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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 19375–19386
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Passive mitigation strategies for mode instabilities in high-power fiber laser systems

Cesar Jauregui, Hans-Jürgen Otto, Fabian Stutzki, Florian Jansen, Jens Limpert, and Andreas Tünnermann  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 19375-19386 (2013)
http://dx.doi.org/10.1364/OE.21.019375


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Abstract

Mode instabilities have quickly become the most limiting effect when it comes to scaling the output average power of fiber laser systems. In consequence, there is an urgent need for effective strategies to mitigate it and, thus, to increase the power threshold at which it appears. Passive mitigation strategies can be classified into intrinsic, which are related to the fiber design, and extrinsic, which require a modification of the setup. In order to evaluate the impact of mitigation strategies, a means to calculate its power threshold and predict its behavior is required. In this paper we present a simple semi-analytic formula that is able to predict the changes of the mode instability threshold by analyzing the strength of the thermally-induced waveguide perturbations. Furthermore, we propose two passive mitigation strategies, one intrinsic and one extrinsic, that should lead to a significant increase of the power threshold of mode instabilities.

© 2013 OSA

1. Introduction

In the relatively short time elapsed since the first reports on mode instabilities, this effect has become the most limiting phenomenon for a further scaling of the output average power of fiber laser systems. Thus there is an urgent need for mitigation strategies that allow for a significant increase of the mode instability threshold.

Mitigation strategies can be classified, according to Table 1

Table 1. Classification of mitigation strategies for mode instabilities

table-icon
View This Table
, into passive and active. Passive mitigation strategies are those that do not require any actuation/control on the system during operation, whereas active mitigation strategies are those requiring such actuation/control. Additionally, passive mitigation strategies can be classified into intrinsic and extrinsic. Intrinsic mitigation strategies are those that involve changes in the fiber design to increase the threshold while leaving the rest of the system untouched. On the other hand, extrinsic mitigation strategies are those that, given a particular fiber, achieve the increase of the threshold by means of modifications of the rest of the system. Furthermore, as illustrated in Table 1, all active mitigation strategies are necessarily extrinsic ones. An example of an active mitigation strategy has recently been presented in [17

17. H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Controlling mode instabilities by dynamic mode excitation with an acousto-optic deflector,” Opt. Express . submitted.

]. Here the beam fluctuations characteristic of mode stabilities for average output power levels above the threshold are stabilized with a dynamic excitation of the modes at the input of the fiber (carried out with an acousto-optic deflector). With this technique the beam could be stabilized up to power levels three times higher than the mode instability threshold.

In this paper we propose two passive mitigation strategies of mode instabilities: one extrinsic and one intrinsic. In order to theoretically evaluate the expected increase of the threshold, we introduce a semi-analytic formula. This simple formula, in contrast to others already published based on the coupled mode theory [18

18. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1944. [CrossRef] [PubMed]

], relies on analyzing the strength of the thermally-induced waveguide changes.

The paper is organized as follows: in section 2 the semi-analytic formula used for predicting the behavior of the mode instability threshold is presented and the theoretical premises in which it is based are discussed. In section 3 an extrinsic mitigation strategy based on reducing the heat load in the active fiber is proposed. In section 4, an intrinsic mitigation strategy based on reducing the pump absorption is presented and discussed. Finally some conclusions are drawn.

2. Semi-analytic formula for the evaluation of the mode instability threshold

At this point there are already several numerical tools for modeling mode instabilities [14

14. 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(12), 12912–12925 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12912. [CrossRef] [PubMed]

16

16. B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407–11422 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11407. [CrossRef] [PubMed]

]. However, these models, even though very general in their scope, are very complex and computationally intensive. Therefore, using them to evaluate mitigation strategies for mode instabilities can be very inefficient due to the long computation times involved. Consequently, we believe that a simple and quick way to calculate the mode instability threshold is required, even at the price of sacrificing some accuracy.

In the semi-analytic formula that will be proposed in the following the physics of the amplification process are modeled in detail whereas there is a certain level of abstraction from the physics behind the origin of mode instabilities. On the contrary, other authors have chosen to model in detail the process of energy transfer between transverse modes while abstracting themselves from the laser physics [18

18. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1944. [CrossRef] [PubMed]

]. However, the strength, shape and evolution of the thermally-induced grating below the threshold are mainly determined by the amplification process. Therefore, we believe that not taking into account the detailed physics of this process limits the ability of other formulas to analyze and find mitigation strategies for this effect.

2.1. Theoretical considerations

Having accepted the presence of the quasi-static grating as almost unavoidable in high-power fiber-laser systems, it is reasonable to think that it should be influencing the mode instability threshold. For example, as proposed in [14

14. 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(12), 12912–12925 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12912. [CrossRef] [PubMed]

], the quasi-static grating can become so strong that it directly triggers mode instabilities by giving rise to non-adiabatic waveguide changes. On the other hand, even in the frame of the moving grating theory [13

13. 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]

, 15

15. A. V. Smith and J. J. Smith, “Steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express 21(3), 2606–2623 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-2606. [CrossRef] [PubMed]

], the quasi-static index grating should still be considered because it may significantly lower the threshold. The reason for this is that, as the moving part of the interference pattern (which drives the moving grating) becomes out of phase with the strong quasi-static grating, a strong instantaneous energy transfer can take place. This instantaneous energy transfer will be much stronger than the one that would be obtained without considering the presence of the quasi-static grating (which is what current models assume). Nevertheless, it is true that, in steady state, the net average energy transfer caused by the quasi-static grating will be approximately zero (because the energy transfer changes sign over a shift of the moving grating equal to one period of the quasi-static grating. This implies that for example over the first half of the period the energy would flow from the fundamental mode to the HOM and in the second part of the period the energy will flow from the HOM back to the fundamental mode). This is the reason why steady state models simply neglect the presence of the strong quasi-static grating. However, it is still reasonable to assume that the stronger instantaneous energy transfer (that will lead to an instantaneously/locally stronger moving grating) could lead to a lower mode instability threshold in the presence of transients (e.g. when increasing the pump power). However, this point still requires further investigation. Independently of this, it can be argued that below the threshold the strength of a possible moving grating will be proportional to the strength of the quasi-static grating (since their growth along the fiber is mostly determined by the amplification process).

2.2. Semi-analytic formula

According to the discussion above, in this paper we propose to analyze the strength of the quasi-static thermally-induced grating to predict the mode instability threshold and its behavior when different system parameters are changed. This approach to obtain a formula for the mode instability threshold, which significantly departs from the path chosen by other authors [18

18. K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1944. [CrossRef] [PubMed]

], is based on the important premise that below the threshold the energy transfer between the interfering modes is very low. This assumption, based on experimental observations [20

20. 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(14), 15710–15722 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15710. [CrossRef] [PubMed]

], in turn implies that the strength of the quasi-static grating below the mode instability threshold is mainly dependent on the amplification process and, therefore, a steady-state rate equation model can be used to compute it.

All the theories about the origin of mode instabilities agree upon the fact that a thermally-induced long period index grating is responsible for the observed energy transfer between transverse modes. So we propose analyzing this grating in an analogous way as normal index gratings. In conventional long period gratings the coupling strength is, in the limit of weak coupling between the modes, proportional to the product κL, where κis the coupling constant and Lis the length of the grating [21

21. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

]. This, in turn, can be demonstrated to be proportional to ΔnL, where Δnis the amplitude of the index perturbation (assuming an homogeneous grating).

Lb(z)=λ(neffLP01(z)neffHOM(z))
(1)

In Eq. (1) λ represents the wavelength and neffiis the effective index of the mode i. Note that Lbis inversely proportional to the perturbation of the waveguide, whereas κis directly proportional to it. Therefore, we propose using 1/Lbas a measure of the strength of the thermally-induced waveguide changes.

Now, in analogy to conventional gratings, we propose employing the following ansatz to calculate the power threshold of mode instabilities Pth:
Δ(1Lb(z))¯L|Pth=γ,
(2)
where the ¯ symbol imply average along the fiber length and γ is a fitting parameter. Besides, Δ(f(z))represents the maximum amplitude of the changes of the function f(z) over each period.

This way, Eq. (2) proposes that, for a given fiber design, mode instabilities are triggered once that a certain coupling strength is reached. The problem is determining the value of this certain coupling strength. In fact, with the very simple model proposed here (which ignores the actual mode coupling and the dynamic processes taking place during and before mode instabilities) it is only possible to use a free parameter γ to fit the calculated values to the actual mode instability thresholds. This reduces the ability of this formula to predict the mode instability threshold of new fibers. However, once that the factor γ has been fitted for a certain fiber, Eq. (2) should be able to predict the behavior of the threshold when changing different parameters of the system. Therefore, the ansatz presented in Eq. (2) is, in spite of its simplicity, still suited to investigate mitigation strategies for mode instabilities.

Equation (2) can be further simplified taking into account that LNLb¯, where Nis the total number of periods of the structure and Lb¯is the average value of the beat length along the fiber. Thus we arrive at the following expression:
m=1NΔ(neffLP01neffHOM)[m]|PthλγLb¯
(3)
In Eq. (3) the maximum amplitude of the difference in effective refractive indexesΔ(neffLP01neffHOM) is evaluated once per period.

In order to evaluate Eq. (3), we simulate the three-dimensional steady-state thermally-induced waveguide changes that will appear in the active fiber under a certain excitation (i.e. relative power between the fundamental mode and the HOM) and pump conditions. This simulation is carried out using the thermally-coupled, transversally-resolved steady-state rate-equation model presented in [19

19. 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]

]. Finally, once that the 3D thermally-modified index profile of the waveguide has been calculated, a mode solver is run at each point along the fiber to calculate the new local beat length.

3. Extrinsic mitigation strategy: reducing the heat load of active fibers

Figure 1
Fig. 1 Evolution of the mode instability threshold with the reduction of the quantum defect heating which was achieved a) by pumping at 976nm and by changing the signal wavelength or b) by emitting at 1030nm and by changing the pump wavelength. In both plots the black dashed line represents the expected evolution of the threshold due to the reduction of the quantum defect.
illustrates the prediction of Eq. (3) for the change of the threshold when reducing the quantum defect. The calculations have been done for a 1.2m long fiber with 80µm core diameter (from which only 64µm are doped with 3.51025m−3 concentration of Yb ions), 228µm pump cladding diameter and 1.2mm outer fiber diameter. The V-parameter of the fiber is 7 and the fitting parameter γ is 1.8102, which results in a predicted mode instability threshold of ~210W when pumping at 976nm and emitting at 1030nm. This threshold value is realistic for fibers of these dimensions. In the simulations the seed power in the fundamental mode is 50W and the LP11 is excited with 0.5W. The reason for this high seed power is to allow reaching the mode instability threshold in spite of the lower gains that accompany the change in signal/pump wavelength. In Fig. 1(a) the pump wavelength is set to 976nm, whereas in Fig. 1(b) the signal wavelength is set to 1030nm and the pump is assumed to be monochromatic.

The weakening of the grating and the increase of its effective length have opposite effects on the mode instability threshold: whereas a weaker grating results in a higher threshold, a longer one results in a lower threshold. The results in Fig. 1 indicate, however, that the weakening of the grating due to the reduction of the quantum defect is the dominant feature for signal wavelengths <1030nm and or for pump wavelengths >976nm; that is why, when the wavelength separation between pump and signal is reduced, the threshold increases, albeit at a lower rate than that dictated by the reduction of the quantum defect due to the simultaneous increase of the effective grating length.

Changing the pump wavelength might be in principle more attractive than changing the signal wavelength because the modification of the system can be reduced to the last amplification stage. However, changing the pump wavelength might become challenging very quickly unless the fiber design is properly modified as well. This is illustrated in Fig. 2
Fig. 2 Evolution of the amplification efficiency for a fixed seed power of 50W a) when changing the signal wavelength while pumping at 976nm and b) when changing the pump wavelength while emitting at 1030nm.
, where the evolution of the amplification efficiency (ηamp=(PoutPseed)/Ppump) as a function of the signal/pump wavelength is represented. As can be seen, in the case of changing the signal wavelength the amplification efficiency remains high (>0.7) up to a factor 2 reduction of the quantum defect. However, in our example, when changing the pump wavelength the amplification efficiency quickly drops to unacceptably low values (<0.3). More importantly, the dramatic loss of efficiency at the longer pump wavelength side means that in real high power pump diodes (with a typical spectral bandwidth of ~3nm) the short wavelength side of the pump radiation will dominate, which will lead to a lower MI threshold than expected from the central wavelength alone. Note, however, that increasing the seed power, the fiber length and/or the ion concentration will help increasing the amplification efficiency when changing the pump wavelength; but this is not possible or desirable in every application.

Both approaches present substantial differences regarding the amplification process. It can be demonstrated that the maximum achievable inversion in an Yb-doped fiber amplifier is given by (when neglecting spontaneous emission):
N2oNσapσap+σep,
(4)
where N2o represents the maximum population density of the upper laser level, N is the total ion concentration, σap is the absorption cross-section at the pump wavelength and σep is the emission cross-section at the pump wavelength. On the other hand, it is also possible to define a transparency inversion as the average population density of the upper laser level N2¯ along the fiber required to obtain an overall gain of 1. In that case this transparency inversion level can be shown to be:
N2¯Nσalσal+σel,
(5)
where σal and σel are the absorption and emission cross-sections at the signal wavelength, respectively. At this point it is possible to calculate the maximum extractable energy E from the fiber as:

E=EstoredEtransparency=hcλlAL(N2oN2¯)
(6)

go=[(σal+σel)N2oNσal]NLΓl
(8)

Here Γl stands for the overlap of the signal beam with the doped region. Therefore, now using Eq. (7) it is possible to calculate the evolution of the available energy and gain in the fiber as either the signal or the pump wavelength is swept. The results of this calculation for a fixed pump power of 300W and for 50W seed power are shown in Fig. 3
Fig. 3 Evolution of the available energy EG and gain G for a fixed pump power of 300W a) when changing the signal wavelength while pumping at 976nm and b) when changing the pump wavelength while emitting at 1030nm.
.

The red thick lines in Fig. 3(a) and Fig. 3(b) mark the situation with a similar mode instability threshold as predicted by Fig. 1. As can be seen, changing the signal wavelength offers, for a similar threshold, a significantly higher available energy. Thus, this approach might be attractive for pulsed systems pursuing high average powers and high pulse energies. Unfortunately changing the signal wavelength implies having to deal with a reduced gain (when compared to 1030nm) throughout the whole amplification chain. This, at the end, can imply the need of more pre-amplification stages, but the advantage is that no changes in the fiber designs are strictly required (at least up to a factor 2 reduction of the quantum defect).

On the other hand, choosing to change the pump wavelength as the way to reduce the heat load has, as mentioned before, the advantage that it can be done exclusively in the last amplification stage. Thus, the change is limited to the very final amplifier whereas the rest of the amplification chain remains intact. This approach, in order to counteract the potentially lower amplification efficiency, will require a redesign of the main amplifier fiber (regarding its length, total ion concentration and/or the ratio of the pump cladding to the doped region) and/or pump sources with higher brightness. These measures should also be ideally accompanied by higher seed powers.

4. Intrinsic mitigation strategy: reducing the pump absorption

Figure 5
Fig. 5 Comparison of the mode instability threshold for fibers with different pump absorption levels. All the fibers have an 80µm core, have been seeded with 50W at 1030nm and are pumped at 976nm.
shows the evaluation of the MI threshold for several fibers with different lengths and pump core sizes (i.e. pump absorptions levels). The pump core diameters have been chosen so that the same total amount of pump absorption is maintained along the black line (the pump core area has been increased by a factor of 2 in the red line and by a factor of 3 in the green line). As before, the fibers were pumped at 976nm and were seeded with 50W of LP01 and 0.5W of LP11 at 1030nm. Moreover, the outer diameter of all fibers was kept constant at a value of 1.2mm. Figure 5 clearly shows that a lower level of pump absorption per unit length is beneficial for MI. This is consistent with anecdotal evidence suggesting that longer fibers exhibit higher MI thresholds. However, length alone cannot explain these observations. In fact, it can be seen in Fig. 5 that for a fixed pump core diameter (i.e. pump absorption level) the MI threshold can be almost independent of the fiber length over a relatively wide range of lengths. Only for lengths shorter than about half the optimum pump absorption length for each fiber does the MI threshold start to sink significantly. Thus, according to Fig. 5, the higher mode instability thresholds typically reported for long fibers seem to be mainly the result of the lower pump absorption levels characteristic of those fibers.

5. Conclusion

Passive mitigation strategies for mode instabilities can be divided in two general categories: intrinsic and extrinsic. Intrinsic mitigation strategies involve modifications of the fiber design, whereas extrinsic mitigation strategies involve acting upon system parameters other than the fiber design.

In order to evaluate the relative performance of different mitigation strategies a means to calculate the mode instability threshold is required. Even though this can be done with complex BPM models, this would be extremely time-consuming. From the practical point of view a simple expression that can be quickly evaluated would be more advantageous, even at the price of sacrificing some accuracy. In this paper we propose a new approach to obtain such an expression, which is based on analyzing the strength of the thermally-induced grating. Since the formula obtained this way contains a free parameter γ (that has to be fitted once per fiber type to experimental data), the ability of this expression to predict the threshold of new fiber designs is rather limited. However, once the γ parameter has been fitted, the formula can evaluate the expected change in the MI threshold associated to different mitigation strategies (that involve using the same fiber type). The main differential feature of this formula is that the detailed physics of the amplification process are taken into account.

Thus, using this expression for the MI threshold, two passive mitigation strategies, one intrinsic and one extrinsic, have been presented and analyzed. The extrinsic mitigation strategy is based on reducing the quantum defect in fiber amplifiers by either changing the signal or the pump wavelength. The advantages and disadvantages of these two approaches from the practical point of view have been discussed. The intrinsic mitigation strategy is based on reducing the pump absorption level. Both strategies promise significant increases of the MI threshold with only moderate changes in current fiber amplifier systems.

Acknowledgments

The research leading to these results has received funding from the German Federal Ministry of Education and Research (BMBF), the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. [240460] “PECS,” and the Thuringian Ministry for Economy, Labour, and Technology (TMWAT, Project no. 2011 FGR 0103) with a European Social Fund (ESF) grant and the Thuringian Ministry of Education, Science and Culture TMBWK) under contract B514-10061 (Green Photonics). Additionally, F.J. acknowledges financial support by the Abbe-School of Photonics Jena.

References and links

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2.

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D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27(11), B63–B92 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=josab-27-11-B63. [CrossRef]

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8.

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(5), 689–691 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=ol-36-5-689. [CrossRef] [PubMed]

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J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14(7), 2715–2720 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2715. [CrossRef] [PubMed]

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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]

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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(2), 94–96 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-2-94. [CrossRef] [PubMed]

12.

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]

13.

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]

14.

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(12), 12912–12925 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12912. [CrossRef] [PubMed]

15.

A. V. Smith and J. J. Smith, “Steady-periodic method for modeling mode instability in fiber amplifiers,” Opt. Express 21(3), 2606–2623 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-2606. [CrossRef] [PubMed]

16.

B. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Express 20(10), 11407–11422 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11407. [CrossRef] [PubMed]

17.

H.-J. Otto, C. Jauregui, F. Stutzki, F. Jansen, J. Limpert, and A. Tünnermann, “Controlling mode instabilities by dynamic mode excitation with an acousto-optic deflector,” Opt. Express . submitted.

18.

K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Express 21(2), 1944–1971 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1944. [CrossRef] [PubMed]

19.

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]

20.

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(14), 15710–15722 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15710. [CrossRef] [PubMed]

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OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2400) Fiber optics and optical communications : Fiber properties
(140.6810) Lasers and laser optics : Thermal effects

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: June 5, 2013
Revised Manuscript: July 15, 2013
Manuscript Accepted: July 17, 2013
Published: August 8, 2013

Citation
Cesar Jauregui, Hans-Jürgen Otto, Fabian Stutzki, Florian Jansen, Jens Limpert, and Andreas Tünnermann, "Passive mitigation strategies for mode instabilities in high-power fiber laser systems," Opt. Express 21, 19375-19386 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19375


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References

  1. T. Maiman, “Stimulated optical radiation in Ruby,” Nature187(4736), 493–494 (1960). [CrossRef]
  2. T. J. Kane, R. C. Eckardt, and R. L. Byer, “Reduced thermal focussing and birefringence in zig-zag slab geometry crystalline lasers,” IEEE J. Quantum Electron.19(9), 1351–1354 (1983). [CrossRef]
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