Highly-stable mode-locked PM Yb-fiber laser with 10 nJ in 93-fs at 6 MHz using NALM

We demonstrate highly stable mode-locked Yb-doped fiber oscillators using a nonlinear amplifying loop mirror, delivering linearly polarized laser pulses with high energy at a low repetition rate of several MHz. These lasers are composed of polarizationmaintaining fibers and fiber-based components without intra-cavity dispersion compensation. The spectral and temporal characteristics are systematically investigated at different repetition rates. Spectral bandwidth of 31 nm is realized in the case of 6 MHz repetition rate, and the pulse energy reaches 10 nJ. A pair of gratings compresses the output pulse to 93 fs. RMS power stability is as low as 0.04% in 10 hours, which shows excellent stability. We believe that this type of fiber oscillator is an ideal seed for further high power amplification. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (140.3510) Lasers, fiber; (140.4050) Mode-locked lasers; (320.7090) Ultrafast lasers. 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The pulse properties (e.g., broad spectrum, high energy, and outstanding stability) of mode-locked fiber oscillator are crucial to fiber amplifiers because they affect temporal and spectral features of the amplified pulses.Various mode-locking methods have been developed to obtain energetic ultrashort pulses at 1 µm, such as nonlinear polarization evolution (NPE) [18][19][20][21], saturable absorber mirror (SAM) [22,23], NOLM (nonlinear optical loop mirror), and NALM (nonlinear amplifying loop mirror)) [24][25][26].A. Chong et al. reported an ANDi fiber laser using NPE mode-locked mechanism, which generated 140-fs pulses with 20-nJ pulse energy after external compressor [18].W. H. Renninger et al. reported shorter pulse duration of 55 fs with energy of 5 nJ using the same mode-locking mechanism [19].X. Zhou et al. obtained 28-fs dispersion managed (DM) mode-locked fiber laser based on NPE by inserting a pair of gratings in the oscillator cavity, but the pulse energy was less than 1 nJ [20].Recently, SESAM mode-locked fiber laser producing 85-fs pulses with 0.5-nJ pulse energy was developed by H. Wang et al., in which a chirped fiber Bragg grating was employed as compensator and output coupler [23].To date, ultrashort pulses under 100 fs can be obtained by traditional NPE and SESAM fiber lasers, but the pulse energies are limited and cavities are non-polarization-maintaining (PM).Although ANDi fiber oscillator can achieve short pulses with high energy, the mode-locking state is sensitive to environmental conditions due to free space configuration.A 20.54-MHz all-PM mode-locked fiber oscillator using NPE was demonstrated in 2017, which generated 0.85-nJ, 150-fs pulses [21].However, the pulse energy is low and the pulse is relatively long.
NOLM and NALM were proposed as the mode-locking component in 1988 and 1990, respectively [27,28].Since then, Er-doped and Yb-doped fiber oscillators incorporating these two devices have been extensively studied [29][30][31].Due to no need of intra-cavity free-space configuration and saturable materials, Yb-doped PM NOLM and NALM oscillators are insensitive to vibration and temperature, leading to high environmental stability [32].Moreover, a 10-MHz NALM fiber oscillator producing 4.5-nJ 120-fs pulses was demonstrated in 2013 [33].Besides, NOLM or NALM fiber oscillators can operate at long cavity with low repetition rate.NALM oscillator with 506-kHz repetition rate and 6.9-nJ pulse energy was reported recently [34].However, PM NOLM and NALM fiber oscillators with short (100 fs) pulse duration, low (<10 MHz) repetition rate, and high (~10 nJ) pulse energy have not been reported.
In this paper, we report highly-stable mode-locked all-PM Yb-doped fiber oscillators using NALM, delivering linearly polarized pulses at repetition rates of several MHz.The spectral and temporal characteristics of laser output at different repetition rate (4 MHz, 6 MHz, and 8 MHz) were intensively studied.Comparison of spectral bandwidth at different repetition rate shows that much better dispersion management in cavity was realized at the 6-MHz repetition rate.The 6-MHz oscillator delivers 10-nJ, 14.4-ps pulses with 31-nm spectral bandwidth.The pulses were compressed to 93 fs by a pair of gratings.The output power stability was measured to be as low as 0.04% (RMS) in 10 hours, which shows excellent environmental stability.

Experimental setup
The schematic of the experiment setup is shown in Fig. 1.Two optical loops (main loop on the left and NALM loop on the right) with all-PM fiber components is employed in this figure-of-eight cavity, pumped by laser diodes centered at 976nm.Loops are connected by a 2 × 2 coupler with splitting ratio of 40:60.The main loop provides cavity for oscillation while the NALM loop enables mode-locking.Yb-doped fibers (YDF, YB 401-PM, Coractive) are employed in both loop to provide gain to pulses.A fiber isolator (ISO) located behind the gain fiber ensures the unidirectional operation of the oscillation.A bandpass filter (BPF) centered at 1030 nm with 3 dB-bandwidth of 2 nm is placed in the main loop to remove the enormous chirp accumulated from each round trip.To maintain enough intra cavity power density, a coupler with output rate of 20% is used as the output coupler (OC).Single mode fiber (SMF) is used to change the cavity length to achieve different repetition rates.The rest of the cavity is mainly constructed by fiber pigtailed components.The cavity length and repetition rate was easily changed by changing the length of SMFs in two spools.

Experiment results
We constructed three Yb-doped NALM fiber oscillators at different repetition rates (8 MHz, 6 MHz, and 4 MHz) in order to reveal the relation between output parameters and lengths of YDFs and SMFs.In order to start mode locking, we gradually increased the pump power of the main loop and NALM loop.The pump powers for mode-locking the oscillators at 8 MHz, 6 MHz, and 4 MHz are shown in Table 1.The spectrum of the mode-locked pulse was measured using an optical spectrum analyzer (OSA, YOKOGAWA AQ6370C).For the 8-MHz oscillator, the total cavity length is 25 m, including 10-m SMF.SMF is placed right behind the output coupler (at SMF-2) to reduce the power density.The mode-locking states changed with the length of YDF-1 and YDF-2.We monitored the output spectrum while changing the length of the 2 segments of YDF.The spectral bandwidth of 28 nm in saddleshape, as shown in Fig. 2(a), was achieved when the lengths of YDF-1 and YDF-2 were set to 1.85 m and 1.4 m.When SMF-2 was increased to 18 m and the length of YDF-1 and YDF-2 remained unchanged, the mode-locking at 6 MHz repetition rate was optimized to obtain broad and smooth spectrum for producing much shorter compressed pulses after the externalcavity grating compressor.Mode-locked pulses with 31-nm spectral bandwidth was realized easily, as shown in Fig. 2(b).
Furthermore, the fiber length of SMF-2 was increased to achieve mode-locking at lower repetition rate.When the length of SMF was increased to 35 m, corresponding to 50-m cavity length and 4-MHz repetition rate, the mode locking cannot be realized under previous setups.The intra-cavity pulse experienced stronger pulse splitting in the longer fiber length compared with the 8-MHz oscillator and the 6-MHz oscillator.We divided the 35-m SMF into two segments and placed them at different positions in the cavity to reduce the splitting.We optimized the length of YDF-1 and YDF-2 gradually.Stable mode-locking was achieved when the SMF was divided to SMF-1 (15 m) and SMF-2 (20 m), and YDF-1 and YDF-2 were set to 2.5 m and 1 m.Spectrum of 16 nm in full width at half maximum (FWHM) was generated, as shown in Fig. 2(c).Comparing the bandwidth of spectrum at different repetition rates shows that the broadest bandwidth is 31 nm generated by the 6-MHz oscillator.The 6-MHz oscillator operates with the highest pulse energy, which leads to the strongest self-phase modulation (SPM) in the cavity, the broadest spectrum, and the shortest pulse duration.In the case of 8-MHz repetition rate, the pulse energy is lower due to higher repetition rate and less pump power of pump-2.Compared with 6-MHz repetition rate, the lower pulse energy at 8-MHz repetition rate results in less intra-cavity nonlinearity, including self-phase modulation (SPM).Consequently, spectrum at 8-MHz repetition rate is slightly narrower.Although pulse energy approaching to 10 nJ was achieved from the 4-MHz oscillator, the intra-cavity pulses experienced much more dispersion in longer fiber cavity, resulting in a narrower spectrum.Detailed experiment parameters are listed in Table 1., repetition rate in MHz; L YDF-1 and L YDF-2 , fiber lengths of YDF-1and YDF-2 in meters; L SMF-1 and L SMF-2 , lengths of SMF-1 and SMF-2 in meters; P pump1 and P pump2 , pump powers of pump-1 and pump-2 in mW; P av , average power exported from the laser oscillator in mW; E p , pulse energy in nJ; Δλ, full width at half maximum of spectrum in nm; τ uc , uncompressed pulse duration in ps; τ c , compressed pulse duration in fs.Table 1 shows the average output powers from the oscillators.Benefiting from the low repetition rate and large gain employed in our cavity, pulse energy extracted out of the oscillators exceeded 6 nJ for the three oscillators.Lower pump power was required to realize stable mode-locking in the case of lower repetition rate.With a NALM as the secondary loop, the intra-cavity pulse was amplified in YDF-2.YDF-2 of 1.4 m was used in the 8-MHz oscillator as well as in the 6-MHz oscillator while higher pulse energy was achieved in the 6-MHz oscillator, caused by higher pump power of pump-2.For the 4-MHz oscillator, pump power of pump-1 was much lower than that for the 8-MHz oscillator and the 6-MHz oscillator because the mode-locking threshold decreased along with the increased cavity length.Although the average power is lower than others, the pulse energy from the 4-MHz oscillator approaches 10 nJ resulting from lower repetition rate.
The output pulses from these NALM fiber oscillators are highly chirped because all the components exhibit normal dispersion and intra-cavity dispersion compensation is absent.The estimation of intra-cavity dispersion based on material dispersion is listed in Table 2.According to the Sellmeier equation, the group-velocity dispersion (GVD) of an optical fiber can be estimated by the following equation: The pulses was not compressed to transform-limited duration due to the uncompensated excessive high-order dispersion from the long cavity.By use of prism pair that can offer negative third-order dispersion [35], it is possible to compress the pulses close to the Fouriertransform-limited duration.Figure 4 shows radio-frequency (RF) spectra of the mode-locking at different repetition rates measured with a fast photodetector connected to a RF spectrum analyzer (E4402B, Agilent).The RF traces indicate that mode-locked pulses are of high quality without any sign of Q-switching, which often occurs along with mode locking and pulse splitting.Moreover, the intra-cavity pulses may split into several pulses when the pulse energy reaches nano-joule level in conventional fiber cavity design.We obtained 10 nJ pulse energy without pulse

β 2 (
λ) is the GVD parameter, calculated to be about 23 fs 2 /mm at 1.03 µm.Figures3(a)-3(c) show the autocorrelation curves of the chirped pulses at the repetition rate of 8 MHz, 6 MHz, and 4 MHz, respectively.The autocorrelation curves of the chirped and dechirped pulses were measured by intensity autocorrelator (pulseCheck, A.P.E.).Figures3(d)-3(f) indicate the autocorrelation traces of the dechirped pulses, which are compressed with a pair of external transmission gratings (TG) (1000 line/mm, LightSmyth).The pulse duration is compressed to 93 fs (Sech 2 fitted) at repetition rate of 6 MHz.The transform-limited pulse duration is 37 fs.

Fig. 4 .
Fig. 4. RF spectrum of output laser pulses from all-PM Yb-doped NALM fiber oscillators at repetition rate of 8-MHz (a), 6-MHz (b), 4-MHz (c) with resolution bandwidth of 1 kHz.The inset of (a)-(c) correspond RF spectrum measured at 50 MHz span with resolution bandwidth of 100 kHz.