Narrow-linewidth, polarization-maintaining (PM) fiber amplifiers are broadly applied in beam combining [1–4] and gravitational-wave detection [5]. These applications require both near-diffraction-limited beam quality and high output power from the amplifier. However, maintaining beam quality with increasing output power is mainly limited by mode instabilities (MI) [6, 7], and the increase in output power is primarily constrained by the effects of stimulated Brillouin scattering (SBS) [8].

To enhance the MI threshold, researchers have made significant efforts to optimize the pump source. Early studies indicated that the enhancement of the MI threshold can be realized by weakening the absorption of the pump [9]. In 2015, Tao et al. [10] demonstrated an increase of 90% in the MI threshold for a 20/400 Yb-doped fiber (YDF) by adjusting the pump wavelength from 976 to 915 nm [10]. However, for the same fiber length, compared to 976 nm pumping fiber pumped at other wavelengths exhibits lower optical-optical efficiency. Therefore, to strike a balance between MI threshold and optical efficiency, a feasible approach is to utilize a combination of multiple pump wavelengths. This strategy allows the enhancement of the MI threshold while maintaining relatively high optical-optical efficiency.

To enhance the SBS threshold, other than optimizing the amplifier itself, many efforts have been made regarding the injected seeds. Different types of seeds have been explored, such as the single-frequency seed (SFS) [11], phase-modulated seed (PMS) [12–17], and the fiber Bragg-grating oscillator (FBGO) [18]. In fiber amplifiers with SFS injection, the output power is limited to several hundred watts, due to the severe SBS effect. In amplifiers with FBGO injection, the output spectrum after amplification is broadened, compared to the seed [19], which is not conducive to achieving output at <10 GHz and several kilowatts. As for the amplifiers with PMS injection, the output spectrum after amplification remains stable [19], and the SBS threshold can be enhanced to several kilowatts. Therefore, PMS injection can be considered the preferred scheme for achieving narrow-linewidth output. Commonly used phase-modulation signals for PMS include sine-wave sources [16, 20], pseudorandom binary sequences (PRBS) [12, 13], white-noise sources (WNS) [21], and optimized signal [14, 17, 22]. Regarding PM amplifiers with a linewidth of 10–15 GHz, in 2016, Yu et al. [17] realized a 3.1 kW output with a 12 GHz linewidth and 12-dB polarization extinction ratio (PER) using PRBS phase modulation, though this setup is not an all-fiber system. Similarly, in 2017, Platonov et al. [23] obtained 1.5 kW output, 15 GHz linewidth, and 13-dB PER, using WNS modulation. In 2019, our group reported 1.5 kW output with 13-GHz linewidth, utilizing WNS modulation [24]. Furthermore, in 2022, Chu et al. [25] achieved 3 kW output with 14-dB PER and a linewidth of 10.6 GHz, by employing optimized signal modulation. For PM amplifiers operating at a linewidth of 1–10 GHz, there have also been notable advancements. In 2017, our group achieved 0.96-kW output with 6.5 GHz linewidth using WNS modulation [26]. Additionally, in 2018, Jun et al. [27] realized 818 W output with linewidth of less than 7 GHz, based on PRBS modulation. In 2019, Meng et al. [20] reported 1.08 kW, 7.6 GHz output by employing sine-wave modulation, as well as an 827 W output with 1.8 GHz linewidth using WNS modulation [28]. In 2021, Lai et al. [29] reported 1.02 kW output with 4.6 GHz linewidth by employing multiphase coded signal modulation, which can also be considered an optimized signal. Furthermore, in 2022, our group achieved 1.2 kW output with 4 GHz linewidth using optimized phase modulation [15]. In 2023, Dong et al. [30] demonstrated 2 kW, 8 GHz output by applying a flat-top PRBS signal. Finally, in the current work our group obtains 3.2 kW, 9.7 GHz output by optimizing phase modulation. These results are summarized in Table 1, which demonstrates the significant improvement in the SBS threshold by optimizing the PMS.

TABLE 1. Recent progress of narrow-linewidth PM all-fiber amplifiers.

Linewidth (GHz)	Year	Modulation	Power (kW)	Linewidth (GHz)	M 2	PER (dB)	Ref.
10–15	2017	WNS	1.50	15	<1.1	20	[23]
	2019	WNS	1.50	13	<1.2	13	[24]
	2022	Optimized	3.00	10.6	<1.2	14	[25]
1–10	2017	WNS	0.96	6.5	1.1	14	[26]
	2018	PRBS	0.82	7	-	13	[27]
	2019	Sine	1.08	7.6	1.2	14	[20]
	2020	WNS	0.83	1.8	<1.5	12	[28]
	2021	Optimized	1.02	4.6	<1.3	13	[29]
	2022	Optimized	1.20	4	<1.3	15	[15]
	2023	PRBS	2.00	8	<1.4	15	[30]
	2023	Optimized	3.20	9.7	<1.3	20	This work

In this paper, we aim to construct a >3 kW PM all-fiber amplifier. Therefore, we first optimize the pumping scheme by using pumps with different wavelengths to find a proper scheme with a high MI threshold (>3.5 kW). Subsequently, by optimizing the seed injection, we obtain 3.2 kW output and 9.7 GHz spectral linewidth with a PER of 20.3 dB, $M_x^2$ of 1.29 and $M_y^2$ of 1.28.

Figure 1 illustrates the experimental setup of the PM all-fiber amplifier. This setup begins with a 1,064-nm single-frequency seed operating at 30 mW of power. The spectrum of this seed is then broadened through an electro-optic phase modulator. A radio-frequency (RF) amplifier is used to drive the phase modulator. Following this, the power of this seed is pre-amplified to 28 W. To monitor the backward-propagating light, a 0.1% fiber coupler (FC) is employed after a PM isolator (ISO). The main amplifier, designed in a counter pumped configuration, consists of a ~13-m piece of PM YDF (effective mode area ~350 μm²), a signal-pump combiner [(6 + 1) × 1], two cladding power strippers (CPS), and a PM end cap. A bending radius of 6 cm is applied to the YDF to achieve a high MI threshold, by effectively filtering out high-order modes. The end cap is employed to collimate the output beam. A high-reflectance (HR; 99.9%) mirror is used to split the beam for measurements of power, PER, MI effects, and beam quality (M ²). The spectrum is measured by a spectroscope. PER is determined using a half-wave plate, a polarizing beam splitter (PBS) and two power meters. What is more, when the MI effect occurs it leads to power fluctuation in the output, because the fiber is bent to filter high-order modes into the cladding, and the filtered power in the cladding is then stripped by the CPS. Therefore, a photodetector (PD; 17 MHz) and an oscilloscope are used to observe the MI effect.

Figure 1. Scheme of the all-fiber polarization-maintaining (PM) amplifier.

3.1. MI-threshold Investigation with Pumping Schemes at Different Wavelengths

In this experiment, the RF signal of the seed is a WNS covering a range of 0–10 GHz, and it is amplified by an RF amplifier with a strength of 30 dBm. The seed spectrum can be stretched to 105 GHz by driving the EOPM with the amplified signal.

To begin, we pump this amplifier with six 976-nm laser diodes (LDs). Figure 2(a) depicts the fluctuation of output power as the pump power increases. The measured optical-optical efficiency is 82.5% at 2,607 W of output. Figure 2(b) indicates the temporal behavior of the output on the 0.01-s time scale, demonstrating that the output is stable in the time domain at 1,315 W and 2,226 W. The time-domain output becomes unstable at 2,607 W, implying that the MI threshold is less than 2.6 kW.

Figure 2. Output power behavior versus pump power and time (a) output power versus the 976-nm pump power, and (b) output power over the forward time domain.

Next, we adjust the pump wavelength to 974 nm. Figure 3(a) depicts output power versus pump power. At 3,539 W of output, we achieve a measured optical-optical efficiency of 75.2%. Figure 3(b) shows the output’s time-domain stability at 2,967 W and 3,410 W. Nevertheless, once the output surpasses 3,539 W it becomes unstable, suggesting that the MI effect occurs.

Figure 3. Output power behavior versus pump power and time (a) output power versus the 974-nm pump power, and (b) over the forward time domain.

Subsequently, we shift the pump wavelength to 981 nm. The resulting power data are depicted in Fig. 4(a). Our measurements indicate that the optical-optical efficiency reaches 67.8% at an output of 3116 W. Figure 4(b) demonstrates the stability of the output, meaning the MI threshold of this amplifier is >3.1 kW (constrained by the pump).

Figure 4. Output power behavior versus pump power and time (a) output power versus 981-nm pump power, and (b) over the forward time domain.

The MI threshold is increased from 2.6 to 3.5 kW by altering the pump wavelength from 976 to 974 nm, yet the optical-optical efficiency is reduced from 82.5% to 75.2%. Likewise, altering the wavelength from 976 to 981 nm raises the MI threshold to >3.1 kW (limited by the pump), while decreasing the optical-optical efficiency from 82.5% to 67.8%. The experimental results confirm that through lowering the pump’s absorption, the MI threshold can be raised. This method, however, comes at the expense of diminished optical-optical efficiency. Given the impact of pump absorption on both the MI threshold and optical-optical efficiency, we implement a mixed pumping scheme comprising six LDs, two operating at 974 nm and four operating at 981 nm. Using this combined-pumping approach, we study the MI threshold and optical-optical efficiency; The findings are shown in Fig. 5(a). At 3,511 W output (limited by the pump power of 4,992 W), the measured optical-optical efficiency is 70.2%. The output’s time domain is stable in Fig. 5(b), and the MI threshold of this amplifier reaches 3.5 kW (constrained by the available pump power).

Figure 5. Output power behavior versus pump power and time (a) output power versus the 974- and-981-nm pump power, and (b) over the forward time domain.

The experimental results demonstrate that the output of this amplifier can reach 3.5 kW, with either 974-nm pumping alone or a combination of 974- and 981-nm pumping. However, when employing 974- and 981-nm mixed pumping scheme, the output in the time domain is more stable at 3.5 kW, indicating greater potential in mitigating the MI effect. Taking these findings into account, we select the 974- and 981-nm mixed pumping configuration for our next experiment.

3.2. 9.7-GHz, 3.2-kW All-fiber Amplifier with 974- and-981-nm Mixed Pumping

To achieve narrow-linewidth output, optimization of the modulation signal is the primary focus. At the outset, a computational signal is produced and fed into an arbitrary waveform generator (AWG). Through meticulous manipulation of the signal parameters, an ideal spectrum is achieved with spectral linewidth of 9.7 GHz (root-mean-square [RMS] 20 dB). Figure 6 displays the spectral data at various output powers, demonstrating that as the output power increases, the spectral linewidth remains constant at 9.7 GHz.

Figure 6. The modulation signal’s spectrum at different output powers.

The measured M ² (4σ) value of this amplifier is shown in Fig. 7, which indicates a value of <1.3 throughout the amplification process. At 3,211 W, $M_x^2$ is about 1.29 and $M_y^2$ is about 1.28. What is more, the PER (represented by the blue dots in Fig. 7) ranges between 19.7 dB and 20.7 dB.

Figure 7. Beam quality M² and PER versus output power.

In this work, the SBS threshold is defined as the output power when the backward-propagating light’s power reaches 0.01% output [12, 31]. As shown in Fig. 8, the backward power is 265 mW at 2,650 W of output, corresponding to 0.01% of the output.

Figure 8. The power of the backward-propagating light versus laser power.

Notwithstanding the amplifier’s attainment of the SBS threshold at 2,650 W, the backward temporal trace exhibits no self-pulses, with peak intensities several times as large as the average power in the temporal trace; See Fig. 9. Prior research has demonstrated that the threshold for backward self-pulsing in a fiber amplifier is greater than the threshold for SBS, when injected with a phase-optimized signal modulation seed [14, 32]. Considering that the isolator in this amplifier is capable of withstanding an optical power of 5 W (which is greater than the backward power), it is feasible to augment the pump power further to achieve an output surpassing the SBS threshold. Even at an output of 3,160 W, the backward power remains stable. At an output of 3,211 W, however, self-pulses with maximum intensity surpassing three times the average power are detected. As a result, the self-pulsing threshold is established at 3.2 kW, signifying that further amplification of power may damage the amplifier.

Figure 9. Backward temporal traces at different output powers.

In conclusion, we have successfully demonstrated a high-power narrow-linewidth polarization-maintaining (PM) all-fiber amplifier, by utilizing an optimized phase-modulated seed and a mixed pumping scheme with wavelength-multiplexed LDs. The measured MI threshold exceeds 3.5 kW (constrained by pump power) when employing 974 and 981-nm pumping. Subsequent investigations will be directed toward undertaking more comprehensive analyses of the mixed pumping method, with the intention of further augmenting the MI threshold. Our objective is to maximize the optical efficacy and MI threshold for improved results. Based on this mixed pumping configuration, we have achieved a remarkable output of 3.2 kW with a spectral linewidth of 9.7 GHz. The PER is 20.3 dB, $M_x^2$ is 1.29, and $M_y^2$ is 1.28. To our knowledge, this represents the highest output power for a narrow-linewidth PM all-fiber laser with a linewidth below 10 GHz. Additionally, this marks the narrowest linewidth achieved at an output power exceeding 3 kW for PM narrow-linewidth fiber lasers.

Innovation Development Fund of CAEP (C-2021-CX 20210047).

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.