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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12912–12925
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Physical origin of mode instabilities in high-power fiber laser systems

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


Optics Express, Vol. 20, Issue 12, pp. 12912-12925 (2012)
http://dx.doi.org/10.1364/OE.20.012912


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Abstract

Mode instabilities, i.e. the rapid fluctuations of the output beam of an optical fiber that occur after a certain output power threshold is reached, have quickly become one of the most limiting effects for the further power scaling of fiber laser systems. Even though much work has been done over the last year, the exact origin of the temporal dynamics of this phenomenon is not fully understood yet. In this paper we show that the origin of mode instabilities can be explained by taking into account the interplay between the temporal evolution of the three-dimensional temperature profile inside of the active fiber and the related waveguide changes that it produces via the thermo-optical effect. In particular it is proposed that non-adiabatic waveguide changes play an important role in allowing energy transfer from the fundamental mode into the higher order mode. As it is discussed in the paper, this description of mode instabilities can explain many of the experimental observations reported to date.

© 2012 OSA

1. Introduction

Due to the impressive development of fiber laser technology in recent years [1

1. 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). [CrossRef]

], optical fibers have earned a solid reputation as a highly power scalable laser concept. This unparalleled progress, that has seen laser systems evolve from low power setups to multi-kW industrial systems in about a decade, has much to do with the extremely high-power handling capability offered by the geometry of the fiber. The very high surface to active volume ratio allows for an efficient heat removal and, therefore, for high-power operation. However, even though the geometry of the fiber relaxes the demands on thermal management, it generates other problems. Thus, the tight confinement of the light in the core of the fiber gives rise to high intensities that interact with the fiber material over long lengths, which increases the impact of non-linear effects. Hence, active fibers for high-power operation (especially in pulsed operation) have to be specifically designed to alleviate the adverse consequences derived from the non-linearity of the material. The most effective way of mitigating non-linear effects in active fibers is to enlarge the core. This results in a twofold advantage: on the one hand it reduces the intensity of the light propagating in the fiber core and, on the other hand, in double-clad fibers if the pump cladding diameter is not changed, it increases the pump absorption, which allows for shorter devices, thus further mitigating the impact of non-linear effects. Unfortunately, realizing fibers with large cores that still support single-mode operation is far from trivial, especially for high-power operation. In fact, even though the most advanced fiber designs have some in-built mechanism of mode discrimination [2

2. 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). [CrossRef] [PubMed]

,3

3. C. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively single-mode chirally-coupled core fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2.

], fibers with mode-field diameters larger than 50µm typically support the propagation of a few modes. Consequently, in high-power fiber laser systems today the combination of high thermal loads with few-mode operation is to be found for the first time [4

4. 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). [CrossRef] [PubMed]

]. This can potentially give rise to new phenomena such as the recently observed onset of mode instabilities at high average powers [5

5. 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). [CrossRef] [PubMed]

].

The phenomenon of mode instabilities refers to the output beam of a fiber laser system becoming suddenly unstable once that a certain output power threshold has been reached. Thus, it can be observed that with only a small increase of the output power, the once Gaussian-like output beam of the fiber starts to fluctuate. In this regime the intensity profile at the output of the fiber shows a constantly changing beam formed by the coherent superposition of the fundamental mode and one or more higher-order modes [6

6. 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). [CrossRef] [PubMed]

]. Recent measurements with a high-speed camera have confirmed that there is actually energy transfer between the fundamental mode and the higher-order mode [7

7. 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]

]. Furthermore, Fourier analysis of the beam fluctuations has revealed that, near the threshold, these are not random but follow quasi-periodic patterns with well-defined frequencies [8

8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

]. However, when increasing the power further, the beam fluctuations seem to become chaotic.

The paper is organized as follows: in section 2 a detailed explanation of the origin of mode instabilities will be provided and in section 3 the theoretical explanation will be supported with simulations. Section 4 provides an overview of the main experimental characteristics of mode instabilities together with a discussion of how they can be understood at the light of the theoretical explanation presented in this paper. Finally some conclusions are drawn.

2. The physical origin of mode instabilities

From Fig. 1(c) onwards there is an additional fourth illustration just below the schematic plot of the longitudinal temperature profile. This new illustration also symbolizes the fiber, but in it the thermally-induced index grating has been schematically represented (as an arrangement of solid dark blue rectangles, each standing for a period of the grating) and/or the thermal load (as an arrangement of empty rectangles).

In the following the explanation of the physical process leading to mode instabilities will be divided in three parts: the first one describes the mechanism allowing energy transfer from the FM into the HOM, the second one details the process that provides the required conditions to allow energy transfer from the HOM into the FM, and the third section presents a description of the circumstances that might lead to the reversal of the direction of energy transfer.

2.1. Energy transfer from the FM to the HOM

It is worth noting at this point that this effect becomes stronger the more the HOM content grows towards 50%. At this point the amplitude of the temperature oscillations and, therefore, the non-adiabatic waveguide changes will reach their maximum strength. From this point on, however, the further the HOM content grows towards 100%, the weaker the effect becomes, because the oscillations in the temperature profile become weaker and, therefore, the waveguide changes become progressively more adiabatic.

2.2. Energy transfer from the HOM to the FM

The modification of the interference period is ultimately dependent on the local transverse temperature gradient, which varies along the fiber. Therefore, the period of the interference pattern will be modified (compressed) in different degrees at different positions along the fiber (Fig. 3(a)). That is the same to say that the period of the interference will be chirped, with a chirp function that roughly follows the longitudinal temperature profile. This modified interference pattern will generate a new heat load which is slightly shifted with respect to the index grating that has been already thermally induced in the fiber (see Fig. 3(a)). Thus, with more time, the temperature profile, and therefore the index grating, will evolve in the direction given by this new heat load. This evolution causes the local movement of the index grating (Fig. 3(b)). In high-power amplifiers this movement will be typically upstream the fiber (i.e. towards the input of the fiber). Thus, this movement will cause the energy to flow from the higher-order mode into the fundamental mode. It is important to note, additionally, that this effect becomes weaker when the local period of the interference pattern approaches the period determined by the local waveguide characteristics.

2.3. Reversal of the direction of energy transfer

Thus, the physical processes described above are what we believe lead to mode instabilities. However, there are some points that are still under investigation on our side and that will require clarification in the future. One of these points is to study if the model as described above is inherently chaotic (as observed in the measurements) or if, instead, it will always relax to a stable state. Provided that the latter were the case, it might be required to include weak external perturbations (which are, on the other hand, always present in any experimental setup) to trigger the chaotic evolution of the system, as already suggested in [15

15. 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). [CrossRef] [PubMed]

]. However, it is still soon to draw any conclusions on this point since, as mentioned before, it is still subject of ongoing research.

It is important to underline that in this explanation of the physical process leading to the movement of the grating and to the energy transfer between the transverse modes, only the interplay between the evolution of the three-dimensional temperature profile and the resulting modification in the index profile of the fiber have been considered. Thus in this model, as opposed to [11

11. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011). [CrossRef] [PubMed]

], both transverse modes at the beginning of the fiber have identical spectra. Nevertheless, the movement of the index grating, via the Doppler Effect, will lead to a small frequency shift between the modes at the output of the fiber. The crucial detail here is that in the physical process described in this paper, the appearance of a frequency shift between the transverse modes is simply a consequence of the movement of the grating but it is not the mechanism originating this movement.

In the following the viability of the physical process described in this section will be demonstrated with the help of simulations.

3. Simulation results

In the following a 0.25m long step-index fiber is simulated with 80μm core diameter (completely doped with Ytterbium ions; total ion concentration N = 1.31026 ions/m3), 0.027 numerical aperture, 200μm pump core diameter, 1.8mm outer fiber diameter, passively cooled in air, and pumped with 300W at 976nm in the counter-propagating direction. These fiber parameters do not correspond to any realistic fiber. However, they have been chose because the high thermal loads generated in the fiber (due to the high power extraction in a short length) and, therefore, the fast temperature evolution, allows us to accelerate the simulation. Thus, the physics behind mode instabilities can be analyzed with a relatively short computational time.

The signal injected as seed for this fiber amplifier is centered at 1064nm and consists of a 1MHz train of 1ns Gaussian pulses which, when coupled into the fiber, excite pulses with 1000W peak power in the LP01 mode (FM) and of 100W peak power in the LP02 (HOM). The active fiber has been pumped until full inversion is reached before the seed signal is injected. The evolution of the fiber was simulated over 1ms.

Figure 5(b) shows the instantaneous shift of three maxima of the temperature profile/index grating originally situated at three different positions along the fiber: one towards the end of the fiber at ~0.22m (red line), another towards the middle of the fiber at ~0.15m (green line), and a last one at the beginning of the fiber at ~0.05m (gray line). What this graph reveals is that even though different maxima of the temperature profile/index grating move in the same direction (downstream the fiber in this case), they do so at different speeds. This points out towards a much more complex movement of the grating than that suggested in [11

11. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011). [CrossRef] [PubMed]

].

The evolution of the relative mode content at the output of the fiber over the 1ms simulation time is plotted in Fig. 7
Fig. 7 Evolution of the relative mode content at the output of the fiber for the FM (blue line) and for the HOM (green line) over the 1ms simulation time.
. There it can be seen that the HOM content at the beginning of the simulation was about 2.3% (which is lower than the ~10% that has been set at the input of the fiber mainly due to the effect of preferential gain), but it continuously increases during the simulation until it reaches ~9.64% (i.e. more than a factor of four increase) by the end. Therefore, Fig. 7 confirms that the process generating the movement of the temperature profile/index grating does indeed lead to energy transfer between the interfering transverse modes. Furthermore, the increase of energy in the radiation modes (black line) is an indirect indication of the existence of non-adiabatic waveguide changes.

It is worth noting that Fig. 7 does not show the dramatic energy conversions (of ~100%) characteristic of mode instabilities, nor does it show its complex dynamic behavior (see [7

7. 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]

] and [8

8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

]). The probable reasons for this are, on the one hand, that the typical periods of mode instabilities for fibers with comparable mode-field diameters to the one that has been simulated is of several ms [8

8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

]. Additionally, as has been previously discussed, the threshold of mode instabilities for radially symmetric modes is expected to be much higher than that corresponding to radially anti-symmetric modes. Finally, very recent measurements have revealed that the build-up of the index grating can take several ms [19

19. N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Build up and decay of mode instabilities in a high power continuous wave fiber amplifier,” Opt. Express . submitted.

]. All these factors together make it unlikely that mode instabilities can be observed under the conditions simulated in this example. Anyways, even though we have not reproduced the instabilities in the simulation, the numerical results have demonstrated that the physical mechanisms described in this paper lead to energy transfer between the interfering modes.

4. Discussion

In this section some of the experimental characteristics of mode instabilities will be listed and, then, it will be analyzed how the current theoretical understanding of mode instabilities can (or cannot) explain them. The list of experimental characteristics has been compiled either from published papers (references will be given) or from anecdotal evidence.

  • Mode instabilities appear after a certain output power threshold has been reached [6

    6. 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). [CrossRef] [PubMed]

    ]: As demonstrated in [11

    11. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011). [CrossRef] [PubMed]

    ] a moving index grating can explain the appearance of a threshold in the process of energy transfer between transverse modes.
  • During mode instabilities there is a continuous back and forth transfer of energy between the interfering transverse modes [7

    7. 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]

    ]: As explained in section 2, there are two competing effects that force the index grating to move in opposite directions. Thus, depending on which effect is dominant the energy will flow from the FM into the HOM or the other way around.
  • There is a dependence of the fluctuation speed of the mode instabilities with the mode-field diameter of the modes, i.e. in larger fibers the mode instabilities are slower [8

    8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

    ]: This can be explained by taking into account the thermal origin of mode instabilities. Due to the finite thermal conductivity of silica, the thermalisation time becomes larger the larger the mode area.
  • Fibers with larger mode-field diameters exhibit, in general, lower mode instability thresholds [8

    8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

    ]: This can be understood given that larger modes are typically more sensitive to waveguide changes. This implies that smaller temperature gradients (both transverse and longitudinal) are required to strongly modify them and, therefore, to set the index grating in motion.
  • Near the threshold the spectrum of the mode instabilities shows several resonances with a certain bandwidth [8

    8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

    ]: The appearance of these peaks is due to the frequency shift caused by the movement of the index grating. Additionally, their finite bandwidth can be understood taking into account the complex movement of the grating revealed by our simulations, i.e. different sections of the grating move at different speeds.
  • Mode instabilities have been observed exclusively between the fundamental mode and radially anti-symmetric modes: Most likely this is due to the presence of transverse spatial hole burning favoring the amplification of radially anti-symmetric modes, as discussed in section 3. This would explain why these modes have the lowest mode instability threshold and, therefore, why almost all mode instability experiments published to date have been reported the appearance of this kind of modes. However, this is a point that still requires further clarification.
  • Above the power threshold for mode instabilities the beam fluctuations evolve towards chaos [8

    8. H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

    ]: Possibly the combination of the non-linear coupling between the beam propagation and the temperature (i.e. they influence one another in a non-linear way as can be inferred from the discussion presented in section 2) with the memory effect of the temperature profile/index grating (which has to evolve from a previous state) leads to a chaotic system. However, this is still a hypothesis and it needs to be confirmed with future research. The truth is that our current models allow us to understand the origin of mode instabilities, but the investigations are not so advanced yet as to explain the complex temporal dynamics of this effect.
  • The effect of mode instabilities seems to have a build-up time and lifetime of some ms [19

    19. N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Build up and decay of mode instabilities in a high power continuous wave fiber amplifier,” Opt. Express . submitted.

    ]: This, once again can be explained taking into account the thermal origin of the effect: as the fiber heats up, the index grating gains in strength and it progressively transfers more and more energy to the HOM. Thus, there is a build-up time of the index grating. On the other hand, if the pump or the seed are suddenly switched-off, the index grating will survive for a time until a homogeneous temperature profile is reached in the fiber.

5. Conclusion

In this paper a new understanding of the physical origin of mode instabilities has been presented and discussed. Energy transfer between the two transverse modes is allowed by the movement of an index grating, which has been ultimately originated by the interference of these two transverse modes. The movement of the grating can be explained by the complex interplay between the temporal evolution of the three-dimensional temperature profile in the fiber, the waveguide changes that it causes, and the effect that these changes have on the interference pattern (which in turn gives rise to the temperature profile). The validity of this model has been supported by simulations showing that the proposed physical process does indeed lead to the movement of the index grating and to the energy transfer between the transverse modes. Finally, some of the most important experimental characteristics of mode instabilities have been analyzed at the light of this new theoretical explanation of the effect. The detailed understanding of the physical origin of mode instabilities should help in the quest of finding efficient methods to mitigate it.

Acknowledgments

The authors what to thank Andrei N. Starodoumov for useful discussions and for making us aware of the existence of stimulated thermal Rayleigh scattering. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement n° [240460] and the Thuringian Ministry of Education, Science and Culture under contract PE203-2-1 (MOFA) and contract B514-10061 (Green Photonics). F.J. acknowledges financial support from the Abbe School of Photonics.

References and links

1.

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). [CrossRef]

2.

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). [CrossRef] [PubMed]

3.

C. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively single-mode chirally-coupled core fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2.

4.

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). [CrossRef] [PubMed]

5.

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). [CrossRef] [PubMed]

6.

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). [CrossRef] [PubMed]

7.

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]

8.

H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnerman, “Temporal dynamics of mode-instabilities in high power fiber lasers and amplifiers,” Opt. Express . submitted. [PubMed]

9.

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). [CrossRef] [PubMed]

10.

A. A. Fotiadi, O. L. Antipov, and P. Megret, “Resonantly induced refractive index changes in Yb-doped fibers: the origin, properties and application for all-fiber coherent beam combining,” Frontiers in Guided Wave Opt. and Optoelectr. 209–234 (2010), http://www.intechopen.com/books/howtoreference/frontiers-in-guided-wave-optics-and-optoelectronics/resonantly-induced-refractive-index-changes-in-yb-doped-fibers-the-origin-properties-and-application.

11.

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19(11), 10180–10192 (2011). [CrossRef] [PubMed]

12.

A. Malvache, X. Chen, C. G. Durfee, A. Jullien, and R. Lopez-Martens, “Multi-mJ pulse compression in hollow fibers using circular polarization,” Appl. Phys. B 104(1), 5–9 (2011). [CrossRef]

13.

T. K. Allison, A. Cingöz, D. C. Yost, and J. Ye, “Extreme nonlinear optics in a femtosecond enhancement cavity,” Phys. Rev. Lett. 107(18), 183903 (2011). [CrossRef] [PubMed]

14.

M. E. Mack, “Stimulated thermal light scattering in the picosecond regime,” Phys. Rev. Lett. 22(1), 13–15 (1969). [CrossRef]

15.

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). [CrossRef] [PubMed]

16.

J. Marcou, J. L. Auguste, and J. M. Blondy, “Cylindrical 2D beam propagation method for optical structures maintaining a revolution symmetry,” Opt. Fiber Technol. 5(1), 105–118 (1999). [CrossRef]

17.

M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15(6), 3236–3246 (2007). [CrossRef] [PubMed]

18.

J. Riishede, N. A. Mortensen, and J. Lægsgaard, “A ‘poor man’s approach’ to modeling micro-structured optical fibres,” J. Opt. A 5(5), 534–538 (2003). [CrossRef]

19.

N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Build up and decay of mode instabilities in a high power continuous wave fiber amplifier,” Opt. Express . submitted.

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: April 5, 2012
Manuscript Accepted: April 27, 2012
Published: May 23, 2012

Citation
Cesar Jauregui, Tino Eidam, Hans-Jürgen Otto, Fabian Stutzki, Florian Jansen, Jens Limpert, and Andreas Tünnermann, "Physical origin of mode instabilities in high-power fiber laser systems," Opt. Express 20, 12912-12925 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12912


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References

  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. 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). [CrossRef] [PubMed]
  3. C. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively single-mode chirally-coupled core fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2.
  4. 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. Express20(4), 3997–4008 (2012). [CrossRef] [PubMed]
  5. 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). [CrossRef] [PubMed]
  6. 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]
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