We report on the observation and experimental characterization of a threshold-like onset of mode instabilities, i.e. an apparently random relative power content change of different transverse modes, occurring in originally single-mode high-power fiber amplifiers. Although the physical origin of this effect is not yet fully understood, we discuss possible explanations. Accordingly, several solutions are proposed in this paper to raise the threshold of this effect.
©2011 Optical Society of America
During the last decade, fiber amplifiers delivering near diffraction-limited output beams have undergone an unprecedented increase in average power. Especially in high-power operation fiber systems benefit from the advantages derived from the fiber geometry. On the one hand, the large ratio of surface to active volume confers fibers an excellent heat-removal capability. Besides, the use of Ytterbium as active ion helps to further reduce the thermal load thanks to its low quantum defect. On the other hand, due to the guidance of the signal light within a waveguide structure, the fundamental mode can propagate largely unaffected by disturbing thermal lensing effects  which typically limit common solid-state laser concepts. However, at this point of the development, in which single-mode fiber-based systems in continuous wave (cw) operation have reached an average power of 10 kW  and even ultrashort pulse systems are approaching the kilowatt level , questions about possible fundamental limitations in the further scalability of single-mode fiber laser systems arise. In conventional scaling studies a variety of effects is considered  including the available pump diode brightness, the damage threshold and nonlinear effects. Typically, the latter impose the strongest restrictions, whereby the actual type of nonlinear effect that has to be considered depends both on the fiber design and on the temporal and spectral properties of the amplified signal.
One straightforward approach to reduce the impact of nonlinearities is the increase of the mode field diameter (MFD) and, therefore, a reduction of the intensity in the signal core. Actually, this procedure results in double advantage since the required fiber length is additionally shortened due to the increased pump absorption (assuming a fixed pump cladding diameter). In the case of standard step-index fibers (SIFs), the enlargement of the fundamental MFD is achieved by reducing the core numerical aperture (NA) while its radius r is simultaneously increased. This is done to ensure that the parameter V = 2π r / λ NA is smaller than 2.405 , which for any given wavelength λ ensures strict single-mode propagation. However, due to technological restrictions in production as well as in characterization, the NA cannot be controlled to arbitrarily low values. Currently, the largest strictly single-mode core diameter produced by modified chemical vapor deposition is of the order of 13 µm (NA~0.06, 1 µm wavelength). Any further increase in core size results in the guidance of higher order modes (HOMs). The impact of these HOMs can be minimized to a certain extent by exploiting e.g. single-mode excitation  or the modal dependence of bend-induced losses . On the other hand, the development of solid-core photonic crystal fibers (PCFs)  has led to very large MFDs [9–11]. However, PCFs are intrinsically multi-mode waveguides, although HOMs usually possess higher propagation losses  or lack any significant overlap with a confined core region (e.g. the doped area) . A number of alternative approaches focus on resonant coupling of HOMs out of the doped core, leading to an effective single-mode emission, e.g . Therefore, whether step-index or PCF concepts are pursued, larger mode areas in fibers are accompanied with allowed but typically weak guidance of higher-order transverse modes.
As a consequence, one could assume that this slight multi-mode behavior does not impose a serious power scaling limitation in fiber laser systems. However, in recent experiments [3,11, 13–15] a threshold-like onset of mode instabilities in large-mode area fibers at very high average-power levels has been observed. This is an effect that, to the best of our knowledge, has not been reported so far and will be described and discussed in this paper.
The paper is organized as follows: After a description of the experimental observations in section 2 we briefly discuss possible physical origins of this effect in section 3. In section 4 we discuss possibilities of increasing the threshold and we give a conclusion in section 5.
2. Mode instabilities in fiber amplifiers
2.1. Illustration of the observed effect
The effect of mode instabilities can be observed in high-average power operation of fiber lasers and amplifiers when the amplified signal power exceeds a certain threshold value. Below this threshold, the near field profile and the measured beam quality out of the amplifier fiber appear to be single mode. However, at and above the threshold, an apparently random temporal change in the mode content accompanied by a sudden decrease in beam quality can be observed.
As an example, Media 1 shows the evolution of the near-field of a large-pitch photonic crystal fiber (LPF) with 56 µm MFD that is used as a single-pass amplifier, when the signal power is raised above the threshold. The used fiber is comparable to LPF2 in reference , where the effect has also been observed, but has a slightly larger MFD due to a larger hole-to-hole distance of 35 µm. Additionally, the average output power and the launched pump power are shown in this movie. Figure 1 shows single frames of Media 1 at pump powers below and above the threshold.
It can be seen in this video that starting from a stable fundamental-mode output a slight increase of the pump power of only a few percent results in the onset of beam fluctuations. Please note that in the video the residual slight movement of the stable beam is due to air movement in the relatively long path length between fiber output and the camera. The subsequent reduction to a power level below threshold results again in a stable fundamental-mode output beam, thus, no hysteresis is observed. Furthermore, the average power does not drop at this threshold and can actually be further increased with subsequent beam quality degradation. The frequency of these fluctuations is typically in the range of a few kHz and the fluctuations become more chaotic when the pump power is further raised.
2.2 Further experimental investigations
Further experiments showed that for a given fiber design, the threshold occurs at comparable (but not identical) power levels for either continuous wave or pulsed operation, which in principle rules out any strong dependence of this effect on the peak power. Further details on these experiments can be found in  for continuous wave and in  for pulsed amplification in the same fiber.
It is worth mentioning that we observe the effect of mode instabilities in state-of-the-art large-mode area fibers, i.e. in fibers that can handle extreme average power levels and that possess a pump cladding (usually an air-clad) which is large enough to launch sufficient pump power. In the following, we present experimental results for two such double clad fibers used in amplifier configuration with a cw-seed. For these fibers, Fig. 2 shows the measured M2- value (2nd moment method) as a function of the signal output power. The first fiber is a PCF with a core that is defined by a seven missing air-holes microstructured region with a MFD of 33 µm. The second fiber is a step-index core fiber with a MFD of 27 µm. Both fibers have an air-clad with a diameter of 500 µm and are pumped in counter-propagating direction at 976 nm central wavelength. The bending radius is approximately 0.5 m. Figure 2a shows the measurement for the 10.5 m long PCF. The seed signal is a narrow band (12 pm FWHM) amplified spontaneous emission source at 1030 nm central wavelength (please see reference  for more details). The threshold-like onset of mode instabilities can be clearly observed as a sudden increase of the M2 factor from M2 = 1.3 to M2 = 1.8 at an output power of about 700 W.
In Fig. 2b the measurement for the 9.5 m long SIF is shown for two different seed sources . The applied signal powers are 20 W at a wavelength of 1055 nm (narrow band Δλ~60 pm, linearly polarized) and 200 W at 1071 nm (broad band Δλ~2.6 nm, unpolarized) average seed power. The measured mode-instability threshold is 1240 W for the 20 W seed average power and 1740 W for the 200 W seed. An additional experimental threshold of 950 W was obtained for 8 m of the same SIF from ref . for the amplification of a quasi-cw (80 MHz) signal comprising broadband pulses. In this experiment, 30 W of linearly polarized seed power centered at 1040 nm wavelength was used.
The increase of the mode-instability threshold with a change of the seed source as indicated in Fig. 2b is a remarkable feature. Since changing the seed power and wavelength primarily affects the inversion along the fiber, the results presented in Fig. 2b strongly suggest that these instabilities are linked to gain dynamics. Hence, this point will be further discussed in the next section.
Figure 2 also shows that below the threshold the beam quality steadily improves with increasing pump power. The reason for this effect is that the residual signal light that is not coupled into the signal core (free space coupling) and is guided in the pump cladding corrupts the M2-measurement. However, the relative fraction of this light decreases with increasing signal power and, therefore, the M2 measurement is improved.
As a conclusion of these preliminary experiments (and also of additional experiments not shown here) it can be stated that the mode-instability threshold is influenced by several experimental parameters such as the wavelength, seed power, the quality of the mode excitation, the temporal and the spectral properties of signal and pump, the signal polarization, etc. As it will be discussed in the next sections, these dependencies offer further insight into the physical origin of this effect and they offer, together with changes in the fiber design, opportunities for increasing the threshold.
From comparing additional fibers (details not shown here) it can be summarized that the observed threshold value varies between a few hundred Watts and several kilowatts of average power depending on the actual fiber design, i.e. the core size, the number and losses of HOMs and the fiber length. In these experiments it has been observed that the threshold is, under comparable experimental conditions, typically lower for larger mode field diameters.
3. Discussion of the physical origin
The physical cause of the observed mode instabilities is not completely understood yet. In principle the experimental observations exclude “classical” nonlinear effects, since it seems that the threshold is primarily dependent on the average power and not on the peak power. Additionally, the onset of instabilities only observed at high average-power levels (i.e. they have not been observed in low power experiments with the same fibers and the same gain) suggest that they can be attributed to saturation effects, thermal load and/or induced stress. However, a complete theoretical description of this problem would require the three-dimensional analysis of a high power fiber amplifier including the temporally and spatially resolved description of the gain dynamics, the modeling of the thermal load and stress and the calculation of the beam propagation and deformation along the fiber core. If this exhaustive modeling were possible at all, it would certainly rely on demanding numerical simulations that would still have to be developed. Nevertheless, at the moment of writing this paper there are already some plausible explanations for this effect, which we will discuss in the following.
At first (e.g. in  or ) mode instabilities at high average-power levels were attributed to transversal spatial-hole burning (TSHB) . Here, the fundamental mode depletes the inversion only in the inner part of the doped region of the core. The remaining inversion in the outer regions of the core can preferentially amplify HOMs possessing their intensity maximum in that area. However, simulations based on a spatially resolved solution of the steady-state rate equations predict that the fundamental mode always experiences a higher gain than the HOMs in fibers with confined doping. This is the case of the fiber depicted in Media 1, and of many other active PCFs, since PCFs usually possess a doping radius smaller than the core radius as a result of the stack-and-draw production technique. Therefore, TSHB cannot be the only mechanism at play in the fiber shown in Media 1. Additionally, TSHB cannot explain the threshold-like behavior since it would only predict a steady degradation of the beam quality.
In our opinion, the most likely explanation of this mode-instability effect is the formation of induced long-period gratings as proposed in . Here the interference pattern of the fundamental mode and a HOM is mapped into the inversion that, in turn, locally modifies the refractive index of the core. In theory, the resulting long-period grating can efficiently couple the light from the fundamental mode to HOMs. Moreover, this type of induced gratings has already been experimentally demonstrated by exploiting the Kerr effect . Additionally, inversion related gratings that are induced by counter-propagating signal waves have been known for many years . In the case of the inversion gratings that may be responsible for the observed mode instabilities, the exact origin of the index change still has to be determined. Possible causes are the resonantly enhanced nonlinearity  due to the inversion, the temperature dependence of the refractive index or the induced stress. Although recent considerations  strongly point towards a dominant thermal origin, further experimental and theoretical investigations are necessary for a complete understanding of this effect.
4. Possibilities of increasing the threshold
Despite the lack of full understanding of the effect, there are several possible steps that have already demonstrated an increase of the threshold. Being the effect directly related to the presence of HOMs in the fiber, any technique that suppresses the HOM content in the fiber core will simultaneously increase the mode-instability threshold. Thus, one straightforward solution is to use fibers that are “more single-mode”. This could be achieved by using smaller core diameters, but this approach of course promotes detrimental nonlinear effects. Another possibility is to use novel fiber designs that are able to suppress the HOM content. One promising concept is the so-called large-pitch fiber that has already demonstrated nearly 300 W of average power out of only 1.2 m fiber length with a 62 µm fundamental-mode diameter . This result is three times above the threshold of conventionally designed rod-type fibers with a comparable MFD described in .
Additionally to such sophisticated fiber concepts, preferential gain can be included in the fibers by confined doping of the active ions in the core region . Recently, by exploiting that concept it was possible to produce 300 W of average power of fundamental-mode radiation with 47 µm MFD out of a 1.7 m long few-mode fiber design . The advantage of confined doping lies not only in the preferential gain effect but also in the reduction of the transversal inversion gradient. However, confined doping usually reduces the available gain and the pump absorption which, therefore, results in longer fiber lengths, something that is disadvantageous for pulsed operation at high power levels.
Another interesting concept is shifting the pump to longer wavelengths. This is usually realized via tandem-pumping [2, 24], i.e. one fiber amplifier is pumped by several other fiber amplifiers emitting at a slightly lower wavelength. In the case of Ytterbium doped fibers, the pump wavelength is usually chosen between 1010 nm – 1040 nm and the laser wavelength is chosen to be longer than 1050 nm. The result is a limitation of the maximum achievable inversion to just a few percent since pump transparency is reached already at very low inversion levels (at room temperature typically <10%). Consequently, this reduces the transversal inversion gradient and negative effects resulting from TSHB or the inversion grating discussed in the previous section are also reduced. However, due to the low inversion levels and the corresponding low gain, relatively long fibers are required, which usually restricts this technique to cw-fiber amplifiers.
We have described the experimental observation of the threshold-like onset of mode instabilities occurring in large-mode area high average power fiber amplifiers. This effect is currently the most limiting factor for the maximum extractable average power in fundamental-mode operation, therefore, constitutes one of the main challenges for fiber based laser development.
We briefly discussed some possible explanations and summarized some techniques that may help to further increase the maximum achievable output power of large-mode-area fiber amplifiers. The threshold of these instabilities strongly depends on the fiber design and several experimental parameters. Additional experiments and improved theoretical models have to be investigated to gain further insight in order to inhibit this effect in the future.
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°  and the Thuringian Ministry of Education, Science and Culture under contract PE203-2-1 (MOFA). F. J. acknowledges financial support by the Abbe School of Photonics Jena.
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