With the rapid development of laser technology, ultrafast laser systems play an important role in femtosecond micromachining, biomedical imaging microsurgery and precision spectroscopy^[1^]. In ordinary laser systems, so as to scale average power and/or pulse energy, the cascaded amplifier stages are frequently utilized after the seed sources^[2^]. Continuous exploration of seed sources with superior performance is crucial for streamlining and enhancing the efficiency of these laser systems. Currently, passively mode-locked fiber lasers have emerged as one of the most effective seed sources for generating high average power and ultrashort pulses^[3^]. Normally, pulse generation in these fiber lasers relies on saturable absorbers, categorized into material-based real saturable absorbers^[4^–9^] and artificial saturable absorbers relevant to the nonlinear effects of optical fibers^[10^–14^]. However, fiber lasers have been confronted with a significant challenge in effectively managing nonlinearities within the waveguide media^[3^], which impedes the development of high-average-power ultrashort pulsed fiber seed sources.

Mamyshev oscillators (MOs) have gained much attention due to their promising tolerance for high nonlinear phase shift and large modulation depth^[3^,15^], effectively addressing the challenge mentioned above in fiber lasers. Consequently, MOs have become the preferred method for generating higher average power and shorter laser pulses. The mode-locking mechanism relies on self-phase modulation (SPM) and offset spectral filtering to achieve the power amplification and spectral broadening of pulses^[16^–18^]. Up to now, utilizing various cavity configurations, researchers have achieved substantial research progress in MOs regarding energy promotion, pulse shortening, power scaling and so on^[19^–22^]. In this mechanism, one primary challenge is that MOs generally cannot be self-starting. To initiate MOs, researchers have employed several approaches including external seeding^[23^–25^], external starting arms^[26^–28^] and pump modulation^[29^,30^]. These methods effectively achieve sufficient optical fluctuations to initiate MOs, but concurrently introduce complexity to these laser configurations. In this regard, researchers couple the nonlinear polarization rotation (NPR) mechanism with the MOs to achieve self-starting mode-locking operation^[22^,31^]. In addition, the NPR mechanism could effectively enhance the Kerr nonlinear effect in fibers while simultaneously offering a flexible and controllable output coupling ratio. Using this method, a pulse duration of 4.16 ps can be obtained^[32^]. Further increasing the filter separation, the pulse duration can be compressed down to 65 fs^[33^]. Moreover, combined with a nonlinear photonic crystal fiber, the scheme enables the pulse duration to shorten to 17 fs^[22^]. To date, in NPR-assisted mode-locked MOs (as shown in Table 1), average power is invariably limited to the milliwatt level. Thus, the potential of NPR-based MOs still needs to be further explored, especially in the context of achieving sub-50 fs pulse duration while sustaining watt-level average power output.

In addition, high average power is essential for numerous applications of femtosecond MO lasers. To acquire higher average power in MOs, large-mode-area photonic crystal fibers^[2^] or large-core-diameter flexible double-cladding (DC) fibers^[21^,40^] are typically utilized in MO lasers. These methods, which generally involve free-space pumping, add complexity to the laser system. Moreover, pump misalignment related to mechanical drift degrades the laser stability. As mentioned above, many researchers typically employ various types of fibers and higher pump powers to enhance output characteristics. However, we think it makes more sense to attain comparable laser output characteristics directly from an MO using flexible DC ytterbium-fiber (Yb-fiber) within a fusion-spliced-combiner pumped scheme. This necessitates studying the relationship between cavity parameters and output characteristics. Under this scheme, by increasing the filter separation, carefully adjusting the polarization state and optimizing the pump power, watt-level average power while maintaining short pulse widths may be achievable. This approach effectively increases the gain fiber nonlinearity and overcomes the limited gain bandwidth, thereby facilitating broad-spectrum generation. Consequently, this strategy allows for the replacement of photonic crystal fibers or larger core fibers with cost-effective flexible fibers, and considerable output performance can be achieved directly from the NPR-based MO.

Based on the above, an MO is constructed using a flexible DC Yb-fiber, leveraging the NPR mechanism to initiate mode-locking. For further promoting the laser output performance, the impact of the filter separation on the output characteristics is explored. Both increments in filter separation and pump power enhance the average power and narrow the pulse width, which is consistent with the prevailing research results. Furthermore, under equivalent conditions, better output performance can be achieved as the center wavelength of the grating filter is blue-shifted, in comparison to its being red-shifted relative to transmission filter with constant central wavelength. This phenomenon, to our knowledge, has not been reported previously. This phenomenon may be attributed to the larger modulation depth and less nonlinear dispersion when the grating filter is blue-shifted, which results in higher average power and shorter pulse duration. Based on the above findings, optimization techniques have facilitated the achievement of an average power of 2.23 W and a pulse duration of 49 fs. This research has substantially enriched the performance of MO generating both high power and short pulse width in the no-seed mode.

As illustrated in Figure 1, the experimental setup consists of two Mamyshev regenerators designated as arms 1 and 2, respectively. In each arm, a section of ytterbium-doped double-clad fiber (YDF, Yb1200-10/125DC, LIEKKI) is used as a gain medium. The gain fiber is co-pumped with multimode laser diodes with power up to 9 W at 976 nm through fusion spliced combiners. The gain fibers in arms 1 and 2 are 1.4 and 1.6 m, respectively. To facilitate the investigation of the effect of the offset spectra filter on laser characteristics, a 1000 lines/mm transmission grating in combination with a collimator is used in arm 1 as a variable spectra filter (grating filter), which is adjusted to support a full-width at half-maximum (FWHM) spectral bandwidth of 1.2 nm. By moving the collimator, the transmitted central wavelength could be consecutively tuned from 1020 to 1040 nm or even broader. In arm 2, the bandpass filter (BPF) features a constant spectral bandwidth of 3 nm at 1030 nm central wavelength. An NPR configuration is constructed to initial the laser. It incorporates a pair of quarter-wave plates (QWPs), a half-wave plate (HWP) and a polarization beam splitter (PBS). This configuration simplifies the laser cavity and enables the generation of single-pulse operation through only increments in pump power. To ensure unidirectional oscillation of light within the cavity, an isolator (ISO) is inserted between the two arms. The output pulses are dechirped with a grating compressor, consisting of two transmission gratings (1000 lines/mm).

So as to obtain ultrashort pulses and elevated average power, the influence of spectral filtering separation ( $\Delta\lambda_{\mathrm{f}}$ ) on laser output characteristics is explored. To initiate the mode-locking operation, the center wavelength of the grating filter is tuned to 1030 nm initially, which overlaps with that of the BPF in arm 2. In the case, the low-peak-power noise can be easily transmitted through two filters, thereby initiating pulsed operation. Furthermore, the presence of two QWPs, an HWP and a PBS could act as an NPR, assisting the self-starting of the laser^[39^]. When the powers from pump laser diodes (LD1 and LD2) are increased to 1.8 and 2.2 W, respectively, by simply rotating the waveplates, self-starting mode-locking operation can be achieved.

Once initiated, stable mode-locking with the fundamental repetition rate can still be maintained via proper cavity parameters, such as the pump power and output coupling ratio. Firstly, the transmission band of the grating filter is separated with respect to 1030 nm and red-shifted. With increasing $\Delta\lambda_{\mathrm{f}}$ , the mode-locked spectrum is broadened and red-shifted gradually. This phenomenon is attributed to enhanced nonlinear effects resulting from the crossed offset spectral shaping mechanism. As the $\Delta\lambda_{\mathrm{f}}$ increases up to 10 nm, the broadest mode-locked spectrum (shown in Figure 2(a)) is obtained. The corresponding pump powers emitted from LDs 1 and 2 are 7 and 7.4 W, respectively. The spectrum is presented in Figure 2(a), in which the 10 dB bandwidth is around 42 nm, accompanied by the emergence of the stimulated Raman scattering (SRS) component at 1060 nm. After compression, with a 1000 lines/mm grating pair, the duration of the pulse is measured to be 59 fs (FWHM), as shown in Figure 2(b). The slight pedestal should be attributed to the uncompensated nonlinear chirping induced by high-order dispersion and nonlinear effects, including SRS. Figure 2(c) shows the measured pulse train with an interval of 32.7 ns, corresponding to the fundamental repetition rate of 30.58 MHz. The radio frequency (RF) spectrum around the fundamental repetition rate is illustrated in Figure 2(d), showing a signal-to-noise ratio (SNR) of up to 71.8 dB. The beam profile captured by the laser beam profiler is displayed in the inset of Figure 2(b), confirming the fundamental mode operation.

However, further increasing $\Delta\lambda_{\mathrm{f}}$ leads to instability in mode-locking. This phenomenon occurs because the optical signal received by the collimator weakens when $\Delta\lambda_{\mathrm{f}}$ exceeds 10 nm. This weakening indicates an increase in the coupling loss between the collimator and the grating. Then, after gain amplification, the spectral broadening cannot reach the bandwidth required by the BPF, which affects the mode-locking stability. Subsequently, to better understand the impact of $\Delta\lambda_{\mathrm{f}}$ on the laser characteristics, the transmission band of the grating filter is separated with respect to 1030 nm and blue-shifted. As $\Delta\lambda_{\mathrm{f}}$ increases, the spectra exhibit differences compared to those recorded when the grating filter is red-shifted. To analyze the reasons for these differences, under the same $\Delta\lambda_{\mathrm{f}}$ , pump power and polarization state, the spectra and autocorrelation traces are recorded (shown in Figure 3), in which the grating filter is deviated relative to the BPF in opposite directions.

As shown in Figure 3, as $\Delta\lambda_{\mathrm{f}}$ increases from zero, the mode-locked spectra are broadened and red-shifted gradually due to gain saturation and reabsorption effects in the Yb-doped fiber. With the spectra broadened, the corresponding pulses are compressed to shorter durations. In the meantime, remarkable SRS components also emerge. It is interesting to note that wider spectrum and shorter pulse duration can be achieved as the center wavelength of the grating filter is blue-shifted, compared to the case when it is red-shifted. This phenomenon appears to correlate with the modulation depth of MOs. Firstly, when $\Delta\lambda_{\mathrm{f}}$ is zero, the high spectral overlap between the two filters prevents achieving high modulation depth in the MO. Consequently, the continuous wave (CW) component cannot be suppressed due to the insufficient modulation depth, resulting in a strong CW peak at 1030 nm (shown in Figure 3(d)). This has been observed in many reported MOs^[2^,24^,31^]. Secondly, the modulation depth can be gradually enhanced by increasing $\Delta\lambda_{\mathrm{f}}$ , thereby gradually suppressing the CW component^[24^,41^]. This is evidenced in Figures 3(a)–3(c) and 3(e)–3(g), where the CW component gradually diminishes with the increment in $\Delta\lambda_{\mathrm{f}}$ . This observation suggests that the CW component in spectra can, to some extent, reflect the intensity of modulation depth in the MO. It is noteworthy that when the grating filter is red-shifted, $\Delta\lambda_{\mathrm{f}}$ needs to be increased to 10 nm to fully suppress the CW component. In contrast, in the event of blue-shift, the CW component is fully suppressed at $\Delta\lambda_{\mathrm{f}}$  = 3 nm. Therefore, compared to red-shifting, blue-shifting could effectively enhance the modulation depth in the MO, resulting in higher average power and shorter pulse duration.

On the other hand, the dispersion in optical fibers is also a factor that affects the laser output performance (including spectra and pulse widths). For ultrashort light pulses whose duration is shorter than 100 fs, the basic equation that governs the propagation of the optical field ( $\phi \left(s,t\right)$ ) in fiber and includes the effects of both the group-velocity dispersion (GVD) and third-order dispersion (TOD) can be written as follows^[42^]:

$$\begin{align}i\frac{\partial \phi }{\partial s}&={D}_2(s)\frac{\partial^2\phi }{\partial {t}^2}+i{D}_3(s)\frac{\partial^3\phi }{\partial {t}^3}-{R}_1(s){\left|\phi \right|}^2\phi \nonumber\\&\quad-i{R}_2(s)\frac{\partial }{\partial t}\left({\left|\phi \right|}^2\phi \right)+ iG(s)\phi,\end{align}$$  (1)

$$\begin{align}\begin{array}{c} \displaystyle \mathrm{GVD}=\frac{1}{C}\;\left(2\frac{\mathrm{d} n}{\mathrm{d}\omega}+\omega \frac{\mathrm{d}^2n}{\mathrm{d}{\omega}^2}\right)=\frac{\lambda^3L}{2\pi {c}^2}\frac{\mathrm{d}^2n}{\mathrm{d}{\lambda}^2},\end{array}\end{align}$$  (2)

$$\begin{align} \begin{array}{c}\displaystyle \mathrm{TOD}=\frac{L}{C}\left(3\frac{\mathrm{d}^2n}{{\mathrm{d}\omega}^2}+\omega \frac{\mathrm{d}^3n}{\mathrm{d}{\omega}^3}\right)=\frac{-{\lambda}^4L}{4{\pi}^2{c}^3}\left(3\frac{\mathrm{d}^2n}{\mathrm{d}{\lambda}^2}+\lambda \frac{\mathrm{d}^3n}{\mathrm{d}{\lambda}^3}\right),\end{array}\end{align}$$  (3)

$$\begin{align} \begin{array}{c}\displaystyle {n}^2=1+\sum \limits_{j=1}^N\frac{\lambda^2{B}_j}{\lambda^2-{\lambda}_j^2},\end{array}\end{align}$$  (4)

In addition, most of the reported MOs utilize either two BPFs or two grating filters. Therefore, the impact of the center wavelength shift of the filter on the laser output characteristics has long been neglected. This may be the reason why this phenomenon has not been reported yet. To further explore this phenomenon, under the same conditions, the variation in SNR with respect to $\Delta\lambda_{\mathrm{f}}$ is recorded (shown in Figure 4). When $\Delta\lambda_{\mathrm{f}}$ ranges from 0 to 3 nm, the SNR remains essentially unchanged. This is because the MO cannot function as a saturable absorption with high modulation depth when $\Delta\lambda_{\mathrm{f}}$ is less than 3 nm. With the increment in $\Delta\lambda_{\mathrm{f}}$ , the modulation depth correspondingly increases, leading to an enhancement in the SNR. Notably, the SNR is higher when the grating filter is blue-shifted, in contrast to the case when it is red-shifted. When the grating filter is blue-shifted, the center wavelength is blue-shifted from the peak of the gain spectrum, thereby reducing the impact of CW background noise. Furthermore, when the grating filter is blue-shifted, the increments in modulation depth can more effectively suppress noise components within the pulse and filter out unwanted spectral elements, thereby enhancing the SNR. In this case, pulse evolution would only distort slightly even at higher pump powers, achieving a high SNR. Therefore, a higher SNR can be achieved when the grating filter is blue-shifted.

As mentioned above, when the grating filter is blue-shifted, the increments in modulation depth in the MO can lead to enhanced performance, including a wider spectrum, shorter pulse duration and higher SNR. The modulation depth may be attributed to several factors, such as the gain medium, the dispersion properties and the nonlinear effects. A blue-shifted central wavelength typically falls within a region where the gain spectrum of the laser medium is less saturated. This lower saturation allows for more effective modulation of the laser intensity, thereby increasing the modulation depth. In addition, the dispersion properties of the fiber at blue-shifted wavelengths can enhance the interaction between the optical field and the nonlinear medium, further contributing to a larger modulation depth.

Under the guidance of the above experiments, the laser parameters are further optimized. Firstly, the central wavelength of the grating filter is adjusted to 1020 nm. In addition, the total dispersion is further optimized by reducing the combiner pigtail length and increasing the gain fiber length. As the pump power is increased, the QWP and HWP before the PBS must be slightly rotated to adjust the output coupling ratio. When the pump powers emitted from LDs 1 and 2 are 8.0 and 8.2 W, respectively, the broadest spectrum as wide as 85 nm (10 dB bandwidth) is obtained, as seen in Figure 5(a). The modulated sideband is caused by the SPM effect. The modulation sidebands are attributed to higher-order dispersion resulting from nonlinear phase accumulation during pulse evolution and SPM effects within the gain fiber during cavity evolution. These factors can lead to pulse asymmetry and pedestal generation. As shown in Figure 5(b), after compression, the pulse duration is reduced to 49 fs, which is shorter than the previously measured duration. The pulse has a small amount of pedestal structure, which we estimate to comprise less than 15% of the pulse energy. Figure 5(c) shows the corresponding pulse trains. The interval between adjacent pulses is 32.8 ns, corresponding to a fundamental repetition rate of 30.48 MHz, which is determined by the new cavity length. The SNR, as shown in Figure 5(d), is about 80 dB, indicating stable operation in the MO. This high SNR can be attributed to the optimization of laser parameters. The inset in Figure 5(b) depicts the output beam, and the strict single mode characteristic of the high-average-power working is verified. In the case of optimum parameters, the maximum output average power of the oscillator is 2.23 W. To the best of our knowledge, our results represent the highest average power in sub-50 fs pulse duration in NPR-based MOs.

MO stability is also assessed under the maximum average power. The output average power is continuously recorded at 1-second intervals, with the data presented in Figure 6. The root mean square (RMS) fluctuation of the recorded power values is calculated to be about 0.20%, indicating a high level of power stability.

In conclusion, we construct an NPR-based MO using a flexible DC Yb-fiber, pumped with a fusion spliced combiner. The influence of the offset spectral filter on the laser characteristics is explored. It is found that increasing the filter separation and pump power enhances the average power and narrows the pulse width. Notably, the experiments reveal for the first time that blue-shifting the grating filter, as opposed to red-shifting it, significantly enhances the laser performance. This enhancement includes more broadened spectra, much shorter pulse width and much higher SNR. Further optimization enables an average power of 2.23 W, a pulse duration of 49 fs and an SNR of approximately 80 dB. Recent research results on MOs without seed injection are summarized in Table 1. The results from our work are nearly comparable with the state-of-the-art results reported by Haig et al.^[38^]. To the best of our knowledge, our results represent the highest average power in sub-50 fs pulse duration in the NPR-based mode-locked MO laser architecture. These results not only enrich the experimental phenomena of MOs, but also provide a valuable reference for the realization of higher-average-power laser pulses in much shorter pulse duration in MOs.