Advances in resonator-based Kerr frequency combs with high conversion efficiencies

Introduction

Benefitting from advanced micro/nanofabrication technologies, Kerr frequency comb generation based on ultra-high-quality (Q) microresonators is a technique with the potential to revolutionize a variety of applications such as high-speed data transmission^1,2,3,4,5, LiDAR^6,7,8, spectroscopy^9,10,11,12, optical clocks^13,14,15,16, microwave photonics^17,18,19,20, machine learning^21,22, astronomical detection^23,24, and quantum optics^25,26,27,28. Over the past decade, significant progresses have been made towards integrated microresonator combs (also called “microcombs”) by using continuous-wave (CW) lasers—in two different group-velocity dispersion (GVD) regimes. For platforms displaying anomalous GVD, dissipative Kerr soliton (DKS) microcombs are generated through a double balance between parametric gain and optical losses, Kerr nonlinearity and dispersion²⁹. These self-confined waves exhibit a hyperbolic-secant squared (sech²) profile in both the time and frequency domains, and illustrate remarkable coherence³⁰. Physically, DKS can be spontaneously organized when the driven CW laser, with an appropriate power, sweeps across a resonance of the microresonator from the blue to red detuning regime. In this process, the states of microcombs experience a continuous evolution from the primary combs to modulation instability (MI) combs, and (breathing) multi-soliton combs³⁰. When the multi-soliton state is generated from the chaotic MI state, the intracavity power drops dramatically and results in pump frequency shifting out of the cavity resonance through thermo-optical effect. Moreover, the randomness of the number of solitons further complicates this process. To overcome the strong thermal-optical effect, one solution is using microresonators with a low thermal-optic coefficient, such as magnesium fluoride (MgF₂)^{30,31,32,33,34}. Another solution is realizing the intracavity thermal equilibrium, and various schemes have been implemented, such as power-kicking^35,36,37, thermal tuning^38,39,40,41, auxiliary-laser-assistance^42,43,44,45, phase modulation^46,47, photorefractive effect^48,49, pulse pumping^{50,51,52,53,54}, and self-injecting-locking^{55,56,57,58,59,60,61}. Accompanying the exploration of enabling robust DKS access, rich types of DKS states have been discovered in anomalous GVD regime, such as breathers^62,63,64,65, Stokes soliton^66,67, soliton crystals^49,68,69,70, soliton molecules⁷¹, and laser cavity soliton^72,73,74. Different from the Kerr soliton frequency combs with various derivatives generated in the anomalous GVD regime, dark soliton (or dark pulse) is deemed as the exclusive mode-locked localized reduction structure in the normal GVD regime. Dark soliton generally manifested as intensity dips embedded in a high-intensity constant background with a complex temporal structure and a spectrum with a flat-topped envelope in the frequency domain^{39,40,65,75,76}. Compared with the bright solitons and soliton frequency combs generated in microresonators with anomalous dispersion, dark solitons are less sensitive to the system perturbations and have higher power conversion efficiency. These unique advantages have facilitated research on dark solitons and attracted increasing interest in many practical areas^39,76,77,78. All of the above achievements suggest that microresonator-based Kerr frequency combs can provide an ideal testbed for nonlinear physics and allow for the realization of a portable integrated photonic device for use in out-of-the-laboratory applications.

Despite the discovery of rich physical phenomena—including breathers, Stokes solitons, soliton crystals, soliton molecules, laser cavity solitons, and dark solitons—relevant to DKS, and deeper insights into the dynamics of this new category of laser sources have been revealed, expanding the potential applications for comb-based integrated photonics, the quality of the generated microcombs, especially the power conversion efficiency limits its practical application scenario. Taking frequency combs as the carriers in communications as an example, the key parameter is the comb-line power, which should be greater than 1 mW as the data channel for modulation and detection⁷⁹. A low pump-to-comb conversion efficiency would require high-power sources and complex servo systems (e.g., thermal management), which greatly offset the advantages of low power consumption and portability of integrated photonics. However, extensive theoretical and experimental works have demonstrated the efficiency of single-soliton Kerr microcombs for a CW laser pump is limit to about 1%^{35,52,80,81,82,83}. The pump power required for holding the soliton in the anomalous dispersion regime is relatively higher compared to the maintained soliton power, and a majority of pump power is transmitted directly at a through port without coupling into the microresonator in order to satisfy the detuning state for obtaining the soliton³⁰. Fortunately, the demonstration of dark soliton alleviated the difficulty of boosting the pump-to-comb power conversion efficiency⁷⁷. Besides, with the development of fabrication process and improved dispersion/perturbation engineering, several approaches have been proposed to increase the efficiency in a Kerr resonator, such as synchronously pulsed pumping^50,52, steadily accessed multi-soliton based on self-injection locking⁸⁴, synthesized soliton crystals⁸⁵, laser cavity soliton, and assisted auxiliary microresonator^40,86. Representatively, a dark soliton microcombs generated in a Si₃N₄ resonator with an on-chip conversion efficiency above 20% has been utilized in a coherent communications scheme, realizing a bit-error rate (BER) below 10⁻¹⁵ with an aggregate data rate of 4.4 Tbps⁷⁸. Dual three-soliton-state combs with slightly different line spacing and a conversion efficiency of up to 40% have been demonstrated by using the self-injection locking method and integrated as a coherent dual-comb spectrometer⁸⁴. Nevertheless, significant improvement of conversion efficiency remains challenging, and there is no decisive approach to produce a high-efficiency Kerr frequency combs while combining other advantages (such as wide bandwidth, high comb-line power, low noise, narrow linewidth, etc.) that can offer a strong promise as a universal laser source for a variety of applications.

In this review, we provide an overview of the recent developments in resonator-based Kerr frequency combs technology towards boosting the pump-to-comb power conversion efficiency. The paper is organized as follows: Firstly, we will start with the demonstration and analysis of the efficiency of single-soliton microcombs. Secondly, we will focus on the emerging schemes for improving the conversion efficiency of Kerr frequency combs in both anomalous and normal GVD regimes, including synchronously pulsed pumping, multi-soliton microcombs, soliton crystals, dark solitons, laser cavity solitons, and assisted auxiliary microresonators. Finally, a brief summary and outlook on the underlying challenges for this field are presented.

Single-soliton microcombs in anomalous GVD regime

The demonstration of mode-locking DKS in a high-Q MgF₂ microresonator triggered a boom in the study of soliton microcombs and became a paradigm for the generation of temporal solitons and microcombs³⁰. The adopted experimental setup is shown in Fig. 1a, where a tunable narrow-linewidth laser is used as the pump and coupled into the MgF₂ crystal whispering gallery microresonator with anomalous dispersion. By changing the laser frequency with an appropriate scanning speed to sweep over one cavity resonance from blue detuning to red detuning regime, DKSs are obtained and measured at the through port. In this work, several key features of temporal solitons and soliton microcombs have been found and demonstrated repeatedly in subsequent studies: (1) the transmission power trace presents a triangular resonance shape with increasing intensity oscillations before the pump reaches the zero-detuning point, as shown in Fig. 1b. This process can be divided into three states to depict the successive evolution of the intracavity optical field in the blue detuning regime, which includes the primary comb (I), subcomb (II), and MI comb (III). The corresponding optical spectra are shown in Fig. 1c. (2) The triangular resonance shape deviates into discrete steps when the pump scans in the red detuning regime, indicating the formation of dispersive solitons and a decrease in the number of solitons. (3) The spectral shape of the comb spectrum exhibits a sech² functional form of a single-soliton state and a modulated envelope for multi-soliton states. In the time domain, the output consists of ultrashort pulses with a period equal to the round-trip time or a subharmonic thereof (Fig. 1e). (4) The DKSs states are fully coherent, as evidenced by the excellent low-noise characteristics of the corresponding beat notes (insets of Fig. 1d), and this coherence is reflected in the consistency between the sech²-shaped power profile and spectral envelope for the single-soliton state (Fig. 1f).

Advances in resonator-based Kerr frequency combs with high conversion efficiencies — **Fig. 1: Experimental demonstration of single-soliton Kerr combs in a MgF₂ microresonator using the frequency-scanning method.**

Taking advantage of the smooth spectral envelope and fixed temporal spacing, single-soliton microcombs are favored for practical applications. However, as aforementioned, the DKSs can be formed through MI by tuning the laser from the blue side of the resonance towards the red in a resonator with bistability, and it can only be maintained with the laser effectively red-detuned. The high laser detuning results in most of the pump power being reflected, thus not coupled into the micro-resonator and involved in the formation of DKSs. This imposes a fundamental limitation on the conversion efficiency, especially for the single-soliton state. It suffers from a sudden drop in microcombs power and exhibits a staircase step in transmission trace (Fig. 1b) when transitioning from multi-soliton states. In addition, the conversion efficiency is further limited due to the saturation of the parametric gain determined by the characteristics of the microresonators^80,87,88,89. In the case of single DKS microcombs generated in anomalous GVD regime, the comb lines carry less than 1% of the input pump power. The low conversion efficiency significantly undermines the practical appeal of single-soliton microcombs. Moreover, with the rapid development of modern micro/nanofabrication technologies, the power consumption of soliton microcombs decreases, leading to a lower power of comb lines due to the relatively fixed parameter space for generating DKSs. The low pump-to-comb power conversion efficiency of conventional single-soliton microcombs has not been bolstered by the development trend of low-power consumption and advanced micro-nanophotonics, and even has gradually fallen out of line with the development needs of practical applications.

While the conversion efficiency of single-soliton microcombs is primarily determined by the inherent properties of DKS formed in microresonators, several parameters can affect the exact value of conversion efficiency. Firstly, the power coupling coefficient between the microresonator and bus waveguide plays a crucial role. Figure 2a illustrates the dependence of nonlinear conversion efficiency and intracavity pulse energy on the power coupling coefficient⁸⁰, revealing a square root dependence of the conversion efficiency on the power coupling coefficient. Obviously, a larger power coupling coefficient allows more pump power to be coupled into the resonator for conversion into a microcomb, resulting in a higher microcomb power being coupled out. Consequently, the increase in conversion efficiency is accompanied by a decrease in intracavity pulse energy. In practice, increasing the power coupling coefficient is a straightforward method to extract intracavity power from high-Q microresonators. Therefore, there is considerable research on microresonators with anomalous and normal dispersions, operating in highly over-coupled regime to generate microcombs with high pump-to-comb power conversion efficiency^{52,77,90,91,92}. Secondly, a higher (anomalous) dispersion coefficient is beneficial to improve conversion efficiency. As shown in Fig. 2b, a microresonator waveguide with a higher dispersion coefficient (slot waveguide 2, β₂ = −87 ps²/km) can generate a microcomb with a narrower bandwidth, corresponding to a wider pulse and theoretically resulting in a higher conversion efficiency⁸⁰. Thirdly, the input (or pump) power exhibits a relationship between the reciprocal of square root and the conversion efficiency, as illustrated in Fig. 2b, g^80,81. As the pump power increases, the conversion efficiency converges to a constant value due to the parametric gain saturation effect. Fourthly, in the parameter space where DKS exists, the conversion efficiency increases with larger pump detuning (i.e., positive-slope soliton stairs as shown in Fig. 2c)^30,80. The underlying physical mechanism behind that lies in the increase in soliton peak power being more prominent than the decrease in soliton pulse width (caused by the larger detuning) to maintain soliton self-thermal-locking. In addition, since the pulses share almost the same shapes and coherence in single-soliton and multi-soliton states, the conversion efficiency is proportional to the reduction of the number of pulses in the further red-detuned regime.

**Fig. 2: Conversion efficiency of single-soliton microcombs.**

Starting from an approximate analytical expression derived from the single soliton solution for the Lugiato–Lefever equation (LLE)^93,94,95, which serves as the universal and successful model for depicting microcombs dynamics in the Kerr microresonator, the conversion efficiency can be expressed as^80,81

$${eta }=frac{2pi theta }{theta +{alpha }_{i}L}sqrt{frac{theta |{beta }_{2}|}{gamma {P}_{{in}}}},cdot, {rm{FSR}},$$

(1)

where η is the conversion efficiency defined as the ratio of the total output comb power excluding the pump mode to the input pump power, θ is the power coupling coefficient, α_i is the propagation loss coefficient, L is the resonator length, β₂ and γ are the dispersion and Kerr coefficients, respectively, P_in is the input pump power, and FSR is the cavity free spectral range. It is noted that the Eq. (1) is derived from an assumption that the soliton locates at the theoretical maximum detuning of Δ_max = δ_{0, max}/α = π²γLθP_in/(8α³), with α = (θ + α_iL)/2, and δ₀ is the phase detuning of the nearest resonance with respect to the pump frequency. Equation (1) provides straightforward insight into how the conversion efficiency scales with various parameters. Therefore, in addition to the parameters discussed above, factors such as the Kerr coefficient, propagation loss, and FSR of the resonator will also impact the conversion efficiency. Notably, Jang et al. further revealed three distinct scaling regimes of conversion efficiency with the FSR, contingent upon the coupling state of microresonators⁸¹. Specifically, the conversion efficiency displays square-root, square, and linear dependence on FSR for near critical coupling, highly under-coupled, and highly over coupled, respectively, as shown in Fig. 2d–f) It is obvious that improving the conversion efficiency of single-soliton microcombs is a complex problem involving multiple parameters, and the microcomb need to synthesize the delicate balance between these parameters, making it difficult to define a fundamental limitation on the conversion efficiency of single-soliton microcombs. Recently, there are some studies on surpassing the conversion efficiency of soliton microcombs by optimizing multiple parameters of resonators^96,97,98, which revealed, in numerical or experimental ways, that the conversion efficiency can be effectively improved by amplifying multiple favorable parameters (e.g., dispersion coefficient, power coupling coefficient, and FSR) and/or minishing the unfavorable parameters (e.g., loss and Kerr coefficient).

In addition to the fundamental properties of microresonators, there are some nonlinear effects that are detrimental to the conversion efficiency. Notably, Fig. 2h, i presents the effects of mode crossing and self-frequency shift (SFS) on conversion efficiency^81,83. Comparing the maximum conversion efficiency in the absence of a mode crossing (dotted red line in Fig. 2h), the existence of a mode crossing reduces the detuning range of soliton and the maximum conversion efficiency that can be achieved (blue circles and red triangles in Fig. 2h). The SFS effect caused by the Raman nonlinearity would shift the energy of the soliton spectrum from the blue side to the red. Such redistribution of soliton energy increases the minimum pumping power for generating soliton and results in the decrease of energy conversion efficiency.

Schemes for generating high-efficiency Kerr microcombs

The low conversion efficiency of soliton microcombs can be attributed to the small temporal overlap between the CW pump laser and the ultrashort soliton pulse generated in anomalous GVD regime. In contrast, the dark pulse formed in normal GVD regime can be inversely regarded as a wide bright soliton that has a high duty cycle and thus a high conversion efficiency. The optimization of single-soliton microcombs parameters to improve conversion efficiency involves increasing dispersion coefficient, increasing FSR of resonator, and achieving over-coupling state, is intended to increase the temporal overlap between soliton pulse and the CW background. Combining the various nonlinear dynamics of soliton, the extraordinary soliton states of multi-solitons, soliton crystals, dark pulses, and laser cavity solitons inherently present a larger temporal overlap with the CW background (even background-free for laser cavity solitons) and hence a larger pump-to-comb power conversion efficiency. In particular, it is an effective method to improve the conversion efficiency by replacing the CW laser with a pulse laser that has a focus intensity profile. Additionally, feedback architectures can also be utilized to recycle the CW pump power, further contributing to improve conversion efficiency. Based on the advantages of high coherence and low noise, soliton microcombs with high conversion efficiency are desired for many practical applications, and has aroused extensive research interest. In this section, we will focus on the schemes for generating microcombs in Kerr resonators with high conversion efficiency.

Pulse pumped soliton microcombs

Distinct from the conventional narrow-linewidth CW lasers, temporally structured light sources can also be used as a pump for soliton microcombs generation. The principles for CW-driven and pulse-driven schemes are presented in Fig. 3a, b, respectively⁵⁰. In a Kerr microresonator, the CW pump field builds up through cavity enhancement and leads to parametric gain for other cavity modes. Once the gain exceeds the cavity loss, parametric oscillation occurs and Kerr frequency comb generated based on a nonlinear optical process of four-wave mixing (FWM). Under suitable conditions of the balance between Kerr nonlinearity and dispersion along with the balance between parametric gain and loss, the stimulated cavity modes would be phase-locked, forming soliton pulse within the CW background in the time domain. Similarly, the soliton driven by optical pulse formed in a nonlinear optical microresonator undergoes nearly identical nonlinear evolution. In the first pulse-driven soliton microcombs generation experiment, an electro-optic modulation (EOM) picosecond pulse generator served as the pump source to drive a monolithic fiber Fabry–Perot (FP) resonator with an FSR of ~9.8 GHz⁵⁰. As the repetition rate of the picosecond pulse, controlled by the radio frequency (RF) generator, matches the FSR of the resonator, the stable femtosecond soliton would be generated ‘on top’ of the resonantly enhanced driving pulse, as shown in Fig. 3b. As the central driving mode scans across a resonance from the blue-detuning to red-detuning regimes, the resonator transmission shows characteristic soliton step features, as shown in Fig. 3c. The generated soliton microcomb is presented in Fig. 3e, with the spectrum corresponding to a single pulse of 137 fs duration, exhibiting a sech²-shape envelope. The soliton step appears for a wide spanning interval (100 kHz) of driving pulse repetition rate f_rep (Fig. 3d), suggesting the soliton obtained in a pulsed driving system is robust for resisting the random fluctuations of value of f_rep. In contrast to CW-driven systems, the pulse laser offers a significantly higher peak power, alleviating constraints on the soliton microcombs generated in a high-Q microresonator with a small FSR and decreases the average driving laser power for generating solitons. Besides, the soliton can be robustly “trapped” at a specific position (not always sit atop the peak) within the intracavity pump pulse, thus the microcomb’s repetition rate is locked to the driving pulse train and synchronized to the FSR of resonator while concomitantly suppressing its time jitter. Particularly, benefiting from the temporally focused structure of the driving pulse, there is a large overlap between the binding soliton and the driving pulse, leading to high power conversion efficiency. A 5% soliton conversion efficiency was measured in the first pulse-driven soliton microcombs experiment.

**Fig. 3: Soliton microcombs driven by optical pulses.**

After the pulse-driven cavity soliton generation in fiber loop and FP resonator^50,99, the same scheme has also been transplanted to chip-scale microresonators^51,52,54. Since then, pulse-driven microcombs have been demonstrated with higher conversion efficiency. Anderson et al. used a high-Q silicon-nitride (SiN) microresonators with a designed low GVD and a strong third-order dispersion, generating a soliton microcombs with an electronically detectable repetition rate of 28 GHz, and measured a conversion efficiency of 8%¹⁰⁰. For the same device, a broadband soliton microcombs close to two-thirds of an octave formed with the aid of the strong dispersive wave emission, demonstrated an efficiency of 2.8% under a pulse driving with an average energy of 6.4 pJ¹⁰⁰. The bandwidth of such broadband soliton microcomb is comparable to that of a supercontinuum, as noted by the authors. Li et al. analytically and experimentally investigated the influence of pulse-driven system parameters on the conversion efficiency of soliton microcombs, revealing unique soliton dynamics compared to CW driving and its limitations⁵². The experimental setup used is shown in Fig. 4a, with an EO comb (as shown in inset of Fig. 4b) utilized to generate pump pulses. The pulses had repetition rates synchronized to the FSR of the silica (SiO₂) microdisk resonator. Soliton generation was triggered when the center frequency of the pump pulse swept across the microcavity resonance from blue to red detuning regime. Examples of the soliton microcombs for the resonators with external Q factors (Q_ex) of 14 million and 37 million are illustrated in Fig. 4b, in which a higher soliton output for the lower Q_ex is consistent with the trend of power coupling coefficient imposed on conversion efficiency. Figure 4c presents the measured soliton conversion efficiency versus Q_ex for different durations of pulses, with the pulse duration adjusted by controlling the number of EO comb lines. The soliton efficiency increases as the duration of pumping pulse decreases. Theoretically, this trend is valid until the pump pulse width is smaller than the width of the formed soliton pulse. Remarkably, single-soliton operation with a steady-state conversion efficiency up to 34% is attained using 2 ps pump pulses, while a transient efficiency up to 54% is measured using 1 ps pump pulses under frequency-scanning conditions. These record high efficiencies demonstrate the conversion efficiency of soliton microcombs can be significantly boosted by optimizing the pulse-driven system.

**Fig. 4: Pulse-driven soliton microcombs with high conversion efficiency.**

Besides the pulse-driven system working in anomalous dispersion, recently, the pulse driven methods were demonstrated for generating dark pulses in normal-dispersion resonators. The first normal-dispersion soliton microcombs driven by pulse was formed in a weakly normal SiN microresonator in the near-zero-dispersion regime¹⁰¹, in which the complex interplay between switching waves (SWs) and dispersive solitons was fully investigated and achieved a near-octave broadband microcomb. At the same time, the soliton dynamics in a strong normal-dispersion resonator was studied by ref. ¹⁰². Both studies demonstrated that pulsed driving enables the spontaneous generation of isolated SWs, without requiring perturbations to the resonator’s dispersion to induce MI. Following these works, the dynamics of normal-dispersion combs in fiber loop and FP resonators were studied^{53,103,104,105}, in which a conversion efficiency of 19% was measured in a FP resonator (with FSR ~ 10.214 GHz) driven by a pulse with a duration of 1.9 ps¹⁰⁴, and a following conversion efficiency of 23.4% was achieved by the same research group in a FP resonator with an FSR of 1.8393 GHz¹⁰⁵.

Researches have been done to explore combination of pulsed driving scheme with other effects. Simply, taking advantage of the bonding effect between pump pulses and solitons (or soliton self-synchronization effect), the microcombs with tunable comb line spacing were achieved by applying a pulsed pump rate that is the rational harmonic of the resonator FSR^101,106. Physically, the dual-wavelength pumping schemes consisting of two laser beams very close in frequency are the roughest pulsed pumping sources⁸⁵, which were used to stimulate Brillouin lasers in fiber loops and driven internally to spontaneously generated soliton microcombs with low noise and high stability^107,108. Furthermore, the combination of self-injection locking and pulsed driving method enables the realization of fully integrated soliton microcomb sources⁵⁴, which were implemented to demonstrate a stable direct atomic spectroscopy with absolute optical-frequency fluctuations at the kilohertz level over a few seconds and <1 MHz day-to-day accuracy¹⁰. In addition, the pulsed driving scheme supports researches on other soliton physics, such as soliton tweezing¹⁰⁹, spontaneous symmetry breaking¹¹⁰, and Faraday instability¹¹¹. In summary, a superior soliton microcomb with greater performances (e.g., a higher conversion efficiency, a wider spectral bandwidth, a lower power consumption, and so on) is expectable in an optimized pulsed driving system combining other favorable effects.

Multi-soliton microcombs

Aforementioned, the microcombs in multi-soliton state have a larger energy that is scaled up proportionally with the number of solitons, which should be a strong candidate for improving the conversion efficiency considering its prevalence accompanying almost all single-soliton microcomb production^30,31,35,42. However, due to the inherently stochastic intracavity dynamics, the number of solitons generated in resonators is probabilistic in the usual approach in which detuning is swept to a predetermined value with input held constant. Figures 5a, b presents an example illustrating the overlapped power traces of one CW pump laser swept over a microresonator’s resonance for 200 times using forward frequency-tuning method from blue to red detuning regime, which clearly shows the randomness of soliton number N. To achieve deterministic generation of single-soliton microcombs, a forward and backward frequency-tuning technique was introduced³¹. Briefly, this technique involves initially applying forward frequency tuning to stimulate multi-soliton state, and then the pump laser is swept backward adiabatically with a low scanning speed. During the operation of the latter, the soliton state switched successively by reducing the number of solitons one by one, as shown in the conceptual diagram in Fig. 5c. The experimental cavity dynamics of the forward and backward frequency-tuning method are shown in Fig. 5d, in which a regular staircase pattern is formed with the successive extinction of intracavity solitons. Incidentally, the nearly equal stair heights confirm the consistency between the pulse energies of multiple solitons. Figure 5e~g present the measured soliton microcombs in soliton states with N = 1,2,3, respectively, through the forward and backward tuning method. Although this method aims to deterministically obtain single soliton state, it involves continuously traversing the soliton state starting from the maximum number of solitons. Such characteristic makes it a technique for generating multi-soliton states containing a specific number of solitons. However, for a given dispersion coefficient, the number of solitons that can be generated has a maximum value, which is randomly determined during the forward tuning process (Fig. 5b). Therefore, it is not a robust approach to significantly improve the conversion efficiency based on the multi-soliton states with high N values.

**Fig. 5: Forward and backward frequency-tuning methods.**

Benefitting from the investigation on the self-injection locking effect, reproducible multi-soliton microcombs with high conversion efficiency were demonstrated on a hybrid integrated platform⁸⁴. The self-injection locking effect is a profound phenomenon in oscillatory circuits, extensively studied for decades in radio-physics, microwave electronics, and photonic integrated circuits to improve the spectral purity of the devices^{55,59,112,113,114}. Recently, this effect has been used in nonlinear photonics to facilitate the integration of microcombs. The principle of self-injection locking enabling the generation of soliton microcombs in a SiN microresonator is presented in Fig. 6a. In such setup, a single frequency laser launched by a free-running distributed feedback (DFB) diode is coupled into the resonator, and a portion of the laser radiation is resonantly backscattered (e.g., due to Rayleigh scattering here, or direct reflection in FP cavities) to the laser cavity. This process induces self-injection locking, effectively locking the laser emission frequency to the cavity mode of similar frequency¹¹⁵. The locked laser exhibits a dramatically reduced linewidth and noise, and further driving the nonlinear resonator to generate soliton microcombs. Since the back-reflection time is shorter than the thermal relaxation time, the laser frequency tracks the thermally shifted cavity resonance, effectively suppressing thermal instability and alleviating the requirement for delicate frequency manipulation to trigger solitons, which further enables a unique state of permitting soliton generation called “turnkey” operation through simply turning on the pump laser free from any additional auxiliary systems⁵⁷. The employed self-injection locking scheme enabled microcomb generation using high-performance semiconductor laser diodes instead of bulky narrow-linewidth lasers, thereby paving the way for the development of fully integrated chip-scale single microcomb sources. Using this method, Dmitriev et al. demonstrated a fully integrated, power-efficient dual-microcomb source operating in multi-soliton states⁸⁴. The merit of self-injection locking against thermal frequency drift broadens the soliton range (Fig. 6b) and enables turnkey operation. Remarkably, two types of microcombs in eight-soliton (FSR ~ 150 GHz) and three-soliton states (FSR ~ 1 THz) with conversion efficiencies of up to 25 and 40%, respectively, were generated, as shown in Fig. 6c, d. It presents a record conversion efficiency for multi-soliton microcombs with broad spectra. Subsequently, the microcombs were further down-converted to the radio-frequency domain for applications in dual-microcomb spectroscopy.

**Fig. 6: Multi-soliton microcombs generation based on self-injection locking effect.**

Despite the realization of multi-soliton microcombs with high conversion efficiency enabled through self-injection locking, it is regrettable that the multi-soliton microcombs generally exhibit a structured spectrum determined by the relative positions of solitons in the microresonators, which are mostly random for the forward and backward tuning method and are ambiguous for self-injection locking^90,116,117. Overall, the challenge of accurately reproducing the same state and the significant intensity variations in the optical spectrum hinder the application of multi-soliton microcombs in fields that require smooth spectrum. This limitation also makes it less attractive in nonlinear physics research.

Soliton crystals microcombs

Among the various soliton phenomena in nonlinear resonator, soliton crystals are the most promising soliton-microcomb states with high conversion efficiency to be applied in practical applications. Soliton crystals were so-named due to their crystal-like patterns of ensembled copropagating solitons within Kerr resonators, which were self-organized and arranged with a regular sequence in distribution. Physically, the soliton crystals are a special class of multi-soliton states, and their generation is found to be related to the modulated background wave^68,70. Typically, this modulated wave is formed due to the presence of avoided mode crossings (AMXs), which occur as localized alterations of the microresonator dispersion resulting from interference between the pump mode and other transverse modes (as shown in Fig. 7b)⁷⁰. The modulated background serves as an optical lattice trap to “catch” the solitons at regular positions, leading to the ordering of DKS pulses in a crystal-like structure. Consistent with the multi-soliton state, the power of microcombs in soliton crystals states linearly increased with the soliton number. A soliton crystal containing a sufficient number of packed solitons and filling the entire angular domain of the resonator exhibits an intracavity power similar to the MI state, it is presented by a typical soliton crystals step appearing at the peak of the transmission power trace following chaotic fluctuation stage (inset of Fig. 7d). This property not only indicates a high power conversion efficiency from the pump to microcombs, but enables the soliton crystals formed stably through adiabatic pump-laser scans, without the need for the complex techniques used in other demonstrations of Kerr solitons to avoid dissipation of the solitons due to thermal changes suffering from sudden drop in intracavity power.

**Fig. 7: PSCs in Kerr microresonators.**

Evolving from the MI state, soliton crystals exhibit various states because of different soliton arrangements, resulting in many unique “palm-like” spectra in the frequency domain, such as the perfect, Schottky defects, Frenkel defects, disorder, superstructure, and irregular states^68,118. Among these soliton-crystal states, the perfect soliton crystal (PSC) is their simplest and most ideal representative, defined as all solitons evenly distributed within the resonators, as shown in Fig. 7a. In contrast to other soliton crystals with defects, the behavior of PSCs is unperturbed by missing or shifted soliton pulses, such a high regularity leading to a pure microcomb consisting of a few lines with a spacing of N (or X in Fig. 7a, which is the soliton number of PSCs) times of FSR. Accordingly, the multiplicity of soliton repetition rate superimposed on the increase in the number of solitons boosts the power of each comb line by N² (or X²) times in comparison to the single-soliton state^70,85, as shown in Fig. 7c, d. The enhanced comb lines offer promise for a number of applications requiring high-power comb lines, ranging from optical coherent communications to astrophysical spectrometer calibration. Furthermore, PSCs could be regarded as a single-soliton state with a multiple FSR reaching terahertz in a common resonator circumvents the bending losses and dispersion control for extremely small microresonators.

After demonstrating the generation of PSCs, a significant amount of effort has been made to obtain deterministic PSC states and controllable switching between different PSC states. In general, excitation of a PSC state is often random, since the regular distribution of solitons is easily interfered by the thermo-optic nonlinearity. Hence, accessing PSCs requires a delicate tuning process in the parameter space of pump power and detuning. Research on the dynamic of PSCs has demonstrated the generation of PSCs is typically achieved at relatively low pump powers in comparison with the standard procedures of multi-soliton excitation⁷⁰. Below the power threshold, the microresonators featured with AMXs exhibit a long PSCs step, indicating the systems for PSCs are robust and reproducible (as shown in inset of Fig. 7d). By varying the pump resonances to adjust the modulated CW background aided by AMXs, PSCs with different soliton numbers were achieved¹¹⁶, as presented in Fig. 8a, b. The controllable switch between different PSC states offers a convenient approach for tuning the repetition rate of soliton microcombs in a monolithic device. Furthermore, this technique was promoted by combining photorefractive effect⁴⁹, thermo-optic effect¹¹⁸, and auxiliary-laser-assistance¹¹⁹. However, suffering from the complex soliton dynamics and the weak AMX-induced modulation on CW background, the soliton numbers of PSCs do not exactly align with the relative resonance shifts between pumping modes and AMXs, as shown in Fig. 8b. This discrepancy hinders the flexible switching of the PSC states. In order to address this issue, a pumping scheme consisting of two CW lasers was proposed to manipulate PSC states directly⁸⁵. The principle of synthesized PSCs generated in a microresonator driven by dichromatic pumping is presented in Fig. 8c, d, where a strong periodic modulation is formed due to the beating of two pump lasers, offering an artificial background potential field to evenly trap solitons in distribution. By controlling the beating of dichromatic pumping, the reconfigurable PSCs with soliton numbers from 1 to 32 were synthesized in a monolithic silica glass microresonator, as shown in Fig. 8d. Such a highly ordered temporal distribution could coherently enhance the PSC-comb lines power up to 3 orders of magnitude compared with the single-soliton state. In a certain sense, this technique could be regarded as an extremely simple pulsed pump containing two comb lines with a repetition rate is an integral harmonic of cavity FSR.

**Fig. 8: Deterministic accessing PSC states through AMX and controllable dichromatic pumping.**

Along with the research on accessing and switching PSCs, the high conversion efficiency of soliton crystals has been demonstrated in several investigations. In one experiment by Corcoran et al., a defective soliton crystal with an internal conversion efficiency of 42% was demonstrated and used as a single integrated chip source in wavelength-division multiplexed (WDM) system². By leveraging the high stability and coherence of soliton crystals, an ultrahigh bandwidth optical transmission with 44.2 Tbps using 64 quadrature amplitude modulation (QAM) was demonstrated. Furthermore, another defective soliton crystal was demonstrated experimentally and numerically in a SiN microresonator for the first time, which has a flat top and a conversion efficiency ~10%¹²⁰. A more recent demonstration by Weng et al. realized the tunable switching soliton states of single-soliton, 2-PSC, and 3-PSC with a conversion efficiency of 7.7%, 11.4%, and 13.5%, respectively, in a dispersion-engineered dual-mode microresonator⁹⁰. Benefitting from the enhanced comb lines of PSCs, both PSCs exhibited broadband spectra exceeding an octave-spanning range from 127 THz to 270 THz. Following this demonstration, the same research group showed the versatility of octave-spanning PSCs with higher conversion efficiency in a SiN microresonator. By optimizing the power coupling coefficient, a series of different PSCs driven by different pump resonances achieved conversion efficiencies above 50%¹²¹. In addition to the results mentioned above, there are several investigations on microcombs with high conversion efficiency in soliton crystal states have been realized by other schemes. We will discuss these specifically in following sections.

Dark soliton microcombs

In contrast to the DKS requires the optical cavity to display anomalous dispersion at the pump wavelength, dark soliton is a type of localized stationary structure found in cavities operating in normal dispersion regime, which is consistent with the inherent material dispersion of most photonics platforms, thereby reducing the requirements on the geometry of resonators for generating microcombs¹²². Accordingly, the phase-matching of the MI process is not satisfied for normal-dispersion microresonators, which is necessary to trigger the state of mode-locked microcombs⁸⁸. To avoid excitation of dark pulses under a large red-detuning in the thermally unstable regime, several excitation methods have been proposed to enable the formation of dark solitons in the normal dispersion regime, such as AMX^65,75, amplitude-modulated optical pumping^123,124, pulsed pumping^{53,101,102,103,104,105}, double-cavity coupled photonic dimers^40,86, and photonic crystal microcavity (PhCR)^92,125. Among these methods, AMX is the most prevalent approach for generating a normal-GVD comb. In contrast to the detrimental effect on soliton generation in the anomalous GVD regime⁸¹, the mode coupling between different mode families in normal-dispersion microresonators causes a shifting of the coupled resonances and locally alters the dispersion to allow for MI. In the representative experiment with dark solitons, AMX was employed to initialize the MI, and then realized dark solitons in a SiN microresonator via a thermal-tuning method. The measured integrated dispersion disturbed by AMX is presented in Fig. 9a³⁹. The pump frequency is gradually tuned from the blue side of a resonance, the power transmission trace is depicted in Fig. 9b. It is notable that the whole tuning range is almost exclusively located in the effectively blue-detuned regime, that implies the intracavity pump field stays on the upper branch of the bistability curve, in which MI is weak or even disappeared. The optical spectra and intensity noise at different detuning stages are presented in Fig. 9c, d, where the low-noise mode-locking microcombs with flat and modulated envelopes were observed in the power drop step regime, indicating the existence of a state transition similar to the soliton step in anomalous GVD regime. Benefitting from the weak MI and the blue-detuned pump, the generation of dark solitons follows a deterministic pathway (Fig. 9b) and exhibits a robust character similar to PSC. The corresponding pulse profile of the normal-GVD comb is presented in Fig. 9e, it is a complex structure depicted as low-intensity oscillations embedded in a high-intensity background. Different from the isolated ultrashort pulses with time-bandwidth-product limited durations in the anomalous dispersion region, dark solitons are the chirped pulses far from the Fourier-transform limitation, which can be interpreted as two stably interlocked SWs, connecting the upper and lower homogeneous steady-state solutions of the bistable cavity response⁷⁶. These localized waveforms exhibit wide pulse durations, the large duty cycle analogous to square waves indicates high conversion efficiency, as proven in various following researches. The key benefits of dark soliton in the normal GVD regime, including ease access, high stability, high conversion efficiency, and slower power falloffs in spectrum, make it a more ideal light source for applications.

**Fig. 9: Dark pulses in a normal-dispersion microresonator.**

Dark pulse shares many similar properties with its counterpart in the anomalous GVD regime in response to parameters of Kerr resonators. For example, a small dispersion coefficient and large nonlinear coefficient result in a broad spectral bandwidth and low conversion efficiency; the increase of power coupling coefficient accompanies an increase in conversion efficiency at the expense of a decrease in Q factor; a large FSR of cavity would enhance the intensity of comb line and boost the conversion efficiency. In contrast, the evolutionary dynamics of dark soliton with respect to detuning are unique. Using the setup as shown in Fig. 10a, Nazemosadat et al. revealed the switching dynamics of dark-pulse in a Kerr microresonator by forward and backward tuning method¹²⁶. Figure 10b presents a measured a transmission trace under a fixed pump power. As the pump laser is swept forward into resonance, the comb power increases in a gradual manner while displaying continuous steps in consistent with Fig. 9b. After accessing the maximum detuning of dark pulse in the forward tuning, the comb power drops along the same trace in the reverse direction by tuning the pump backward. Furthermore, the comb power continually drops in a smoothed, steplike pattern in further backward tuning until the pump non-resonant completely. The evolution of comb power in the forward and backward pump tuning shows hysteresis behavior, similar to what has been observed for bright solitons in anomalous-dispersion resonators. The optical spectra and their corresponding simulated intracavity pulse profiles at different detuning stages, marked in Fig. 10b, are shown in Fig. 10c. The optical spectra depicted similar normal-GVD combs except for the variation of bandwidth in parallel with comb power evolution. Strikingly, the simulated waveforms revealed the switching of low intensity oscillation at the center of the dark-pulse structure, as the arrows pointed in Fig. 10c. The number of low-intensity oscillations increases as the comb power increases in forward pump tuning, while vanishing one by one in the reverse direction. In bifurcation analysis, these temporal structures arise from the different snaking branch solutions of SWs; the orders of SWs and their stable regimes decrease with increasing detuning, thus called the collapsed snake structure⁷⁶. When the ratio of low-intensity structure is larger than high intensity, a flat-top pulsed structure called platicon is formed and deemed as a bright pulse evolving from a dark pulse in normal dispersion regime, which is a higher-order dark pulse can be accessed at the stable Maxwell point in bifurcation analysis^76,127. Intuitively, a dark pulse can be regarded as the inverse bright multi-solitons with a coherently assembled structure embedded in a high-intensity constant background, where the low-intensity ripples correspond to the pulse peaks of assembled solitons. Therefore, dark pulses present modulated spectral envelopes and high conversion efficiencies similar to multi-soliton, and a reproductive pathway free from the disordered distribution of multiple solitons in microresonators. In addition, the maximum comb power is consistent with the duration of dark pulse or the number of low-intensity ripples, which is determined by the Maxwell point related to the parameters of the system, and is similar to the limitation of the maximum soliton numbers confined in a resonator.

**Fig. 10: Deterministic switching of dark pulses.**

Encouraged by the various advantages of dark solitons, a number of platforms for generating dark soliton microcombs with high conversion efficiency have been studied. For instance, Lihachev et al. used laser self-injection locking to demonstrate a fully integrated platicon microcomb operating at a microwave K-band repetition rate¹²⁸. By using a high-Q SiN microresonator self-injection-locked by a DFB laser (Fig. 11a), multi-platicon states with low phase noise were excited directly without sophisticated active control. The formation dynamics and properties of platicons were investigated, in which a high conversion efficiency of 40% was demonstrated. In addition, the same configuration was adapted to demonstrate hertz-linewidth semiconductor lasers using CMOS-ready ultra-high-Q microresonators, where a self-injection-locked platicon microcomb with low phase noise and narrow linewidth is obtained⁵⁹. Another approach to excite dark pulse in normal dispersion regime is by using PhCR. A PhCR is a microresonator with periodic modulation to create frequency-domain point defects¹²⁹, which can locally modify the dispersion akin to AMXs to enable MI. By employing an edge-less tantala PhCR (as shown in Fig. 11b), Yu et al. showed the dark-to-bright continuum via controlling the strength of defect along with the pump-cavity detuning¹²⁵. They demonstrated flexible control over the bandwidth and conversion efficiency of microcomb, achieving a 200-GHz normal-GVD microcombs spanning 180 ~ 210 THz with a conversion efficiency of 21%. Furthermore, Li et al. proposed a PhCR with a modulated structure on both the inner and outer edges of the microresonator (Fig. 11c) to generate stable, power-efficient normal-GVD microcombs with high spectral symmetry¹³⁰. The structure of such PhCR results in two symmetrically positioned local dispersion alterations on either side of the pump mode (Fig. 11c), eliminating the odd components of dispersion responsible for the asymmetry of dark-soliton microcombs. Moreover, by adjusting the interval between the positions of the dispersion alterations and the pump mode, deterministic perfect platicon crystals were achieved. In contrast to the PSCs in anomalous GVD regime, the conversion efficiency of microcombs increases slightly rather than linearly with the number of platicons due to the duration of the dark pulses further compressed within limited angular space. Here, a normal-GVD microcomb in a single-platicon case with a conversion efficiency of 27.6% was demonstrated. Recently, by using a pump-recycling photonic crystal reflector in the coupling waveguide (Fig. 11d), a measured 65% conversion efficiency and 97% pump consumption of a 40 mW input pump laser was demonstrated in an over-coupled PhCR with normal dispersion⁸⁸. Besides advances on excitation schemes of dark-soliton microcombs, optical materials with favorable properties provide another route to support microcombs with high conversion efficiency. Xia et al. demonstrated both a bright soliton-based microcomb with a bandwidth of 240 nm and a dark-soliton microcomb with a conversion efficiency of 21.8% in a single GeSbS microresonator in two fundamental polarized mode families (Fig. 11e)¹³¹. Alternatively, by using microresonators on an AlGaAs on-insulator platform (Fig. 11f), Shu et al. generated a dark-soliton microcomb with an unprecedentedly wide tuning range of over one free spectral range. The conversion efficiency reached ~15%¹³². Combining the same configuration with foundry-based silicon photonics, dark-soliton microcombs were demonstrated to driven system-level data links. Such synergy of microcombs and other integrated components would facilitate the next generation of integrated photonics¹³³.

**Fig. 11: Dark pulses with high conversion efficiency generated on different platforms.**

Laser cavity soliton microcombs

Recently, a novel bright dispersive soliton named laser cavity soliton was demonstrated in a microresonator nested into a pump-generating active ring cavity. The principle of laser cavity soliton is presented in Fig. 12a, which contains a Kerr microresonator and a longer amplifying fiber loop. The exact experimental setup is shown in Fig. 12b⁷². It is observed that the Kerr microcavity is embedded within a fiber loop assembled to resemble a mode-locked laser without a saturable absorber. The pulse propagating in the fiber loop is boosted and spectrally limited by the erbium-ytterbium co-doped fiber amplifier (EYDFA). By adjusting the length of the delay line, the resonance distribution of such two cavities is finely tuned to ensure only a single fiber cavity mode in each microresonator mode to prevent supermode instability (Fig. 12c). The pulse sustained in microresonator, and spectrally broadened by the Kerr nonlinearity over the laser-gain bandwidth. A tunable bandpass filter (BPF) is employed in the fiber loop to suppress excessive nonlinear phase shift and maintain the locked coherence of comb lines enabled by the FWM effect. The principle of such laser cavity soliton is similar to the filter-driven FWM laser, where a resonator is used as a filter as well as a nonlinear gain element in an erbium doped-fiber cavity¹³⁴. The measured optical spectrum of laser cavity soliton is presented in Fig. 12d, presenting a broadband comb with a unique envelope due to the interference between the fields in the two cavities. The pulse profiles both in experimental and theoretical revealed it is the bright-soliton combs (insets in Fig. 12d). Remarkably, the laser cavity soliton does not require the pump background wave to maintain its existence (i.e., background-free), which releases most pump energy to be converted into comb modes. Compared to the conversion efficiency of a few percentage points for conventional bright soliton, here the laser cavity soliton achieved a conversion efficiency of 75%, with a theoretical maximum reached to 96%. Such high conversion efficiency, combined with the regular pulsed nature, motivates further pursuit of bright solitons. Very recently, Nie et al. deeply studied the laser cavity soliton generation and interaction dynamics in a FP-microresonator-filtered fiber laser, and demonstrated a self-starting soliton microcomb with a high conversion efficiency of 90.7%¹³⁵. Here the FSR of the employed FP-microresonator is ~10 GHz, the corresponding synchronous repetition rate of soliton is favorable for application in X-band. It is incomparable to conventional bright soliton limited by the corresponding large volume and low conversion efficiency. Besides the excellent conversion efficiency, it has been discovered that the microresonator-filtered fiber laser system exhibits a property of slow nonlinearity arising from the EDFA and the thermal response of the Kerr microresonator, which can transform the desired soliton state to be the dominant attractor of the system^{73,74,136,137}. Therefore, the self-emergence (i.e., self-starting) of specific soliton states and flexible switching between different states by tailoring the global parameters of the system were enabled. Moreover, the generated soliton states exhibited high stability and self-healing capability, which are desired merits for microcombs applied in practice.

**Fig. 12: Laser cavity solitons generation in microresonator nested into a gain fiber cavity.**

Replacing the gain fiber loop in the microresonator-filtered fiber laser system by a passive waveguide, a novel hybrid Mach-Zehnder micro-ring resonator architecture was proposed to support soliton microcomb with high conversion efficiency. The principle of the proposed micro-ring resonator is presented in Fig. 13a, consisting of a Kerr microresonator for motivating DKSs, embedded in a secondary cavity that acted as a feedback section⁸⁷. The optical path length of the secondary cavity was designed to be twice that of the microresonator, and can be delicately tailored and tuned (by microheater in the experiment as shown in Fig. 13b) to set a phase difference of π between the pump fields out-coupled from the microresonator and through-passed from the feedback section at node 2. The opposite phases between the fields cause a sharp pump depletion, which indicates an extreme conversion efficiency into the comb lines. In theory, the interference of the fields permits an unprecedented pump depletion above 80% and a high conversion efficiency only limited by the necessarily remaining pump background field to sustain DKS operation in the resonators. Driving the fabricated device as shown in Fig. 13b using a CW-laser with the conventional frequency scanning method, Boggio et al. demonstrated various soliton crystal states with high conversion efficiency (Fig. 13d), featured by a deeply depleted pump mode with a weaker intensity in comparison with other supermodes in spectra, as shown in Fig. 13e, f. Here, a microcomb in PSC state with a conversion efficiency as high as ~55% was achieved. Although the solitons demonstrated here are less robust, its robustness can be improved by referring to other geometry of resonator with feedback^138,139,140. Meanwhile, combining the advantages of isolated pulse profiles and spectrally smooth envelopes of bright solitons, the ultra-efficient microcombs enabled by microresonator with an interferometric back-coupling architecture are suitable for various applications such as astronomy, spectroscopy, and telecommunication.

**Fig. 13: Efficient soliton-crystal microcomb generation in a microresonator with interferometric back-coupling.**

Microcombs in dual-cavity coupled microresonator

Expanded from the mode splitting caused by coupling between different polarization or spatial modes in an individual resonator, dual-cavity coupled microresonator architecture has recently emerged as a favorable alternative approach to generate normal-GVD microcombs with high conversion efficiency aided by AMX. The typical structure of the dual-cavity coupled microresonator is presented in Fig. 14a, which is composed of two linearly coupled cavities, main and auxiliary, with microheaters on top of one or both of them¹⁴¹. Because of the close proximity of the two similar microresonators, such an architecture also called photonic dimer or photonic molecule. The transverse modes of the resonators evanescently couple with each other, leading to AMXs (Fig. 14b) and localized anomalous dispersion to initiate the formation of normal-GVD microcombs. In comparison with AMXs in an individual cavity, the photonic dimer is immune to the randomness of the AMXs’ locations and coupling strengths⁴⁰. By controlling the gap between resonators, the coupling coefficient between modes can be easily controlled. Furthermore, the resonance locations of the coupling modes can be tuned separately via heating the resonators. The benefits of photonic dimer enable the generation of wavelength-tunable normal-GVD microcombs in multiple resonances (Fig. 14c), improve the robustness of normal-GVD microcombs, and eliminate other parasitic effects in conventional microresonator that support more than one mode.

**Fig. 14: Dissipative soliton in a dual-cavity coupled microresonator.**

The normal-GVD microcombs utilizing AMXs in photonic dimer were first demonstrated by ref. ⁴⁰. By tuning the power applied to the microheater of the auxiliary ring, the position of the AMX was controlled, facilitating the deterministic generation of normal-GVD microcombs with selected repetition rates in a monolithic device. Almost simultaneously, the same configuration was employed with two anomalous-GVD resonators by ref. ¹⁴². They demonstrated a similarly controllable AMX and proved that it could improve the pump-to-comb conversion efficiency. Benefitting from advances in micro/nanofabrication technologies, the potential of the photonic dimer in promoting microcomb properties has been further unlocked. As shown in Fig. 15a–c, Kim et al. demonstrated turnkey normal-GVD microcombs in a SiN photonic dimer device driven by a CW fixed-frequency laser⁸⁶. The generated mode-locked normal-GVD microcombs exhibited a high conversion efficiency of 40.6%, and the power of comb lines was greatly enhanced (as presented in Fig. 15c), which is encouraging for applications requiring sufficient power per line, such as data transmission⁴. Furthermore, the normal-GVD microcombs with high conversion efficiency generated in different photonic dimers were proved to be synchronized and coherent combined for a 2.9 dB increase in comb power. The spectral profiles were relatively flat while maintaining a high total conversion efficiency of 26%¹⁴³. It enables fully integrated systems to break the power limitation of an individual comb system. Taking advantages of the purity of the parameter space of photonic dimer, the normal-GVD microcombs can be robustly triggered in a broad range of existence. Figure 14c shows the broadly tunable normal-GVD microcombs achieved by selecting the frequency location of the split resonance. Remarkably, the conversion efficiency increased from 32 to 49% along with the increase in coupling rate at long wavelengths over the tuned frequency span¹⁴¹. The same configuration was further employed to generate a microcomb-based, widely and arbitrarily tunable laser source with a very narrow linewidth¹⁴⁴. More recently, a variant photonic dimer consisting of two anomalous-dispersion microresonators was demonstrated to generated bright Kerr solitons with high conversion efficiency¹⁴⁵. Figure 15d presents the microscopy image of the photonic dimer, in which the two linearly coupled cavities are significantly different in size. Both resonators have identical cross-sections, but the auxiliary resonator is smaller, resulting in a larger FSR that minimizes the interaction between cavities at longitudinal modes except the pump mode (Fig. 15e), which is responsible for the asymmetry and fluctuation of normal-GVD microcombs in similar-scale dual-cavity coupled microresonators. The pump is coupled into the main resonator and the pump resonance is shifted towards the red side with the perturbation of AMX while other resonances remain. Physically, this mechanism breaks the synchronization between pump mode and other comb-teeth modes that require a high red-detuning to reach soliton regime, allowing DKS microcombs with a high conversion efficiency under more sufficient pump coupling. As shown in Fig. 15f, a broadband bright soliton microcombs with a deeply depleted pump mode was demonstrated, achieving a conversion efficiency as high as 54%. It presents an order-of-magnitude improvement compared with conventional soliton microcombs in CW driven anomalous dispersion microresonators. Benefiting from the sample structure and relatively small footprint, it was proven to be suitable for wafer-level fabrication with high yield¹⁴⁶. Furthermore, the same architecture was applied in the normal dispersion regime, a wideband platicon microcomb with fewer spectral defects was generated and exhibited a conversion efficiency of 51%, as shown in Fig. 15g¹⁴⁷. Besides the microcombs with high conversion efficiency aided by AMXs, photonic dimers were also demonstrated to support other emergent nonlinear phenomena, such as Fano-shaped dispersive waves and soliton hopping¹⁴⁸, which are not contained in a single-particle resonator and may further promote advance in integrated microcombs.

**Fig. 15: Efficient microcombs in dual-cavity coupled microresonators.**

Accompanying the investigation on the photonic dimer, Xue et al. demonstrated an installation with two linearly coupled fiber cavities supporting soliton combs with ultrahigh conversion efficiency¹⁴⁹. Figure 16a illustrates the concept of super-efficient soliton generation in the mutually coupled optical cavities, where a normal dispersion resonator is coupled with an anomalous-GVD resonator. In contrast to the photonic dimers, where the auxiliary resonator served as an MI initiator or pump mode frequency shifter, the normal-GVD resonator is described as a storage unit that recycles the pump field, leading to a high-efficiency soliton microcombs generation in the anomalous-GVD resonator. Despite being limited by the high intrinsic loss of the fiber cavities and a relatively large dimension corresponding to an extremely low soliton duty cycle, the average soliton power measured was only 4.6 × 10⁻⁵ of the input pump power (Fig. 16b). An ultrahigh conversion efficiency close to 100% was numerically predicted for intrinsically lossless microcavities. It is an excellent paradigm promising a different route to generate microcomb with high conversion efficiency in integrated photonic dimers.

**Fig. 16: Super-efficient temporal solitons in mutually coupled optical cavities.**

Summary and outlook

In this review, we presented an overview of the microresonator-based Kerr microcombs technologies that enable combs with high conversion efficiency. The reported Kerr microcombs with high conversion efficiency are summarized in Table 1. With the in-depth understanding of nonlinear physics, soliton states such as multi-soliton, soliton crystal, dark soliton, and laser cavity soliton can overcome the energy-conversion limitations of conventional single soliton in anomalous regime. Meanwhile, advances in micro/nanofabrication and photonic engineering capacity enable Kerr microcombs with high conversion efficiency generated with low loss, unprecedented topological architectures, and novel material platforms.

Table 1 Summary of reported high conversion efficiency Kerr microcombs based on microresonators

Full size table

Aside from the impressive high conversion efficiency achieved by Kerr microcombs in recent advances, substantial obstacles remain in bringing these microcombs from laboratory into real-world applications. One critical problem is the level of integration. Although multi-soliton and dark soliton microcombs with high conversion efficiency have been demonstrated via the laser-injection locking method, a fully integrated photonic system remains a challenge due to the requirement of Kerr microresonator performance and the limited power of current on-chip lasers¹⁵⁰. Another key challenge is establishing a robust route to achieve the desired Kerr microcombs with high conversion efficiency. As presented in the above section, current techniques for generating Kerr microcombs with high conversion efficiency mostly rely on complex servo systems to operate microcombs in desired states. Combining the rich dynamics involved in microcombs formation, the required monitoring and control capabilities for microcombs operation pose obstacles to full integration and deployment. Besides, the bandwidth and flatness of Kerr microcombs with high conversion efficiency obtained by current technologies are limited. While the comb-line power is enhanced due to the improvement of power conversion efficiency, the bandwidths of microcombs do not broaden significantly, which hinders the generation of stabilized microcombs facilitated by self-referencing technique. Meanwhile, the flatness of microcombs is not ideal due to the defective perturbations in the power distribution caused by additional nonlinear effects such as AMXs and stimulated Raman scattering. Furthermore, a majority of the reported Kerr microcombs with high conversion efficiency are focused on communication bands. However, there is a significant demand for visible and mid-infrared microcombs in the fields of chemical/biological sensing and molecular spectroscopy. The bandwidth of visible microcombs is quite limited, and the conversion efficiency is low¹⁵¹. Moreover, there are no reports yet about mode-locked mid-infrared microcombs with high conversion efficiency based on Kerr microresonators.

Despite there being numerous challenges for current techniques in generating Kerr microcombs with high conversion efficiency, the current trend of integrated optics remains a promising path that can be extended to achieve the desired goal. On the one hand, there are amounts of emerging nonlinear physics phenomena that require further investigation^111,148,152. With a broader insight beyond current focuses, it is anticipated that more favorable Kerr microcombs will be obtained based on new mechanisms. On the other hand, microcavities are yet to be thoroughly developed and understood. For instance, there is still great potential to further improve the performance of Kerr microcombs in the microresonators with higher Q values. Besides, there are several microcombs generated with high conversion efficiency in novel material platforms with both Kerr nonlinearity and second-order nonlinearity, which is beneficial for microcombs with extraordinary nonlinear dynamics in the visible band^153,154,155. In summary, there is an anticipating margin on the material platform to improve the performance of microcombs until it reaches the ultimate capabilities of microresonators. Along such two separated development routes, there are many open questions to be studied and answered. It is encouraging to see that this field has become an active field in optics today, and we foresee that there will be more achievements in the future that will make Kerr microcombs with high conversion efficiency the cornerstone in the next-generation integrated photonics. Over the next decade, we anticipate that the synergy between Kerr microcombs and their expanded applications will lead to further exciting breakthroughs in improving the microcombs’ performance and promote the widespread deployment of microcombs, accelerating the transition of this technology into commercial production.