6 kW Single Stage Narrow Linewidth Fiber Amplifier Based on the Balance Between Mode Instability and Nonlinear Effects

Single-stage high-power narrow-linewidth fiber laser has been investigated intensively recently because of its simple and robust configuration and great potential in spectral/coherent beam combination. In this work, a 6 kW narrow-linewidth fiber amplifier was experimentally achieved based on a fiber oscillator seed. By employing a few-mode ytterbium-doped fiber, the spectral broadening and SRS effects are both significantly mitigated. Combined with a wavelength-stabilized 981 nm pump source, the threshold of transverse mode instability is improved, then, a maximum output power of 6020 W at the central wavelength 1080 nm was achieved with 3-dB bandwidth of ∼0.37 nm and optical-to-optical efficiency of ∼85.6%. The mode instability and nonlinear effects were balanced well. The measured beam quality and the signal to Raman ratio were M2∼2.7 and ∼27 dB, respectively. This work shows the great potential of such amplification structure for the power scaling of high-power narrow-linewidth fiber lasers.


I. INTRODUCTION
H IGH power narrow-linewidth fiber lasers (NLFLs) play an important role in spectral/coherent beam combinations, which are helpful for expanding single fiber output power [1], [2]. Recently, the power scaling of high-power NLFLs has been investigated intensively. It is challenging for power scaling in a NLFL since transverse mode instability (TMI) effect and various nonlinear effects, such as four wave mixing (FWM), self-phase modulation (SPM), stimulated Brillouin scattering (SBS), and stimulated Raman scattering (SRS). Furthermore, due to the high spectral density the thresholds of nonlinear effects are much lower than those in traditional high-power fiber lasers, whose linewidth are usually more than several nanometers. Normally, high power NLFLs can be acquired by using a structure of master oscillator power amplification (MOPA), in which the seed is a narrow-linewidth laser. There are two promising kinds of seed sources, i.e., phase-modulated singlefrequency lasers and fiber Bragg grating (FBG)-based oscillators. The front has shown a good time domain characteristic and so its spectral broadening and SRS effects are weak relatively during the power amplification [3], [4], [5]. Some breakthroughs have been made recently [6], [7], [8]. In 2021, Huang et al. achieved the output power of 5.07 kW narrow linewidth continuous wave fiber amplifier with near diffraction limit beam quality and 0.37 nm 3 dB linewidth [7]. In 2022, Wang et al. achieved a 6.12 kW record narrow-linewidth fiber laser with 0.86 nm bandwidth and near single mode beam quality [8]. However, the SBS threshold of the single frequency seed is very low and thus need a complicated and expensive multi-stages configuration to widen signal linewidth to increase the SBS threshold [9]. MOPA based on oscillator seed consists of single stage amplification structure. It is an alternate solution to obtain high power NLFLs with lower cost and better robustness. The characteristic of less longitudinal modes in this type of seed makes it almost unnecessary to consider SBS effect. However, the resulting spectral broadening is more serious than singlefrequency phase-modulated laser seed [10]. And SRS effect induced by instability in temporal domain is one of the biggest obstacles for power boosting in the single stage MOPA structure NLFLs [5]. However, its obvious advantage of simple structure is worthy studying and has attracted intensive attention Up to now, the average output power of this type of NLFL has reached to 3∼4 kW level [10], [11], [12], [13], [14], [15]. In 2022, Du et al. reported a 0.4 nm, 3.3 kW output power from a backward pumped fiber amplifier and the beam quality was M 2 ∼1.32 [13]. Then, our previous work achieved an output power of 4.2 kW single mode narrow linewidth fiber amplifier with 3 dB linewidth of 0.62 nm [15]. In these studies, the power scaling is always accompanied by a process of balancing nonlinear effects and TMI. Because there are certain contradictions when using traditional design strategies to suppress TMI and nonlinear effects. For instance, weakening heat load along the active fiber could enhance the TMI threshold, whereas the longer YDF This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ required in this case would strengthen the SBS and SRS effects and broaden the output spectrum. Besides, a large core diameter of the fiber could mitigate the SRS and spectral broadening effects, but at the same time higher-order modes (HOMs) would be introduced so that increasing the danger of the TMI and FWM effects. Moreover, TMI and nonlinear effects are usually interrelated in high-power continuous wave fiber lasers [17], [18], [19]. Therefore, comprehensive method balancing TMI and nonlinear effects for further power scaling of high-power fiber lasers and amplifiers becomes an imminent necessity.
In this work, we have experimentally demonstrated a 6-kW narrow-linewidth one-stage MOPA fiber laser based on a fiber oscillator seed. The fiber amplifier adopts a custom-made wavelength-stabilized 981 nm pump source to enhance the TMI threshold. Besides, the active fiber of amplifier stage with a large mode area of 30 μm is employed to mitigate SRS and spectral broadening effects. By this way, the TMI and SRS effects are effective balanced. At the maximum laser power of 6020 W, the optical-to-optical (O-O) efficiency is 85.6%, and the measured 3-dB and 10-dB linewidths are 0.37 nm and 1.47 nm, respectively. The Raman suppression ratio is ∼27 dB. Because of the large core size of the fiber, the output laser operates in a multimode regime and the measured M 2 is ∼2.7 at the maximum power.

II. EXPERIMENTAL DESIGN AND SETUP
For the design of the oscillator seed, the reduced longitudinal mode number of the seed is the key to narrower linewidth of the amplifier [10]. In a laser cavity, the longitudinal mode interval can be derived as Δυ = c 0 /2nL, where Δυ denotes the longitudinal mode interval, c0 is the light speed in vacuum, n is the refractive index of silica fiber, and L is the length of cavity. It indicates that a shorter cavity implies a larger Δυ and small number of longitudinal modes. Therefore, here the seed oscillator was adopted with a short resonant cavity with an active fiber length of 3 m. And a narrow-linewidth FBG with a full-width-at-half-maximum (FWHM) of 0.04 nm was adopted. Besides, a seed laser with good temporal characteristics is helpful to suppress SRS effect in the fiber amplifier because fewer pulses with high peak of laser is amplified. During experimental exploration, it was found that a broader bandwidth of high reflector (HR) FBG could mitigating the SRS effect induced by polarization dependence. The mechanism can be explained that the polarization-mode-interacted FWM (PFWM) would be easier to be excited in oscillator containing HR-FBG with wide bandwidth or fiber with a larger core ellipticity [20]. Besides, the PFWM-induced polarization dispersion would cut the Raman gain down due to the polarization variation of both signal and Raman laser so that elevate SRS threshold [21]. Thus, a HR-FBG with a relatively broad FWHM of 2.6 nm was utilized in the seed. In addition, the reasonable seed power is also the key for suppressing SRS, it neither be too low, otherwise a sustained self-pulsing of seed laser could be strong in the time domain; nor be too high, as the SRS noise of seed laser would be amplified [15]. For the design of the amplification stage, it needs to comprehensively weigh the influence of the nonlinear effects and the TMI. In this NLFL, the SBS is no need to pay more attention because the signal linewidth is widened enough during the seed laser transmitting long fiber of amplifier. However, other nonlinear effects such as SRS, FWM, combined with TMI effect would restrict the spectral purity and improvement of output power. Besides, the spectral broadening effect of signal light need to be controlled. Here, we balance SRS, spectral broadening and TMI effects by increasing the core size of fiber in the amplification stage, combined with optimizing the pump wavelength, that is 981 nm. Large core size fiber could mitigate SRS effect and spectrum broadening but decrease the TMI threshold with conventional pump wavelength of 976 nm. The pump wavelength of 981 nm could reduce heat load along active fiber for relatively low pump absorption, thus increasing the threshold of TMI compared to the case that using pump wavelength of 976 nm, while the needed active fiber is longer than pump wavelength of 976 nm but shorter than that pump wavelength of 915 nm [22]. Furthermore, the pump direction and pump power distribution also have an impact on SRS and TMI thresholds. Adopting counter-pumped configuration is helpful to mitigate SRS effect, because signal laser with high power only transmits by relatively short length of the fiber, which reduces the effective fiber length of high-power fiber lasers. But TMI effect would block the improvement of output power if only with the sole counter-pumped. Instead, the bidirectional configuration offers an advantage on redistributing heat load in active fiber and thus improving the final output power.
Based on the above design strategies, the single-stage MOPA configuration fiber laser based on FBG-seeded is illustrated in Fig. 1 The main amplifier is based on a bidirectional-pump configuration by adopting two (6+1) ×1 pump/signal combiners (PSC). The pump source of amplifier adopted multiple groups The YDF was coiled with a minimum radius of 12 cm and a maximum radius of 16 cm in the grooves on a water-cooled heat sink. The selection of coiling radius is to balance TMI threshold and beam quality [23]. When bending diameter is larger than 12 cm, the MI threshold would be improved with deterioration of beam quality; with smaller coiling radius, the beam quality could maintain well but the MI threshold would decrease. The residual pump light was removed by a cladding light stripper (CLS). The laser was ultimately transmitted in a fiber with a core/cladding diameter of 30/250 μm and output by a quartz block head (QBH) in the end. In the all-fiberized laser system, effective heat management was realized by cooling all fiber devices and perfect fusions, making sure the stability of fiber laser system in high power operation. The performance of the NLFL including output power, signal linewidth, optical spectrum and beam quality were measured and recorded in the experiment

III. EXPERIMENTAL RESULTS AND DISCUSSION
According to the selection principle of seed power mentioned above, here the seed power was set about 30 W considering the timing domain and SRS noises of fiber oscillator seed. The spectrum was measured by an optical spectrum analyzer with a spectral resolution of 0.02 nm and the FWHM of the seed transmitting through the amplification stage was 0.28 nm. In the experiment, we firstly injected the backward pump and then forward pump to the main amplifier. Under a total pump power of 7000 W, we achieved the maximum laser output power of 6020 W. As shown in Fig. 2, the output power and optical-optical efficiency versus pump power are depicted respectively. The O-O conversion efficiency of this NLFL did not decrease during the increase of output power, and this value was 85.6% at the maximum power.
The measured spectra at different output powers are depicted in Fig. 3(a). The central wavelength of the signal laser remains almost stable in the experiment. It can be observed the obvious FWM in the output spectrum. With only backward pump of 5235 W injecting, the output power reached 4400 W with the signal to Raman ratio (SRR) of 44 dB. The signal to FWM ratio (SFR) was about 33 dB. Then when the output power exceeded 4400 W, there was a serious spectral broadening at the bottom of the signal spectrum arising from self-and cross-phase modulation effects. In addition, the Stokes light and anti-Stokes light were also amplified with the enhancement of the nonlinear interaction. But the Stokes line and anti-Stokes line were unequally which can be attributed to the SRS effect [24]. With the forward pump light of 1765 W added, that is a total pump power of 7000 W, the output power reached the maximum value of 6020 W with SRR of 27 dB. The FWM ratio at 1092 nm is about 20 dB at the highest output power of 6020 W. The evolution of SRR and SFR versus output power are displayed in Fig. 3(b) and (c), respectively. Whether the SRR or SFR, the signal component decreased quickly with the additional forward pump injecting. The SRR decreased from 44 dB at 4400W to 27 dB at 6020 W and SFR decreased from 30 dB to 20 dB under the same circumstances. Fig. 3(d) shows the evolution of 3-dB and 10-dB bandwidth with output power increasing. The bandwidth increases almost linearly with only the backward pumped then this trend became steep with increasing forward pump. At the highest power of 6020 W, the 3-dB and 10-dB bandwidth reached up to 0.37 nm and 1.47 nm.
From the output spectrum of 2570 W, we can infer the threshold of FWM is lower than SRS effect. This because the optical parametric gain of FWM is higher than the peak of Raman gain in this large mode area fiber that satisfied phase matching. In fiber lasers, the strong intermodal FWM effect arises from the phase matching between the fundamental mode and HOMs [25], [26]. Due to the momentum conservation, the wave numbers of two generated photons must be of opposite signs. The real propagation constant of LP mn mode can be derived as Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. where n mn is the mode effective index. The first term contains the material dispersion, the later one contains waveguide dispersion and mode dispersion. Assuming the anti-Stokes light is the fundamental mode with a frequency shift of +Δf, and the Stokes light is the same higher-order mode with the frequency shift of −Δf. The frequency of the signal light is f 0. The phase matching Δβ can be derived as For the adopted fiber with core diameter of 30 μm and NA of 0.06, the normalized frequency parameter, i.e., V parameter, is calculated about 5.23 at the wavelength of 1080 nm, which indicates that five modes can be supported for simultaneous transmission including LP 01 , LP 02 , LP 11 , LP 12 , and LP 31 . Fig. 4(a) depicts the calculated phase mismatch for a few mode fiber with propagation constant of V = 5.23. One pump light is the fundamental mode with wavelength of 1080 nm, and the other pump light is one of the HOMs. In this case, the phase matching condition is satisfied at Δf = 3.35 THz between LP 01 and LP 11 mode. When pumped at 1079.3 nm, the calculated anti-Stokes and Stokes wavelengths are 1066.4 nm and 1092.5nm. The discrepancy might result from choosing of the fiber parameter. This is in accordance with the experimental results, as shown by the blue mark in Fig. 4(b). Besides, there are also slightly envelope of about 1105.2 nm in the output spectra, as shown by the red mark, which corresponding to phase mismatch between LP 01 and LP 02 mode, and Δ f = 6.3 THz. Whereas it is submerged in spectral broadening with increasing the output power, as shown in the spectrum in Fig. 3(a). Consequently, the intermodal FWM effect mainly occurs between the fundamental mode and the secondary mode in fiber lasers. The green mark in Fig. 4(b) shows the SRS effect, whose center wavelength is ∼ 1134.2 nm.
During the process of power amplification, we used a photodetector and an oscilloscope to record the temporal characteristics of laser. The beam quality was also measured simultaneously by a M 2 analyzer (Ophir Photonics, Beam Squared SP920). Fig. 5(a) shows the beam quality evolution. Because of large core size of the fiber adopted, the output laser operated in a multimode regime. Under the influence of TMI and FWM effects, the output laser spot jitters continuously, resulting in the gradual deterioration of the beam quality. And the M 2 factor is measured ∼2.7 at the maximum power of 6020 W. From the contour image of beam waist spot, one can see that the output laser mode is mainly composed of fundamental mode (LP 01 ) and higher-order mode (LP 11 ). The slight fluctuations of the temporal signal and corresponding Fourier spectrum of the dumped cladding is observed at the maximum power, as shown in Fig. 5(b), reasonably indicating TMI effect occurred [27]. Therefore, TMI is the direct obstacle for further power scaling of this NLFL.
Next, the experimental design strategies will focus on improving beam quality and mitigating the TMI and FWM effects for a higher output power. And suppressing inter mode FWM effect and optimizing beam quality are complementary. The essence of these problems is to decrease or control the number of modes in fiber. Some methods are proposed such as using the specially designed active fiber with low NA or vary core to achieve near single mode laser transmission [28]. In addition, mode control technology can also be used to suppress FWM effect in fiber laser, including gain fiber winding, gain fiber taper and mode conversion, and so on [29], [30]. Bending gain fiber is the simplest and easiest way to operate. In high-power fiber lasers and amplifiers, the bending loss of HOMs is greater than that of fundamental mode, appropriate winding radius could effectively reduce the proportion of high-order modes in fiber core for suppressing FWM and TMI effects.
In addition, the temporal characterizes of injected seed laser is the key to maintain narrow linewidth during the process of amplification. Although the linewidth of the laser decreases with reducing the longitudinal mode number of the seed source [10]. But the number of longitudinal modes is not the essential difference between phase modulated seed and multi-longitudinal modes oscillator seed. Two types of seeds possess different random phase distribution of the multiple waves or temporal features, thus, the multi-longitudinal mode seed experiences serious spectrum broadening induced by the self-phase modulation and FWM among various longitudinal modes. While the phase modulated seed can almost maintain the spectrum profile during the amplifying process even with some noise fluctuation [31]. Some methods to enhance temporal stability of oscillator have been proposed such as utilizing composite cavity structure oscillator [32]. These factors would be considered in the future work.

IV. CONCLUSION
In conclusion, we have experimentally demonstrated a highpower bidirectional pump narrow-linewidth single-stage MOPA system. The adopted large mode area active fiber with 981 nm pump wavelength help to obtain an output power of more than 6 kW. The O-O conversion efficiency is ∼85.6%, the FWHM bandwidth is ∼0.37 nm, and the SRR is ∼27 dB. The laser has operated at 6 kW for ∼3 mins and the calculated power instability was less than 1%. Because of the large core size of the fiber, the output laser operates in a multimode regime and the signal laser generates sideband energy. In the future work, the optimization of the seed's time domain characteristics and the improvement of beam quality are the key points. In short, this work shows a good potential of such simple amplification structure for power amplification of high-power NLFLs.