum value of γ necessary to suppress SBS.

In Fig. 8 we plot the STRS threshold powers versus the quantity PthresLeff for our example fiber with dcore = 50 μm. Selecting an arbitrary value for PthresLeff on the horizontal axis (or equivalently the value of γ), the values of the STRS threshold can be read from the computed curves. From the four curves it appears that for any value of γ the counter-pumped fully doped amplifier provides the highest STRS threshold power, the co-pumped fully doped amplifier offers the lowest STRS threshold power, while the confined doping, co-pumped amplifiers give intermediate threshold powers.

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.

6. Scaling for other core/cladding sizes

To first order changing the core diameter while keeping the ratio dcore/dclad fixed, and keeping NA = 0.054, the threshold powers do not change. The frequency offset changes proportional to 1/Aeff but the degree of saturation, and thus the value of χ′ is unaltered.

However, for dcore < 30 μm, the value of V is reduced to less than 5, so the mode overlap with the core becomes noticeably weaker, which tends to raise the STRS threshold [6

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] .

, 8

8. L. Dong, “Stimulated thermal rayleigh scattering in optical fibers,” Opt. Express 21, 2642–2656 (2013) [CrossRef] [PubMed] .

]. At the other extreme, for dcore > 80 μm, thermal lensing becomes significant, and this constriction of the modes may alter the STRS threshold.

As dcore changes the area Aeff changes and this changes the value of γ required to suppress SBS for a given value of PthresLeff according to Eq. (8). Similar powers are possible, while avoiding both SBS and STRS, but the value of γ necessary to avoid SBS scales approximately as 1/dcore2. If there is a constraint on γ imposed by beam combining requirements, for example, this implies a lower limit on the core size.

7. Scaling for other LP11 starting powers

The thresholds computed in this study are based on an input signal power of 10−16 W in LP11, with a frequency shift to the STRS gain maximum, or threshold minimum. This input power level corresponds approximately to the quantum noise limit, and serves as a standard point of comparison among models. Actual starting powers will be considerably higher than this if there is amplitude modulation on the pump or signal seed with a modulation frequency near the optimum STRS frequency shift [3

3. A.V. Smith and J.J. Smith, “Influence of pump and seed modulation on the mode instability thresholds of fiber amplifiers,” Opt. Express 20, 24545–24558 (2012) [CrossRef] [PubMed] .

, 4

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).

]. Thermal noise is probably 2–3 factors of 10 higher than this as well [17

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

]. More realistic thresholds would be based on input powers of perhaps 10−10 W, but the exact level will require measurements of the modulation properties of the pump and seed. The reference thresholds presented here (Pref) can be used to estimate the threshold for a higher input power (Pstart) using
Pthres=Preflog(Pstart/10)log(1016/10)
(9)
where the divisors of 10 are present because our definition of threshold as 1% of the power in LP11 implies a threshold output power of order 10 W in LP11.

The thresholds computed in this study are also based on negligible signal loss due to absorbing impurities in the glass or due to photodarkening. The presence of these processes adds heat with a profile that contributes to STRS gain, and so reduces the thresholds [5

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

].

8. Conclusion

We showed that transverse hole burning, or saturation of the population inversion, in a Yb3+ doped fiber can strongly influence the STRS or mode coupling gain, and this effect can be exploited to substantially raise mode instability thresholds. The degree of saturation can be manipulated by changing the ratio of pump irradiance to signal irradiance through choice of core and cladding sizes, injected seed power, and doping profile. Generally we find that otherwise identical co- and counter-pumped configurations have nearly equal thresholds even though the z dependence of saturation is quite different in the two.

The benefits of high saturation persist when SBS suppression is considered, even though high saturation implies longer fibers with higher PthresLeff values. The benefits of confined doping also survive the requirement of SBS suppression.

Fibers with high saturation have the added advantage of minimizing photodarkening, assuming photodarkening increases with higher upper state population density, as experiments seem to indicate [18

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. Express 16, 10633–10640 (2008) [CrossRef] [PubMed] .

].

We have shown that saturation has a strong effect on thresholds for step index fibers. Other, more complex refractive index profiles might be designed to raise the instability threshold by changing the shapes of the interacting modes. However, saturation can be expected to have a strong influence in those as well.

References and links

1.

A.V. Smith and J.J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19, 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. Express 21, 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. Express 20, 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. Express 21, 1944–1971 (2013) [CrossRef] [PubMed] .

8.

L. Dong, “Stimulated thermal rayleigh scattering in optical fibers,” Opt. Express 21, 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. Express 20, 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. Express 20, 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. Express 16, 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. SPIE 6873,68730O (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. Express 15, 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. Express 16, 10633–10640 (2008) [CrossRef] [PubMed] .

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(140.6810) Lasers and laser optics : Thermal effects
(190.2640) Nonlinear optics : Stimulated scattering, modulation, etc.

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 4, 2013
Revised Manuscript: June 9, 2013
Manuscript Accepted: June 10, 2013
Published: June 18, 2013

Citation
Arlee V. Smith and Jesse J. Smith, "Increasing mode instability thresholds of fiber amplifiers by gain saturation," Opt. Express 21, 15168-15182 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-15168


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References

  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]
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