1. Introduction

The average-power scaling of single mode fiber lasers and amplifiers is currently under intense theoretical and experimental investigation. This involves exploring transverse mode instabilities (TMI) [1], especially in Yb-doped fibers. This effect currently limits the extraction of high average power with single-mode output in all kinds of Yb-doped fibers, from step-index to special photonic-crystal fibers. Above the TMI threshold, energy is dynamically transferred between different transverse modes resulting in the reduction of beam quality and in a fluctuating beam profile at the fiber output [2, 3].

Guidelines to increase the TMI-threshold have already been given based on the understanding of the effect [4]. Some of them include actively influencing the amplifier dynamics, carefully designing the fibers core in terms of optical and material properties as well as optimizing system aspects such as bending and mode excitation [5].

Apart from TMI, avoiding nonlinear effects, such as inelastic scattering processes (stimulated Brillouin and Raman scattering (SBS, SRS)), is also typically necessary while scaling the output power of fiber amplifiers [6]. In order to mitigate these effects, the most effective strategy is scaling the effective mode area of the fundamental mode. Moreover, assuming constant material absorption properties and pump core geometry, a larger core leads to a reduced absorption length, which further reduces the nonlinear interaction length. Unfortunately, since TMI seems to be driven by the heat load of the fiber in the high average power regime, it gets more difficult to avoid them, if the fibers core is enlarged and the fiber gets shorter [2]. Furthermore, the TMI-threshold seems also to depend on the supported transversal mode content of the fiber core and on the propagation losses of the higher-order modes [7, 8].

Because of the interplay of the different variables mentioned above, the highest reported single-mode output power of narrow-linewidth fiber amplifiers was limited to an output power of 3.1 kW from a 17 µm core, short fiber (4 m) [9] and to 3 kW out of a 24.5 µm core with a relatively long fiber (30 m) [5]. A few other systems stating single mode or nearly diffraction limited beam quality have been presented, but, unfortunately, they show higher order mode content or have not been characterized in terms of TMI, thus making the comparison with other systems impossible [10–13].

Here we report on the continuation of our effort to scale the TMI threshold by controlling the fiber properties of low-NA large mode area fibers. We show a fiber with a core diameter of 30 µm that is able to generate a stable narrow linewidth output of 2.8 kW limited by TMI. Additionally, we also show a further scaling of the output power to 4.3 kW using a fiber with 23 µm outer core diameter that shows no indication of TMI or SRS.

2. Fiber design and characterization

It is well known that low NA-fibers are well suited for power scaling of fiber amplifiers to the kW-level [5]. In this context, the optimization of the core refractive index profile and the core diameter plays an essential role in determining the modal properties of the fiber. In order to examine the limits imposed by nonlinear effects NLE and TMI, two fibers with different core diameters and refractive index profiles were produced by modified chemical vapor deposition technology (MCVD) with solution doping.

The TMI-threshold seems to decrease by higher average heat load deposited in the amplifier fiber and quantum defect as well as photodarkening have been found to mainly influence this heat [14]. To lower the average heat load, low ytterbium concentrations were chosen for the fibers under test. On the one hand, a low ytterbium concentration distributes the heat to a longer absorption length and on the other hand, a low ytterbium concentration lowers the photo darkening equilibrium loss [15].

The refractive index profiles of the resulting fibers have been measured (IFA-100 Fiber Index Profiler) and are shown in Fig. 1. Here, we define the outer core diameter by the intersection of the linear regression of the outer core flanks and the surrounding cladding profile. Fiber 1 had an outer core diameter of 30 µm whereas that of fiber 2 was 23 µm. Both double-clad fibers were produced with an octagonal pump core with a flat-to-flat diameter of 460 µm. The dopant concentrations were measured using electron probe micro analysis (EPMA) [16]. A core doping concentration of 0.9 mol% of phosphorus, 0.5 mol% of aluminum and 0.07mol% of ytterbium was measured for fiber 1. Fiber 2 was made with a dopant concentration of 0.6 mol% of phosphorus, 0.4 mol% aluminum and 0.09 mol% of ytterbium to achieve a slightly higher index profile compared to fiber 1.

 

Fig. 1 Refractive index profile relative to the pump cladding index of fused silica for the active core regions of fiber 1 and 2.

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In addition, an Optical Frequency Domain Reflectometer (OFDR) was employed to measure the average fiber core attenuation at a wavelength of 1.3 µm for various bend diameters [18]. As shown in Fig. 2, the attenuation of the fiber core is constant for both fiber samples with large bend diameters. In this regime, the attenuation represents the core background losses at 1.3 µm. With a measured value of 16 dB/km a very efficient fiber operation is expected.

 

Fig. 2 Loss of the fundamental mode as a function of fiber bend diameter for fiber 1 and fiber 2. The attenuation was determined by OFDR-measurements.

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From the measurement, the critical bend diameter can be defined at the intersection of the constant regime and the asymptotic linear regression of the core attenuation in the logarithmic regime for both fibers. In our fibers, the critical bend diameter for guiding at 1.3 µm is 65 cm and 53 cm for fibers 1 and 2, respectively. This bending behavior is important for various applications. In our case, when analyzing the average power scaling capabilities of a fiber laser system, bending influences the high order mode loss and the TMI threshold such that usually this threshold increases for tighter bending [7]. Of course, the critical bending diameter and high order mode losses would be lower at 1 µm compared to 1.3 µm but, since the attenuation slightly differs for both fibers, we operated both fibers at a diameter much larger than the critical one, more specifically at 1.1 m to see the worst-case performance for both fibers in terms of TMI.

3. Experimental setup and results

Both fibers have been tested in a high power setup schematically shown in Fig. 3. The pump diode laser and the seed signal were free-space coupled into the fiber, which was prepared with spliced end-caps and water flushed connectors in a bath of standing water used for cooling. The setup allowed measuring the output power and the residual pump power. In order to obtain desired pump absorption of more than 95 %, fiber lengths of 35 m and 30 m were used for fiber 1 and fiber 2, respectively.

 

Fig. 3 Experimental high-power amplifier setup used for the characterization of the fibers. The amplifier was pumped at 976nm in counter-propagation direction. The spectral and temporal behavior of the output beam, as well as its beam quality and output power were analyzed. (PM: Power Meter, DM: Dichroic Mirror)

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The seed was a phase-modulated external-cavity diode laser (ECDL), which was pre-amplified to achieve a seed power of 10 W at 1067 nm and a spectral linewidth of 180 pm. The pump at a wavelength of 976nm (Laserline GmbH, wavelength stabilized by water cooling) was coupled in counter-propagating direction into the fiber. A dichroic mirror was used to separate the amplified signal from the pump light. The measured average power values were corrected for the power loss experienced in the two-way reflection of the wedge plate. Additionally, the beam quality, the optical spectrum and the temporal behaviour were measured. In order to detect the TMI threshold, a small fraction of the power was analysed with a photodiode connected to an oscilloscope using the method described in [17].

The 35 m piece of Fiber 1 has been pumped up to an output power of 2.8 kW with a slope efficiency of 90 % (with respect to absorbed pump power), as can be seen in Fig. 4(a). A spectral linewidth of 180 pm and a ratio of 75 dB from the peak spectral intensity to the ASE maximum intensity were measured for the output signal (Fig. 4(b)). The output power was limited by TMI as shown in Fig. 4(c) and (d). The photodiode signal was stable below the TMI threshold and photodiode traces similar to the one exemplarily shown for a power of 1.5 kW in Fig. 4(c) were obtained. At the threshold of 2.8 kW, the beam showed periodical fluctuations on the ms-scale because of TMI. Figure 4(d) shows the normalized standard deviation of ten of such time traces for every measured output power. It can be seen that at an output power of 2.8 kW the standard deviation rises significantly.

 

Fig. 4 (a) Slope efficiency of the amplifier for fiber 1, (b) Optical spectrum at 3.5kW output power with 75dB level ratio of output signal (with 180pm linewidth) to ASE, (c) Photodiode intensity traces of the output signal at two output powers: below and above the TMI threshold, (d) Evolution of the standard deviation of the normalized PD traces with the output power.

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In a second experiment, a 30 m piece of Fiber 2 seeded with the same front-end was pumped up to an output power of 3.5 kW, limited by SBS. The slope efficiency reached 90%, as shown by the dark blue dots in Fig. 5(a). The spectral characteristic was measured by an optical spectrum analyzer and is shown in Fig. 5(b) (also in dark blue). The intensity ratio between the spectral maximum and the ASE peak is 75 dB.

 

Fig. 5 (a) Slope efficiency of fiber 2 up to an output power of 4.3kW, (b) Optical spectrum at 3.5kW output power with 75dB ratio of the output signal (180pm linewidth) to ASE and spectrum at 4.3kW output power broadened up to a bandwidth of 7nm, (c): Photodiode intensity trace of the output signal at 4.3kW, (d) Normalized standard deviation of PD traces at various output power.

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In a third experiment, a second ECDL with a central wavelength shifted by 300pm with respect to the original one was combined with the first ECDL to obtain a two-wavelength seed. This was used to increase the SBS threshold of the fiber in comparison to the experiment before. The combined signal was send through the same phase modulator in order to keep its coherence and was then pre-amplified to 10 W. In the same main amplifier as before, a very similar output power value and slope efficiency of 90% were obtained (see Fig. 5(a)), but it could be scaled to 4.3 kW without any indication of TMI. The slight roll-off at very high power levels is related to a non-corrected degradation of brightness of the pump diode at these power levels. The output spectrum broadens up to a maximum bandwidth of 7 nm with increasing output power due to self-phase modulation of the temporal sinusoidal signal resulting from the interference of the two-wavelength seed. The spectrum also shows a signal to ASE level ratio of 65 dB, as shown in Fig. 5(b), without any indication of stimulated Raman scattering.

Figure 5(c) shows a time trace of the photodiode signal at 4.3 kW output power and underlines the temporal stability in comparison to the results from fiber 1. Moreover, the standard deviation of the output signal on the photo diode does not change significantly with the output power and gives evidence that no TMI occurs at this output power.

In all experiments, we measured the beam quality carefully. Due to increasing thermal lensing in the output optics above 2 kW, the measurements were performed in pulsed pump mode with a duty cycle of 40% with a 100 ms period, which is much longer than the time scale for TMI [19]. It should be noted that TMI occurs neither in continuous wave nor in pulsed operation. The M² (4σ) was measured to be below 1.3 in both directions, as shown in Fig. 6.

 

Fig. 6 Beam quality measurement (M²x = 1.27, M²y = 1.21) for 4.3 kW peak power at 40% duty cycle.

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An overview on the essential fiber parameters and limitations of the described experiments is given in Table 1.

Table 1. Overview of the relevant fiber parameters, maximum output power, and limitations, for the fibers under test.

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4. Discussion

It is well known that the TMI threshold not only depends on the thermal load [2], but also on the mode content of the fiber [7, 19]. To get a better understanding of the modal behaviour of fiber 1 and fiber 2 we calculated the higher order mode cut-off wavelength using the 2D-refractive index data and assuming a straight fiber with an infinite pump cladding as boundary condition. A simpler prediction done in terms of the V-number is not applicable for the index profiles investigated here (since they deviate significantly from an ideal step-index profile) [20]. The so-calculated cut-off wavelength is located near 1275 nm and 1100 nm for fibers 1 and 2, respectively. This means that fiber 2 is substantially closer to single-mode operation than fiber 1. Bending would even increase the higher order mode losses and shift the cut-off to smaller wavelength, however, it has been tried to use the largest bending diameter possible. Under thermal load, the thermal gradient in the core region will shift the cut-off wavelength towards longer wavelengths potentially increasing the number of modes that can be guided or, at least, it will pull the higher order modes towards the core and increase their overlap with the doped region. Bending can be seen as an influencing parameter for TMI as the theory requires interference and overlap of the fundamental and higher order mode [21]. Thus, we conclude here that the susceptibility of fiber 2 to guide higher order modes under thermal load is lower than that of fiber 1 which suggests a reason for its higher TMI threshold.

Another aspect that has been discussed in the literature is the connection of SBS and TMI [22]. In fiber 2, it is clear that the SBS threshold has been reached but the TMI threshold not, so that there is no connection between the effects here. In case of fiber 1, however, it has to be clarified if the SBS threshold power is related to the observed TMI threshold. The effective mode area and the effective length of fiber 2 can be calculated to be _{$A_{\text{eff}}=333 \mu {\text{m}}^2$} and $L_{\text{eff}}=5.3 \text{m},\text{ assuming}$_{a gain of 0.2 dB/m from 10 W to the threshold at 3.5 kW on a length of 35 m. Transferring this nonlinearity to fiber 1 with $A_{\text{eff}}=405\mu {\text{m}}^2$ allows for calculating the SBS threshold to be 3.7 kW related to an effective length of $L_{\text{eff}}=5.3\mu {\text{m}}^2$. We conclude that similar to fiber 2, no direct relation between TMI and SBS for fiber 1 is observed.}

5. Conclusion

In conclusion, we have shown that the modal behavior of a step-index fiber is a critical parameter and has to be designed carefully for fibers intended to deliver average powers in the multi-kW range. As a result of our comparison of a 30 µm and a 23 µm low-NA LMA fiber, we have shown that the TMI threshold is increased when the susceptibility of the fibers to the guidance of higher order modes is reduced. Experimentally, we obtained 3.5 kW of average power when amplifying a narrow linewidth signal and could scale the power to 4.3 kW for a broadband signal in a 23 µm core fiber. This power level is shown to be truly single-mode and the fiber has not reached its TMI threshold suggesting that a further power scaling is possible. Especially as the seed power in our experiments was low (10 W), the power of 4.3 kW is the highest single-mode power reported from a directly-diode pumped fiber amplifier so far.