High power polarization-maintained (PM) fiber lasers with near-diffraction-limited beam quality have been widely used in many fields, such as gravitational wave detection [1], coherent radar system [2, 3], nonlinear frequency conversion [4–7], and coherent/spectral beam combining system [8–10]. For PM fiber lasers, beam quality and polarization extinction ratio (PER) are the key factors to evaluate laser performance, and attract great attention in the fiber laser society. Up to now, the output power of fiber lasers has been significantly improved, reaching a maximum level of 5 kW [11]. However, further power scaling of PM fiber lasers with great beam quality and PER are mainly limited by the nonlinear effects and the mode instability (MI) effect [12–15]. The MI effect originates from the thermal effect, which results in dynamic power coupling between the fundamental mode (FM) and high order modes (HOMs), and thereby dramatically deteriorates the beam quality and limits the output power. Even worse, recent experimental results in forward-pumped PM fiber lasers show that the MI effect can also result in a decrease in PER, which further limits the application of PM fiber lasers [16, 17]. However, the physical mechanism of MI induced degradation of PER in forward-pumped PM fiber laser has not been analyzed. On the other hand, the impact of MI on PER has only been reported in forward-pumped PM fiber lasers, and no related research in backward pumped configuration has been reported, to the best of our knowledge [18–25]. Compared with the forward-pumped fiber lasers, the backward pumped ones have the advantages on suppressing the MI and nonlinear effects, and have been widely employed in high power PM fiber lasers [26–30], which deserve further investigation.

In this paper, a high power PM fiber amplifier has been established based on backward pumped master oscillator power amplifier (MOPA) structure. Based on the laser system, the influence of MI on PER has been investigated, and the results showed that the occurrence of MI in backward pumped PM fiber amplifier did not decrease PER, which is different from the results in forward pumped PM fiber amplifier. The physical mechanism has been discussed, and the simulation results illustrated that different pump power distributions can influence the leaking and reinjecting process of HOM, leading to the different results.

The experimental setup of the MOPA system is shown in Figure 1. The seed was a single-frequency linear-polarized fiber laser with central wavelength being 1,064 nm and spectrum linewidth being about 10 kHz, which delivers an output power of 20 mW. In order to suppress the stimulated Brillouin scattering effect (SBS), the spectrum linewidth of the seed laser was broadened to 0.2 nm by a phase modulator, which was driven by an amplified white noise signal (WNS). A filter was employed to adjust the frequency bandwidth of the WNS. The broadened seed laser was amplified by a three-stage all-fiber amplifier. Two pre-amplifiers boosted the laser power to about 20 W, where a PM Yb-doped fiber (YDF) with core diameter of 10 μm and cladding diameter of 125 μm was used. Then, the pre-amplified laser was injected into the main amplifier through a PM mode field adaptor (MFA). The 10/125 μm YDF and MFA were used to ensure that the optical field injected into the main amplifier was near single-mode. Between the PM MFA and pre-amplifiers, a PM isolator (ISO) was inserted to prevent damage from backward light, and the multi-mode fiber port of ISO was used to monitor backward power and backward spectrum. The main amplifier was constructed by PM YDF with mode field diameter being 20 μm and cladding diameter being 400 μm, which was coiled tightly on a water-cooled aluminous plate to dissipate the heat and suppress MI. Six laser diode modules centered at 976 nm were coupled into the YDF through a (6 + 1)×1 p.m. signal-pump combiner. By employing a 976 nm pump source to shorten the gain fiber length and utilizing 20/400 μm PM YDF to enlarge the mode field area, the SBS effect was effectively suppressed. Two home-made PM cladding power strippers (CPSs) were used in main amplifier to strip the residual pump light and cladding signal light. A quartz block head was used to deliver the amplified laser, which was collimated by a collimator.

The output power was measured by the power meter, and the increase of output power versus pump power is shown in Figure 2. With the scaling of pump power, the output power of fiber laser increased linearly firstly. When the pump power was 2,419 W, the output power reached 1,880 W, and the optical-to-optical efficiency was about 78%. However, as the output power exceeded 1,880 W, the output power was barely growing with the increasing of pump power, which indicated the efficiency decrease and the onset of MI [13].

An optical spectrum analyzer (OSA) with a resolution of 0.02 nm was used to record the output spectrum. The output spectrums at different output powers are shown in Figure 3a. The linewidth of seed laser was 0.2 nm, which remained constant and with output power scaling, and the SRS suppression ratio was higher than 70 dB at the maximum output power. The backward spectrums at different output powers are shown in Figure 3b. The backward spectrum manifested no sign of typical pulse, which confirmed that the laser system was free of SBS [31].

The beam quality factors M² at different output powers were measured, and value of which were calculated by M 2 = M x 2 2 + M y 2 2 / 2 . One can see from Figure 4 that, the M² of the seed laser was 1.163 while it became 1.237 at the maximal output power of 1,935 W. When the output power was less than 1,880 W, the PM fiber laser kept near diffraction limited beam quality, and no obvious degradation of beam quality was observed. However, when the output power exceeded 1,880 W, the beam quality degraded obviously, indicating the onset of MI [32].

It is well known that the MI effect can result in the beam quality distortion and the output efficiency decrease [32]. To further confirm that MI threshold was reached in the laser system, a photodiode (PD) with a hole of 1.0 mm diameter and bandwidth of 350 MHz was employed to sample the time fluctuations of the transverse beam profile, which has been widely used to monitor the MI effect [32–34]. The PD was placed on the center of the collimated beam to detect the temporal characteristic of beam profile fluctuations, which were monitored by an oscilloscope with bandwidth of 500 MHz. It should be mentioned that the hole of PD was smaller than the beam size, which excluded the impact of power fluctuation. The time-domain traces at different output power are shown in Figure 5a. One can see the output power remained stable at 1,745 W, while it fluctuated at 1,961 W. The time traces proved that the onset of dynamic MI. Moreover, Fourier spectra (FSs) of the time traces at different output power levels were illustrated in Figure 5b. With the scaling of output power, obvious discrete noise lines appeared in the FSs, implying that the MI effect was onset. To quantitatively evaluate the MI effect, the relative intensity σ versus output power was inserted in Figure 5c, which was defined as σ = ∫ 0 10 kHz P ν d ν / ∫ 10 kHz 20 kHz P ν d ν ‐ 1 , where P(ν) was the power density at frequency of ν [34]. Once the output power exceeds MI threshold, the frequency component will increase obviously in the range of 0–10 kHz, and σ will increase nonlinearly. Similar with Refs. [32, 34], the MI threshold was defined as the output power when σ reaches 5%. It can be concluded from Figure 5c that as the output power reached 1,880 W with σ being 7.63%, the relative intensity suddenly increased to 19% at 1,935 W, which suggested the MI threshold was 1,880 W [31, 33]. The evolution of relative intensity was similar with the results in Figure 2. After the onset of MI effect, large amount of HOMs will be generated and naturally decrease the beam quality. Furthermore, a part of the HOMs will leak into the fiber cladding due to fiber coiling, which will be stripped by CPS, resulting in the optical efficiency rollover shown in Figure 2.

The power of p-polarization light and s-polarization light and the PER at different pump powers are shown in Figure 6, which was measured by using assemble components of a half-wavelength plate and a polarization plate. With the increasing of the output power, the measured PER changed between 95.1% and 96.6% with about 1.5% of fluctuation, which was mainly induced by environmental noise and thermal noise. When the output power exceeded 1880 W, the MI occurred, but the PER did not decrease, and at maximum output power, the PER was 96.3% (14.32 dB), whereas for the forward-pump schemes, the PER dropped from over 94%–90% during MI occurrences [16], which indicates that the MI has little influence on PER of PM fiber laser with backward pumping configuration.

The influence of the MI effect on PER of backward pumped PM fiber amplifier has been investigated in the experiment, and the results show that the MI effect has little impact. The phenomenon is different from the results in [16, 17], where the MI effect can result in the decrease of PER in the forward-pumped PM fiber amplifier.

The different relationships between MI and PER in PM fiber laser under different pump configurations may be attributed to the influence of the different pump power distributions [35]. In order to analyze the different results, the MI model is used to simulate the HOM distribution along the gain fiber, which can be expressed as ξ L ≈ ξ 0 ⁡ exp ∫ 0 L d z ∬ g r , ϕ , z ψ 2 ψ 2 − ψ 1 ψ 1 r d r d ϕ + ξ 0 4 2 π ∫ 0 L P 1 z χ ″ Ω 0 , z d z exp ∫ 0 L d z ∬ g r , ϕ , z ψ 2 ψ 2 − ψ 1 ψ 1 r d r d ϕ × R N Ω 0 exp ∫ 0 L P 1 z χ Ω 0 , z d z Where the ξ ₀ is the initial HOM fraction, L is the length of the gain fiber, ψ _i is the normalized electric field of fiber mode i, and P ₁(z) is the power of fundamental mode. χ(Ω) is the nonlinear coupling coefficient, and Ω₀ represents the frequency of the maximum of χ(Ω). χ''(Ω) denotes the second derivative of χ(Ω). g(r, ϕ, z) is the gain of the amplifier, which can be calculated by laser rate equation N 2 r , ϕ , z N 1 r , ϕ , z = ∑ P P z σ P a φ P r , ϕ h γ P + ∑ P S z σ S a φ S r , ϕ h γ S ∑ P P z σ P e φ P r , ϕ h γ P + ∑ P S z σ S e φ S r , ϕ h γ S + 1 τ ± d P P ± z d z = ∫ 0 2 π ∫ 0 a σ P e N 2 r , ϕ , z − σ P a N 1 r , ϕ , z φ P r , ϕ r d r d ϕ × P P ± z − α P P P ± z ± d P S ± z d z = ∫ 0 2 π ∫ 0 a σ S e N 2 r , ϕ , z − σ S a N 1 r , ϕ , z φ S r , ϕ r d r d θ × P S ± z − α S P S ± z g r , ϕ , z = σ S e N 2 r , ϕ , z − σ S a N 1 r , ϕ , z

Where index P and S stand for pump wave and signal wave respectively, + and–correspond to forward and backward propagation waves respectively, σ _a and σ _e are the corresponding absorption and emission cross section, N ₁ and N ₂ represent the numbers of Yb-ions in ground state and excited state, φ is the overlap factor, λ is the wavelength, γ is the nonlinear Kerr coefficient, α is the loss coefficient, τ is the life of the excited state population. For different pump configuration, the gain distribution g(r, ϕ, z) of amplifier is different, which leads to the difference of HOM distribution along the fiber.

With the theoretical model, the HOM distribution caused by MI along the active fiber has been simulated for the fiber amplifier with different pumping configurations, as shown in Figure 7. When the power ratio of HOM exceeded 5%, the MI threshold was reached, and the power ratio of HOM would increase along the active fiber for both forward and backward pump configurations. However, compared with the backward pump scheme, the MI-induced HOMs was closer to the input end for the forward-pump schemes, as Figure 7 illustrated. Therefore, for forward pumped PM fiber amplifier, due to the fiber coiling, the HOMs would leak into the cladding, and a small part of the cladding signal light was able to reinject into the active core during propagating along the fiber. The polarization state of the reinjected signal light was random due to the scramble of the cladding, and reinjected signal light was amplified by the Yb-ions and in the PM fiber amplifier, and the polarization state was maintained [36], leading to the degradation of the PER. For backward pump scheme, the HOMs was mainly generated at the output end, which resulted in that the leaking and reinjecting process happened in passive fiber. The small portion of the reinjected signal light cannot be amplified, thereby the PER showed no obvious degradation.

In conclusion, the impact of MI effect on PER of the backward pumped PM fiber amplifier have been investigated, which revealed that the MI effect had little impact on PER for backward pump PM fiber amplifier. Comparing the experimental results of forward pumped amplifiers, where the MI induced the decrease of PER, one can conclude that the different pump power distribution can influence the leaking and reinjecting process of HOM, and then leading to the different results with different pump configuration. Therefore, to circumvent MI-induced polarization degradation, backward pumping configurations should be preferentially adopted in high-power PM fiber laser systems.