High-power fiber lasers serve as vital tools in scientific, industrial, and defense applications. The primary obstacle to further scaling the power of single-frequency fiber laser amplifiers is stimulated Brillouin scattering (SBS). When optical power exceeds the SBS threshold, the forward-transmitted signal light excites intense backward Stokes light. This not only depletes pump energy and reduces output efficiency but may also damage front-end precision components. Increasing the fiber core diameter and broadening the signal spectrum can elevate the SBS threshold, thereby suppressing SBS effects in single-frequency fiber amplifiers. Current SBS mitigation efforts are largely confined to single-mode or few-mode fiber amplifiers with high beam quality, making it challenging to simultaneously achieve high power, narrow linewidth, and high-quality beam output. This paper explores a multimode fiber (MMF) amplifier where SBS is significantly suppressed due to reduced optical intensity in the large core and broadening of the Brillouin scattering spectrum caused by multimode excitation. By applying spatial wavefront shaping to the input light of the nonlinear amplifier, the output beam is focused to a diffraction-limited spot, achieving high power (503 W), narrow linewidth (1 kHz), and high-quality beam output .
Figure 1 Schematic of the experimental optical setup
Figure 1 shows the optical setup of this study. Seed light at 1064 nm wavelength undergoes pre-amplification and beam expansion in single-mode fiber before its wavefront phase is modulated by a spatial light modulator (SLM). The modulated signal light is first coupled into a passive multimode fiber, combined with the pump light, and then amplified in a Yb-doped multimode gain fiber supporting 76 modes. After amplification, the signal light enters the measurement path for evaluating parameters including power, spectrum, linewidth, focal spot, and phase. This study investigates SBS characteristics in multimode fibers. Results indicate that the SBS threshold (maximum power without SBS generation) in MMF is significantly higher than in single-mode fiber. Simulation results show that for the MMF used (core diameter 42 μm), the SBS threshold is approximately 24 W when only the fundamental mode is excited, which is 8 times higher than that of a 15 μm diameter single-mode fiber. Due to unavoidable mode coupling in the fiber, MMF cannot achieve pure fundamental mode excitation. Measurements indicate an SBS threshold of 59 W under few-mode excitation and 97 W under multi-mode excitation in MMF, as shown in Figure 2(A).
Figure 2 (A) SBS thresholds in single-mode and multimode fibers; (B) SBS gain spectra for fundamental and multimode excitation in MMF
This paper establishes a semi-analytical theory for SBS in MMF amplifiers, analyzing the coupling between different mode signal lights and Stokes light to derive corresponding SBS gain coefficients. This theory indicates that the SBS gain coefficient in multimode excitation conditions within MMF is lower than in any single-mode excitation scenario. Multimode excitation in MMF significantly broadens the SBS gain spectrum, reduces the gain peak, and achieves an increase in the SBS threshold, as shown in Figure 2(B). Due to the backward propagation nature of the Stokes light, longer MMF lengths result in greater SBS gain and a correspondingly lower threshold. Experiments demonstrate that the pump light is depleted within approximately 6 m. By shortening the fiber length and measuring the SBS threshold, results indicate that the SBS threshold is inversely proportional to the effective length of the MMF. At an MMF length of 3.7 m, the amplifier achieves a maximum SBS threshold (i.e., peak output power) of 503 W, which is five times the SBS threshold (theoretical calculation result) for fundamental mode excitation alone.
Figure 3 Relationship between effective length of MMF and SBS threshold; inset: output focal spot intensity versus phase
To control MMF output, this study modulated the wavefront phase using a spatial light modulator (SLM) before the signal light entered the MMF. The modulation range covered the entire input aperture of the MMF. Within this modulation range, the pixels were divided into 256 macropixels. Starting from the central pixel, the phase of each pixel was scanned in a spiral pattern to achieve optimal output on the focal plane. Under the influence of wavefront phase control, interference occurs between different modes within the MMF, forming a high-quality spot on the output focal plane. The spot intensity and phase distribution are shown in the inset at the top right of Figure 3, revealing uniform intensity and phase distribution, indicating excellent spot quality on the focal plane. Figure 4: Spots on the MMF focal plane (A) and at slightly defocused positions (B, C); measured output beam quality (M2) (D)
Figure 4 displays the beam profiles at the focal plane and under slight defocusing (200, 400 μm). Measurements indicate a focal efficiency of 76% at the focal plane, meaning 76% of the beam energy resides within the focal range. The measured M2 values in the x and y directions are 1.05 and 1.35, respectively, indicating good beam quality. The results demonstrate that phase modulation based on SLM effectively improves the spot quality on the focal plane of the MMF output.
Figure 5: Slope efficiency (A), output spectrum (B), and linewidth (C) of the MMF amplifier [1]
The amplifier's output efficiency, spectrum, and linewidth were also measured. The MMF amplifier achieved a slope efficiency of 82%, as shown in Figure 5(A), consistent with theoretical predictions. The output spectrum (Figure 5B) shows a signal peak at 1064 nm with a relative ASE intensity of 52 dB, while the left-side peak represents a faint residual pump signal. Due to the extremely narrow output linewidth, conventional spectrometers struggled to measure it. Therefore, heterodyne methods were employed to determine the input and output linewidths. The MMF amplifier constructed in this work exhibits an output linewidth of 35 kHz (20-dB) / 1 kHz (3-dB, i.e., full width at half maximum), showing no significant difference from the input linewidth. Its excellent temporal coherence meets the requirements for precision interferometric measurements. This paper systematically elaborates on multimode fiber SBS theory considering pump depletion and gain saturation. It proposes integrating multimode fiber amplification with wavefront phase modulation to simultaneously achieve SBS suppression and output spot optimization. The constructed MMF amplifier operates at high power, high efficiency, and narrow linewidth, ensuring high coherence. This technology holds potential applications in coherent beam combining, large-scale interferometry, and directed energy systems.
References: [1] Stefan Rothe et al., Wavefront shaping enables high-power multimode fiber amplifier with output focus. Science 390, 173–177 (2025).
