The power scaling of high-power fiber lasers based on the use of rare-earth doped fibers as gain medium is limited by the presence of nonlinear effects such as Raman and Brillouin scattering, as well as by transverse mode instability (TMI). Particularly, TMI is a main limiting factor in large mode area (LMA) CW fiber lasers, leading to both sudden fluctuations and severe quality reduction of the beam at the amplifier output, for powers about a certain threshold value [1].

A possible solution to mitigate TMI is provided by the use of tapered ytterbium-doped fibers (T-YDFs), where the fiber core size varies along its axis, so that high-order modes (HOMs) are filtered out, and a good beam quality is obtained at their output. At the same time, the progressively increasing mode area permits to mitigate nonlinear effects, such as frequency conversions, which could otherwise distort and deplete the laser beam. Several researchers have reported the use of T-YDFs for high-power single-mode fiber lasers operating in both pulsed and CW regimes [2-5]. In these studies, the T-YDFs are singlemode at their input end with a smaller diameter, so that quasi singlemode operation is maintained throughout their large diameter output end, with relatively small bending loss sensitivity, and high TMI thresholds when compared with uniform YDFs.

In order to overcome the beam quality degradation that is inherent to active MMFs, nonlinearity may turn from a disadvantage into an opportunity via the beam self-cleaning effect. Guenard et al. demonstrated self-cleaning in a 5-m long double-clad uniform YD MMF with nearly step-index refractive index profile and uniform core doping profile [6]. Beam self-cleaning was also exploited to obtain mode-locking in a composite cavity laser configuration, where a passively Q-switched Nd:YAG microchip laser was combined with an extended cavity including the same YD [7].

More recently, Niang et al. demonstrated Kerr beam self-cleaning in a 10-m long T-YD MMF, with GRIN profile of the core, by using sub-nanosecond 1064 nm pulses propagating from the wider (120 μm) into the smaller (40 μm) diameter [8]. In this case, however, self-cleaning in the presence of amplifier gain was accompanied by ultrawideband frequency conversion and supercontinuum generation extending from 520 nm to 2600 nm. In fact, the decreasing core diameter in combination with amplification concur to accelerate the nonlinear effects, similar to the case of lossless singlemode and multimode fiber tapers.

In order to use the T-YD MMF in a high power fiber laser, any frequency conversion should be avoided, so that the signal must necessarily propagate from the smaller to the larger diameter, similar to conventional T-YDF amplifiers. In this configuration, which decreases the fiber nonlinearity as the pulse get amplified, it remains an open issue whether any beneficial Kerr-induced beam self-cleaning may still be achieved. In this work, we answer this question, by experimentally demonstrating that indeed beam self-cleaning is obtained in a 5 m long double-clad T-YD MMFs, in spite of a longitudinally increasing core diameter, which leads to a decelerating nonlinearity. We used 500 ps pulses at 1064 nm, propagating in the normal dispersion regime, from the smallest to the largest taper diameter. Remarkably, we observed self-cleaning with its associated beam quality improvement not only in the active configuration, that is in the presence of gain (induced by the pump laser diode), but even in a lossy configuration (i.e., with no pump laser diode)

We injected in the core of the T-YD MMF a Nd:YAG microchip laser at 1064 nm with Gaussian spatial beam shape, generating 500 ps pulses at the repetition rate of 500 Hz, with up to 90 kW peak power. We used a 5 m long, double-clad Yb-doped MMF taper with 1.1 dB/m linear average attenuation at 1064 nm, corresponding to an overall attenuation of 5.5 dB, and parabolic core refractive index, with nearly uniform doping profile.

The first experiment was performed in a passive configuration. The signal beam was focused into the smallest end of the core of the T-YD MMF. The peak power of the coupled input signal (Pin) was initially set to 280 W: in this case a highly speckled output beam was observed, see top figure in the left panel of Fig. 1. As can be seen, when increasing the input coupled power above 20 kW, the output beam spatial pattern self-organises into a bright spot with a bell shape, surrounded by a low-power background, a typical manifestation of spatial beam self-cleaning. The right panel of Fig. 1 shows that beam self-cleaning is not accompanied by any significant spectral broadening. As shown in Fig. 2, the increase of the output beam quality as a function of the input peak power was confirmed by the measurement of the M2 beam quality parameter, which drops from M2=12 to below M2=4 as the peak power grows above 20 kW.

Next, we switched on the CW LD pump source for inducing amplification in the T-YD MMF. In spatial beam cleaning experiments, we kept the signal input peak power fixed at 10 kW, that is below the self-cleaning threshold in the passive configuration. Thus, the amplification boosts the signal and push it to enter the self-cleaning process. Fig. 3 (left panels) shows that the output field remains highly speckled, hence with low beam quality, until the gain reaches the value of 1.6. Conversely, for gain values above 1.6, the output beam remains stably self-cleaned. The output spectra corresponding to the manifestation of spatial beam self-cleaning are reported in the right panels of Fig. 3. As can be seen, also in the active case, Kerr-induced beam cleaning is not accompanied by any significant spectral broadening of the signal.

In the active case, the self-cleaning of the beam injected from the smaller side of the T-YD MMF was also characterised in terms of M2 output beam quality parameter measurements, as shown in Fig. 4. Here, the beam quality parameter drops from very high values (M2=15) for G = 1.1, to about M2=5 for the maximum gain value of 4.1.

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8. A. Niang et al., "Spatial beam self-cleaning and supercontinuum generation with YB-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape", Opt. Express, vol. 27, no. 17, pp. 24 018-24 028, Aug. 2019.