The optical frequency comb (OFC), as its name suggests, consists of a series of equally spaced spectral lines, resembling a comb. Its ability to link microwave and optical frequencies makes it a key motivation for many applications. After nearly 20 years of development, OFCs have become a persistent research hotspot and opened up growing subject areas. Before the emergence of microcombs, OFCs were generated by a mode-locked laser. However, their applications are limited by the large volume, high power consumption, and restricted usage conditions.

In microcavity optics, the Kerr effect of optical microresonators provides the possibility of generating OFCs as well, leading to a large reduction of volume and power consumption, and it is further developing toward chip integration. In most microcomb generation processes, turning patterns, chaotic microcombs, and soliton comb states are formed in sequence. Compared to high-power chaotic states, the soliton comb is more stable and more widely used for high-precision applications. The soliton comb is also named dissipative soliton—self-confined pulses balancing dispersion and nonlinearity, gain, and loss^[1]. Many applications have been demonstrated with soliton combs, such as spectroscopy^[2-4], ultra-low-noise microwave generation^[5,6], light detection and ranging (LiDAR)^[7], and optical communications^[8,9].

The performance of photonic integrated circuits (PICs) is largely determined by the selection of the integration platform. Silicon photonics leverages mature complementary metal–oxide–semiconductor (CMOS) facilities to ensure manufacturing on a large scale. To generate soliton microcombs, there are several methods based on PICs: auxiliary laser thermal compensation^[10,11], thermal tuning of resonances^[12], pulse pumping^[13,14], pump frequency tuning^[15-17], self-injection locking (SIL)^[18,19], etc. Auxiliary laser thermal compensation needs an extra laser, which makes the setup more complex. The thermal tuning method has a slow tuning speed with high demands on the quality factor (Q factor) of the microresonators. Pulse pumping requires a pumping light with a narrow pulse width. Pump frequency tuning is the most common method for generating soliton microcombs, while SIL is the most integrated method, so here we choose the two methods for comparison.

In this work, stoichiometric silicon nitride (Si3N4) is selected as a nonlinear material for generating soliton microcombs. The same Si3N4 microresonators are used to generate soliton microcombs based on both methods. Soliton microcombs of 50 GHz and 100 GHz are achieved, and their on-chip pump power, 3 dB spectral width, conversion efficiency, and stabilization time are listed, respectively. It shows that SIL largely reduces the on-chip power for generating a single soliton, whereas the 3 dB spectral width for frequency tuning is nearly twice as large as that of SIL. The physical process is analyzed and discussed in detail.

Our chip characterization and subsequent experiments are performed on a six-axis coupled platform. Si3N4 chips with free spectral ranges (FSRs) of 100 GHz are used for experiments, which were fabricated in Qaleido Photonics Co., Ltd. For the sake of improving the coupling efficiency, spot-size converters (SSCs) are designed to be tapered waveguides with varying widths on both edges of the Si3N4 chips. This allows a higher coupling efficiency of ∼50%. Since the thickness of the waveguide is fixed at 820 nm, different waveguide widths, ranging from 1.6 µm to 2.4 µm, are designed to change the dispersion and to search for the best one to generate a soliton comb. In addition, the coupling rate plays an important role in soliton generation. There are three kinds of coupling states: under coupling, critical coupling, and over coupling, which can be tuned by changing the gap between the ring and the bus waveguide. As evidenced in Ref. [20], the critical coupling state is most suitable for soliton comb generation. Therefore, considering manufacturing errors, different gaps are designed in this work for each waveguide width to find the critical coupling state.

Figure 1(a) shows the setup used to characterize the Si3N4 chip, using the methods in Ref. [21]. The quality factor is achieved by measuring the resonance linewidth of Si3N4 microresonators. Light is coupled into and out of Si3N4 microresonators via lensed fiber and inverse tapers. The power applied to the DUT is in hundreds of microwatts, which is low enough to avoid nonlinear effects. The pump frequency is then swept, and the resulting data are processed to characterize the Q factor and dispersion of the Si3N4 microresonators. The microresonator’s integrated dispersion is defined as Dint(μ)=ωμ−ω0−D1μ=D2μ22+D3μ36.(1)

As a test example shown in Figs. 1(b) and 1(c), we can obtain the dispersion and Q factor of a Si3N4 microresonator with a waveguide width of 2.4 µm and a coupling gap of 0.3 µm. Figure 1(b) shows measured dispersion, and the FSR is 100.44 GHz. By deriving the integrated dispersion and fitting it with Eq. (1), the microresonator has a second group velocity dispersion (GVD) D2/2π of 0.598 MHz, which indicates anomalous dispersion. Besides, there are some noticeable jumps in the dispersion curve, corresponding to mode crossing. Avoided mode-crossing can bring unexpected results for soliton comb generation^[22]. Figure 1(c) shows the Q factor at different resonance peaks, which is obtained by Lorentzian fitting of transmission spectra. It indicates that the intrinsic Q factor can exceed 107, and the average loaded Q factor is calculated to be 4.08×106, which is high enough for soliton generation. This characterized Si3N4 waveguide is used in subsequent optical comb generation experiments.

Figure 2(a) displays the setup of the pump frequency tuning experiment. The same ECDL is used as the pump light, followed by an erbium-doped fiber amplifier (EDFA) and a fiber polarization controller (PC). Finally, the pump couples to the Si3N4 microresonator via a lensed fiber. In the experiment, the frequency of the ECDL is first roughly swept to find the resonance, and then an arbitrary waveform generator (AWG) is used to scan finely from high frequency to low frequency, at a scan speed of a few tens of Hz. During this process, the cavity power rises gradually, reaches its peak, and then plummets, which indicates that the microcomb transitions from a chaotic state to a soliton state. Figure 2(b) showcases the comb and pump power evolution during frequency tuning. The power step indicates the soliton state, and different soliton numbers can be accessed as we tune the driving voltage of AWG. After the pump frequency has stopped at a multi-soliton step, the wavelength of the pump is tuned manually, and the single soliton is achieved by changing thermal effects and detuning.

Figures 2(c)–2(h) showcase different output spectra during this process, including the primary comb, secondary comb, chaos, multiple solitons, dual solitons, and single soliton. By tuning the pumping power and detuning, the 3 dB spectral bandwidth could be optimized, reaching 29 nm with 70 mW on-chip power as shown in Fig. 2(h).

Rayleigh scattering from the Si3N4 microresonator provides fast frequency-selective optical feedback to the laser for mode competition, leading to a self-injection locking between the laser and the microresonator. When pump power is low, the high-Q microresonator serves as an external cavity to enlarge the cavity length and reduce the linewidth of the laser^[23,24]. With the increase of pump power, the microresonator also acts as a place where nonlinear effects occur, resulting in the generation of second harmonics^[25] or OFCs^[26]. The schematic diagram of the hybrid integration laser is shown in Fig. 3(a), which consists of a commercial DFB laser and a Si3N4 microresonator. When the DFB laser is controlled at 25°C with thermo electric cooler (TEC), the threshold current of the DFB laser used is 40 mA, the output power can reach nearly 70 mW at 300 mA drive current, and the wavelength tunability is approximately 2.5 nm by tuning the drive current from 50 mA to 400 mA using a battery-driven power supply. The overall coupling loss from the DFB laser to the micro-cavity chip and to the lensed fiber is about 9 dB.

First, tune the current of the DFB laser to access the self-injection region, which appears as a flat pit on the transmission curve. After entering the self-injection region, keeping the current constant and changing the distance between the DFB laser and Si3N4 chip, which represents changing the locking phase, the primary comb, chaos, soliton crystal, multiple-soliton, and single-soliton states occur in sequence, as shown in Fig. 4(c). When the displacement reaches 1.5 µm, this process is recycled, as 1.5 µm corresponds to the change of the 2π locking phase^[18]. Importantly, SIL can suppress the thermal effect in real time because the Rayleigh backscattering happens instantaneously, which is much faster than the cavity thermal drift; thus, we can manually tune the DFB current and the locking phase to access the soliton microcomb states. When the SIL stabilizes in single-soliton states, the pump power on the chip is about 15.5 mW. The parametric oscillation threshold power of the microresonator with an FSR of 100.44 GHz is 7.73 mW, which has been demonstrated by the simulation to be sufficient to excite a single soliton^[27].

To investigate the effect of the locking phase on microcomb formation, the DFB laser current is scanned at different displacements using a piezo stage. We measure the comb power by applying 1 Hz triangular diode current modulation from 359 mA to 374 mA so that the laser scans over a nonlinear microresonator resonance. As shown in Fig. 4(b), the comb power curve is different from the pump frequency tuning method, which is characterized by a triangular shape with soliton steps. Moreover, soliton states occur in both tuning directions. Results shown in Fig. 4(a) reveal that only special phase conditions permit comb generation, which explains why only adjusting the injection current sometimes does not access soliton states in experiments, consistent with the theory^[26]. However, when tuned to the correct phase, single solitons can be obtained by manually adjusting the current of the DFB laser.

It is worth mentioning that, when the displacement is changed, the coupling efficiency between two chips changes simultaneously, so the power on the Si3N4 chip would fluctuate and then affect the microcomb generation. Therefore, this mapping includes the effects of both the locking phase and power on the comb generation.

We compare the chaos and soliton spectra of pump frequency tuning and SIL in Figs. 5(a) and 5(b). The single soliton of 100.44 GHz is generated using both methods. The spectrum sech2 fit shows a 3 dB bandwidth of 30.72 nm and 16.35 nm, corresponding to a pulse duration of 83 fs and 153 fs. To generate a single soliton, the on-chip power needed is 70 mW for pump frequency tuning, which is about 4.5 times that of SIL (15.5 mW). From Figs. 5(c) and 5(d), we can explain why pump frequency tuning needs higher pumping power for soliton generation. For pump frequency tuning, as shown in Fig. 5(c), the comb state evolves from chaotic to soliton as the frequency decreases, resulting in a significant decrease in intracavity power. Due to the thermal effect, the detuning in the cavity also changes greatly. When the pump power is low, the soliton step (red line) is short, and the detuning variations L₁ go beyond the range of the soliton step, which results in the optical comb not being able to stay in the soliton state. However, with the increase of pump power, the soliton step becomes longer^[28], which makes it easier for the comb to stay in. Therefore, for pump frequency tuning, the pump power should be high enough to ensure soliton generation. On the other hand, SIL has a different mechanism of soliton generation. As shown in Fig. 5(d), due to the frequency pull of SIL, regardless of the detuning between the laser and the microresonator, it will automatically stay at the red detuning once it enters the SIL region^[18,29]. The laser frequency can follow the resonance shift instantly so that the soliton state is maintained. Therefore, SIL can access soliton states even at low pump power.

Furthermore, as shown in Fig. 5(b), we find that the pump power is not at the center of the soliton spectrum for pump frequency tuning, which is due to the Raman-induced soliton self-frequency shift (SSFS)^[30]. In Eq. (2), the detuning Δδ and the soliton pulse width τs play an important role in Raman-induced SSFS. For pump frequency tuning, the detuning Δδ is larger than for the SIL, and the soliton pulse width τs is 83 fs, about 50% of the SIL (153 fs), so the ΔΩRaman is much larger. It can be seen that the Raman-induced SSFS of SIL is very small and the spectral symmetry is high, which is the inherent advantage of the SIL mechanism, ΔΩRaman=−8D2τR(Δδ)Q15ω0D121τs4.(2)

At the same time, the optical linewidth of the soliton microcombs is analyzed. The results are shown in Fig. 6, where the intrinsic linewidth of about 20 comb lines on both sides of the pump is measured. As shown in the blue dots, the linewidths of the soliton comb by pump frequency tuning follow a parabolic distribution with the mode number, with a minimum value of 10 Hz at mode number −1. The theoretical basis for this phenomenon is analyzed in Ref. [31]. However, the red triangles show that this rule does not apply to SIL. Figure 6 shows that pumping frequency tuning has a better performance in microcomb linewidth, which can be attributed to the pump laser used. The former uses an NKT laser with an intrinsic linewidth as low as 0.0039 kHz, while the latter uses a DFB laser chip with an intrinsic linewidth up to 22.04 kHz at the current of 320 mA. Therefore, it can be concluded that pump frequency tuning degrades the linewidth and that the lower the Q factor of the microresonator, the faster the linewidth of the edge comb line degrades. However, SIL narrows the linewidth from 22.04 kHz to 0.119 kHz and uses a DFB laser that is more than 10 times less expensive than the NKT laser.

We also generate single solitons in microresonators with FSRs of 50 GHz using both methods, whose waveguide width is 2.2 µm and coupling gap is 0.4 µm. Table 1 shows the comparison between the two methods from different aspects. For the same microresonator, it can be seen that the on-chip power of the SIL for generating a single soliton is much smaller than that of the pump frequency tuning, about 1/14 at 50G microresonator and 1/4 at 100G microresonator. The reason is that the Rayleigh backscattering happens instantaneously, which is much faster than the cavity thermal drift and suppresses the thermal effect in real time^[32]. The 3 dB spectrum bandwidth is correspondingly reduced by about half due to the lower pump power. By designing the waveguide to minimize the dispersion as much as possible, a Kerr comb with a wider spectrum^[33] can be obtained.

The energy conversion efficiency (ECE) of conventional soliton combs is quite low, which is not favorable for applications. In our work, even for microresonators with a total Q value of above 4×106, the ECE of the pump frequency tuning scheme is less than 2%. As mentioned in Ref. [34], the ECE is affected by the FSR and the pump power. With the increase of FSR, the ECE is larger. Table 1 shows that the ECE of SIL is generally higher, about 4 times that of pump frequency tuning, for the reason that it generates soliton microcombs at lower pump power, as discussed before.

During the experiment, as long as the parameters have been well studied, it is easy and repeatable to use both methods to generate single solitons. The stabilization of a single soliton generated by pump frequency tuning is better than SIL because SIL is sensitive to the locking phase and has strict requirements for ambient vibration. Packaging the laser and Si3N4 chip can greatly improve its stabilization. The most obvious advantage of the SIL is the high level of integration. It can be butterfly packaged in several-coin sizes, which is much smaller than in some other methods.

In conclusion, we demonstrate the Kerr microcomb generation in high-QSi3N4 microresonators with FSRs of 50 GHz and 100 GHz by using two methods of pump frequency tuning and self-injection locking. The advantages and disadvantages of the two methods are compared. In pump frequency tuning, a wider spectrum of 30.58 nm in 100G can be achieved, about twice that of SIL. However, in SIL, it is possible to change the soliton states not only by adjusting the current but also by changing the phase. It is also important to note that SIL can realize turnkey operations, with low cost and higher spectral symmetry, and its conversion efficiency is 5.75%, about 4 times that of pump frequency tuning. In addition, for pump frequency tuning, the linewidth of the edge comb line deteriorates, obeying a parabolic distribution, whereas SIL narrows the linewidth from 22.04 kHz to 0.119 kHz, and the linewidth of the edge comb line does not deteriorate significantly. Therefore, SIL is a perfect candidate for applications in highly integrated and narrow-linewidth types.