Microresonator-based frequency combs (microcombs) [1,2] have emerged as a state-of-the-art scheme by pumping a continuous-wave (CW) pump laser into a high-Q optical microresonator. The microresonator provides great design flexibility in the adjustment of comb teeth intervals ranging from several gigahertz (GHz) to even above 1 THz. In particular, due to the two balances of dispersion and Kerr nonlinearity and of parametric gain and cavity losses, the microcombs could be characterized by temporal dissipative Kerr solitons (DKSs) [3]. These solitons are highly coherent with a smooth comb-like spectral envelope and have already been used for coherent communications [4,5], time-frequency metrology [6,7], laser ranging [8], low-phase-noise microwave generation [9,10], and photonic convolutional neural networks [11]. Microresonators with different material platforms have been studied [12–22]. A silicon nitride (Si3N4) platform is favored, benefiting from the wide transparence windows, ultralow-loss features, and compatibility with complementary metal-oxide-semiconductor (CMOS) technology, which contributes to large-scale fabrication and widespread application.

One essential problem that prevents the generation of DKSs is the resonance frequency shift caused by the thermo-optic effect when the microcombs transit from a chaotic state to a soliton state with a sudden decrease of the intracavity power [23]. The resonance frequency shift can be overcome with a lot of methods such as a rapid frequency sweep of the pump laser [24], power kicking [25], backward tuning [26], a pulse-driven scheme [27], auxiliary laser-assisted thermal compensation [16,28–31], and self-injection locking [32,33]. Among them, the auxiliary laser-assisted scheme is particularly fascinating, owing to the ease of operation for the single-soliton generation. However, the adoption of another independent laser, fiber circulators, and an amplifier in the opposite direction makes the microcomb generation system much more complicated. Recently, an alternative option that utilizes an optical sideband generated from a modulator to replace the auxiliary laser has been put forward, which could simplify the setups and promote the soliton microcomb generation to some extent, such as exciting either the same mode [34] or two neighboring cavity modes [35] in the same direction or exciting the same mode in the opposite direction [36].

Another key challenge that disturbs the DKSs microcomb’s stability is the microresonator refractive index change with a temperature exchange between the microresonator and the surrounding environment. Therefore, the frequency detuning between the pump laser and resonance frequency would drift out of the soliton existence range [37]. To circumvent this issue, some feedback and locking techniques can be employed to maintain long-term operation stability and reduce the phase noise of the microcombs. Once the repetition rate (frep) is locked, DKS microcombs can have the potential for compact and low-phase noise millimeter of water (mmW) and terahertz (THz) wave generators through direct optical beat, which is often difficult for electrical methods. Recently, there have been several works demonstrating this outstanding performance with low fractional instability compared to electrical CMOS oscillators [38,39].

In this work, a novel high-fidelity 100 GHz single-soliton microcomb generation scheme is put forward by combining an optical sideband thermal compensation method with a rapid frequency sweep method, in which no circulators and extra amplifiers are required. Compared to merely using the rapid frequency sweep method, the new scheme has a low pump power requirement about 580 mW and extends the soliton existence range from 146 MHz to 3 GHz. Here, the soliton existence range is defined as the frequency range that the pump laser can sweep without losing the soliton microcombs. Besides, due to the thermal compensation effect, the thermo-refractive noise can also be reduced. It is found that the soliton microcombs possess an enhanced repetition rate stability and a decrease in the effective linewidth. When locking frep signal to an atomic clock, the generated 100 GHz microwave signal has a low in-loop fractional instability of 5.5×10−15 at 1 s integration time compared to the free-running fractional instability of 2.9×10−7 at 1 s. Besides, a triangular linear repetition rate sweep with 2.5 MHz can also be executed. In consequence, the demonstrated technology could meet the demand for portable and compact mmW and THz wave generators. It also has the potential for precision laser ranging and innumerable applications in science and technology.

Figure 1(a) shows the schematic of the experimental setup for 100 GHz DKS microcomb generation. A CW pump laser at around 1550 nm followed by a suppressed-carrier single-sideband modulator (SC-SSBM), a phase modulator (PM1), and an erbium-doped fiber amplifier (EDFA) is coupled into a Si3N4 ring microresonator. The temperature of the microresonator chip is kept at 23.6°C with the help of a thermoelectric cooler. Concerning the generation part of the DKS microcombs, all employed fibers and devices are polarization-maintaining ones to eliminate the need for polarization control and keep the system stable away from environmental disturbances. The free spectral range (FSR) and loaded quality factor (Q) of the transverse magnetic mode (TM00) are about 100 GHz and 1×106, respectively. At the microresonator output, one part of the microcombs, excluding the strong pump by a fiber-Bragg grating (FBG), is sent to test instruments for monitoring, and the other part is used for locking.

In the scheme, a rapid frequency sweep method is employed to initiate the DKS microcomb. When the microcombs transform from a high-power chaotic state to a low-power soliton state, the resonator will have a frequency blueshift with a fall of temperature, thus hindering the soliton microcomb formation. This method can overcome the thermal effect of the cavity by optimizing the tuning speed and range parameters. Specifically, the suppressed-carrier single-sideband frequency sweeps from 8.75 to 10.93 GHz within 80 ns, and the voltage-controlled oscillator (VCO) drive voltage is ramped from 4.0 to 8.2 V through an arbitrary waveform generator (AWG). It must be figured out that the fast frequency shifting (up to 27.25 GHz/μs) corresponding to the thermo-optic response time enables the generation of soliton microcombs with high fidelity. This specific tuning range and velocity of the pump laser could satisfy the thermal equilibrium condition of the single-soliton microcomb in the resonator and the ambient environment. Usually, according to Ref. [40], about 1 W on-chip power is indispensable for 100 GHz soliton microcomb generation by the rapid frequency sweep method. The loaded Q (about 2.2×106) of that microresonator is even twice that of this work. It means that watt-level power is approximately needed to generate the single-soliton microcomb if using the microresonator in this work, which is energy intensive for practical application.

Therefore, based on the auxiliary laser-assisted method, this issue can be addressed by taking advantage of the cavity thermal compensation effect. Owing to the extended existence range of solitons and the smaller cavity thermal change, a much lower power requirement can be realized [29]. Different from the complicated individual auxiliary laser, an optical sideband can be generated by directly modulating the pump laser with the PM1 and utilized as an auxiliary laser. Thus, a miniaturized system can be realized without excess fiber amplifiers and circulators.

The thermal compensation effect can be explained in Fig. 1(b). When the DKS microcombs are initiated, the pump laser and the red detuned pump sideband are located at the red side of the cavity resonance frequency, and the blue detuned pump sideband is located at the blue side of the cavity resonance frequency. It should be noted that the sideband at the red detuned position relative to the pump mode has little effect because it is far from the cavity resonance. In this case, the blue detuned pump sideband stays in the thermal self-lock region and mitigates the resonance frequency shift by compensating for the thermal change. When the pump laser jitters and moves toward the longer wavelength (shorter wavelength), the pump sideband follows the pump laser to the longer wavelength (shorter wavelength) with a fixed detuning, causing the cavity power increment (decrease) and a redshift (blueshift) of the cavity resonance frequency. As a consequence, there is a lesser variation of the relative detuning between the pump laser and cavity resonance frequency compared to the situation without an auxiliary optical sideband.

In the experiment, estimated on-chip power of only 580 mW was utilized to generate the single DKS microcombs. However, when based solely on the rapid sweep method, the single-soliton state was incapable of existence due to the short soliton step. Hence, an RF signal from the direct digital synthesis (DDS1) referenced to a rubidium atomic clock is set at 1000 MHz, which is nearly in the middle of the measured working range (0.5–1.4 GHz) and modulated on PM1 to generate two optical sidebands. Only the pump laser and blueshifted optical sideband that are close to the cavity resonance can be allowed to enter the cavity. Note that the power ratio between the sideband and the pump stays the same even after the optical amplification. The RF power used for microcomb generation is about 7 dBm, corresponding to a blueshifted sideband power of about 53 mW and a pump laser power of about 474 mW. The concrete influence of the power allocation will be discussed below. By combining the rapid frequency sweep method with the sideband thermal compensation method, a single-soliton microcomb can be accessed easily. The microcomb’s power and VCO control voltage are monitored by an oscilloscope (OSC), and a clear power transition called the soliton step can be seen in Fig. 1(c) during the scan procedure. There is a drift between the control signal and the detected comb signal, which can be possibly ascribed to the detection signal delay.

Figure 1(d) shows a typical optical spectrum of the single-soliton microcomb measured with an optical spectrum analyzer (OSA). The spectrum is well fitted by a sech2 function except for some spikes and departures at shorter wavelengths. The spikes are mainly from the avoided mode crossing effect [41], and the departures at shorter wavelengths may be caused by the decreased coupling rates at shorter wavelengths [42]. The 3 dB bandwidth of the spectrum is around 41.05 nm, corresponding to a Fourier-transform-limited pulse duration of 62 fs. Furthermore, compared to the pump laser wavelength, the microcomb spectrum shape center has a shift of about 7.53 nm toward the longer wavelength due to the presence of the pulse-induced Raman self-frequency shift effect [43].

The other part of the output from the microresonator is used for repetition rate detection and locking. Due to the large 100 GHz repetition rate, it is difficult to measure it directly. Usually, downconverting it to a detectable RF signal (below 25 GHz) is appropriate for analysis. Nevertheless, some electric devices such as frequency dividers with large conversion loss and additional phase noise are not suitable. Photoelectric combination methods such as electro-optic (EO) frequency combs or microresonator DKS microcombs with much smaller repetition rates have shown great potential and chip capability for downconverting.

As indicated in Fig. 1(a), different schematic microcomb states are shown after different devices. Auxiliary EO frequency combs are adopted to realize downconverting. As shown in Fig. 2(a), two frequency lines of the pump and the adjacent microcomb are filtered by a tunable bandpass filter (BPF), then amplified by an EDFA, and sent to a PM2 driven by a 25.38555 GHz microwave signal generator referenced to a rubidium atomic clock for EO frequency comb generation. The center of spectral overlaps (second EO frequency comb) generated around the two DKS microcombs, is filtered with a 0.1 nm bandwidth BPF and sent to a photodetector (PD). By adjusting the polarization of the down-converting system, an optimized EO frequency combs shape with a maximum beat signal can be acquired. Then, the total soliton repetition rate can be obtained by adding the beat signal and four repetition rate signals of the EO frequency combs. For example, a beat signal of about 200 MHz indicates a total repetition rate of about 101.7422 GHz for the DKS microcomb.

Thereafter, the effect of the sideband power on generating optical microcombs was investigated. Repetition rate variations versus pump frequency tuning range under different modulation strengths (7, 4, 1, −2, −5, −8dBm) and unmodulated state were analyzed, and the results are shown in detail in Fig. 2(b). As the modulation strength increases, the soliton existence frequency range gets larger and expands to the low-frequency area. It can be explained in Fig. 1(b) as described above, the larger power the sideband has, the more thermal-induced resonance frequency redshifts the sideband brings about. Nevertheless, the DKS microcomb collapses when the sideband power exceeds the parametric oscillation threshold (measured as about 70 mW). Furthermore, by increasing the frequency of the pump laser and decreasing the modulation power synchronously, the modulation can finally be switched off, and a pure microcomb spectrum without any weak sidebands can be obtained.

In general, the soliton existence frequency range, judged by the piezoelectric change of the pump laser with a resolving accuracy of 4 MHz, can be improved from 146.1 to 3080 MHz, which is 21 times the range without modulation. Furthermore, the value of repetition rate is influenced by the dispersion waves or Raman effect, which is correlated to the cavity-pump detuning [44]. Therefore, by changing the pump laser frequency, the repetition rate can also have a linear variation. Besides, the range of repetition rate variation has been strengthened a lot from 2.2 to 3.87 MHz with the increment of the pump sideband power. Although the pump sideband does not increase the cavity-pump detuning range, the thermal compensation effect can help measure the repetition rate at the cavity-pump detuning position much closer to the boundary. By linear fitting, the slope changes from 14.8 to 1.21 kHz/MHz. To further prove that the increment of the soliton existence range comes from the thermal compensation effect of sideband power, as shown in Fig. 2(c), another experiment on the cavity resonance frequency response transmission spectrum of various pump sideband power has been executed with OSC. In this experiment, only a tunable CW laser, which represents the auxiliary sideband, is injected to the microresonator, detected by the PD, and then collected in the OSC. Along with the increment of sideband power from 1 to 51 mW, a triangular-shape resonance appears with a sudden jump corresponding to the thermal bistability and shifts to a longer wavelength. In addition, by linearly fitting the cavity resonance frequency with different on-chip powers, a slope of 62.05 MHz/mW can be obtained. When the on-chip power comes up to about 50 mW below the optical parametric oscillation threshold, a resonance redshift for near 3.1 GHz can be obtained, which is approximate with the measured maximum soliton existence range. Therefore, the resonance frequency compensation effect caused by the optical sideband is the main reason for the increased soliton existence range.

To stabilize the repetition rate signal of the DKS microcomb, the downconverted RF signal (∼200MHz) is then phase-locked to a 10 MHz reference signal from the rubidium atomic clock through a DDS2 and an RF mixer [see Fig. 1(a)]. After being amplified and filtered by a low-noise RF amplifier and a 300 MHz low-pass RF filter, respectively, the generated error signal is then sent to a proportional–integral–derivative (PID) controller to actuate on the frequency modulation port (VCO) of the SC-SSBM through the voltage adder, besides the control signal from AWG for the DKS microcomb initiation. Since the beating of neighboring modes will cancel out the carrier-envelope offset frequency fceo, the tuning of VCO does not directly affect the repetition rate RF signal. Furthermore, as discussed above, the changed detuning between the pump laser and cavity resonance has a linear relationship with the repetition rate signal. Therefore, the control of frep can be achieved by rectifying the frequency of the pump laser. When the feedback loop is closed, the temperature and environmental variations can be fully compensated. The microcomb can be operated and kept in a single-soliton state for more than 12 h as shown in Fig. 3(a) by recording the optical spectrum of the microcomb.

For evaluating the long-term locking performance of the repetition rate, a 3 h frequency stability measurement of the downconverted RF signal (∼200MHz) through a frequency counter is conducted at 1 s gate time. The yellow points (left axis) in Fig. 3(b) represent the locked frep signal, which can be well controlled within 5 mHz. The histogram in Fig. 3(c) shows that the locked signal is distributed around 101.7422 GHz, which has a standard deviation (SD) of 0.61 mHz and a standard error of the mean (SEM) of 5.84 μHz. For comparison, the measurements of the red points (free-running with modulation, right axis) and blue points (free-running without modulation, right axis) in Fig. 3(b) show frequency drifts near a range of 0.5 MHz and 2 MHz, respectively. It also needs to be mentioned that when under the free-running state without modulation, owing to the pump laser drift, fluctuations of the intracavity optical power, and the temperature change of the microresonator, the single-soliton microcombs can only exist for near 1 h. Furthermore, under the free-running state with modulation, the sideband thermal compensation effect discussed above can possess a soliton existence time longer than 3 h and less frequency drift.

Allan deviations have also been calculated in Fig. 3(d) to demonstrate the frep stability. The in-loop instability is calculated through dividing the locked downconverted RF signal instability (∼mHz) by the original repetition rate signal (∼101.7GHz). The in-loop instability is 5.5×10−15 at 1 s, corresponding to 0.56 mHz fluctuations of the 101.7 GHz carrier, which is 309 times smaller than the instability of the rubidium frequency standard used here (1.7×10−12 at 1 s), thus constraining the signal stability to the rubidium maser, and then reaches 3.7×10−17 at 2000 s. The frequency instability of the rubidium frequency standard is measured by dividing the instability of the 10 MHz reference signal by 10 MHz. But under the free-running condition, the microcomb has fractional instability of 2.9×10−7 (without modulation) and 5.2×10−8 (with modulation) at 1 s, respectively. It is proved that the repetition rate stability of the soliton microcomb can be greatly improved by locking.

In Fig. 4, a quantitative analysis on the downconverted frep signal (200 MHz) from 101.7 GHz is conducted, and the figure shows the measured frequency and single-sideband (SSB) phase noise spectra. Figures 4(a) and 4(b) show the electronic spectrum signals when the soliton microcombs are free-running without modulation (resolution bandwidth of 1 kHz) or with modulation (resolution bandwidth of 200 Hz), respectively. The electronic spectrum in Fig. 4(b) has a 3 dB linewidth with a few kilohertz (kHz) compared to dozens of kHz in Fig. 4(a), owing to the sideband thermal compensation effect. When the locking loop is closed, as shown in Fig. 4(c), the in-loop frep signal has a 3 dB linewidth around 1 Hz (resolution bandwidth of 1 Hz) with the signal-to-noise ratio of about 55 dB.

To further explore the SSB phase noise characteristics of the downconverted frep signal in different states, they are measured and depicted in Fig. 4(d) with a signal source analyzer (SSA). The blue curve represents the phase noise of free-running frep without modulation, and the phase noise is mostly ruled by the thermo-refractive noise due to the small mode volume of the microresonator. When under the modulation state, the thermo-refractive noise can be counteracted by the pump sideband with recoil, and the phase noise (red curve) can be suppressed to a certain extent (∼31dB at 1 Hz offset frequency). When the locking loop is closed, frep signal jittering can be well overcome. The yellow curve shows a great phase noise suppression within the locking bandwidth of about 30 kHz, and ∼116dB phase noise decrease can be realized at 1 Hz offset frequency. Better phase noise will be carried out when the DKS microcombs are locked to the ultrastable laser or depending on the frequency division effect.

The capability for repetition rate variation and locking with pump detuning offers the possibility for frep precision tuning in this microcomb generation scheme, which is of great importance in many essential applications such as laser ranging [8]. On the one hand, the repetition rate is typically about 101.7 GHz, which corresponds to a shortened ambiguity distance of about 1.475 mm. As a result, a short and high-precision displacement platform could satisfy the non-dead-zone distance measurement. On the other hand, as the repetition rate sweep provides another degree of freedom for regulation, based on the multiplication effect [45], arbitrary distance measurement can be realized with a long fiber-based reference path, even with a slight change in δfrep. Similarly, the repetition rate sweep can also lift the ambiguity for the dual-comb ranging measurement.

The setup for repetition rate tuning is the same as the above locking scheme. In detail, the frep chirping of the microcombs is performed by directly modulating the DDS2 signal. As a proof-of-concept demonstration, a triangular frequency modulation scan of 2.5 MHz has been employed with the frep centered at 101.74255 GHz. As measured in Fig. 5(a), under gate time of 1 ms, the repetition rate can sync with DDS2 back and forth in time faultlessly on account of the locking scheme within several periods. To be specific, 800 points with a time interval of 20 ms are ascribed to a period (16 s). When the frep adjustment range exceeds 2.5 MHz, the scan becomes unstable and is prone to the loss of lock. The tuning range much larger than 2.5 MHz can be realized by adding temperature control with a micro-heater at the expense of tuning speed and turning direction. In order to have a clearer picture of the tuning behavior, the frep variation within a time range of 100 ms has been recorded in Fig. 5(b), in which the blue circles and yellow circles represent the signal source and measured locked frep signal, respectively. The adjustment step is about 6.27 kHz, and the time for locking to take effect is about 5 ms. Furthermore, a faster repetition rate sweep can be realized by adopting a signal source with much more scan points and less sweep time. Similarly, a greater feedback bandwidth is also indispensable.

The frequency noise and linewidth of the microcomb reflect the coherence performance, which are essential for most applications. Here, frequency noises of different optical microcomb modes and states have been measured and compared using a delayed self-heterodyne setup [46]. The test scheme is illustrated in detail in Fig. 6(a). The soliton microcomb modes can be separated from each other through a commercial arrayed waveguide grating, and one of the microcomb modes is sent into an EDFA to be amplified to 20 mW. Then an unbalanced Mach–Zehnder interferometer (MZI), consisting of a 32 m long fiber delay line, is used for subcoherence measurement. To avoid strong zero-frequency noise, the acousto-optic modulator (AOM) is placed in the shorter arm driven by a low-noise microwave source of 80 MHz for heterodyne interference. The output beating signals are detected by a PD, and then they are recorded and analyzed by the SSA.

The frequency noise and linewidth of the microcombs can be analyzed by the single-sideband power spectral density SΔφ(f) obtained from the SSA. Specifically, the frequency noise Sv(f) can be investigated by [47] Sv(f)=f24[sin(πfτ)]2SΔφ(f),(1)where τ stands for the time delay of the two arms, and f is the Fourier frequency. Furthermore, the β separation line, expressed by Sv(f)=8×ln2×f/π2, can separate the frequency noise spectra into low-frequency 1/f noise and high-frequency white noise. In addition, considering that the effective linewidth of the microcombs is mainly dependent on the low-frequency noise, it can be calculated through Δν=(8×A×ln2)12, and A is expressed as [48] A=∫1T0∞H[Sv(f)−8×ln2×fπ2]×Sv(f)df,(2)where H(x) is unit step function; A stands for the corresponding area of Sv(f), where Sv(f)>8×ln2×f/π2; and T0 is the measurement time, which is set to 1 ms, corresponding to 1 kHz offset frequency of the frequency noise.

Furthermore, frequency noise spectra of 41 microcomb modes centered at the pump laser have been measured from 100 Hz to 40 MHz. For clarification and comparison, Figs. 6(b) and 6(c) show the frequency noise of pump mode C34 (channel 34 of C band, 1550.12 nm) and marginal mode C54 (channel 54 of C band, 1534.25 nm). The spectra are hindered by the spikes at 6.3 MHz and their harmonics up to a point, which are the frequency fringes corresponding to the FSR of MZI, but it is insusceptible to observing the low-frequency noise behavior. Then the calculated effective linewidth variations are shown in Fig. 6(d). Three different microcomb states are listed, in which the blue, red, and yellow lines are frequency noise spectra of free-running without modulation, with modulation, and of locked operation, respectively.

For the linewidth of free-running microcombs in Fig. 6(d), due to the instability of the repetition rate, the decoherence of the microcombs is discovered as the linewidth increases quadratically with the microcomb mode away from the pump. Furthermore, as can be seen from the low-frequency noise in Figs. 6(b) and 6(c) dominated by the thermal noise, the microcombs with modulation have a weaker low-frequency noise above the β line than the microcombs without modulation. This phenomenon is much more obvious when the microcomb mode is further away from the pump because of the modulated pump sideband mitigating the thermal noise by thermal compensation effect. Therefore, linewidths can achieve a reduction from 148–400 kHz (without modulation) to 145–180 kHz (with modulation).

For the linewidth of the repetition rate locked microcombs in Fig. 6(d), as expected, linewidths of different microcomb modes are nearly the same because of the high stability of frep. However, the linewidths are rising to around 1155 kHz, and there is an undesirable and distinct increase of frequency noise in Figs. 6(b) and 6(c). The reason can be attributed to the feedback of the VCO, changing the frequency of fceo continually when the repetition rate is locked. Hence, the low-frequency noise has a certain increment, and a locking bandwidth of nearly 30 kHz can also be observed in the frequency noise spectrum. To overcome this problem and reduce the linewidth to a lower value in the future, feedback to the cavity resonance frequency through temperature control or power change of the pump laser can be utilized. Moreover, through locking fceo signal of the microcomb to a laser frequency standard will further achieve a fully locked optical frequency comb.

In conclusion, the generation, stabilization, and tuning of the 100 GHz DKS microcomb are experimentally demonstrated in this work. By taking advantage of the optical sideband thermal compensation effect, a much larger soliton existence range of 3 GHz, a simplified setup, and less pump power have been accessed. Besides, this thermal compensation effect can effectively counteract thermo-refractive noise and achieve enhanced repetition rate stability and a decrease in the effective linewidth of the microcomb lines. The repetition rate microwave signal could be downconverted and phase-locked to a rubidium atomic clock. The in-loop fractional frequency instability of the locking state is about 5.5×10−15 at 1 s, indicating high stability of the source compared to the free-running state. By using a resonator with different FSR or selecting different microcomb lines with several FSRs, this locking method can be expanded to other wavebands, especially for THz, which is hard for the pure electrotechnics method. A better phase noise of the repetition rate signal for ultralow-noise microwave generation will be carried out once the microcombs are locked to the ultrastable laser or depending on the frequency division effect. Moreover, a repetition rate scan with a range of 2.5 MHz can also be employed. These microcombs with a low-noise and tunable microwave frequency rate signal would pave the way for precise laser ranging measurement. Furthermore, this microcomb generation and locking scheme has a great potential toward miniaturization and integration, and it is also applicative for other material platforms as well.