1. Introduction

Laser frequency combs emitting an evenly spaced grid of frequencies [1,2], have revolutionized wide applications ranging from optical communication, computation, metrology, to spectroscopy [3–8]. In an anomalous dispersion fiber laser cavity, one can generate mode locked soliton and thus output frequency combs [1,9,10]. In such a soliton laser cavity, there naturally exists periodic disturbance due to the discrete dispersion and nonlinearity. This periodically disturbances couple the soliton to co-propagating dispersive waves (DW), forming Kelly sidebands on the soliton spectrum [11,12]. Although Kelly sidebands are widely used to retrieve chromatic dispersion [13], they can also cause interference to adjacent soliton pulses, leading to pulse timing jitter and reduces the stability of the soliton state [14,15]. Moreover, strong Kelly sidebands with energy comparable to the pulse itself also imply a possible limitation on soliton amplification efficiency [16]. Recently, in dissipative Kerr soliton microcombs [17], DW via the process of soliton Cherenkov radiation has been successfully leveraged to generate fully coherent frequency comb spectra, with remarkably increased bandwidth that extends into the normal group velocity dispersion (GVD) regime [18]. By analogy, the exploration of the nonlinear interactions of the soliton and Kelly sidebands in an anomalous dispersion cavity, can demonstrate intriguing physical paradigms of soliton-like dynamics, and provide a new opportunity for supercontinuum generation, pulse energy promotion and noise suppression, thus would significantly expands their potential in communication, metrology and spectroscopy.

In this work, we demonstrate the concept of a soliton comb merging the soliton envelop and the Kelly sidebands, in an anomalously dispersive fiber cavity, which is just simply composed by high nonlinearity erbium doped fiber and single mode fiber sections. Soliton mode locking around 1560 nm is generated via nonlinear polarization rotation [19]. Due to the stimulated Raman scattering (SRS) [20], the Kelly sidebands are amplified in the Stokes region, forming an asymmetric spectrum. Finally, once the amplified Kelly intensity reaching the four-wave-mixing (FWM) threshold, the spectral broadening merges the Kelly sidebands and the soliton envelop, forming a broad laser comb with smooth shape, corresponding to ultra-narrow pulses with periodic breathing. Such utilization of DW in a dispersion managed mode locking system helps to suppress the noise (integrated RIN down to -101 dB, 3 orders lower than conventional case), and enables higher pulse peak power (47 kW, sufficient for external-amplifier-free f-2f supercontinuum), which cannot be achieved simultaneously in a cavity with net normal dispersion.

2. Concept and experimental results

2.1 Concept

Figure 1(a) shows the conceptual design of our fiber laser comb. For ensuring efficient nonlinear interactions between the soliton and the DW, we design the cavity specifically. Different from conventional fiber loops containing many passive devices, our fiber cavity is a simple construction, only composed by a high-power 980 nm pump laser diode, a section of 3 m long highly-nonlinear erbium doped fiber (HNL-EDF), a section of 6 m long single mode fiber (SMF), an integrated polarization controller (PC) and a polarization dependent-optical integrated component (PD-OIC). The HNL-EDF simultaneously provides rare-earth gain for laser excitation and high nonlinear gain for nonlinear effects (e.g. SPM, XPM and SRS), third order nonlinear coefficient γ of the cavity ≈ 1.2×10² W^-1 m^-1 [21]. The PD-OIC offers the comprehensive functions including wavelength-division-multiplexing, coupling, and polarization-selective-isolation. It also helps to suppress the backward Brillouin scattering [22]. Different from conventional fiber laser cavities, this construction combines proper repetition rate, clear dispersive disturbance and strong nonlinearity together. Moreover, we compactly encapsulate all the components in a 12×12×5 cm³ package, in which f-2f expander and optoelectronic controllers are also integrated in. Picture of the packaged laser comb device is shown in Supplement 1.

 

Fig. 1. Conceptual design of the soliton laser comb using Kelly sidebands. (a) Conceptual design of our laser cavity, in which we encourage nonlinear interactions between soliton and DW. In experiment, the fiber laser cavity is a simple structure, only consisting of a PD-OIC, an integrated PC, a section of HNL-EDF and a section of SMF. (b) Schematic diagram of the soliton comb using Kelly sidebands. Kelly sidebands are excited by the periodic interferences. Then the Kelly sidebands are amplified by the SRS. When the intracavity power is high enough, due to the nonlinearities such as FWM, the amplified Kelly sidebands merge in the soliton envelop gradually, forming a broadband spectrum. In this process, the soliton pulse would be compressed, which could be verified by the Kelly shifting. (c) Numerically simulated spectral evolution of the fiber laser, from continuous wave operation to mode locking state. Here the white dashed curve marks shift of the first order Kelly sideband.

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2.2 Experimental results

Before experiment, first we qualitatively analyze the interaction of the soliton and DW in a laser resonator (Fig. 1(b)). The optical dynamics of a soliton laser is described by the Ginzburg-Landau equation [23]:

Here A is the temporal envelope, z is the transmission distance, γ is the nonlinear coefficient, g is the gain coefficient, Ω_g is the gain bandwidth, β = 2πfn/c is the transmission coefficient and β_m = (d^mβ/dω^m)_ω=ω0, (m = 0,1,2,…). By leveraging the Fourier relationship i∂/∂t ∼ ω - ω₀, one can rewrite the master equation of a mode family in frequency domain, in resonance frequencies [11]:

Here ω_u is the u-th cavity resonance frequency, D_k is the k-th order dispersion parameter, and D_int(u) = ω_u-(ω₀+ D₁u) is the integrated dispersion, specifically u is the relative mode number, D₁/2π denotes the free spectral range, and D₂ = -(c/n)D₁²β₂ is the group velocity parameter. For β₂ < 0 and ignorable higher order dispersions, we can find a soliton solution of Eq. (1) in sech² envelop, A(ω) = A₀sech[R(ω-ω₀)]∑_uδ(ω-ω_u). The spectral span R of a soliton is balanced by the nonlinear phase modulation and the D₂. Due to the temporal overlapping of the soliton pulses and the DW, Kelly sidebands can be excited via the 3rd nonlinearity, at the offsets from the soliton central frequency:

Here τ is the pulse width, Z_p is the effective cavity length, m is an integer. When the intracavity power is high, the SRS can amplify the Kelly sidebands in the Stokes region [24], forming an asymmetric distribution. When the intracavity optical power of an amplified Kelly band is higher than the FWM threshold, resonant laser lines between the soliton envelope and the Kelly band would be increased, leading to their spectral merger. In this process, the effective bandwidth of the laser spectrum is broadened, correspondingly the pulse width would be compressed, based on the Fourier relationship. Referring Eq. (3), |Δω| decreases correspondingly. By using the finite-difference time-domain (FDTD) method, we show a simulated laser evolution accordingly, in Fig. 1(c). Soliton-Kelly mergers only occur in a fiber cavity with high nonlinearity and sufficient intracavity power. More detailed theoretical analysis is shown in Supplement 1.

Figure 2(a) demonstrates the measured spectra of the laser output. The spectral envelop could be approximately written in A_ssech[R_s(ω-ω₀)]+∑_mA_m(ω-ω₀±ω_m), with considering both the soliton and the Kelly sidebands. First, we obtain continuous waves (CW) laser when gain is larger than loss, and then soliton mode locking occurs when the nonlinear phase modulation matches the dispersion. The Kelly sidebands shifts toward the soliton spectral center during the spectral broadening, and an ultra-broadband laser spectrum is finally achieved. The experimentally measured results meet the evolution well. In our cavity, the laser threshold is 22 mW. When the pumping laser power is higher than 62 mW, mode locking state begins to appear. Thanks to the DW and the SRS, we observe asymmetric Kelly bands, which are remarkably stronger in the Stokes region. By further increasing the pumping laser power (>240 mW), the optical span is broadened gradually. Meanwhile, the number of observable Kelly sidebands in the Stokes region increases. During this evolution, the spectral shift of the Kelly bands toward the soliton central wavelength is observed. Such a phenomenon strongly suggests pulse suppression and spectral broadening since the cavity net dispersion is fixed, referring the Eq. (3). In the end, the Kelly sidebands are completely swallowed into the soliton frequency comb, forming a smooth and ultra-broad envelop (over 230 nm on the -75 dBm noise base). The finally formed envelop is also in sech² shape approximately. Determined by the Raman amplification, the laser comb envelop under 1200 mW pumping power is also slightly asymmetric, it demonstrates wider distribution in the Stokes region. In the Supplement 1, we also show the measured dispersion of the laser cavity, verifying the spectral asymmetry is not induced by the Cherenkov radiation determined by the 3β₂/β₃.

 

Fig. 2. Spectra of the mode locked laser comb using Kelly sidebands. (a) Measured laser spectra, when the pumping power increases from 30 mW to 1200 mW. The mode locking threshold is 62 mW, and once the pumping power is higher than 240 mW, the Kelly sidebands disappear, because they merge in the soliton envelope due to the inter-resonance FWM. In the bottom panel, the zoomed-in curves show the 3-dB bandwidth of the soliton lasers, demonstrating a maximum 3-dB span 2.28 THz under the 1200 mW pumping power. (b) Parameters summarized in the spectral measurement. From left to right, we plot the correlations of the pump power vs the laser power, the full-width of half-maximum (FWHM), and the first order Kelly offset, respectively. (c) By using external supercontinuum technique, the soliton laser comb could be broadened covering 1100 nm to 2300 nm, wide enough for f-2f self-referencing. (d) Beat notes of the f_ceo, before (blue curve) and after stabilization (red curve).

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More in details, we zoom the spectra in, when the pumping power is 480 mW, 800 mW, and 1200 mW, in the bottom panel of Fig. 2(a). It is clear to see that the 3-dB bandwidth in the three cases is 1.11 THz, 1.48 THz and 2.28 THz. Specifically, when the pumping power is 1200 mW, the comb span is over 160 nm, comparable to microcombs with much smaller net dispersion. Figure 2(b) plots the properties according to the spectral measurement, regular soliton mode locking threshold of the laser comb is 62 mW, and the nonlinearity induced soliton-Kelly merger occurs once the pumping power is higher than 240 mW. Under a 1200 mW pumping power, the laser comb power reaches 86 mW. The maximum 3-dB spectral bandwidth of the regular soliton is 0.88 THz, which is much smaller than the soliton-Kelly merged state. Such a spectral broadening certainly decreases the Δω_m of the Kelly bands, from 1.47 THz to < 1.05 THz. This trend also meets the correlation of pumping power and spectral width. We also note that the Kelly merging only occurs when the cavity has a section with enough high nonlinearity. In the Supplement 1, we compare the cases with and without using HNL-EDF.

By using a 1.5 m long dispersion compensated high-nonlinear fiber (HNLF) (4 µm core diameter, nonlinear coefficient 10.8 W^-1 km^-1) externally, the output laser comb could be further expanded, covering over one octave. Figure 2(c) shows the broadened f-2f spectrum of our laser comb. It covers from 1150 nm to 2300 nm, enough for second-harmonic-generation (SHG) based self-referencing. In this process, thanks to the originally high output power, an external-cavity EDFA is not essential. This is also helpful to realize a fully-stabilized comb source more compactly. For further applications such as spectroscopy, the power per comb line could be further amplified before the supercontinuum process. Figure 2(d) show the measured beat notes of the carrier envelop frequency (f_ceo), obtained from a commercial BBO crystal. By using a microwave oscillator, such f_ceo could be stabilized via loop-feedback technique [25]. Here the feedback signal is used to both adjust the 980 nm pump laser power and the polarizer. After stabilization, linewidth of the f_ceo beat note is suppressed from ≈50 kHz to sub 200 Hz.

According to the Fourier transform relationship, the broadened spectrum suggests the compressed soliton pulse. We verify the remarkable pulse compression by measuring its SHG based frequency resolved optical gating (FROG) traces. In order to ensure there is no pulse distortion, we use a 0.5 m long SMF linking the laser output and the FROG. The experimental setup is shown in the Supplement 1. Figure 3(a) shows the retrieved profiles of the measured single soliton pulse because the retrieved traces are almost identical to the raw traces, under varied pumping powers. When the 980 nm pumping power is 70 mW, the laser works in a typical mode locked state. The soliton pulse width is only determined by the balance of the nonlinear phase modulation and the GVD intracavity. Similar to other mode locked lasers, the pulse width is ≈ 1 ps, meeting the -0.01 ps² dispersion nature. But when the 980 nm pumping power reaches 1200 mW, the retrieved intensity changes from a horizontally wide shape to a vertically wide shape. It verifies that the temporal pulse is obviously compressed meanwhile the laser spectrum is expanded. Here we also show the auto-correlation (AC) traces of the pulses clearly via the blue curves. During the pumping power increment, the pulse keeps in sech² shape well. Moreover, we note that in all the pulse suppression process, phase of the pulse keeps flat ≈ 0, that means, the soliton-Kelly interaction during the energy amplification brings no additional chirping. Such pure pulse compression perfectly maintains the temporal shape and the smooth phase of a soliton, which is of outstanding value for applications such as optical communications. For further verification, we also show the time-stretched pulses in the Supplement 1 [26].

 

Fig. 3. Measured pulse alteration with incremental power. (a) With the 980 nm pumping power increasing from 70 mW to 1200 mW, the left panels show the FROG traces of the soliton pulse, and the right panels plot the autocorrelation traces (blue curves) and the phase (red curves). (b) The characteristics of the temporal pulse, from top to bottom, we show the alteration of the pulse width, the peak power and the pulse energy.

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In details, Fig. 3(b) plots the half-width of the measured AC traces, the peak power and the pulse energy, when the 980 nm pumping power varies from 70 mW to 1200 mW. First, meeting the spectral observation well, the pulse width is compressed with the increasing pumping power. For a regular soliton state (P_p < 240 mW), pulse compression is not apparent. But once the strong nonlinear interaction of the soliton and the Kelly sidebands is excited, the pulse width decreases sharply. Then, the pulse width doesn't depend solely on dispersion, the broadened soliton laser spectrum enables the AC pulse width (τ_AC) down to 118 fs. Referring τ_AC = 1.54τ for sech² pulse, the pulse width is only 77 fs. This number is much smaller than a conventional soliton fiber laser. Furthermore, as the Kelly sidebands and the soliton merge more and more completely in the optical frequency domain, timing jitters and cross-modulations also become weaker, hence the pulse are increasingly meeting the Fourier transform limit. Meanwhile, another enhancement is the increment of pulse peak power and pulse energy. Following the promotion in average power, the peak power of a pulse boosts from 0.11 kW to 47 kW, over 2 orders, and its pulse energy raises from 0.06 nJ to 3.18 nJ, over 1 order. Such a high pulse power can enable subsequent nonlinear supercontinuous broadening directly by just using a short section of HNLF, without the requirement of further amplification (see Fig. 2(c)).

Such high energy pulse generation is rarely observed in a conventional soliton laser, limited by the soliton energy quantization effect. Typically, when a mode-locked pulse becomes so narrow that its spectrum is larger than the effective laser gain bandwidth, the erbium gain would no longer amplify the pulse but impose an extra loss on it, thus split the pulse into two or more pulses with broader pulse width [27,28]. In our implementation, thanks to the third order nonlinearity, the cavity provides broader amplification for the comb envelope. Meanwhile, in this process, since the Kelly sidebands are merged in the soliton envelop, the CW energy is suppressed and the pulse energy could go further higher. Besides, we note that our near-zero-dispersion cavity is composed of ‘HNL-EDF + SMF’ (normal GVD + anomalous GVD), this enables pulse stretching and narrowing periodically for additive-pulse mode-locking, and approaches high energy in the framework of dispersion-managed soliton [29–31]. We discuss the pulse evolution in Fig. 5. Nevertheless, when the pumping power is higher than 1260 mW, pulse splitting would be difficult to avoid (Fig. S4).

In Fig. 4, we discuss the stability of the laser comb, during the excitation. Measuring the laser output at the port used in Fig. 1 to Fig. 3, Fig. 4(a) demonstrates the self-beat-notes with 22.96 MHz repetition, here the pumping power is 1200 mW. Even driven by such a high pumping power, the laser comb outputs a single pulse per roundtrip. We show more measured radio-frequency (RF) beat notes under varied pumping powers in Supplement 1. The radio-frequency down conversion reflects that the laser comb is smooth and stable optically. Specifically, we check the intermodal beat frequency at 22.96 MHz, its signal to noise ratio (SNR) is > 95 dB, verifying that the laser comb has very clean continuous wave base (or ultrahigh pulse purity). In Fig. 4(b), we illustrate more details. For a pumping power increasing from 70 mW to 1200 mW, the nonlinearity-based Kelly sideband merging also helps to suppress the intensity noise. First, when the pumping power increases from 70 mW to 240 mW, because the Kelly sidebands become stronger, the SNR of the intermodal beat frequency decreases. Afterwards, the further increased pumping power enables the Kelly bands merged in the soliton envelope, this means the temporal continuous noises are considerably suppressed. Thus, we obtain a higher temporal SNR, the maximum number reaches 100 dB. But when the pumping power is too high, the SNR would decrease back, due to the power overload induced noise-like pulse competition [32], also see Supplement 1.

 

Fig. 4. Stability of the soliton laser comb using Kelly sidebands. (a) Beat note (repetition 22.96 MHz) of the soliton laser frequency comb, illustrating the flat envelope and the high SNR (> 95 dB). (b) SNR of the first order beat note @ 22.96 MHz, varying with increasing pumping power. (c) SSB phase noise of the soliton laser comb. Thanks to the nonlinear merging of Kelly sidebands, it demonstrates lower phase noise when the pumping power > 240 mW. (d) RIN of the soliton fiber laser comb, the increasing pumping power can bring a low RIN state, but when the pumping power is > 1200 mW, instabilities such as Q-switching and multi-soliton competition would appear.

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Fig. 5. Pulse evolution intracavity. (a), (b) Schematic and qualitative depiction of the pulse evolution. Pulse duration periodically decreases and increases due to the positive-negative dispersion segments. (c) Measured retrieved FROG traces at different ports, verifying the temporal-spectral breath. (d), (e), (f) At varied ports, the pulse duration (blue dots), the spectral bandwidth (red dots), and the time-bandwidth product (black dots) are also different, with the pulse propagation.

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Figure 4(c) plots 6 single-sideband (SSB) phase noise curves of our laser comb (for frequency carrier 22.96 MHz), under the pumping power 70 mW, 120 mW, 210 mW, 680 mW, 800 mW, and 1200 mW, respectively. In the first 3 cases, the Kelly sidebands are obviously seen in spectrum (blue curves), while in the later 3 cases, the supercontinuum soliton envelope has been already formed (orange curves). The measured data illustrate that merging the Kelly sidebands and the soliton realizes lower phase noise. For instance, at the frequency offset 7 kHz, the phase noise is -160.1 dBc/Hz under 1200 mW pumping power, but -137.8 dBc/Hz under 70 mW pumping power (optimization > 22 dBc/Hz). Moreover, in relatively high frequency region (10 kHz to 1 MHz), we can see huge noise peaks induced by the Kelly sidebands, but they can be dramatically suppressed in the orange curves. Generally, in the frequency offset 1 Hz to 10 kHz, the phase noise obeys the trend of f^-2, suggesting the phase noise of the laser soliton comb is majorly limited by the white noise. For further applications, such numbers could be further stabilized via external locking techniques [33].

Although a higher pumping power can achieve larger spectral span and narrower pulse with higher peak power, overloading intracavity energy can also induce multi-solitons, even Q-switching instability. When increasing the pumping power from 70 mW to 1400 mW, the laser operation experiences the regular soliton mode-locked state, the Kelly-soliton merged state, and finally the unstable state, which is the major reason of SNR decrement in Fig. 4(b). Figure 4(d) plots the typical relative intensity noise (RIN) of the three states. First, under a relatively low pumping power, the mode locking accompanies considerable Kelly sidebands, hence we see a high RIN in low frequencies, and a peak at 131 kHz, induced by the laser breather [34]. Then, on the Kelly-merged state, thanks to merging the Kelly sidebands in the soliton, the broadband mode locked laser comb also demonstrates low RIN down to -144 dB @ 10 kHz (integrated RIN ≈ -101 dB). Finally, once the pumping power is too high, the laser RIN returns higher. Here we also observe Q-switching peaks with repetition 18.8 kHz and mode competition noise peaks over 100 kHz [35].

3. Discussion

For better understanding the periodic evolution of pulses in the cavity, we monitor laser output at different locations in the cavity, by using multiple 1:99 couplers. Figure 5(a) and 5(b) shows the Qualitative depiction. Dispersion of the HNL-EDF is positive, while dispersion of the SMF is negative, this enables the broadening-narrowing breather of pulses in each roundtrip. The HNL-EDF offers the third order nonlinearity majorly, and enables a large nonlinear phase shift φ_NL = γPL ≈ 80 >> π, the pulses are heavily chirped. In the SMF section, the anomalous GVD stretches the pulses, while in the HNL-EDF section with normal dispersion, the pulses are compressed. Excepts the physical mechanism, such evolution is similar to the ‘breaking-free’ similariton in an all-normal-dispersion cavity [10].

Then we measure the pulse evolution under varied pumping powers. Left panels of Fig. 5(c) illustrate the retrieved FROG traces of the soliton pulses measured at different positions, when keeping the pumping power 90 mW. In this case the Kelly sidebands are not merged. Alteration of the time-frequency profile of a pulse is not obvious. For instance, from Port 1 to Port 2, the pulse duration is just compressed from 884 fs to 803 fs. On the other hand, right panels of Fig. 5(c) demonstrate the retrieved FROG traces measured at different positions in cavity, when keeping the pumping power 1200 mW. Pulse alterations in both temporal and spectral domain are obvious. From Port 1 to Port 2, a temporally wide pulse with relatively low peak power evolves to an ultrashort pulse with high peak power. The strong four-wave-mixing broadens the laser spectrum, especially when β₃ of the fiber cavity is small. From Port 2 to Port 3, the laser spectrum becomes narrower due to the chirp induced filtering effect. Besides, FROG traces at the Port 2 and the Port 4 are tilted, such tilt is especially obvious when the pumping power is higher. This verifies that the pulses are heavily chirped during the intracavity evolution.

In Figs. 5(d) to 5(f), we summarize the pulse duration, spectral bandwidth, and the time-bandwidth product of the measured pulses. For 90 mW pumping power, the laser comb operates in a soliton-like state, the pulses propagating along the cavity keeps shape and spectrum well. During the evolution, the time-bandwidth product keeps ≈ 0.6. While in the case when the pump power is 1200 mW and the intracavity power is high enough, the soliton-Kelly becomes a merged state, due to the large nonlinear modulation. At Port 1, we obtain the widest pulse duration ≈ 1040 fs, with spectral bandwidth ≈ 1.62 THz; while at the Port 3, there appears narrowest pulse duration ≈ 52 fs, with spectral bandwidth ≈ 6.1 THz. Here the chirp is close to 0, and the time-bandwidth product reaches 0.317, approaching to the Fourier transform limit. Since the average power and the repetition in cavity is the same, we estimate the highest peak power appears at Port 3 could be ≈ 70 kW.

4. Conclusion

In summary, by taking advantage of the Kelly sidebands rather than annihilating them, we find a novel way to use the DW via strong nonlinearities, in a high-power fiber laser cavity, with managed dispersion. Thus, we obtain a supercontinuum comb, with 3-dB bandwidth up to 6.1 THz, breaking the limitation of erbium gain bandwidth. In FROG measurements, we clearly verified that the soliton pulses breathe dramatically, with pulse duration down to 52 fs, which was hard to obtain in a typical anomalous dispersion fiber cavity. This technique also has unique potential to compress both phase noise and RIN over two orders. Moreover, thanks to the pulse compression, our soliton comb laser can output ultrahigh peak power (up to 70 kW), showing capability for amplification-free f-2f broadening for full-stabilization. Finally, benefit from the simple geometry, all the laser soliton comb can be encapsulated in a centimeter scale package with an internal integrated temperature controller. This work demonstrates a novel physical paradigm for understanding the laser evolution in a soliton-similariton fiber cavity, and can provide a high-performance fiber comb source with both high energy, low noise and compact size, offering a tool for out-of-lab applications ranging from optical coherence metrology [36], comb based distributed fiber sensing [37], supercontinuum spectroscopy [38], high resolution tomography [39], to large volume optical communication [40].

5. Experimental detail

The fiber laser cavity is driven a compact high power 980 nm laser diode (Connet Venus VLSS-980-B-1400-SM-FA-SP), the optoelectrically packaged pump module is < 10×8 cm² scale. The pumping laser is coupled in the cavity via a polarization dependent-optical integrated component (CHONGYU, PD-OIC-98-S-10-N-N22N-BLLB-1-S). The fiber laser cavity is composed by 3m heavily doped HNL-EDF (YOFC EDF 1036⁺, C band adsorption 40 dB/m, core diameter 5 µm, GVD 28.6 fs² mm^-1), and 6 m SMF (Corning, SMF-28e, GVD -21 fs² mm^-1) [41]. The SMF ensures the total dispersion of the cavity is anomalous (≈ -0.01 ps² for 1560 nm wavelength). For ensuring the setup compactness, a 6 cm long polarization controller is linked in the SMF. Typically, we measure the spectra of laser outputs by using an optical spectrum analyzer (Yokogawa AQ 6370D, Yokogawa AQ 6375B), and the temporal traces by using a fast oscilloscope (Siglent SDS 5104X). We check the RF noise of the laser comb in an electrical spectrum analyzer (R&S FSW 43). In the FROG measurement, we use the instrument (Mesa-Photonics). It has a free-space tunable time delay line enabling auto-correlation window 6656 fs. A BBO crystal with a minimum response peak-power of ≈ 1 kW is used to generate the SHG signal. In the phase noise measurement, a low-noise detector (Thorlabs LDS12B, bandwidth 400 MHz) is used to obtain the RF signals, then the first order beat note (23 MHz) of the laser comb is measured in a phase noise analyzer (APPH-2660). Besides, for measuring the RIN, we use an oscilloscope to calibrate the average power, and then demonstrate the frequency dependent noise in an electrical spectrum analyzer. More details are shown in Supplement 1.