High-power fiber lasers have been highly desired for many industrial and scientific applications, including material processing, manufacturing, nonlinear conversion, and gravitational-wave detection [1–4]. Unfortunately, power scaling of a single monolithic fiber laser system is currently limited by the optical nonlinearities, optical damage, and transverse mode instability [5–9]. Coherent beam combining and spectral beam combining provide two effective approaches to further improve the output power of fiber lasers while maintaining excellent beam quality [10–13]. The key unit in the two beam combining systems is the high-power narrow-linewidth fiber amplifier. The properties of the high-power narrow-linewidth fiber amplifier, especially for the output power and spectral purity, tightly determine the performances of the two beam combining systems. However, it is challenging to realize high power and high spectral purity simultaneously due to the inevitable spectral broadening effect in high-power fiber amplifiers.

Different types of narrow-linewidth seed sources have been applied in high-power fiber amplifiers for narrow-linewidth operation, including filtered superfluorescent fiber sources [13], random distributed feedback fiber lasers [14], fiber-Bragg-grating-stabilized laser diodes [15], multi-longitudinal fiber oscillators [16–18], and phase-modulated single-frequency lasers [19–21]. Those seed sources could be classified into two categories according to the strategies for narrow-linewidth operation. One is to apply the seed source with narrower spectral linewidth as much as possible and to optimize the fiber amplifier to avoid the impact of the spectral broadening [13–18]. The other is to control the spectral broadening effect through applying a seed source with stable intensity [19–21]. Despite that higher than kilowatt-level narrow-linewidth fiber amplifiers with diffraction-limited beam quality have been reported based on the above two categories, the extensibility of the first one is limited because the seed laser with a narrower spectral linewidth might lead to more serious issues of nonlinear effects and the spectral broadening effect [22,23]. Accordingly, most of the reported high-power narrow-linewidth fiber amplifiers are based on phase-modulated single-frequency seed lasers [24–27], which naturally have stable intensity and can maintain the spectral linewidth during amplification. However, there could also exist obvious spectral wing broadening in those narrow-linewidth fiber amplifiers based on phase-modulated single-frequency seed lasers [25,26], which would decrease the spectral purity of the output laser and degrade their performance in further applications.

In this work, we aim to clarify the mechanism of the spectral wing broadening effect in narrow-linewidth fiber amplifiers based on phase-modulated single-frequency seed lasers and propose possible techniques to suppress this phenomenon. Through investigating the effects of background spectral noise in the phase-modulated single-frequency seed laser on the spectral evolution in the Yb-doped fiber amplifier (YDFA), we propose a spectral evolution model for the phase-modulated single-frequency part and the background spectral noise in narrow-linewidth fiber amplifiers. The mechanism for the spectral wing broadening effect is clarified, and design strategies to maintain high spectral purity are given according to the theoretical analysis. We have also conducted contrast experiments to verify the theoretical model and the design strategies for high-spectral-purity operation.

The phase-modulated single-frequency laser is commonly based on a single-frequency laser, which is externally modulated through an electro-optic modulator to broaden its linewidth to effectively suppress the stimulated Brillouin scattering (SBS) effect. Therefore, the phase-modulated single-frequency laser could have stable intensity and maintain its spectral shape during amplification. Accordingly, the obvious spectral wing broadening effect in a high-power narrow-linewidth fiber amplifier based on phase-modulated single-frequency seed laser indicates that additional noise is introduced into the seed laser. One strong possibility for this noise source is the background spectral noise, which could originate from the amplified spontaneous emission noise in the preamplifiers. To demonstrate the possible impact of the background spectral noise in the phase-modulated single-frequency seed laser on the spectral evolution in the high-power narrow-linewidth YDFA, we need to construct a phase-modulated single-frequency seed laser with background spectral noise and describe the spectral evolution of the total seed laser in the YDFA. There exist two different spectral components in the total seed laser: the phase-modulated single-frequency part and the background spectral noise. Accordingly, it is preferable to analyze the spectral evolution of the total seed laser through separate descriptions of the two different spectral components (two seed lasers). Then both the output properties of the total signal laser and the interactions between the two different spectral components could be included in the theoretical analysis.

As for the spectral evolution of a single seed laser in a YDFA, it could be generally divided into two main energy conversion processes, i.e., the energy absorption from pump laser to signal laser and the energy conversion among different spectral components. Consequently, the basic approach to model the spectral evolution of a single seed laser in a YDFA is the joint analysis of the two energy conversion processes. Specifically, the two energy conversion processes could be described through the rate equation and the nonlinear propagation equation. When it comes to the case of two seed lasers, the interactions between the two seed lasers could also lead to energy conversion between them. Accordingly, the effects, such as gain competition, cross-phase modulation (XPM), and four-wave mixing (FWM), should also be included in the rate equation and the nonlinear propagation equation. Then the set of unidirectional spectral-spatial equations describing the spectral evolutions of two spectral components in a YDFA could be expressed as N2N0=Γp⏧ωpAeσpaPp+12πTmAe∫Γs⏧ωσωa(|A˜0|2+|A˜1|2)dωΓp⏧ωpAe(σpa+σpe)Pp+1τ+12πTmAe∫Γs⏧ω(σωa+σωe)(|A˜0|2+|A˜1|2)dω,(1)dPpdz=Γp(σpeN2−σpaN1)Pp−αpPp,(2)$$\begin{gathered} ∂A˜0∂z=12Γs(σseN2−σsaN1)A˜0−αs2A˜0+i2β2ω2A˜0 \\ +iγF{(|A0|2+2|A1|2)A0+A1A1A0*}, \end{gathered}$$(3)$$\begin{gathered} ∂A˜1∂z=12Γs(σseN2−σsaN1)A˜1−αs2A˜1+i2β2ω2A˜1 \\ +iγF{(|A1|2+2|A0|2)A1+A0A0A1*}, \end{gathered}$$(4)where the subscripts p and s stand for pump laser and signal laser, respectively; the subscripts 0 and 1 stand for the phase-modulated single-frequency part and the background spectral noise; A˜ and A are the envelope of the signal field in the spectral and temporal versions; σa and σe are the corresponding absorption and emission cross sections; N1 and N2 are the ion densities in the ground state or excited state; N1+N2=N0; N0 is the dopant density in the fiber core; Γ is the power overlap factor; ℏ is the Planck constant; ω is the angular frequency; Ae is the effective mode area of the fiber; τ is the lifetime of the excited state; Tm is the time window during the calculation; α is the loss coefficient; β2 is the second-order dispersion coefficient; γ is the nonlinear coefficient; and F{} denotes the Fourier transform. Equations (1)–(4) describe the evolutions of the ion density in the excited state N2, the pump power Pp, the spectral envelope of the phase-modulated single-frequency part A˜0, and the spectral envelope of the background spectral noise A˜1 along the fiber, respectively. An iterative solution of Eqs. (1)–(4) is obtained numerically using the Runge–Kutta method with the initial conditions.

Based on the spectral evolution model and the constructed initial inserted seed lasers, we simulate the spectral evolutions of both the phase-modulated single-frequency part and the background spectral noise for a typical co-pumped high-power narrow-linewidth fiber amplifier. Here we set the power ratio and bandwidth of the background spectral noise to be −30dB and 2 nm, respectively. The major simulation parameters of the fiber amplifier are shown in Table 1. The core and inner cladding diameters of the YDF are 20 μm and 400 μm, respectively. The absorption coefficient of the initial pump laser is set to be about 1.5 dB/m. For simplicity, the loss coefficient is set to be the same at different wavelengths, and the insertion loss of the pump laser is omitted. Due to our main purpose being to investigate the spectral evolution of the fiber amplifier, not power scaling limitations, we ignore the SBS and stimulated Raman scattering (SRS) effects and focus on a case well below the SBS and SRS thresholds.Table 1.

Major Simulation Parameters for the Fiber Amplifier

The two spectral components have similar spectral bands, and the power ratio of the background spectral noise is much lower than that of the phase-modulated single-frequency part in the initial inserted seed laser; thus, the gain competition between them would not lead to obvious enhancement of the background spectral noise. Therefore, it could be inferred that obvious energy conversion occurs between the phase-modulated single-frequency part and the background spectral noise during amplification, which finally leads to the spectral wing broadening in narrow-linewidth fiber lasers.

According to the above analysis, two types of strategies could be applied to suppress the spectral wing broadening effect in narrow-linewidth fiber amplifiers, i.e., to optimize the properties of the background spectral noise in the phase-modulated single-frequency seed laser or to suppress the FWM effect in the fiber amplifier. The background spectral noise in phase-modulated single-frequency seed laser could be optimized through filtering out part of the background spectral noise. In this way, both the power ratio and bandwidth of the background spectral noise would be changed. Here we analyze the impact of the power ratio and bandwidth of the background spectral noise on the spectral wing broadening effect separately.

In this work, we propose a spectral evolution model for narrow-linewidth fiber amplifiers to analyze the effects of the background spectral noise in the phase-modulated single-frequency seed laser on the spectral purity of the signal laser. Through demonstrating the spectral evolutions of the phase-modulated single-frequency part and the background spectral noise, the interactions between the two spectral components are given. The theoretical results clarify that it is the FWM effect that transfers energy from the phase-modulated single-frequency part into the background spectral noise and leads to the spectral wing broadening in narrow-linewidth YDFAs. Accordingly, the spectral wing broadening effect could be suppressed by filtering out the background spectral noise in the seed laser or applying a counter-pumped configuration in the YDFAs. We have also conducted contrast experiments, which have verified the validity of the theoretical model and the design strategies for high-spectral-purity operation. We believe that this work could provide a good reference for improving the spectral purity of high-power narrow-linewidth fiber lasers.