1. Introduction

Kerr soliton frequency combs (microcombs) have attracted significant interest due to the merits of compactness, low noise, reduced power consumption, and their almost unlimited potential for applications in frequency metrology, ultrafast ranging, dual-comb spectroscopy, and coherent communication [1–4]. To overcome the prevalent thermal instability during soliton formation, various techniques have been developed, such as pump frequency ramp programming [1,5], power kicking [2,6], and pump modulation [7,8]. Bi-directional switching [9–11] and dual-pumping [10–14] have also been proposed for a single-soliton generation. However, most of these schemes require extra equipment such as radio-frequency (RF) sources, modulators, and, in some cases, an additional laser and another fiber amplifier, making them complex and costly. Another promising scheme involves thermally tuning the resonance by integrating a micro-heater on top of the resonator [15–17]. It would be more attractive to trigger the soliton microcombs in a turn-key manner [18], which could eliminate the need for a high-performance tunable laser or complex control, simplifying the system and aiding in practical applications. Microresonators with normal dispersion have also demonstrated turn-key generation of dark-pulse microcomb, such as dual-coupled Si₃N₄ microresonators [19] and AlGaAs platforms [20]. However, all these reported microcombs have a limited bandwidth less than 150 nm, which compromises the application prospects. Considering the paramount importance of the f−2f self-referencing technique for precision metrology [21–23], our focus is on developing a turn-key Kerr soliton comb with broad bandwidth. Such a microcomb can potentially serve as a scalable module to be assembled in astronomical telescopes and optical clocks.

Besides the timing and spectroscopy applications, soliton microcombs have also been widely investigated for low-noise microwave generation, particularly frequencies lower than 40 GHz that can be detected by conventional electronics [6,16,24–26]. The microwave oscillation frequency is determined by the soliton repetition rate (f_rep), implying that a relatively large resonator with a footprint of mm² is required to support the electrically detectable signals. However, unlike fiber mode-locked lasers, the microcomb’s f_rep is higher and not tunable as it is determined by the microresonator size. Exciting multiple solitons in a single resonator and harnessing their correlated beat note (f_beat) has been explored for microwave generation, such as the coexistence of primary and Stokes solitons in the silica platform [27,28] and the soliton molecules in an MgF₂ resonator [29]. However, due to the small difference between the repetition rates of the coexisting solitons, the beat note is typically less than 1 GHz, which is ideally suited for sensing but is too low for microwave photonics.

In this work, we address the aforementioned challenges by employing simple dual-mode Si₃N₄ microresonators with a f_rep of ∼384 GHz, which enables the achieving of the turn-key operation of single-solitons and the synthesis of the tunable microwave. It has been revealed that the auxiliary mode, located on the red detuned side of the pump mode, exhibits advantageous thermal behaviour within the cavity, which ensures the maintenance of the soliton over an enhanced tuning range of pump frequency, i.e., soliton existence range (SER) [30]. The auxiliary resonance can be a high-order transverse mode with the same polarization as the pump mode [31,32], or another high-Q fundamental mode with crossed polarization [33,34]. Based on the dual-mode Si₃N₄ microresonator with a desirable mode separation, we demonstrated the turn-key soliton generation using an external cavity laser or an on-chip semiconductor laser as the pumping source. The SER exceeds 30 GHz, which is two orders of magnitude higher than the resonance linewidth of the pump mode. Furthermore, we demonstrate the coexistence of the single-soliton and primary comb, resulting in a beat note at ∼41 GHz. In another resonator with a closer proximity between the two modes, there is a higher probability to acquire multi-solitons and the coexistence of two frequency combs. The device exhibits discretely tunable microwave signals, versatile multi-solitons, and perfect soliton crystals, showcasing promising applications in microwave photonics.

2. Principle and device characterization

The setup and principles for soliton formation and the generation of the coexisting combs in the dual-mode microresonator are illustrated in Fig. 1. Unlike the widely investigated systems that pump a single mode, the microresonators used in this study feature an auxiliary resonance (TM₁₀) located on the red side of the pump mode TM₀₀ [Fig. 1(a)]. The mode separation Δf is defined by 2πΔf=ω₀₀-ω₁₀, where ω₀₀ and ω₁₀ denote the angular frequency of cold cavity resonance TM₀₀ and TM₁₀, respectively. The laser-resonance effective detuning can be expressed by 2πδ_eff00 (δ_eff10) =ω_p−$\widetilde {{{\mathbf{\omega}}_{\mathbf{00}}}}$ ($\widetilde {{{\mathbf{\omega}}_{\mathbf{10}}}}$), where $\widetilde {{{\mathbf{\omega}}_{\mathbf{00}}}}$ ($\widetilde {{{\mathbf{\omega}}_{\mathbf{10}}}}$) and ω_p denote the angular frequencies of the hot cavity resonance and the laser, respectively. Initially, by gradually tuning the laser from a highly blue-detuned side (no comb, stage I) towards the resonance (stage II), δ_eff00 approaches 0+, and a modulation instability (MI) comb is excited from the TM₀₀ mode. However, the δ_eff10 remains large and there is no nonlinear excitation of the auxiliary mode. Traditionally, as the pump transitions from the effectively blue-detuned (δ_eff00$> $0) to the red-detuned (δ_eff00$< $0) region, the MI comb can transform into a soliton state. However, during this transition, the intracavity power and temperature undergo a significant reduction, resulting in a blue shift of the cavity resonance and the loss of soliton status.

 

Fig. 1. (a) Five stages of microcomb generation with different detuning levels. (I) No comb, the pump is highly blue-detuned; (II) Modulation instability (MI) comb from the TM₀₀ mode; (III) Start-up of soliton state of TM₀₀ mode; (IV) Coexistence of soliton and primary comb from the TM₀₀ and TM₁₀ modes, respectively; (V) No comb, the pump is red-detuned. The dash lines indicate the initial resonance positions without pumping. (b) Four scenarios with different mode separation, illustrating the variation of cavity powers as a function of laser wavelength, considering the two modes independently (left) and collectively (right). (c) Setup scheme for the generation of turn-key solitons and discretely tunable microwaves. ECDL: external cavity diode laser; AWG: arbitrary waveform generator; FPC: fiber polarization controller; FBG: fiber Bragg grating; PD: photodiode; BPF: band-pass filter; OSA: optical spectrum analyzer; ESA: electrical spectrum analyzer.

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Next, by performing a qualitative analysis of the thermal behaviour for soliton generation in the dual-mode resonators, we predict three main benefits of this scheme. First, it enables self-starting and stabilization of the soliton state. During soliton formation, the reduction in cavity power causes a synchronous blue shift of the TM₁₀ resonance (stage III). With an appropriate separation Δf, the pump can enter the effectively blue-detuned region of the TM₁₀ resonance, leading to the excitation of a second mode in the resonator. The additional absorbed power will offset the expected reduction in the cavity power and result in a mitigated thermal shift when transiting from MI to soliton state, thus preserving the stability of the soliton. Consequently, the auxiliary resonance can coincide with the so-called soliton resonance [1,9], enabling the generation of another microcomb from the TM₁₀ mode by further decreasing δ_eff10 through forward tuning of the pump. This represents the second achievement, the generation of coexisting combs (stage IV). Third, it extends the SER, which is defined as the absolute pump frequency tuning range that can support the soliton state. The SER is typically 1∼10 times the linewidth in Si₃N₄ microresonators [35]. When the laser moves away from the TM₀₀ resonance, the soliton is annihilated and the cavity resonances return to the original cold resonance positions (stage V). In our scheme, during the red-tuning of the laser, when the soliton persists, a continuously increasing cavity power from the auxiliary resonance will force the TM₀₀ resonance to shift towards the red side in the same direction as the pump. This delays the decoupling between the pump and the TM₀₀ resonance, thereby enabling an extended SER. The self-feedback from the auxiliary resonance and associated thermal compensation can ensure long-term stabilization of soliton against pump fluctuations.

Figure 1(b) explains how the mode separation affects the soliton behaviour by introducing the concept of the effective compensation region (ECR), which refers to an appropriate contribution to the cavity power from the auxiliary mode that can stabilize the soliton state. Considering the relatively low quality factor (Q) and large dispersion, we assume the TM₁₀ mode cannot exhibit soliton behaviour. There are four situations for the ECR position when the TM₀₀ soliton is initially triggered. (i) If the dual modes are significantly far apart (Δf $\gg $δ_eff00), the δ_eff10 will remain large, resulting in no excitation of the auxiliary mode and no soliton stabilization. (ii) By decreasing the Δf to an optimal separation, the auxiliary resonance induces absorption from the pump and compensates for the intracavity power changes, thereby maintaining the soliton state. This can be a single-soliton (SS) if the ECR aligns with the predicated detuning region supporting SS, which we refer to as critical compensation. (iii) Further slight reduction of Δf leads to two observable trends in the microcomb state: (1) the pump is sufficiently close to the TM₁₀ resonance, generating a primary comb that can coexist with the soliton, and (2) the generation of multi-solitons (MS) generation due to slightly over-compensation. (iv) If Δf becomes too small, causing δ_eff10 to approach zero or even become positive, the excessive power of the TM₁₀ mode will fail to maintain the soliton.

Figure 1(c) shows the experimental setup. A C-band ECDL (Santec TSL-710) is first amplified using an erbium-doped fiber amplifier (EDFA) and then injected into the Si₃N₄ waveguide through a lensed fiber with a spot size of 2.5 µm. The ECDL allows for wavelength adjustment using built-in sweeping or step mode functions. By triggering a Santec optical power meter during laser tuning, the pump wavelength can be measured and calibrated with a commercial Swept Test System [36]. The other pump source utilized in this work is a single-mode slot semiconductor laser developed by our group, which was mounted on a copper heat sink and coupled via a single-mode fiber. The laser design incorporates a high-order grating, which is relatively simple to fabricate by etching slots in the laser ridge [37]. It exhibits a sub-MHz linewidth, a laser power of several mW, and a side mode suppression ratio (SMSR) of ∼40 dB. The wavelength of the slot laser is controlled by changing the current injected into the gain section using an arbitrary waveform generator (AWG). The current can be linearly increased or adjusted in a step-wise manner for tuning. It is important to note that the pump system, which includes the lasers, EDFA, and optical isolators, is designed to prevent injection locking as there is no feedback from the microresonator. The generated microcombs are collected using another lensed fiber. For the soliton generation and characterization, 10% of light is tapped into an optical spectrum analyzer (OSA) to monitor the microcomb spectra. The remaining 90% of the light is split into two outputs using a 3-dB coupler. One output is directed towards a fiber Bragg grating (FBG) to suppress the pump, and then the real comb power can be detected by a power meter or an oscilloscope after a photodiode (PD). The other output is connected to a tunable band-pass filter (BPF) to select a specific comb line, which is then combined with another ECDL. The combined light will be incident on a PD, and the comb noise performance can be evaluated using an electrical spectrum analyzer (ESA, R&S FSV3-K40). For the dual microcomb-based microwave generation, 90% of the output is sent through the BPF to filter the two closest comb lines belonging to different mode families for beat note measurement. The phase noise characterization is carried out using the ESA.

The Si₃N₄ microring resonators employed in this study share the same structural geometry, specifically a radius of 60 µm and a cross-section (width × height) of 2.6 µm × 0.8 µm. The coupling gap between the resonator and bus waveguide is 600 (or 650) nm. These dimensions allow for ideal dispersion profiles and the crossing of TM₀₀ and TM₁₀ mode families near the C-band. The devices were fabricated by Ligentec [38], yielding the intrinsic Q factor of ∼1.6 × 10⁶ for the TM₀₀ mode. It should be noted that the fundamental transverse electric (TE₀₀) modes in the resonator have an under-coupling state (see Supplement 1), which led to the generated microcomb lines being pretty weak. The coupling efficiencies between the two waveguide facets and lensed fibers are measured to be ∼55% and ∼58%, corresponding to a total coupling efficiency of ∼31.9%. The details of the measurement are provided in Supplement 1. As shown in Fig. 2(a), a TM-polarized transmission spectrum consists of two transverse mode families that cross each other near 1570 nm due to the different free-spectral ranges (FSRs). The drastic change in resonance linewidths at µ=−1 suggests a strong mode coupling at this position. We will pump the TM₀₀ mode with µ=0, while the adjacent TM₁₀ mode on the red side acts as an auxiliary resonance. An enlarged view in Fig. 2(b) shows the two resonances with a Δf of 6.3 GHz and linewidth κ/2π of 0.29 and 0.71 GHz, respectively.

 

Fig. 2. Characterization of the dual-mode resonator, ECDL, and slot laser. (a) Transmission spectrum of the resonator under TM polarization, along with the extracted resonance linewidths (dash line-symbol). The dual-mode near 1570 nm used for pumping are denoted as µ=0. (b) Zoom-in view of the dual-mode resonances with a frequency separation of ∼6.3 GHz. The resonance linewidths of the TM₀₀ and TM₁₀ modes are fitted to be 0.29 and 0.71 GHz, respectively. (c) Simulated integrated dispersion profiles (D_int, solid lines) for the TM₀₀ and TM₁₀ mode families, shown as solid lines, demonstrating the agreement with the measured results of 50 resonances. Inset: Zoomed-in view of the dispersion profiles near the pump. (d) Lasing spectra of the slot laser (solid line) and ECDL (dot line). Inset: Oscillation wavelength of the slot laser as a function of the bias current injected into the gain section (I_gain).

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By solving the Eigen frequencies with the finite element method and fitting them with a polynomial function (tenth-order), Fig. 2(c) shows the simulated integrated dispersion. It can be expressed by ${D_{\textrm{int}}}(\mu )= {\omega _\mu } - ({\omega _0} + {D_1}\mu ) = \mathop \sum \nolimits_{i > 1} {D_i}{\mu ^i}/i!,\; i \in \mathrm{\mathbb{Z}}$, where µ is the mode number relative to the central mode (for which µ = 0), ${\omega _\mu }$ is the angular frequency of that mode, and D₁/2π is FSR of the central mode. For TM₀₀ and TM₁₀ resonances with µ=0, the extracted FSR is ∼384.62 and ∼378.89 GHz, and the second-order dispersion coefficient D₂/2π is ∼5 and ∼33 MHz, respectively. Note that here both D_int curves are plotted with a common ${\omega _0}$ and FSR of the pump mode TM₀₀. The inset shows excellent agreement between experimental dispersion and simulations, confirming the near-ideal anomalous dispersion of the TM₀₀ mode, which ensures efficient soliton microcomb generation. The two mode families cross as µ varies from 0 to −1 and their separation Δf exhibits a linear change with µ with a slope of ∼5.6 GHz. Figure 2(d) compares the lasing spectra of the pump sources, where the ECDL has a high signal-to-noise ratio of ∼70 dB while the slot laser has a SMSR of ∼40 dB.

3. Experimental results

3.1 Deterministic soliton generation with ECDL

We initially achieve stable access to the SS state by sweeping the laser wavelength across the resonances with a speed of 1 nm/s. Figure 3(a) displays the measured comb power traces as a function of the laser detuning (relative to 1570 nm) under different on-chip pump powers (P_in) after amplification. In the top subgraph, at P_in= 330 and 400 mW, the comb power curves of the two modes are independent, and no soliton steps are observed. The threshold power for the parametric oscillation of the TM₁₀ mode is approximately 330 mW. Upon further increasing the P_in to 475 mW [middle plot of Fig. 3(a)], a prominent step between 1570.5 and 1570.76 nm emerges, indicating the formation of SS. In our dual-mode resonator design, the SER is significantly expanded to 0.26 nm (∼32 GHz), which is approximately 100 times the resonance linewidth. In contrast, conventional systems with only one pumped cavity mode typically have an SER-to-linewidth ratio of 1∼10 of the pumped mode [9,35]. The sharp increase in comb power before dropping off the resonances is attributed to TM₁₀ comb excitation although it cannot be stably accessed when we stop the laser at the corresponding detuning position. It is noteworthy that the SS can be deterministically created at P_in= 475 mW by repeatedly sweeping the laser, as depicted by the green shading in Fig. 3(b). Different soliton power levels are observed at P_in= 750 mW, corresponding to the formation of SS (N = 1) or two-soliton (N = 2) states, where N is the soliton number and can be identified by the associated spectra. The occurrence of two-solitons at higher pump power is attributed to enhanced compensation strength [as shown in Fig. 1(b)] resulting from a smaller mode separation induced by thermal effects. This is similar to the findings achieved by modifying the mode spacing using an external temperature controller [30]. Therefore, in addition to controlling the mode separation via precise fabrication, adjusting the pump power and temperature represents an alternative method to manipulate the compensation strength and soliton behaviour. Moreover, based on the SS step, the comb power increases dramatically at the end of the tuning, even surpassing the one of TM₀₀ MI comb, indicating an efficient microcomb excitation from the TM₁₀ mode.

 

Fig. 3. (a) Comb power traces while sweeping the laser across the resonances, with on-chip pump power (P_in) of 330 and 400 mW (upper), 475 mW (middle), and 750 mW (lower). The laser detuning is referenced to 1570 nm. Green and red shading represent the regions of the TM₀₀ soliton state and TM₁₀ comb. (b) Comb power trace showing repeatable soliton steps (green shading) during successive scans. (c) Measured microcomb spectra corresponding to the detuning (i)-(iv) marked by arrows in (a). Dash-dot lines in (iv) indicate the envelope of the primary comb spectrum. Left inset: Measured RF noise spectra by beating a microcomb line (µ=4, black arrow) in states (ii) and (iii) with another ECDL. Right inset: RF beat note spectrum obtained from the two neighbouring comb lines with µ=7 in the state (iv).

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Figure 3(c) presents the measured microcomb spectra, where the different states (i)-(iv) correspond to the different pump parameters indicated by the arrows in Fig. 3(a). The top two spectra are the primary and MI combs that are excited from the TM₁₀ and TM₀₀ modes, respectively. In state (iii), the comb spectrum exhibits a sech² shape, indicating a SS state, and an expanded bandwidth from 130 to 250 THz, equivalent to 0.95 octaves. The high-order dispersion and the associated soliton recoil [2] give rise to a distinct dispersive wave (DW) envelope near 154.4 THz, contributing to the spectral broadening. Notably, the DW intensity is significantly enhanced (up to ∼mW), surpassing that of the lines near the pump, which should be attributed to the smaller second-order dispersion coefficient. The transition from chaotic to locked state is further confirmed by beating one comb with another laser, as shown in the left inset of Fig. 3(c), where the RF spectrum changes from a broad beat note to a single line. At the bottom of Fig. 3(c)-(iv), the spectrum obtained at 750 mW clearly demonstrates the coexistence of soliton and primary comb (red crosses), generated from the pump and auxiliary modes, respectively. The primary comb lines are separated by 7×FSR. By filtering the two adjacent lines at µ=7 and mixing them with a photodiode, an RF signal (f_beat) of ∼40.68 GHz is obtained. The signal is approximately equal to 7×Δf and has a linewidth of 30 kHz, but it drifts several MHz over time. No broad MI comb or soliton was achieved from the TM₁₀ mode.

Next, we will demonstrate the automated SS formation at 475 mW using a “step” mode in the ECDL, and the results are presented in Fig. 4. The diagram in Fig. 4(a) illustrates the process, where routes 1, 2, and 3 indicate the forward tuning, i.e., increasing the laser wavelength from the blue side to the red side by only setting the start (λ_start) and stop (λ_stop) wavelength and triggering the tuning. By way of contrast, routes 4, 5, and 6 represent backward tuning. For the forward tuning, the ECDL is adjusted by a step motor to tune the wavelength, with a speed of tens of nm (depending on the range), towards the target position with an error of several pico-meter (pm), which can eventually be calibrated to 0.5 pm with a piezo controller. However, the backward tuning involves two stages. Firstly, the laser will be set to a value about 1 to 2 nm shorter than the target position to avoid the backlash of the motor, then shifts towards a long wavelength using a similar process as in forward tuning. Figure 4(b) shows the map of the microcomb state under backward (upper) and forward (lower) “step” tuning, respectively. The left areas 1 and 4 represent a steady MI comb state, where the λ_stop is effectively blue-detuned side of the TM₀₀ cavity resonance. Conversely, the red-shaded areas 3 and 6 show that the pump laser stops at the red side of the resonance where absorption by the cavity is very weak. The middle green areas demonstrate stable SS formation, triggered from either the blue (area 2) or red side (area 5). The generated SS can last for hours and potentially longer by reducing the external perturbations and improving the stability of the fiber alignment system, which could be realized by packaging the resonator with lensed fiber [39]. During forward tuning, the soliton region varies, whereas it is almost fixed between 1570.41 and 1570.65 nm in backward tuning. These differences are related to the mechanical operating principle of the laser mentioned earlier. For the forward tuning, despite having the same λ_stop, the different λ_start result in varying absorption power by the cavity and also different thermal changes during the tuning. This is likely the main reason for the variation in the soliton existence range. We also note the obvious periodically oscillating modes in the pump transmission, with an FSR of ∼0.2 nm, which is caused by the light reflection between the waveguide facets and probably impacts the soliton step. However, in backward tuning, as explained before, the laser wavelength is first tuned to the blue side of the resonance (e.g., shorter than 1570 nm here) where no energy is absorbed by the cavity, and then it is forward-tuned to the target position. Consequently, the thermal change is fixed if the λ_stop is the same, resulting in no obvious variation in the soliton region. For both forward and backward tuning settings of the ECDL, it is always the forward tuning process that contributes to the soliton formation in our case. Therefore, we would clarify that the presented backward tuning for soliton generation here is not the same as that has been demonstrated in LiNbO₃ [40]. The overall SER is approximately 30 GHz, generally consistent with the one obtained by scanning the laser with 1 nm/s. Such a broad SER will be conducive to enhancing the tolerance of the drift of pump power or wavelength, thus improving the long-term stability of the soliton without any active feedback control.

 

Fig. 4. (a) Schematic of the “step” tuning of the pump laser. Routes 1, 2, and 3 represent forward tuning from the blue-detuned side to MI comb, SS, and no-comb. Likewise, routes 4, 5, and 6 indicate the laser is backward-tuned from the red-detuned side to a state of MI comb, SS, and no-comb states. All the microcombs mentioned here are from TM₀₀ mode. (b) Map illustrating the microcomb state based on different start (λ_start) and stop (λ_stop) wavelengths of the laser. Upper: backward tuning; lower: forward tuning. The left, middle, and right areas correspond to the MI comb, stable SS, and red-detuned side without comb, respectively. (i), (ii), and (iii) denote the specific paths, which have a fixed λ_stop of 1570.6 nm, and a varied λ_start of 1570 nm, 1570.3 nm, and 1570.8 nm, respectively. (c) Measured comb power traces using the corresponding to path (i), (ii), and (iii). The duration of each laser wavelength is 2 seconds. (d) Zoomed-in view of the start-up of SS state in c. (e) Evolution map of measured microcomb at different laser detuning during the automated process. (f) Corresponding RF spectra obtained by beating the comb line at µ= 4 with another ECDL. The artificial yellow line depicts the narrow beat notes (under soliton states) that are difficult to see.

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Figure 4(c) shows three examples of soliton generation (green shading) when tuning the laser from 1570 nm (i), 1570.3 nm (ii), and 1570.8 nm (iii) to a constant value of 1570.6 nm using the “step” mode. The power overshoot in the oscilloscope trace of (i) corresponds to primary or MI comb generation. Notably, at (ii) the comb at λ_start= 1570.3 nm is an MI state with higher comb power than that of the SS. Figure 4(d) provides details of the SS start-up stage, e.g., the transition from an initial state to the final soliton state. In forward “step” tuning, the pump laser will accelerate up to tens of nm per second and then decelerate to reach the target wavelength. Therefore, we can observe the MI comb-related overshoot in both (i) and (ii), which have rising time of ∼9 ms and ∼2.2 ms, respectively. The powers then decrease to the level of the SS with a decay rate of ∼1.6 ms. The situation is slightly more complex for the backward tuning (iii). The flat step (between 0 and ∼36 ms) is related to the decoupling state when the laser is first tuned to the blue side of the resonance. This high-power level indicates a saturated state of the photodiode since the laser is tuned out of the FBG regime, where the pump cannot be effectively suppressed. Then the laser is forward tuned to the soliton state (between 38 and 48 ms). Even though, in the so-called backward “step” mode of the laser in our case, it is still the forward tuning process that makes the contribution to the soliton generation, the obtained results demonstrate the powerful capability of the dual-mode system to automatically access the soliton state by increasing the pump wavelength to the target, regardless of the tuning speed and any intermediate process. Figure 4(e) illustrates the microcomb evolution at different laser detuning. As λ_stop increases, the primary comb is generated at ∼1570.03 nm, followed by an MI comb that persists until 1570.42 nm. Subsequently, soliton spectra with enhanced DW and extended bandwidth become accessible within the λ_stop range of 1570.43 and 1570.68 nm. By beating the comb line at µ= 4 with another ECDL fixed at 1570.43 nm, we record the RF noise and depict the corresponding evolution in Fig. 4(f). Once the microcomb lines are locked, the RF noise transitions from a broadband spectrum to a narrow single peak. The frequency of this peak increases from 0 to approximately 30 GHz (i.e., SER) with laser tuning, as represented by the yellow line.

3.2 Turn-key soliton generation with a slot laser

A critical technological development is to deliver a low-cost soliton microcomb source by hybrid-integrating the semiconductor lasers as pump sources [41]. Miniaturized electrically driven soliton microcombs, operated under a turn-key manner, have been widely reported by butt-coupling active laser chips to passive microresonators with ultrahigh-Q factors for injection locking [18,42–44]. However, these works typically generate spectral bandwidths of only tens of nm due to the limited laser output power and relatively low repetition frequency (f_rep) of the resonators. Efforts have been made to demonstrate hybrid-integrated octave-spanning frequency combs in 1 THz microresonators [45]. However, achieving a narrow laser linewidth and wide detuning range requires challenging capabilities in high-Q microresonators fabrication and rigorous control of the phase and power of the back-scattered light. In contrast to the SIL strategy, we demonstrate the turn-key generation of the single soliton using a semiconductor laser diode as a pump without feedback from the resonator. By amplifying the slot laser to P_in= 500 mW and sweeping its wavelength via increasing injection current, we record the comb power trace as plotted in Fig. 5(a). The SS step is 0.18 nm (∼22 GHz), slightly narrower than that obtained by ECDL. We attribute this to the fact that the slot laser can easily drop off the resonance due to the large jitter of tens of MHz without using feedback mechanism [46], while the stability of the ECDL is several MHz. Figure 5(b) shows the measured soliton spectrum, which has a similar profile as Fig. 3(c)-(iii) but with stronger amplified spontaneous emission (ASE) noise from the EDFA and some weak side modes near the pump. The stronger ASE noise is likely due to the worse signal-to-noise ratio of the slot laser compared with ECDL. More importantly, the soliton can also be generated by simply tuning the laser wavelength with a step mode applied current waveform. As illustrated by Fig. 5(c), by controlling the I_gain with pulsed modulation between 160 and 246 mA, the soliton can be deterministically generated and confirmed to last for hours. In comparison to a previous report that used a packaged DFB laser as the pump [47], the thermal dynamics in our slot laser chip, controlled by a large copper heatsink and thermoelectric controller (TEC), are relatively slow. As shown in Fig. 5(d), after an overall rising and decay time of ∼1 ms, the microcomb eventually evolves into a soliton state. This transition from a chaotic comb to a soliton state using laser diodes has also been achieved elsewhere, requiring multi-stage modulation of the injection current to overcome the thermo-optic effect [47,48]. We have implemented backward tuning of the slot laser, but no soliton microcomb is observed.

 

Fig. 5. (a) Measured comb power traces when scanning the laser across the resonances. The green shading indicates the accessible SS step. (b) Optical spectrum of SS, with a zoomed-in view near the pump as an inset. (c) Measured comb power traces (lower) obtained by implementing a pulse laser current change from 160 to 246 mA (upper). (d) Zoomed-in view of the start-up of SS state.

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3.3 Tunable microwave synthesizer

To investigate the influence of mode separation on the soliton behaviour, we employ another resonator with identical dimensions but a different coupling gap of 650 nm, which also has two adjacent modes near 1565.7 nm but with a relatively smaller separation [Δf = 5 GHz, see inset of Fig. 6(a)]. As predicted by Fig. 1(b), a smaller Δf will trigger the multi-solitons and dual-microcombs, which can be experimentally confirmed by comb power traces in Fig. 6(a). With an on-chip pump power of 240 mW and a laser scan speed of 1 nm/s, the SS state (solid line) can be achieved with a success rate of over 90%, while the no-soliton state (dotted line) and the two-soliton state (N = 2, dash-dot line) are the other two possible situations. As shown by the dotted line, the comb power profiles of the two modes are independent, and the second triangle envelope is so weak as to be negligible. The observed soliton number is stochastic (1 or 2), and the SER is also smaller (0.1 nm, i.e., 12.5 GHz) when compared to the first sample. When P_in =300 mW, discrete steps related to the different soliton numbers are observed among multiple scans (ii). We note that the prominent triangular increase at the end of resonance, which is relevant to the TM₁₀ comb generation, is only accessible with SS formation. Intuitively, the two-soliton regime requires absorbing more pump power compared to the SS formation [1], which will hinder the comb excitation from the auxiliary mode. The same behaviour is obtained with the higher powers of 400 (iii) and 500 mW (iv). It should be mentioned that although not observed in the comb power curves, the SS is commonly triggered concurrently with the primary comb as evidenced by the OSA. Therefore, we recognize that the SS steps overlap with the triangular shape related to the auxiliary primary comb.

 

Fig. 6. (a) Measured comb power traces for different levels of P_in after amplification: (i) 240 mW, (ii) 300 mW, (iii) 400 mW, and (iv) 500 mW. Inset: Resonances spectrum of dual-mode in the second resonator, showing a mode separation of ∼0.04 nm (∼5 GHz). (b) Corresponding optical spectra of the microcombs: (i) pure TM₀₀ SS and the (ii)-(iv) coexistence of TM₀₀ SS and TM₁₀ primary comb microcombs. The primary comb lines (dash-dot lines) are located at (ii) 4×m, (iii) 5×m, and (iv) 6×m, where m=±1, ± 2, ± 3, and so on. (c) Zoomed-in view of the primary comb lines with (top) m = 1, (middle) m = 2, (bottom) m = 3, along with the adjacent soliton lines (dash arrow). Inset: Corresponding beat note of two neighbouring comb lines. (d) Frequency noise of the microwave signal near 34.626 GHz. Inset: Max-hold trace of the beat note.

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Figure 6(b) summarizes the corresponding optical spectra of the single solitons achieved at the different pump powers used in Fig. 6(a). A pure SS from TM₀₀ mode is observed at 240 mW, while the coexisting two combs are attained between 300 and 500 mW. It is worth noting that changing P_in can adjust the line spacing of the primary combs, as depicted in the subplots (ii, 4×FSR), (iii, 5×FSR), and (iv, 6×FSR) of Fig. 6(b). The top subplot of Fig. 6(c) provides a close-up view of the first primary comb sidebands and the adjacent soliton lines, which result in beat notes at ∼23.4, ∼28.9, and ∼34.6 GHz, respectively, as indicated by the measured RF spectra in the inset. These microwave signals, falling within the K and Ka bands, have potential applications in satellite communications and imaging radar. Furthermore, the harmonics of our fundamental beat notes can be measured with a high-bandwidth photodiode. As shown in the middle plot of Fig. 6(c), the separation between the second primary comb sidebands and the adjacent soliton line is ∼46.8,∼57.8, and ∼69.2 GHz. These frequencies hold promise for application in radio links and wireless communication. Similarly, the high-frequency millimeter waves between 70 and 104 GHz can be obtained from the lines with µ=12, 15, 18. Thus, the stable coexistence of two combs within a single pumped cavity offers the potential for a discretely tunable microwave oscillator. We would like to mention a recent study that demonstrated microwave signal generation using a cross-polarized dual-mode microresonator, while the beat note is non-tunable [49]. In Fig. 6(d), a measured phase noise curve of f_beat= 34.626 GHz is presented, along with an inset showing the max-hold RF trace. The RF peak exhibits a jitter of ∼2 MHz, corresponding to a phase noise level of −68 dBc/Hz and −98-dBc/Hz at 100 kHz and 1 MHz deviation, respectively. Considering that the solitons are thermally locked and exhibit significantly lower noise level [49,50], we deduce that the jitter mainly originates from the primary comb. It is promising to enhance the coherence between the two microcombs by implementing a feedback servo loop to control the pump frequency or power, and by utilizing a narrow-linewidth fiber laser as a pump, although these approaches introduce additional complexity.

3.4 Perfect soliton crystal and versatile two-solitons

The second resonator also offers a wide range of soliton states, including two-soliton microcomb (TSM) and perfect soliton crystal (PSC), and some spectra are plotted in Fig. 7. By fitting the spectra with S²(µ)=S¹(µ) × [2 + 2×cos(µΨ)] [2,43], we can extract the relative azimuthal angles ψ (angle between two pulses) ranging from 18.1° to 38.8°, 175.8°, and 180° (2-PSC). Here, µ presents the comb mode index relative to the pump position, and S¹(µ) is the spectral shape of a SS state following a sech² shape fitted from the experimental data. It should be noted that the pulse spacing is influenced by the pump power and laser detuning. For instance, lower pump power appears to favor large pulse spacing. However, even with the same pump power and wavelength tuning, it is not always possible to access a specific two-soliton state with 100% certainty. This means that the pulse spacing may vary during different pump scans. Despite these, the presented multi-soliton states are reproducible but with multiple scans. Mode coupling has been identified as the main factor contributing to the generation of the PSC, which exhibits microcomb lines spaced by multiples of the cavity FSR and with enhanced comb power [51–54]. The employed dual- mode device also enables the 2-PSC and 3-PSC generation, corresponding to a f_rep of ∼0.77 and ∼1.15 THz, respectively. The coexistence of 2-PSC and the primary comb is also observed. These readily accessible diverse soliton states will enhance the microcombs applications in the arbitrary waveform generation and RF photonic filters [55,56].

 

Fig. 7. Versatile two-soliton microcomb (TSM) spectra and the PSCs achieved from the second resonator. Red dash lines: fitting of the TSMs. Dash-dot line: the primary comb originating from the TM₁₀ mode. Insets: Soliton pulse distribution around the microresonator.

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4. Conclusions

In summary, our investigation into the dual-mode Si₃N₄ microresonators has revealed several key effects in the system: (1) deterministic soliton formation, (2) extended soliton existence range, and (3) single-pump based multiple combs emission within a single resonator. We have successfully achieved the deterministic generation of broadband single-solitons spanning 0.95 octaves by controlling the pump wavelength of a tunable laser or a semiconductor laser chip in a turn-key manner. More importantly, the observed 30 GHz soliton existence range represents a two-order-of-magnitude improvement compared to previous reports, ensuring the long-term stability of the soliton microcomb. This wide spectral existence range has potential applications in enhancing depth resolution in massively parallel LiDAR systems, thanks to the large scan range of the comb modes [57]. Further, our comparisons between two resonators under varied pump power have revealed that the coexistence of primary comb and single-soliton, as well as the multi-solitons can be easily accessed when the mode separation is smaller due to slight over-compensation from the auxiliary mode. In addition, the line spacing of the primary comb can be dynamically adjusted with pump power, providing a discretely tunable microwave synthesizer through the photodetection of the two coexisting microcombs. These microcombs oscillate at ∼23.4, ∼28.9, and ∼34.6 GHz, along with their harmonics.

The mode separation is influenced by multiple factors such as the thermal shift range of the resonances and power distribution between the two modes, which depend on the thermal conduction coefficient of the material and mode Q factors. For layout design, the dual-mode condition is very sensitive to the ring width variation, and a fine scan of several nm is required [30], which is challenging for most fabrication. We recently discovered another design strategy to acquire large number of dual-mode resonators, which is tuning the ring radius instead of the width. In Supplement 1, we have compared the effects of tuning the radius and width of the resonators on mode separation. Once the initial dual-mode resonator dimension is confirmed, scanning the ring radius with a step of hundred nm can ensure a large amount of dual-mode resonators for the soliton microcombs generation with varying pump wavelength. This development could pave the way for low-cost self-referencing microcombs, enabling their widespread use in precision spectroscopy, time-keeping, and integrated microwave photonics.