###### Advanced Photonics, Vol. 2, Issue 3, 034001 (2020)

## Advances in soliton microcomb generation

Weiqiang Wang^{1,†}, Leiran Wang^{1,2}, and Wenfu Zhang^{1,2,*}

Author Affiliations

^{1}Chinese Academy of Sciences, Xi’an Institute of Optics and Precision Mechanics, State Key Laboratory of Transient Optics and Photonics, Xi’an, China^{2}University of Chinese Academy of Sciences, Beijing, China

## Abstract

Optical frequency combs, a revolutionary light source characterized by discrete and equally spaced frequencies, are usually regarded as a cornerstone for advanced frequency metrology, precision spectroscopy, high-speed communication, distance ranging, molecule detection, and many others. Due to the rapid development of micro/nanofabrication technology, breakthroughs in the quality factor of microresonators enable ultrahigh energy buildup inside cavities, which gives birth to microcavity-based frequency combs. In particular, the full coherent spectrum of the soliton microcomb (SMC) provides a route to low-noise ultrashort pulses with a repetition rate over two orders of magnitude higher than that of traditional mode-locking approaches. This enables lower power consumption and cost for a wide range of applications. This review summarizes recent achievements in SMCs, including the basic theory and physical model, as well as experimental techniques for single-soliton generation and various extraordinary soliton states (soliton crystals, Stokes solitons, breathers, molecules, cavity solitons, and dark solitons), with a perspective on their potential applications and remaining challenges.

## keywords

## 1 Introduction

Optical microcavities, which emerged from the rapid development of modern micro/nanofabrication technologies, have grown to be revolutionary devices that light the way toward several fantastic applications, including advanced light sources, ultrafast optical signal processing, and ultrasensitive sensors, benefitting from their unprecedented small size and high buildup of energy inside the resonators.^{1}^{2}^{,}^{3}^{4}^{,}^{5}^{6}

Technically speaking, the character of microcomb mainly depends on microresonator properties as well as the pumping parameters (e.g., pump power and frequency detuning). The ^{7}^{2}^{8}^{9}^{10}^{10}^{11}^{10}^{12}^{,}^{13}^{14}^{15}^{,}^{16}^{17}^{18}^{19}^{20}^{21}^{22}^{23}^{12}^{,}^{24}^{–}^{27}

Figure 1. Route map of microcombs.

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Until now, based on advanced experimental techniques, SMCs have been realized in an ^{10}^{13}^{28}^{,}^{29}^{30}^{31}^{12}^{32}^{15}^{31}^{,}^{33}^{10}^{,}^{13}^{,}^{15}^{,}^{30}^{,}^{34}^{,}^{35}^{36}^{31}^{36}^{10}^{–}^{12}^{,}^{37}^{38}^{39}^{40}^{41}^{42}^{43}^{,}^{44}

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#### Table 1. Typical parameters of reported SMCs.

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#### Table 1. Typical parameters of reported SMCs.

Material Structure $\mathsf{Q}$ FSR (GHz) Wavelength range (nm) Types Refs. ${\mathsf{MgF}}_{\mathsf{2}}$ Rod $\mathsf{4.3}\times {\mathsf{10}}^{\mathsf{8}}$ 35.2 1520 to 1590 Solitons 10 ${\mathsf{MgF}}_{\mathsf{2}}$ Rod $>\mathsf{1.0}\times {\mathsf{10}}^{\mathsf{8}}$ 14 1520 to 1590 Solitons 24 ${\mathsf{MgF}}_{\mathsf{2}}$ Rod $\sim \mathsf{4.7}\times {\mathsf{10}}^{\mathsf{8}}$ 25.78 1540 to 1580 Solitons 36 ${\mathsf{MgF}}_{\mathsf{2}}$ Rod $>{\mathsf{10}}^{\mathsf{9}}$ 12.5 1526 to 1548 Solitons 45 ${\mathsf{SiO}}_{\mathsf{2}}$ Disk $\sim \mathsf{4}\times {\mathsf{10}}^{\mathsf{8}}$ 22 1510 to 1600 Solitons 13 ${\mathsf{SiO}}_{\mathsf{2}}$ Disk $\sim {\mathsf{10}}^{\mathsf{8}}$ $\sim \mathsf{20}$ 1025 to 1125 and 760 to 790 Solitons 33 ${\mathsf{SiO}}_{\mathsf{2}}$ Disk $>{\mathsf{10}}^{\mathsf{8}}$ 22 1600 to 1650 Stokes solitons 17 ${\mathsf{SiO}}_{\mathsf{2}}$ Disk $>{\mathsf{10}}^{\mathsf{8}}$ 1.8 to 33 1530 to 1570 Solitons 4 ${\mathsf{SiO}}_{\mathsf{2}}$ Disk $>{\mathsf{10}}^{\mathsf{8}}$ 26, 16.4 1540 to 1580 Soliton crystals 46 ${\mathsf{SiO}}_{\mathsf{2}}$ Disk $\mathsf{1.8}\times {\mathsf{10}}^{\mathsf{8}}$ 22 1510 to 1590 Solitons 47 ${\mathsf{SiO}}_{\mathsf{2}}$ Rod $>{\mathsf{10}}^{\mathsf{8}}$ 55.6 1520 to 1590 Solitons 28 ${\mathsf{SiO}}_{\mathsf{2}}$ Rod $\mathsf{3.7}\times {\mathsf{10}}^{\mathsf{8}}$ 50 1530 to 1590 Solitons 29 AlN Ring $\mathsf{0.65}\times {\mathsf{10}}^{\mathsf{8}}$ $>\mathsf{500}$ 1400 to 1700 Solitons 30 SiN Ring $\sim \mathsf{5}\times {\mathsf{10}}^{\mathsf{5}}$ 189 1330 to 2000 Solitons 12 SiN Ring $\sim \mathsf{0.4}\times {\mathsf{10}}^{\mathsf{5}}$ 1000 1100 to 2300 Solitons 48 SiN Ring $\mathsf{1.4}\times {\mathsf{10}}^{\mathsf{6}}$ 1000 1420 to 1700 Solitons 49 SiN Ring $\sim \mathsf{0.6}\times {\mathsf{10}}^{\mathsf{6}}$ 1000 850 to 2000 Solitons 34 SiN Ring $\sim \mathsf{0.5}\times {\mathsf{10}}^{\mathsf{6}}$ 200 1440 to 1660 Solitons 50 SiN Ring $>\mathsf{2.0}\times {\mathsf{10}}^{\mathsf{6}}$ 200 1470 to 1620 Breathers 51 SiN Ring $\sim \mathsf{1.9}\times {\mathsf{10}}^{\mathsf{6}}$ $>\mathsf{200}$ 1450 to 1700 Breathers 20 SiN Ring $\sim \mathsf{8.0}\times {\mathsf{10}}^{\mathsf{6}}$ 194 1540 to 1640 Solitons 52 SiN Ring $>\mathsf{15}\times {\mathsf{10}}^{\mathsf{6}}$ 99 1570 to 1630 Solitons 53 SiN Ring $\sim \mathsf{0.65}\times {\mathsf{10}}^{\mathsf{6}}$ $\sim \mathsf{1000}$ 776 to 1630 Solitons 35 SiN Ring $\sim \mathsf{0.77}\times {\mathsf{10}}^{\mathsf{6}}$ 231.3 1460 to 1610 Dark pulses 23 Doped silica glass Ring $\sim \mathsf{1.7}\times {\mathsf{10}}^{\mathsf{6}}$ 49 1480 to 1650 Solitons 15 Doped silica glass Ring $\sim \mathsf{1.7}\times {\mathsf{10}}^{\mathsf{6}}$ 49 1480 to 1650 Soliton crystals 19 Doped silica glass Ring $\sim \mathsf{1.3}\times {\mathsf{10}}^{\mathsf{6}}$ 49 1510 to 1580 Cavity solitons 21 Graphene-nitride Ring $\sim {\mathsf{10}}^{\mathsf{6}}$ $\sim \mathsf{90}$ Tunable ^{a}Soliton crystals 54 Silicon Ring $\mathsf{0.2}\times {\mathsf{10}}^{\mathsf{6}}$ 127 2800 to 3800 Breathers 51 ${\mathsf{LiNbO}}_{\mathsf{3}}$ Ring $\mathsf{2.2}\times {\mathsf{10}}^{\mathsf{6}}$ 199.7 750 to 800 and 1460 to 1650 Solitons 31 ${\mathsf{LiNbO}}_{\mathsf{3}}$ Ring $>\mathsf{1.1}\times {\mathsf{10}}^{\mathsf{6}}$ $\sim \mathsf{200}$ 1830 to 2130 Solitons 55

Figure 2. Typical spectral coverage of SMCs on various material platforms using different approaches.

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In this review, we summarize recent experimental achievements with a perspective on the potential and challenges. The remainder of this paper is organized as follows. Sec.

## 2 Physics and Numerical Models for Microcombs

The generation of microcombs arises from parametric frequency conversion through the FWM effect that generates a pair of photons (a signal and an idler) that are equally spaced to the pump. The photonic interaction can be expressed as ^{56}^{,}^{57}

The CMEs have been successfully used to determine the threshold and explain the role of dispersion as well as other mechanisms in the microcomb formation. However, the amount of computation increases dramatically with increases in the mode number. Through considering the total intracavity field an entirety ^{58}^{–}^{60}

Based on the LLE, mode-locked microcombs have been predicted and rich physical phenomena have been explained, including the single soliton with dispersion wave,^{12}^{46}^{23}^{25}^{,}^{27}

## 3 Experimental Schemes for Single SMC Generation

It has been found that SMC can be spontaneously formed while a CW pump stabilizes in the red-detuned regime of a dissipative nonlinear microcavity. However, the soliton existing range exhibits thermal instabibility for microcavities with negative temperature coefficients, which blinded SMC observation for more than 6 years since the first microcomb realization.^{8}^{,}^{10}^{10}

## 3.1 Frequency-Scanning Method

The basic idea of the frequency-scanning method is sweeping the pump to the red-detuned regime before the microcavity is heated up by the thermo-optic effect. Generally, the frequency-scanning speed is determined by the thermo-optic response time, ^{10}^{,}^{25}^{,}^{44}^{,}^{61}^{–}^{63}^{10}

Figure 3. Experimental demonstration of stable temporal solitons in a high-

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The pump frequency-scanning method is a fundamental and intuitional approach for SMC generation. The success of this method relies on the control of the pump frequency sweeping speed and accuracy. The laser scanning time should be comparable to the cavity lifetime and thermal lifetime of the microresonator, which has a very high ^{63}^{30}^{,}^{47}

For some special cases, SMCs can also be generated with relatively slow scanning speeds once the thermal dynamics during soliton formation can be stabilized by other approaches. For example, a partial overlapping mode can be used to compensate for the thermal dissipation when the pump tunes to the red-detuning regime. By taking advantage of an adjacent mode family in a specific ^{48}^{49}

## 3.2 Power-Kicking Scheme

For microresonators with a high thermal-optic effect, the durations of soliton steps are so short that stopping the laser frequency exactly within these steps is technically difficult.^{63}^{12}

Figure 4. SMC generation based on power-kicking scheme. (a) Experimental setup of power-kicking scheme. The microresonator is pumped by an external cavity diode laser that is amplified and modulated by an AOM and an EOM. (b) Typical triangular shape of the transmission power while the pump sweeps across a resonance. (c)–(e) Soliton steps of

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A typical experimental setup is shown in ^{63}^{63}^{[Fig. 4(f)]} benefitting from the soliton-induced Cherenkov radiation.^{12}

Figure 5. Schematic and timing sequences of the power-kicking scheme. (a) Setup used to bring very short-lived soliton states to a steady state, including two modulators to adjust the pump power. (b) Timing sequences of the pump scanning, the fast and slow power modulation, and the converted light power. (c) Initial timing of the fast modulation with respect to the thermal triangle and slow power modulation. (d) The fast power modulation induced soliton steps. (e) Combined effect of the fast and slow modulation. Images are adapted with permission from Ref. 63.

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For cases with long enough soliton steps (e.g., longer than several microseconds), a single AOM can provide enough modulation speed for SMC generation. Additionally, the pump parameters can be adjusted with an active feedback loop to realize active capture and stabilization of temporal solitons.^{64}^{38}^{65}

## 3.3 Thermal-Tuning Method

An equivalent approach for SMC generation is shifting the resonances of a microresonator through a thermal-tuning method rather than tuning the pump frequency. As shown in ^{14}

Figure 6. SMC generation based on thermal-tuning method. (a) Experimental setup of thermally controlled SMC generation in a

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In principle, the thermal-tuning method can be regarded as a variant of the pump frequency-scanning method. Compared with tunable lasers, fixed frequency lasers usually have much narrower linewidth and lower noise. So it is attractive for soliton generation using a fixed frequency laser to improve the microcomb performance. Meanwhile, a fixed frequency laser has a smaller footprint and the integration technique of current source is rather mature, so the thermal-tuning method has the potential to realize a fully integrated microcomb.^{52}

## 3.4 Auxiliary-Laser-Based Method

Because the challenges of SMC generation mainly arise from the thermal instability of the soliton existing range, it is reasonable to imagine that the thermal effect can be solved by maintaining the intracavity optical power at a similar level during SMC generation. It is noted that microresonators exhibit contrary thermal characters when pumps are located at the blue- and red-detuned regimes. As a result, the dramatic decrease of intracavity heat when a pump laser tunes into a soliton existing range can be effectively compensated for by an auxiliary laser located at the blue-detuned regime. This principle has been verified recently,^{15}^{,}^{16}^{,}^{28}^{,}^{29}^{,}^{34}

A typical experimental setup is shown in ^{16}

Figure 7. SMC generation by the auxiliary-laser-based method. (a) Experimental setup. (b) Schematic of the counter-coupled auxiliary-laser-assisted thermal response control method. (c) The pump and auxiliary laser counter-balance thermal influences on the microcavity. (d) Optical spectrum of single SMC. Images are adapted with permission from Refs. 16 and 66.

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Based on the auxiliary-laser-assistant thermal-balance approach, a new SMC regime is discovered in which the soliton power exhibits a negative slope versus pump frequency detuning. It is distinct from the traditional soliton existence regime with a positive slope that is accessible via thermal locking by thermal-avoided methods. The negative slope implies that the increase of average comb power is less than the decrease of pump background, resulting in the total intracavity power decreasing with the increasing of detuning. In another experiment, it is proved that the durations of soliton steps can be extended by two orders of magnitude under the assistance of a codirectional-coupled ^{29}^{15}^{,}^{28}

All of these experimental results suggest that using an auxiliary laser can contribute to intracavity thermal equilibrium. It is regarded as an effective and universal method for stable SMC generation. Further, the auxiliary laser provides an additional degree of freedom for microcomb dynamic research. For example, the frequency spacing of the auxiliary and pump lasers has a significant impact on the microcomb states, and the beating between the auxiliary and pump lasers provides an optical lattice for soliton capture, which would be helpful for soliton crystal generation. This method can also provide a feasible approach to realizing spectral extension and synchronization of a microcomb in a single microresonator.^{67}

## 3.5 Photorefractive Effect for Stable SMC Generation

Because of the negative temperature coefficient of microresonators, the soliton existing range exhibits thermal instability, which results in complex pump tuning techniques for SMC generation. By contrast, if the refractive index of a microresonator decreases with increasing intracavity optical power, the pump can enter the red-detuned regime stably for SMC generation, just like the MI comb generation in a negative temperature coefficient microresonator. It has been discovered that the photorefractive effect in a Z-cut ^{31}^{31}

Figure 8. Bichromatic SMC generation in a

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Because of the photorefractive effect, the thermal instability of the soliton existing range is completely compensated for. Therefore, SMC can be stably generated by coupling a pump into the resonance from the red-detuned side, and the pump can freely tune forward and backward for soliton switching. Meanwhile, the thermal stability of the soliton existing range can contribute to simplification of control circuits for SMC generation, which is crucial for miniaturized integration and practical applications. More interestingly, the ^{68}

## 3.6 Forward and Backward Tuning Method

Due to the inherently stochastic intracavity dynamics, it remains a challenge to realize repeatable soliton switching and deterministic single SMC generation if using the aforementioned strategies. For example, ^{69}

Figure 9. (a) Scheme of the forward frequency-tuning method. (b) 200 overlaid experimental traces of the output comb light in the pump forward tuning, revealing the formation of a predominant soliton number of

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After the frequency-scanning method was proposed, a forward and backward frequency-sweeping technique was introduced for deterministic single SMC generation.^{69}

A parallel progress on deterministic single SMC generation was fulfilled in a high-index doped silica glass microring through the forward and backward thermal-tuning method.^{15}

Figure 10. Deterministic single SMC generation using thermal-tuning method.^{15}

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## 3.7 Self-Injection Locking

One of the ultimate goals for the microcomb field is fully integrated SMC sources. A common feature of all methods mentioned above is reliance on external narrow-linewidth pumps, which introduces great challenge for miniaturized integration. Benefitting from the advanced micro/nanofabrication technologies, ultra-high-^{45}^{70}^{,}^{71}^{45}^{10}^{,}^{63}^{,}^{64}^{,}^{69}

Figure 11. Self-injection locking and spectral narrowing of a multifrequency laser diode coupled to an ^{45}

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A key factor of this technique is the ^{72}^{–}^{75}^{72}^{74}^{75}

## 3.8 Pulse-Pumped Single-Soliton Generation

In addition to the narrow-linewidth CW lasers, temporally structured light sources can also be used as a pump for SMC generation.^{11}^{,}^{76}^{,}^{77}^{76}^{[Fig. 12(d)]}, indicating that precise control of the driving pulse repetition rate is not strongly required for the SMC formation in a pulsed pump system.

Figure 12. Principle and experimental scheme for SMC generation driven by optical pulses.^{76}

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Following the pulse-pumped cavity soliton generation in fiber and Fabry–Pérot cavities,^{78}^{,}^{79}^{77}^{77}^{80}

Physically, a pulse pump can break the symmetry of a microcavity, which induces optical lattice for soliton capture. The soliton quantity is determined by the repetition rate, width of the pump pulse, and intrinsic properties of the microresonator (dispersion, ^{81}

## 4 Extraordinary Soliton Microcombs

Different soliton forms in microcavities besides typical single or multisolitons, such as the soliton crystals, Stokes solitons, breather solitons, soliton molecules, laser cavity solitons, and dark pulses (solitons), also exist. They present distinct behaviors in both frequency and time domains, as well as enrich soliton dynamics and physics for microcomb research. In this section, the generation of these extraordinary solitons and their unique characteristics are reviewed.

## 4.1 Soliton Crystals

Soliton crystals defined as spontaneously and collectively ordered ensembles of copropagating solitons that are regularly distributed in a microcavity were recently discovered in silica WGM,^{46}^{54}^{,}^{82}^{19}^{83}^{46}^{19}^{46}^{19}^{[Fig. 13(I a)]}, Schottky defects with vacancies ^{[Figs. 13(I b)–13(I e) and 13(II a)–13(II i)]}, Frenkel defects ^{[Figs. 13(I f)–13(I i) and 13(II j)]}, disorder ^{[Fig. 13(I j)]}, superstructure ^{[Figs. 13(I k)–13(I n) and 13(II k)]}, and irregular intersoliton spacings ^{[Figs. 13(I o) and 13(II l)]}. In another experiment, soliton crystals with Schottky defects are also observed in a graphene-nitride microresonator, where the cavity dispersion becomes adjustable and affects the spectral bandwidth and shape.^{54}

Figure 13. (I) Soliton crystals in a silica disk resonator.^{46}^{19}

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A special state of soliton crystals, i.e., the perfect soliton crystals (PSCs), is defined as all solitons are evenly distributed in a cavity and experimentally observed recently.^{82}^{,}^{83}^{83}

Soliton crystals introduce a new regime of soliton physics and act as a test bed for the research of soliton interaction. The extreme degeneracy of the configuration space of soliton crystals suggests its capability in on-chip optical buffers.^{46}

## 4.2 Stokes Soliton

Stokes soliton is a special type of soliton that arises from Kerr-effect trapping and Raman amplification when a first soliton (primary soliton) is present.^{17}^{17}

Figure 14. Stokes soliton in a high-^{17}

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The central wavelength of the Stokes soliton relies on the FSR matching of distinct mode families, which offers a potential approach for controllable multicolor soliton generation through advanced-dispersion engineering techniques.^{84}

## 4.3 Breather Solitons

Distinct from the stationary soliton states mentioned above, breather solitons show periodic oscillation in both pulse amplitude and duration^{20}^{,}^{51}^{,}^{85}^{–}^{87}^{88}^{,}^{89}^{20}^{,}^{51}^{,}^{85}^{,}^{88}^{85}^{,}^{88}^{51}^{51}^{[Fig. 15(c)]}. Note that this process is similar to but different from the forward and backward tuning method mentioned above, where the backward-tuning process is a necessary adiabatic step for deterministic single SMC generation. Compared with stationary solitons, the spectra of breather solitons are characterized by a sharp top and a quasitriangular envelope (on logarithmic scale) ^{[Fig. 15(e)]} instead of the sech^{2}-like profile, resulting from the averaging of the oscillating comb bandwidth by an optical spectrum analyzer. Meanwhile, for the RF spectra, breather solitons are identified by sharp tones that indicate oscillation at a low frequency (the fundamental breathing frequency and its harmonics) rather than a single one at the cavity repetition rate, suggesting the low-noise feature of the stationary soliton state ^{[Fig. 15(f)]}.

Figure 15. Breather soliton in a

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The breather soliton state also can be triggered by avoided mode crossings (regarded as the intermode breather soliton), which is a ubiquitous phenomenon in multimode microresonators as illustrated in ^{85}^{2}-shape spectral envelope (similar to the stationary SMCs) in the primary mode family but featuring several spikes (i.e., enhanced power in comb teeth) due to the phase matching to the cavity soliton,^{85}

Figure 16. Intermode breather solitons in microcavities. (a) Simulated intracavity power trace over the laser detuning in the absence of intermode interactions. The intermode breather soliton exists in the region where stationary soliton is expected (orange area). (b) Simulated power trace based on the coupled LLEs, showing a hysteretic power transition (gray area) and an oscillatory behavior (orange area). (c), (d) Measured optical spectra for intermode breather solitons in (c) an

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## 4.4 Soliton Molecules

Soliton molecules are balanced states in which attractive force caused by group velocity dispersion (GVD) of bound solitons is counteracted by the intersoliton repulsive force induced by the XPM effect.^{22}^{[Fig. 17(c)]}, solitons with different pulse energies can form once the pumps are stabilized in the red-detuned regime simultaneously. The relationship of repulsive force (drifts of the distinct solitons) versus the soliton temporal gap can be calculated by

Figure 17. Heteronuclear soliton molecule generation using two discrete pumps. (a) Principle of bound solitons where attractive force and repulsive force are balanced. (b) Calculated repulsive force versus the temporal separation of solitons. (c) The experimental setup for soliton molecule generation. (d) Measured transmission power trace while the pumps sweep across a cavity resonance. The red-shaded area is the comb power of the major pump, while the comb power of the minor pump is indicated by the blue-shaded area. (e) Optical spectrum of soliton molecules of two bound solitons, which corresponds to a linear superposition of optical spectra of the major soliton (f) and minor soliton (g). Images are adapted with permission from Ref. 22.

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Concerning experimental realization, discrete pumps are obtained by modulating a CW laser using an EOM. The frequency separation of discrete pumps is controlled by the driven RF signal. An example work is implemented in an ^{22}

Soliton molecules in microcavities go beyond the frame of their predecessors in fiber lasers, which enriches the soliton physics. In terms of applications, soliton molecules might contribute to comb-based sensing and metrology by providing an additional coherent comb, as well as optical telecommunications if storing and buffering soliton-molecule-based data come true.^{22}

## 4.5 Laser Cavity Solitons

SMCs can also be generated in a nested laser cavity in which a Kerr microresonator is embedded into a gain fiber cavity.^{21}^{90}^{,}^{91}

Figure 18. Laser cavity solitons. (a) Principle of cavity soliton formation. The microresonator is nested into a gain fiber cavity. (b) Mode relationship of the nonlinear microresonator and gain fiber cavity. (c) Typical optical spectrum of laser cavity soliton, which includes two equidistant solitons per round-trip. Images are adapted with permission from Ref. 21.

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Comparatively, the laser cavity soliton is background-free, which is beneficial for improving the energy conversion efficiency. According to the LLE, the energy conversion efficiency is limited to 5% for CW laser pumped single soliton. However, the conversion efficiency of laser cavity soliton can be boosted to 96% in theory, and 75% is experimentally obtained.^{21}

## 4.6 Dark Soliton Generation in the Normal-Dispersion Regime

Dark solitons (or dark pulses) are generally understood as intensity dips on a constant background, which demonstrate some unique advantages (e.g., less sensitivity to the system loss than bright solitons and more stability against the Gordon–Haus jitter in long communication lines) and have attracted increasing interest in many areas. Based on the mean-field LLE in the context of ring cavities or Fabry–Pérot interferometer with transverse spatial extent, it is found that in the time domain the dark solitons manifest themselves as low-intensity dips embedded in a high-intensity homogeneous background with a complex temporal structure, as being a particular type of solitons appearing in dissipative systems.^{92}^{,}^{93}^{94}^{,}^{95}^{96}^{,}^{97}^{98}^{94}^{95}^{99}^{23}^{,}^{92}^{93}^{,}^{95}^{,}^{96}^{97}

An obvious difference between the two opposite-dispersion regimes is that the anomalous region usually favors ultrashort pulse emission with time-bandwidth-product limited (chirp-free or nearly chirp-free) durations, while for the normal-dispersion regime it prefers strongly chirped waves that are far from the Fourier-transform limitation with the absence of intrinsic balancing between the nonlinearity and negative dispersion. Thus intuitively, the route to DS generation as well as its excitation dynamics will deviate from those for bright solitons in anomalous-dispersion microresonators. During the past years, several experiments with normal-dispersion resonators on diverse material platforms, including ^{100}^{101}^{97}^{,}^{102}^{100}^{101}^{102}^{[Fig. 19(d)]}.^{102}^{97}^{95}

Figure 19. Frequency comb generation in normal-dispersion microcavities. (a) Experiment setup using a semiconductor laser self-injection locked to an ^{101}^{102}^{97}

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All of this progress demonstrates that the mode-locking mechanism for normal-dispersion microcavities might have analogies to, but surely is not identical to, that in anomalous-dispersion regimes. One of the most obvious differences, compared with bright solitons observed in negative-dispersion microcavities, is that the soliton regime now favors the blue-detuned region instead of the red-shifted regime, which leads to the intracavity pump field staying on the upper branch of the bistability curve where modulational instability is generally absent.^{103}^{,}^{104}^{23}^{92}^{23}^{,}^{103}^{23}^{,}^{104}^{[Fig. 20(c)]}.^{104}^{92}^{23}

Figure 20. DS generation in a normal-dispersion SiN microring using (a) and (b) the thermal-tuning method^{23}^{93}

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Looking back on the research of extraordinary SMCs related to rich physical phenomena (including soliton crystals, Stokes solitons, breathers, molecules, and cavity solitons, as well as dark solitons), all of these encouraging discoveries have revealed deeper insight into the dynamics and properties of this new category of laser sources for integrated photonics. As a comparison, the developing route is, interestingly and legitimately, mimicking the evolution roadmap of the mode-locked fiber lasers of previous pioneers in nonlinear optics in the last few decades (and still continuously yielding cutting-edge progresses at present^{105}^{106}^{,}^{107}^{108}^{,}^{109}^{110}^{111}^{,}^{112}^{113}^{114}

## 5 Applications

To date, various proof-of-concept experiments concerning extensive applications of SMCs have been demonstrated (

Figure 21. Application areas of SMCs.

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## 5.1 Coherent Optical Communications

Future demand in “big data” interconnection leads to optical communication systems with terabits to petabits per second data rates in a single fiber with hundreds of parallel wavelength-division multiplexing channels. The SMC can act as a promising candidate of multiwavelength carriers due to its favorable characteristics of frequency stability, broad band, suitable mode spacing, and narrow linewidth. Even based on a nonsoliton-state microcomb with an imperfect spectrum, Pefeifle et al.^{115}^{39}^{116}^{117}

## 5.2 Spectroscopy

The DCS, which is similar to Fourier transform spectroscopy, provides an excellent method for gas composition detection with outstanding features of shorter sampling time, higher optical spectrum resolution, and multicomposition detection capability. Two SMCs in the telecommunication band with slightly different repetition rates that were generated in two separate ^{38}^{118}^{119}^{120}^{80}^{,}^{121}

## 5.3 Distance Measurement

OFCs are promising as excellent coherent sources for light detection and ranging (LIDAR) systems to fulfill fast and accurate distance measurements. Using a setup similar to the DCS system, dual-comb ranging systems have been carried out recently, which opens the door to low-SWaP LIDAR systems. For example, by employing the dual counter-propagating SMCs within a single silica wedge resonator, a dual-comb laser ranging system substantiates the time-of-flight measurement with 200-nm accuracy at an averaging time of 500 ms and within a range ambiguity of 16 mm.^{65}^{41}^{122}^{123}

## 5.4 RF Related

SMCs are promising candidates for microwave-related applications including optical atomic clocks, ultrastable microwave generation, and microwave signal processing. Early attempts of photonic-microwave links include locking a nonsoliton state microcomb to atomic Rb transitions^{124}^{125}^{40}^{,}^{126}^{127}^{40}^{128}^{129}^{,}^{130}^{131}^{–}^{135}

## 5.5 Quantum Optics

Benefitting from the significant cavity enhancement, microresonators can offer attractive integrated platforms for single photon or entangled quantum state generation.^{136}^{137}^{137}^{138}^{139}^{140}^{–}^{146}

## 6 Summary and Outlook

The experimental realization of SMCs represents the successful convergence of materials science, physics, and engineering techniques. SMCs have been regarded as an outstanding candidate in the exploration of next generation of optical sources due to the unprecedented advantages of lower SWaP (size, weight, and power), higher repetition rate as well as high coherence across the spectral coverage.^{147}

Although SMC-based applications present unprecedented performance improvements in many fields, generally they are still at the stage of proof-of-concept in laboratories at present. Considering engineering applications, the developments of SMCs (should) favor the tendency toward automatic generation, as well as higher integration density and higher energy conversion efficiency. The main challenge of automatic or programmable-controlled SMC generation comes from the ultrashort thermal lifetime of a microresonator, which is beyond the capacity of practical instruments for timely judgment on the soliton state through spectrum recognition. Fortunately, some advanced tuning speed independent schemes (e.g., the auxiliary-laser-assistant method and photorefractive effect in ^{148}^{–}^{150}^{52}^{,}^{72}^{151}^{,}^{152}^{33}^{83}^{23}^{91}^{152}

It should be noted that a majority of reported SMCs are operating at communication bands. However, there are still great challenges for the generation of visible and mid-infrared SMCs, which would enable broad applications in molecular spectroscopy and chemical/biological sensing. The bandwidth of visible SMC^{28}^{153}^{,}^{154}^{155}^{–}^{158}

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