Owing to the high efficiency, excellent monochromaticity and beam quality, stable and reliable operation, and high environmental adaptability, high-power narrow-linewidth fiber lasers are widely applicable to various fields, such as spectral-beam combining (SBC), coherent-beam combining (CBC), nonlinear frequency conversion, remote-sensing measurement, and gravitational-wave detection. The development of application technologies has increased the demand for power scaling narrow-linewidth fiber lasers. To achieve prominent effects in SBC and CBC, a gigahertz spectral linewidth is typically required. Narrowing the linewidth and increasing the power simultaneously are challenging owing to nonlinear effects, in particular the stimulated Brillouin scattering (SBS) effect. To suppress SBS, researchers have proposed many methods, such as increasing the optical fiber-mode field area, reducing the optical-fiber length, optimizing the pump structure of the main amplifier, introducing gain competition, applying a temperature or stress gradient to broaden the Brillouin gain spectrum, and phase modulation. Among them, phase modulation can mitigate SBS by broadening the seed linewidth to effectively reduce the spectral power density of the laser; thus, it has been extensively investigated recently. However, improvement to the SBS threshold is limited under a certain linewidth. Nonlinear spectrum compression with a negative chirp is widely used in pulsed-fiber amplifiers. To reduce the SBS gain, the self-phase modulation (SPM) generated by the nonlinear Kerr effect is employed for phase demodulation and carrier recovery. Notably, this technique is applicable to continuous-wave laser domains. Multistage phase or frequency modulation (FM) is adopted to obtain a relatively wide spectrum and achieve a high-power output. Subsequently, the SPM generated in the fiber can be controlled via amplitude modulation (AM) to narrow the output spectrum. Consequently, power scaling with a narrow linewidth is achieved.

In this study, the principle of nonlinear phase demodulation based on SPM is investigated. The physical mechanism and factors affecting spectral compression are demonstrated comprehensively in a narrow-linewidth fiber laser with a broadened spectrum. The nonlinear demodulation of the spectrum is realized using combined modulation. When the modulation frequency is restricted to 10 GHz with general modulators, the effect of modulation on SBS is analyzed. The effect of phase error caused by FM and AM delays on the demodulation results is quantified to identify the optimal demodulation phase. In the case of optimal nonlinear demodulation, the relationship between the FM/AM depths and output power is investigated. The SBS thresholds under different modulations are compared experimentally. By combining this technique with phase modulation using a low-pass-filtered pseudo-random binary sequence (PRBS), one can overcome the current disadvantage of the phase-modulation technique and obtain fiber lasers with high powers.

In the experiment, multistage modulations combining white noise source (WNS) modulation, FM, and AM are used to realize the nonlinear phase demodulation of the spectrum (Fig. 5). Signal-to-noise ratios of ±1-order sidebands and root-mean-square (RMS) linewidths are measured with different FM and AM phase shifts to evaluate the demodulating effect (Fig. 6). The optimal demodulation phase is obtained via theoretical simulation. In the case of perfect nonlinear phase demodulation, the FM depth is proportional to the output power, whereas the AM depth is inversely proportional to the power (Fig. 7), which is consistent with theory. The SBS thresholds under different modulation schemes are measured and compared experimentally (Fig. 8). The SBS threshold based on nonlinear phase demodulation is approximately twice higher than that based on pure phase modulation for the same linewidth (Table 1). By combining this technique with low-pass-filtered PRBS phase modulation, output spectrum compression is realized experimentally, and the linewidth reduces from 22.4 GHz (RMS) to 9.5 GHz (RMS) at an output power of 40 W (Fig. 9).

In this study, the physical mechanism and influencing factors of spectral linewidth compression based on the SPM effect are investigated comprehensively in narrow-linewidth fiber lasers via spectrum broadening. Nonlinear phase demodulation is realized by adopting the WNS modulation + FM + AM, and the effect of the demodulation phase is analyzed. The residual phase signal after nonlinear demodulation is an oscillating signal with the same frequency as that of the modulation signal, and the oscillating amplitude is proportional to βFM2-2cosΔ?. In the optimal demodulation phase, the relationship between the modulation depth and output laser power is measured, which shows consistency with theory. The SBS thresholds are measured and compared under different modulations. The SBS threshold spectral power density after the WNS modulation + FM + AM is higher than those after the WNS + FM. Compared with the case of pure phase modulation, the SBS threshold based on nonlinear phase demodulation is 2.4 times higher for the same linewidth. Additionally, the experimental results verify that the expected spectral compression can be achieved by combining PRBS signal modulation with a higher SBS threshold and nonlinear demodulation. A higher fiber-laser power can be obtained for the same linewidth via nonlinear demodulation, or the spectral linewidth can be reduced at the same output power. This approach can potentially overcome the limitation of the current phase-modulation technique and yield a higher power for a narrow-linewidth fiber laser. Additionally, it is advantageous for generating a higher spectral power density for pulsed or continuous-wave fiber amplifiers limited by SBS.