2.2.1.

Coupled mode equations

The equilibrium of pumping and dissipation, intracavity dispersion, and nonlinearity realize a microcavity’s optical frequency comb generation. Chembo and Yu proposed a method based on CMEs^[111] to describe the complex evolution of comb modes in a cavity. In the coupled mode equations, each mode is treated as an individual electromagnetic field component, and all the comb teeth interact with each other through Kerr nonlinear effects such as four-wave mixing.

Modeling spatiotemporal systems usually requires a set of partial differential equations describing the evolution of every spatial point. Although this method can precisely calculate the field within the volume of interest, solving complex mathematical models is quite time-consuming. The modal expansion methods in CMEs rely on the fact that the spatial mode distributions are already known. Here, we considered a series of optical cavity modes. Based on the classical wave equation^[118]

We can expand the electromagnetic field with the eigenmodes as

Then, we can rewrite the equation as

This equation clearly describes the basic intercoupling relationship of the comb modes that can be used for steady-state analysis. For instance, parametric oscillation occurs proficiently once nonlinear gain surpasses mode intrinsic loss. Using the coupled mode equation, the pump threshold power $P_{\mathrm{th}}$ for the first pair of sideband generation can be theoretically deduced as

A complete set of coupled mode equations can describe the dynamic process of a Kerr microcomb, including cascaded FWM to wideband frequency combs. However, when a large number of modes are considered, the computational cost of the model increases sharply (proportional to the cubic of exciting modes). More importantly, the model makes it difficult to describe the pulse evolution in the time domain, which is significant in studying Kerr optical frequency combs.

2.2.2.

Ikeda map

Different from the coupled mode equation, where the evolution of each comb line component is described with an equation, the Ikeda map gives a general description of the whole microcomb in the time domain with the nonlinear Schrödinger equation (NLSE) and boundary conditions. The evolution of a microcomb in the microcavity can be divided by the roundtrip. The intracavity field starts from the coupled points and goes around the cavity for each roundtrip. The propagation process can be described with the nonlinear Schrödinger equation (NLSE)^[91] as

2.2.3.

LLE

Based on the Ikeda map, it is convenient to derive the LLE^[10]. Under a mean-field approximation, the optical field at the end of a roundtrip can be expressed as

Submitting Eq. (12) into (11), we can get

Finally, a slow time variable $t$ is introduced based on the transition of

With the transition, the discreated roundtrip propagation process can be generated into a single deviation equation with the approximation of $[\partial E(t=m{t}_R,\tau )/t]=[E_{m+1}(z=0,\tau )-E_m(z=0,\tau )]/t_R$:

Fig. 4

Numerical simulation of the microcomb evolution. (a) The evolution process of intracavity optical spectra (top), pulse shapes (middle), and total powers (bottom). (b) Optical spectra under different states marked in (a). (c) Pulse shapes under different states marked in (a).

Compared with the experimental results, the LLE comprehensively and precisely describes the evolution process of the microcomb in the time-frequency domain and has become the most commonly used equation in the study of microcavity nonlinear optics. The LLE can be solved by the split-step Fourier algorithm considering the periodic boundary conditions of microresonators, and other numerical solving methods like the Newton–Raphson solver^[121]. Additionally, for different platforms, various modified equations have been introduced to incorporate additional physical mechanisms, such as higher-order dispersion^[73], the thermal effect^[122], the Raman effect^[31], and the free carrier effect^[123]. These modifications further refine the accuracy of the simulations. By establishing explicit spatiotemporal models, researchers can gain deeper insight into the dynamic processes underlying microcomb generation, leading to a better understanding of this complex phenomenon.

2.3.1.

Frequency sweeping and optimized pumping

The response of the Kerr nonlinear effects can be considered to be approximately instantaneous. At the same time, the thermal effect is a relatively slow process, generally on the order of microseconds. The thermal-relaxation-induced transient instability is highly related to the detuning speed and the pump power. In the early research, the researchers mainly focused on optimizing the frequency sweeping strategies and pumping conditions for deterministically reaching mode-locked states with the thermal effect^[11], as shown in Fig. 5. The most straightforward method is the rapid sweeping, where the generation of soliton states is much faster than that of the thermal response. To reach a fast sweeping, researchers propose the pump frequency sweeping based on a single-sideband modulator (SSBM)^[126,127], as shown in Fig. 5(a). By sweeping the applied frequency on the SSBM, the generated sideband features ultrafast sweeping speed, even larger than 400 GHz/μs. It is worth noting that a fast-sweeping process results in short time windows where the soliton states exist. Thus, an optimal sweeping speed is required for the stable and easy access of the soliton states. As the detuning between the pump frequency and the resonant frequency is critical instead of the pump frequency, it is equivalent to tuning the resonant frequency. As depicted in Fig. 5(b), resistive heaters can be deposited above the microcavity to tune the resonance. By optimizing the applied voltage on the microheater, a soliton state can be generated^[137].

Fig. 5

Methods of frequency sweeping and pumping optimization. (a) Fast frequency scanning method^[127,137]. (b) Thermal tuning of the resonant frequency^[137]. (c) Power kicking method^[124,143]. (d) Bi-directional scanning method^[122].

Except for the tuning of the detuning, it is feasible to access the mode-locked state with the tuning of pump power, known as the power kicking process^[124]. Firstly, the pump sweeps into the resonance at a high power level. Due to the thermal effect, the system does not reach the soliton state at this detuning, while the soliton state exists with a lower pump power. Thus, the soliton state can be generated by abruptly decreasing the pump power. Meanwhile, the soliton existence range is relatively short at a low pump power. To increase the stability, the pump power abruptly increases again without losing the soliton state. The core of the power kicking process is the pump power tuning, which can be realized with an acoustic-optical modulator. In addition, the power kicking process can be combined with the rapid frequency tuning process^[143], as depicted in the lower panel of Fig. 5(c).

For the previous process, it is hard to determine the reached soliton state. In a pure anomalous dispersion cavity, the existence ranges of different soliton states overlap with each other, and the transition from a chaotic state leads to the uncertain reach of these soliton states^[11]. Meanwhile, in most cases, the single-soliton state is the required state. A backward sweeping method is proposed to solve this problem with the assistance of the thermal-optical effect^[122]. Considering the thermal effect, the existence range of a high-order soliton redshifts due to high state power. Thus, the steps of different soliton states do not overlap anymore at the blue (high-frequency or small wavelength) side. As illustrated in Fig. 5(d), the soliton order gradually decreases with a backward sweeping process and eventually reaches the single-soliton state.

Despite the stable access of soliton states, the above schemes require complex tuning processes and equipment, which is difficult to integrate with miniaturized microcomb systems.

2.3.2.

Pulse pumping

The continuous wave (CW)-laser-driven DKSs in microresonators face several challenges related to conversion efficiency and the pump power thresholds, which limit their practical applications. The low conversion efficiency results from the small temporal overlap between the driving CW background and the ultrashort bright soliton pulse. For microcomb generation in a pulsed driving scheme^[129–131], a periodic driving pulse train replaces the CW laser, as illustrated in Fig. 6. The resonantly enhanced pulse supports a co-propagating soliton pulse, reducing the required driving power and the absorptive thermal effect. The pulse pumping configuration provides merits of reduction of pump power and improvement in efficiency, as well as deterministic and controlled generation of stable single or multiple DKSs. Also, the repetition rate and the CEO frequency of the generated microcomb are determined by the driving pulse, which reduces the timing jitter. However, the pulse repetition rate and the carrier-envelope frequency of the driving pulse train must match the resonance frequency to achieve coherent build-up. This intricate tuning process and the complex pulse pump conditions make the setup challenging, which hinders its broader application.

Fig. 6

Principle and experimental scheme of pulse pump method. (a) Concept and comparison of the pulse pumping with traditional methods^[129]. (b) Experimental setup, simulation results, and experimental results of pulse pumping microcombs^[129].

2.3.3.

Auxiliary laser cooling

Another stable arrival scheme for mode-locked microcombs is based on the idea of balancing the total intracavity power with an auxiliary laser, as shown in Fig. 7. According to different detailed mechanisms, different schemes such as “auxiliary mode”^[144], “auxiliary light”^[132,135], and “auxiliary sideband”^[134] are proposed. In this scheme, in addition to the pump laser, an auxiliary laser is required. During the tuning process, the auxiliary laser is first fixed on the blue detuning side of a resonant peak, and then the pump laser is scanned into the resonance^[135]. When the microcomb state supported by the pump laser is switched from a non-mode-locked state to a mode-locked state through scanning, the pump power in the cavity drops sharply, as mentioned above. The resonant peak near the auxiliary laser will blueshift as the pump power decreases. Thus, the auxiliary laser power in the cavity will increase to compensate for the total intracavity power change. By carefully setting the power and frequency of the auxiliary laser, simple mode-locked microcomb excitation can be achieved under a slow frequency sweeping process. In addition, the length of the soliton step will be significantly extended due to the cross-phase modulation effect of the auxiliary laser on the pump field^[133]. Recent studies have also revealed that the cavity with the auxiliary laser will exhibit an equivalent negative thermo-optical coefficient^[132], and direct mode-locked microcomb excitation can be achieved with a backward tuning process^[136]. However, owing to the use of the auxiliary laser, this method has disadvantages in terms of device cost and overall system size.

Fig. 7

Auxiliary laser cooling for soliton generation. (a) Concept and principle of the auxiliary cooling methods. (b) Experimental setup and simulation results of auxiliary laser thermal balance^[132,135].

2.3.4.

Self-injection locking

In recent years, researchers have demonstrated turnkey microcomb excitation^[77] based on the self-injection locking effect^[145] by directly butt-coupling a semiconductor laser to a microresonator^[138], as depicted in Fig. 8(a). Traditionally, since the laser is sensitive to reflections, an optical isolator needs to be placed after the output of the laser. In the self-injection locking scheme, narrow-band reflections from high-quality-factor microcavities are utilized^[139] without the optical isolator. As the laser is directly connected with the high-quality-factor microcavity, the narrow-band reflection from the microcavity will lock the output frequency of the laser to the resonant peak of the microcavity, suppressing the frequency jitter of the laser. When the power and detuning of the laser are suitable, the mode-locked microcombs will be directly excited through the locking process. Firstly, this scheme is demonstrated based on the direct coupling between a laser diode and a bulk cavity, as depicted in Fig. 8(b). This locking process provides an integrated scheme for high-coherence optical sources, with integrated laser diodes and microcavities^[138], as shown in Fig. 8(c). Utilizing this scheme, single-chip and high-coherence mode-locked integrated microcombs can be realized with anomalous dispersion^[138] [see Fig. 8(d)] and normal dispersion^[140] [see Fig. 8(e)]. The basis of self-injection locking is the reflection or backscattering from a high-quality-factor microcavity. As shown in Fig. 8(f), the generated microcomb exhibits much better coherence compared with the free-running laser diode. The commonly used backscattering source is Rayleigh scattering^[139] in a high-quality-factor microcavity, which relies on random fabrication roughness and defects. The randomness can be solved by introducing controllable reflection structures^[142]. Although the turnkey operation and the integration are attractive, the spectral bandwidth is limited by the available pump power of integrated lasers. In addition, the generation relies on the preset of the system parameters, such as the feedback phase from the microcavity to the laser cavity. The sensitivity of the feedback phase raises concerns about the robustness of this scheme for real-world applications.

Fig. 8

Illustration of self-injection microcombs. (a) Concept and principle of self-injection locking and turnkey operation^[77]. (b) Self-injection locking of a laser diode to a bulk cavity for microcomb generation^[145]. (c) Self-injection locking of a laser diode chip to an integrated SiN microcavity chip for microcomb generation^[138]. (d) Bright soliton generated by self-injection locking^[86]. (e) The dark pulse is generated by self-injection locking^[140]. (f) Suppressed frequency noise^[140].

3.1.1.

Metal fluoride

Metal fluoride crystal materials are highly suited for optical microcavity nonlinearities due to their broad transparent window, low optical absorption loss, minimal dispersion, and excellent thermal and mechanical stability. For example, ${\mathrm{MgF}}_2$ offers a wide transparent window ranging from ultraviolet (0.16 µm) to mid-infrared (7 µm), enabling the realization of high-quality factors ($\mathit{Q}>{10}^8$) over a broad spectral range. This, combined with weak dispersion, makes ${\mathrm{MgF}}_2$ ideal for multiband applications, such as octave-spanning tunable OPO^[151], nonlinear oscillation in visible bands^[172], and mid-infrared microcombs^[147]. High-quality ${\mathrm{MgF}}_2$ microresonators, as shown in Fig. 10(a), also exhibit low-thermal-refractive-index constants, exceptional mechanical stability, and hardness^[173], all critical factors for creating stable microcomb systems. As shown in Fig. 10(d), with precise cavity design and system optimization, low-phase-noise Kerr combs can be generated. Notably, a micro-sized 10 GHz RF photonic oscillator^[44] has been demonstrated, which exhibits frequency stability (as measured by Allan deviation) several orders of magnitude higher than existing RF photonic devices with similar size, weight, and power consumption. In addition to ${\mathrm{MgF}}_2$, ${\mathrm{CaF}}_2$ also has a broad transparent window (0.13–10 µm) and was among the first platforms used for microcomb generation^[148]. ${\mathrm{CaF}}_2$ cavities, as shown in Fig. 10(b), have achieved a quality factor exceeding $2.5\times {10}^9$ and can generate microcombs of over 80 nm span with an input pump power of 50 mW. Similar ultrahigh-Q factors [above ${10}^9$, see Fig. 10(c)] have also been achieved based on ${\mathrm{BaF}}_2$^[149] and ${\mathrm{SrF}}_2$^[150].

Fig. 10

Metal fluoride microcavities. (a) ${\mathrm{MgF}}_2$^[147]. (b) ${\mathrm{CaF}}_2$^[171]. (c) Q factor measurement of the ${\mathrm{BaF}}_2$ cavity^[149]. (d) Generated bright soliton microcomb in a ${\mathrm{MgF}}_2$ cavity^[44].

While metal fluorides have significantly advanced the development of ultrahigh-Q microcavities, integrating these materials into chip-based platforms remains a challenge. Most demonstrated systems use bulk cavities, which require specialized and costly fabrication techniques, such as polishing and crystalline growth, making on-chip integration difficult. Nonetheless, their superior optical properties continue to drive innovation in high-Q resonators.

3.1.2.

Silica

Since the early days of optics through to modern optical technologies, particularly fiber-based technologies, silicon dioxide (or silica) has played a pivotal role across all eras and applications. As shown in Table 3, despite its relatively low optical nonlinear coefficient^[177], silica enables nonlinear interactions at pump powers in the microwatt range with easily achieved quality factors exceeding ${10}^8$^{[70,135,174,176,177]}. Since the first demonstration in 2007 of silica platforms generating microcombs with over 100 GHz repetition rates and wide spectral spans^[70], as shown in Fig. 11(d), various microcavities have been employed for microcomb generation. Due to the ease of fabrication through the melting and solidification of silica, bulky microcavities such as microspheres^[175] and microrod cavities^[176] have been well-developed, as depicted in Figs. 11(b) and 11(c). A microrod cavity with an ultrahigh quality factor above $4\times {10}^9$ has been fabricated by irradiating silica microrods with ${\mathrm{CO}}_2$ lasers, significantly decreasing the OPO threshold power to 110 µW^[176].

Fig. 11

Silica microcavities. (a) Silica toroid microcavity^[82]. (b) Wideband microcomb generated in silica microcavity^[70]. (c) Bright soliton microcomb generated in silica microcavity^[174]. (d) Silica microsphere cavity^[175]. (e) Silica microrod cavity^[176]. (f) Silica wedge microresonator^[177].

Beyond bulk microcavities, several on-chip microcavities, such as silica wedge microresonators^[177] [shown in Fig. 11(f)] and microtoroids^[82] [shown in Fig. 11(a)], have been developed to expand applications and improve performance. In 2012, fabrication methods of silica wedge resonators compatible with traditional semiconductor processing processes were proposed^[177], with excellent control over the microcavity FSR and a record high Q of up to $8.75\times {10}^8$. These silica-based wedge resonators show constant finesse over a wide range of diameters, supporting microcomb generation with the comb line spacing ranging from 2.6 to 220 GHz^[42,178]. With delicate design and fabrication of the wedge shape, broadband dispersion tuning can be realized^[179]. In addition, integrating high-Q silica microcavities with deposited ${\mathrm{Si}}_3{\mathrm{N}}_4$ bus waveguides on a single chip offers an alternative to traditional bulky prism or fiber coupling methods^[180].

3.1.3.

Hydex

High-index-doped silica glass (Hydex) was developed as a CMOS-compatible optical platform and has been used for linear optics since the early 2000s^[181] and for nonlinear optics since 2008. The low optical loss, typically less than 0.1 dB/m, and negligible nonlinear loss, especially under high-intensity conditions ($>25\mathrm{GW}/{\mathrm{cm}}^2$)^[182], make it attractive for microcomb generation. In addition, Hydex benefits from a mature fabrication process, including low-stress deposition, which facilitates the production of high-quality waveguides and resonators, as depicted in Fig. 12. Although its refractive index is low, the core-cladding contrast remains sufficient to allow for a minimum bending radius of 20 µm. Its Kerr coefficient^[183] of $1.15\times {10}^{19}{\mathrm{m}}^2{\mathrm{W}}^{-1}$ is approximately five times that of silica. The Hydex platform holds the potential for achieving more integrated and flexible applications of soliton microcombs. For example, in 2010, optical “superparameter” oscillation was achieved on the Hydex platform with a quality factor of $1.2\times {10}^6$, where the continuous wave threshold power was as low as 54 mW, and the frequency interval range was tunable from 200 GHz to over 6 THz^[158]. Soliton microcomb generation has been demonstrated in various regimes, including single-soliton, soliton crystal^[184], and laser soliton states^[76], highlighting the platform’s flexibility and robustness in supporting diverse comb dynamics.

Fig. 12

Hydex microcavity^[15].

Fig. 13

Silicon nitride microcavity. (a) Massively produced silicon nitride chips^[87,140]. (b) Thin silicon nitride microcavity^[140]. (c) Thick silicon nitride microcavity^[185].

3.1.4.

Silicon nitride

Silicon nitride (SiN) is an exceptional platform for microcomb generation due to its low optical loss, wide transparency window, and favorable nonlinear properties^[183]. SiN waveguides can achieve ultra-low propagation losses, often below 0.1 dB/m, which is crucial for supporting high-Q resonators. These high-Q resonators enable efficient light confinement, facilitating the strong nonlinear interactions necessary for generating stable and coherent frequency combs. SiN also offers a broad transparency window, spanning from the visible ($\sim 400\mathrm{nm}$) to the near-infrared ($\sim 4.6\mathrm{\mu m}$), making it versatile for applications in telecommunications, spectroscopy, and optical clocks. This broad transparency allows SiN to be used for frequency combs across multiple spectral bands, including the visible^[186] and telecom regions^[87]. SiN exhibits a relatively high Kerr nonlinear coefficient, which enhances four-wave mixing, the key mechanism for microcomb generation. The strong nonlinear response of SiN enables comb generation at relatively low power levels, further enhancing its suitability for compact and energy-efficient photonic devices.

Nowadays, silicon nitride has emerged as a leading platform for microcomb generation, mainly due to the ultrahigh quality factors^[83,85], even close to the material limitation, with the standard planar fabrication process. As illustrated in Fig. 13, there are two common types of integrated silicon nitride (SiN) platforms: thick and thin^[140] SiN platforms. The first is the thick silicon nitride platform, where the waveguide thickness needs to exceed 600 nm to achieve anomalous dispersion in the telecommunication band^[185], which is essential for generating bright soliton microcombs. However, during the fabrication of thick SiN films, stress accumulation at high temperatures often leads to film cracking. This issue can be addressed using the Damascene process^[83] or a multiple-deposition process^[187]. Both methods have successfully produced integrated microring resonators with quality factors higher than ${10}^7$. The second platform is the thin silicon nitride platform, with a typical waveguide thickness around 100 nm^[85]. By reducing the thickness, a more significant portion of the optical field is distributed into the silica cladding, which helps minimize the interaction between the optical field and the etched sidewalls, reducing scattering losses. This design has enabled the fabrication of integrated optical microcavities with quality factors^[140] as high as ${10}^8$. The high quality factor achievable on both platforms has empowered researchers to explore various nonlinear optical phenomena and integrated microcavity optical comb technologies. These include photo-induced second-order nonlinear effects^[188,189], highly coherent light sources based on self-injection locking^[140], optical isolators using nonlinear phase shifts^[190], and the experimental observation of mode-locked microcombs^[11,72].

Although the silicon nitride (SiN) platform has achieved significant success and facilitated the study of various physical phenomena, the demanding fabrication conditions required for low-loss SiN waveguides limit its broader adoption. To achieve dense, high-quality SiN films with near-stoichiometric ratios, low-pressure chemical vapor deposition (LPCVD) is typically necessary. Additionally, the silica cladding surrounding the waveguides also requires LPCVD deposition^[85]. High-temperature annealing of the entire structure is essential to reduce hydrogens (mainly Si—H and N—H bonds) within the material and eliminate residues from the fabrication process, further lowering optical losses. However, these high-temperature fabrication conditions not only complicate the manufacturing process but also impose limitations on the integration of SiN with other material platforms. While plasma-enhanced chemical vapor deposition (PECVD) offers a faster and more cost-effective method for SiN film deposition^[191,192], it introduces higher intrinsic losses, primarily due to hydrogens formed during the deposition process. Efforts to reduce these losses have led to the development of post-deposition annealing techniques to minimize hydrogens. More recently, deposition methods such as using deuterated silane (${\mathrm{SiD}}_4$) instead of silane (${\mathrm{SiH}}_4$) have been proposed to avoid hydrogen-related absorption in telecommunication bands^[193,194]. As a result, SiN fabrication is gradually shifting towards lower-temperature processes.

In the future, advancements in low-temperature deposition techniques for low-loss SiN waveguides, particularly those compatible with multiple material platforms, could pave the way for integrated, multifunctional systems based on microcombs. These improvements will expand the potential applications of SiN, enabling broader use in fields such as telecommunications, sensing, and quantum photonics.

3.1.5.

Chalcogenides

With the great success of microcombs in the communication band, the extension into long wavelengths, such as the MIR^[147] bands, pushed the development of various platforms. Inspired by the chalcogenide glass fiber, integrated chalcogenide platforms are developed due to their high nonlinear optical properties and broad transparency window, particularly in the mid-infrared range^[22]. Chalcogenide glasses, composed of elements like sulfur, selenium, and tellurium, exhibit a much higher Kerr nonlinearity (${\chi }^3$) than silicon-based materials, which significantly enhances nonlinear effects for microcomb generation. This allows for efficient comb generation at lower power levels, making it ideal for power-sensitive and compact applications. One of the significant advantages of chalcogenide materials is their broad transparency range, which spans from the visible ($\sim 1\mathrm{\mu m}$) to the mid-infrared ($\sim 12\mathrm{\mu m}$). This makes chalcogenide platforms particularly attractive for mid-infrared frequency comb generation, opening opportunities in fields like spectroscopy, environmental sensing, and chemical detection, where molecular absorption lines lie within the mid-IR spectrum. Chalcogenide waveguides can be fabricated with high-refractive-index contrast, enabling strong confinement of light and boosting nonlinear interactions. In addition, the easy fabrication process enables the integration with other integrated platforms, such as silicon^[196] and silica^[195], as depicted in Figs. 14(b) and 14(c). With the tuning of the material composition, mode-locked microcombs are observed in integrated chalcogenide microrings in telecom bands, under both anomalous and normal dispersion conditions^[170].

Fig. 14

Chalcogenide platforms. (a) Integrated chalcogenide microcavity^[170]. (b) Chalcogenide on silica^[195]. (c) Chalcogenide on silicon photonics^[196].

However, chalcogenide glasses face challenges such as higher optical losses compared to more mature platforms like silicon nitride, as well as susceptibility to environmental degradation like oxidation and moisture sensitivity. These factors can impact device longevity and performance, particularly in harsh operating environments. Nevertheless, with ongoing advances in fabrication techniques and protective coatings, the chalcogenide platform shows excellent potential for future microcomb applications, particularly in the mid-IR region, where other material platforms face absorption limitations.

3.1.6.

Group IV semiconductors

With the development of electric chips, the silicon (Si) crystal is the purest crystal in the world. Thanks to the compatibility with the electrical chip fabrication process, namely, the CMOS compatibility, silicon photonics has been one of the most essential integrated photonic platforms. Silicon-on-isolator (SOI) structure is commonly used for silicon photonics^[198], where a top thin silicon layer is embedded on an oxide layer on the silicon substrate and another oxide layer deposited on the patterned structure. With the fabrication and design advancements, the quality factors above ${10}^7$ are available from silicon photonics foundries^[199]. Despite the transparent window from 1.2 to 8 µm limiting its application for short wavelength bands and communication bands (1310 and 1550 nm) due to severe linear or nonlinear losses, the high Kerr nonlinear coefficient makes it a promising platform for microcomb generation in the mid-infrared^[160,200]. Microcomb generation has been demonstrated with the nonlinear absorption weakened with a reverse-bias PIN structure to shorten the free carrier lifetime^[123], as illustrated in Figs. 15(a) and 15(b). For the extension to a more extended wavelength band, the absorption of silica should be considered. Suspended silicon waveguides with the surrounding silica being removed are proposed for MIR range applications^[201].

Fig. 15

Group IV semiconductor microcavities. (a) Silicon microring with PIN junction^[160]. (b) Mode-locked microcomb in silicon microrings^[123]. (c) High-quality germanium microcavity^[165]. (d) High-quality SiGe microring cavity^[197].

Similar to silicon, other group IV semiconductors^[202], including the germanium (Ge)^[165,166] [see Fig. 15(c)] and the silicon-germanium alloy (SiGe)^[203,204], feature high Kerr nonlinear coefficients, suitable for nonlinear effects in the MIR band. Considering the absorption of silica, air cladding is preferred for low losses. Recently, as shown in Fig. 15(d), the ultrahigh Q of a $1.71\times {10}^8$ integrated platform consists of the SiGe core, and the Si cladding is proposed^[197], bringing novel integrated platforms for MIR nonlinear effects.

3.1.7.

III–V compound semiconductors

The III–V semiconductor platforms, encompassing materials like gallium phosphide (GaP), aluminum gallium arsenide (AlGaAs), aluminum nitride (AlN), and gallium nitride (GaN), offer substantial promise for microcomb generation due to their high nonlinear optical coefficients and expansive transparency windows, along with strong second-order nonlinearity for self-referenced microcombs^[206]. These materials have distinct advantages that make them suitable for different spectral ranges and applications, particularly in the visible, near-infrared, and mid-infrared regions.

AlGaAs is a standout material for microcomb generation, particularly in the near-infrared range with the tuning of the material composition^[21]. It exhibits exceptionally high Kerr nonlinearity, two orders higher than that of silicon nitride, enabling efficient four-wave mixing for comb generation with ultra-low powers under moderate quality factors^[205]. Advanced fabrication processes, including the annealing process, the deposition of ${\mathrm{Al}}_2{\mathrm{O}}_3$ to reduce surface states, and integrated AlGaAs microrings with quality factors above $3\times {10}^6$, have been demonstrated^[169,205]. Combining the high quality factor and the high Kerr coefficient, the OPO threshold down to 36 µW and mode-locked microcomb generation with 930 µW pump power are demonstrated^[157].

GaP is another promising material with high Kerr nonlinearity for low threshold power and a high index for tight light confinement, similar to AlGaAs. The cutoff wavelength of GaP is shorter, with the transparent windows ranging from 0.54 to 10.5 µm, enabling the nonlinear effects from the visible bands. GaP does not suffer from nonlinear absorption loss in communication bands, making it efficient for microcomb generation.

AlN and GaN, known for their wide bandgaps, high thermal conductivity, and mechanical robustness, are excellent candidates for ultraviolet to near-infrared applications. AlN offers strong nonlinear properties like silicon nitride while being transparent over a broader spectrum from the UV to the infrared. GaN, similarly, is transparent across a wide range and has a relatively higher Kerr coefficient^[168]. In addition, the second-order nonlinearity of both materials makes it possible to realize microcomb generation and second-harmonic generation for a self-referenced frequency comb^[206]. For example, the cofunction of Kerr nonlinearity and second-order nonlinearity can excite microcombs at the telecom band and the visible band simultaneously^[115], as depicted in Fig. 16(e).

Fig. 16

III–V compound semiconductor platforms. (a) AlGaAsOI microcavities^[21,205]. (b) GaP microcavity. (c) AlN microcavity. (d) GaN microcavity^[168]. (e) Comb generation with the second-order nonlinearity in AlN^[115].

Despite their advantages, III–V semiconductors face challenges in complex fabrication processes, such as epitaxial growth and higher production costs than silicon-based platforms. However, their unique combination of strong nonlinearities, expansive transparency windows, and potential for integration with active devices like lasers and modulators makes them highly promising for advanced microcomb generation in diverse fields.

3.1.8.

Electro-optical crystal

Compared to silicon nitride (SiN), lithium niobate [${\mathrm{LiNbO}}_3$, as depicted in Fig. 17(a)] offers similar optical properties, such as refractive index, Kerr nonlinear coefficient, and a broad transparent window suitable for Kerr microcomb generation. However, ${\mathrm{LiNbO}}_3$ stands out due to its strong second-order nonlinearity, resulting from its non-centrosymmetric crystal structure^[23]. This feature allows for simultaneous microcomb generation and second-harmonic generation on a single chip, as depicted in Fig. 17(d). It is ideal for self-referenced microcombs—critical for producing stabilized optical frequency combs. Additionally, ${\mathrm{LiNbO}}_3$ has a high electro-optic coefficient, which facilitates efficient interactions between optical and radio-frequency fields, as illustrated in Fig. 17(b). By applying a radio-frequency field with a frequency close to the FSR of the microcavity, the repetition rate of the generated microcomb can be locked, leveraging the interaction with the background fields^[207]. This provides precise control over the comb generation process. Moreover, the photorefractive effect of ${\mathrm{LiNbO}}_3$ enables easier access to the bright soliton state, as depicted in Fig. 17(c). Unlike other platforms that require forward tuning, the bright soliton state in ${\text{LiNbO}}_3$ can be reached through a backward tuning process, simplifying the transition to this stable operational regime^[104].

Fig. 17

Electro-optical crystal platforms. (a) ${\text{LiNbO}}_3$ microcavities^[23]. (b) ${\text{LiNbO}}_3$ microcavity with electrodes (top) and the tuned repetition rate of the generated microcomb with the applied microwave field (bottom) ^[207]. (c) Self-starting solitons in ${\text{LiNbO}}_3$ microcavities^[104]. (d) Visible comb generation in ${\text{LiNbO}}_3$ microcavities with the second-order nonlinearity^[104]. (e) ${\text{LiTaO}}_3$ microcavities^[88]. (f) Comparison of the dispersion profiles of ${\text{LiNbO}}_3$ (right) and ${\text{LiTaO}}_3$ (left) microcavities^[88].

However, one drawback of ${\mathrm{LiNbO}}_3$ of x-cut films, commonly used for electro-optic modulation, is its anisotropy. This anisotropy degenerates fabrication and induces inter-mode coupling, which can hinder microcomb generation. Recently, lithium tantalate^[88] [${\mathrm{LiTaO}}_3$, as shown in Fig. 17(e)], another electro-optic crystal with similar performance but weaker anisotropy, has been developed. As shown in the measured dispersion profiles in Fig. 17(f), the ${\mathrm{LiTaO}}_3$ microcavity exhibits a smooth dispersion profile, indicating weak inter-mode coupling. With intrinsic quality factors up to ${10}^7$, soliton microcomb generation has already been demonstrated in ${\mathrm{LiTaO}}_3$, positioning it as a promising alternative to ${\mathrm{LiNbO}}_3$ for specific applications.

3.1.9.

Other platforms

Except for the aforementioned material, other platforms, especially integrated platforms are also developed for different applications, such as diamond^[19], SiC^[25], and ${\mathrm{Ta}}_2{\mathrm{O}}_5$^[155].

Diamond was first proposed as a platform for OPO oscillation comb generation in 2014^[19]. It has a relatively high refractive index (2.38) and an ultra-wide transparent window (0.22–50 µm). Diamond exhibits a significant Kerr nonlinearity ($0.8\times {10}^{-19}{\mathrm{m}}^2{\mathrm{W}}^{-1}$) in the communication band, and its large bandgap of 5.5 eV ensures immunity from TPA not only in the near-infrared but also in the visible range^[208]. Its high thermal conductivity and low thermo-optic coefficient provide high-power handling capabilities, resulting in temperature stability of microcombs across a wide wavelength range. Diamond offers unique opportunities to integrate nonlinear photonics with quantum optics, potentially merging quantum information science^[209,210] with classical optical information processing on a single chip.

Similar to diamond, silicon carbide (SiC) has garnered significant attention due to its excellent material properties for quantum information science^[211]. Recent reports have demonstrated that 4H-silicon-carbide-on-insulator (4H-SiCOI) can achieve a quality factor Q^[154] as high as $6.75\times {10}^6$, and a mode-locked microcomb generation has been reported. The formation process of microcombs was observed in the quantum aspect of this platform^[79].

Recently, CMOS-compatible materials have been well-developed for microcomb generation, except for silicon and silicon nitride. One of the most successful integrated platforms is tantalum pentoxide^[155] (${\mathrm{Ta}}_2{\mathrm{O}}_5$). It exhibits low intrinsic material stress, low optical loss, and effective Kerr nonlinearity^[155]. It has achieved quality factors as high as $3.8\times {10}^6$ and residual tensile stress of only 38 MPa. Due to its low-temperature deposition and processing requirements, ${\mathrm{Ta}}_2{\mathrm{O}}_5$ offers extensive opportunities for low-loss nonlinear photonics and heterogeneous integration.

3.2.1.

Cutting and polishing

Since the inception of microcavity-based research, crystalline microcavities^[218,219] have been pivotal due to their ultrahigh quality factors^[212] (Q factors) and broad transparent windows, as discussed earlier. The initial step in the fabrication process involves cutting the bulk crystal into rough shapes^[215], as illustrated in Fig. 18(a), a procedure that must be performed with high precision to avoid introducing defects. This is typically done using diamond tools^[216] [see Fig. 18(b)] or other high-precision cutting tools, which allow for clean and controlled cuts. Following this, the crystals undergo a meticulous polishing phase, which is crucial for achieving the atomic-level smoothness required for high-Q microcavities^[217], as depicted in Fig. 18(c). This process can involve a combination of mechanical and chemical polishing techniques. Mechanical polishing uses abrasives to progressively refine the surface, while chemical polishing may involve etching agents that help remove any residual surface imperfections. To further enhance surface quality, thermal annealing^[212] can be employed. This technique involves heating the polished microcavity to relieve internal stresses and further smooth out any microscopic imperfections that might remain, ensuring that the surface is ideally suited for optical applications.

Fig. 18

Fabrication process of crystalline microcavities. (a) Cutting and shaping process^[215]. (b) The photo of a diamond tool^[216]. (c) Polishing with abrasive particles^[217].

Overall, the fabrication of crystalline microcavities requires a high degree of precision and control at every stage^[173]. Each step—from material selection and cutting to polishing, shaping, and coupling—plays a significant role in determining the final performance of the microcavity^[173,215].

3.2.2.

Melting and solidification

Different from crystalline materials, where the fabrication process involves precise and complex mechanical processes, the fabrication of amorphous microcavities is relatively handy with the melting and solidification process, usually realized with high-power lasers^[220]. A typical one is silica. In the following, the fabrication processes of two typical microcavities, the microsphere^[221] and the microtoroid^[70] cavities, are introduced.

1) Fabrication process of microsphere cavity

Microsphere cavities are among the simplest yet most effective types of high-Q resonators^[221]. These spherical structures are usually fabricated from glass materials such as silica (${\mathrm{SiO}}_2$) due to their low optical absorption and high transparency over a broad wavelength range. The primary method for creating microsphere cavities involves a melting and solidification process, which is relatively straightforward but highly effective in yielding ultra-smooth surfaces, as illustrated in Fig. 19(a).

Fig. 19

Melting and solidification processes. (a) The fabrication process of microtoroid cavity^[82]. (b) Preparation process of microsphere cavities^[222].

Fig. 20

Fabrication processes of thick silicon nitride microcavities. (a) The subtractive process^[187]. (b) The Damascene process^[214].

The fabrication process begins with a small glass fiber, typically silica, which is heated using a focused ${\mathrm{CO}}_2$ laser beam. This laser precisely melts the tip of the fiber, causing it to form a spherical shape through surface tension as the glass reflows. The melting process can also be realized with a microheater^[222] or arc discharge of a fiber fusion splicer^[223]. The molten glass naturally minimizes surface imperfections, resulting in an exceptionally smooth surface critical for high-Q operation. As the melted glass cools and solidifies, a nearly perfect spherical shape is achieved with minimal optical scattering losses. This process ensures high precision and repeatability in forming microspheres with diameters ranging from a few microns to several hundred microns.

One key advantage of microsphere cavities is the absence of complex lithography or etching steps, making them a cost-effective option for generating high-Q resonators. The smooth surface achieved through the melting process ensures minimal optical losses, which is crucial for applications requiring high light confinement. However, controlling the exact size and shape of the microsphere can be challenging, and additional care must be taken during the heating and reflow process to avoid asymmetries.

2) Fabrication process of microtoroid cavity

Microtoroid cavities^[82], on the other hand, represent a more sophisticated type of resonator that combines high-Q performance with a compact and planar form factor, making them more suitable for integration into photonic circuits. The fabrication of microtoroid cavities typically follows a multistep process that involves lithography, etching, and laser reflow techniques^[213], as shown in Fig. 19(b).

The fabrication process of microtoroid cavities begins with a planar substrate, usually silicon coated with a thermally grown silica layer. The first step involves using standard photolithography to define the toroidal shape of the silica layer. A photoresist is applied and patterned using UV light to create a mask for the subsequent etching process. Once the pattern is transferred, reactive ion etching (RIE) is used to etch away the exposed silica, forming a cylindrical pedestal structure. The dimensions of the toroid are defined during this step, including the height and width of the resonator.

Following the etching process, a ${\mathrm{CO}}_2$ laser is used to selectively reflow the edges of the silica pedestal, converting the sharp, cylindrical profile into a smooth toroidal shape. The high heat from the ${\mathrm{CO}}_2$ laser locally melts the silica, and as with microspheres, surface tension helps smooth out any rough edges or imperfections. The reflow process is critical for achieving the ultra-smooth surfaces necessary for minimizing optical scattering losses. By controlling the laser power and duration, the size and quality of the microtoroid can be fine-tuned. The final structure resembles a doughnut-shaped ring, with light tightly confined around the central axis of the toroid.

Microtoroid cavities offer several advantages over microspheres, particularly in terms of integration with other photonic components. Their planar geometry allows them to be fabricated directly on-chip, making them ideal for applications that require compact, integrated photonic circuits. Additionally, the precise control over the resonator dimensions provided by the lithographic process enables the fabrication of microtoroids with highly uniform characteristics, which is beneficial for scaling up production^[224].

3.2.3.

Monolithic process

In integrated photonic platforms, it is often more practical to directly deposit the required material onto a substrate, a process known as monolithic integration. For the platforms mentioned earlier, materials such as silicon nitride^[87], Hydex^[183], silica^[82], chalcogenide^[22], and silicon^[16] can be directly deposited on silica, while materials like AlN^[18] and GaN^[168] can be deposited on sapphire. An example is the fabrication of thick silicon nitride^[225], where managing stress accumulation at high temperatures is a significant challenge. This issue can be addressed using the Damascene process^[83] or a multiple deposition process^[187].

1) The Damascene process

The Damascene process, initially developed for the microelectronics industry, has been adapted for high-Q photonic device fabrication. It involves patterning and filling trenches in a substrate with SiN, followed by a planarization step to achieve the desired waveguide and cavity structure, as shown in Fig. 20(a). This technique is especially well-suited for fabricating waveguides with minimal surface roughness and ultra-smooth sidewalls, which are crucial for reducing optical losses in microcavities.

The Damascene process begins with the deposition of a sacrificial layer, usually silicon dioxide (${\mathrm{SiO}}_2$), onto a substrate, typically silicon. Photolithography is then used to define the pattern of the waveguide or resonator in the ${\mathrm{SiO}}_2$ layer, which is subsequently etched to create trenches. The SiN material is deposited into these trenches via chemical vapor deposition (CVD). One of the key advantages of this process is that it allows for the deposition of thick SiN layers, which is important for avoiding issues related to thin-film cracking and stress during high-temperature processing. After the SiN is deposited into the trenches, the surface is polished using chemical mechanical polishing (CMP) to achieve a planar surface. This step is critical for removing excess SiN and ensuring that the surface of the waveguide or cavity is as smooth as possible. The planarization process helps to minimize surface roughness and defects, which are major sources of scattering loss in optical microcavities.

The Damascene process offers several advantages, including the ability to create thick waveguides with minimal stress, excellent control over geometry, and smooth sidewalls that are essential for maintaining low optical losses. The high degree of process control also allows for the fabrication of complex structures, such as microresonators and integrated photonic circuits. However, the process can be time-consuming and requires several fabrication steps, including the deposition, etching, and polishing of multiple layers.

2) The subtractive process

The subtractive process, in contrast, involves the deposition of a uniform SiN layer over the entire substrate, followed by patterning and etching to define the microcavity structure, as shown in Fig. 20(b). This method is simpler and more widely used than the Damascene process, particularly in research laboratories, due to its straightforward implementation and adaptability.

The subtractive process typically begins with the deposition of a SiN film on a silicon dioxide substrate. LPCVD is commonly used for this purpose, as it produces high-quality SiN films with low intrinsic losses. The thickness of the SiN layer is carefully controlled, as it plays a critical role in determining the optical confinement and the mode properties of the resulting microcavity. It is worth noting that for thick SiN layer deposition, two-step deposition is applied with crack barriers and a thermal cycling process to avoid the film cracking.

Once the SiN layer is deposited, photolithography is employed to define the desired pattern of the microcavity. The patterned photoresist serves as a mask for the subsequent etching step. Reactive ion etching (RIE) is then used to remove the excess SiN, leaving behind the microcavity structure. The quality of the sidewalls formed during the etching process is crucial for minimizing scattering losses. In some cases, additional surface treatment steps, such as thermal annealing, are used to further smooth the etched sidewalls and improve the optical performance of the cavity.

The subtractive process offers several advantages, including simplicity and scalability. It allows for the fabrication of a wide range of SiN-based photonic devices, including ring resonators, waveguides, and photonic crystal structures. Additionally, this process is well-suited for integration with other materials and components, making it a versatile option for creating complex photonic circuits. However, the subtractive process has some limitations, particularly in terms of sidewall roughness and material stress. Since the SiN layer is deposited as a continuous film before patterning, it can develop stress during deposition, which may lead to cracking or warping, especially for thicker films. Moreover, the etching process can introduce sidewall roughness, which increases optical scattering and degrades the Q factor of the microcavity.

3.2.4.

Bonding process

Due to lattice mismatch, it is often challenging to directly deposit high-quality films on substrates made of different materials. Bonding processes have been developed to overcome this issue in integrated devices. Among the integrated platforms that rely on bonding, LNOI^[23] and AlGaAsOI^[21,157,169] are two prominent examples. In this subsection, the fabrication process of AlGaAsOI serves as a representative case for understanding the role of bonding in creating high-performance photonic devices.

As shown in Fig. 21, the fabrication of AlGaAsOI microcavities^[21,157,169] begins with the preparation of high-quality AlGaAs epitaxial layers on a GaAs (gallium arsenide) substrate. These epitaxial layers are grown using molecular beam epitaxy (MBE) or metal-organic chemical vapor deposition (MOCVD), ensuring precise control over layer thickness and material composition. The high crystalline quality of the AlGaAs film is crucial for achieving low optical losses in the final microcavity. Once the AlGaAs layer is prepared, it is transferred onto a silicon dioxide (${\mathrm{SiO}}_2$) insulator layer, typically on a silicon wafer, through a process called wafer bonding. The bonding process involves bringing the AlGaAs/GaAs wafer into contact with the target ${\mathrm{SiO}}_2/\mathrm{Si}$ substrate and applying thermal treatment or pressure to achieve a strong, permanent bond. This step is critical for creating the AlGaAsOI structure, which combines the advantageous properties of AlGaAs with the thermal and mechanical stability of the insulator platform. After bonding, the original GaAs substrate is removed through selective etching, leaving only the AlGaAs layer on the insulator. This step can be achieved using a chemical etching process that selectively removes GaAs without damaging the AlGaAs layer. Once the AlGaAsOI structure is prepared, the microcavity patterning process begins. Photolithography is used to define the microcavity design, such as microring or disk resonators, on the AlGaAs surface. After patterning, reactive ion etching (RIE) is employed to create the desired structures with high precision. This etching process is carefully controlled to achieve smooth sidewalls, which are essential for minimizing optical scattering losses and maximizing the Q factor of the resonator. Finally, the fabricated microcavities are often subjected to thermal annealing, which helps to further reduce surface imperfections and enhance the optical performance of the device.

Fig. 21

Fabrication processes of AlGaAsOI microcavities^{[21,157,169,205]}.

4.1.1.

Influence of dispersion on spectral shape

The dispersion properties of the cavity fundamentally determine the spectrum’s characteristics^[179], as summarized in Table 5. In most cases, anomalous dispersion is necessary for the generation of microcombs^[11]. In an anomalous dispersion cavity, the mode-locked state is the so-called “bright soliton”, as discussed in previous sections, shown in Fig. 23(a). These mode-locked microcombs exhibit a ${\mathrm{sech}}^2$ shape in both the optical spectrum and time pulses^[174]. Generally, the relationship between the spectrum 3 dB bandwidth $\mathrm{\Delta }{\omega }_{\mathrm{comb}}$ and the second-order dispersion ${\beta }_2$ can be described by^[253]

Table 5

Comb State in Different Dispersion Conditions in an Experiment

Fig. 23

Microcombs under different dispersion conditions. (a) Bright soliton under anomalous dispersion^[11]. (b) Dark pulse under normal dispersion^[72]. (c) Dispersion wave due to high-order dispersion^[73]. (d) Quartic soliton supported by fourth dispersion^[64]. (e) Bright pulse under near-zero dispersion^[252].

Apart from the second-order dispersion, higher-order dispersion also plays a significant role. The dispersion wave due to high-order dispersion is investigated^[73,225], showing that a cluster of comb lines with relatively high power is excited due to the local wave packet’s match with the soliton pulses in the cavity. The excitation of dispersion waves is the most common method for generating microcombs with over-octave spectra, depicted in Fig. 23(c). Recently, octave-spanning microcombs have been demonstrated on various platforms through the excitation of dispersion waves, aided by delicate dispersion engineering^{[206,225,254,255]}.

As discussed, weak second-order dispersion can be beneficial for achieving a wide spectrum. When second-order dispersion approaches zero, higher-order dispersion factors begin to dominate the mode-locking process, resulting in distinct and diverse mode-locked pulses^[256]. Such dispersion conditions are called near-zero dispersion. Generally speaking, mode-locked microcombs exhibit flatter central spectra when even higher-order dispersion is dominant^[257]. For example, under pure fourth-order dispersion, mode-locked pulses present a Gaussian shape in both optical spectra and time pulses, showing a flatter central part compared to bright solitons supported by anomalous dispersion^[64,258,259]. These mode-locked states are often referred to as quartic solitons^[64], as shown in Fig. 23(d). The mode-locked states have also been studied in theory and simulation under sixth- and eighth-order dispersion^[257,260]. When odd higher-order dispersion dominates, mode-locked pulses present complex finger-like shapes where multiple tips are confined in a cluster, illustrated in Fig. 23(e). The parameter regions for the existence of different pulses overlap^[252,261], leading to a phenomenon known as snake-collapse soliton trace. Mode-locked state generation and characterization have been demonstrated in both fiber cavities^[262] and integrated microcavities^[263].

The aforementioned mode-locked pulses all appear as bright pulses, characterized by high peak pulses supported by a relatively low continuous wave background. In contrast, under normal dispersion, the mode-locked pulse features anti-pulses or dark pulses, where dips are located on a relatively high continuous wave background, as shown in Fig. 23(b)^[72]. These dark pulses are mode-locked due to the interaction of switching waves with opposite directionalities, where one wave connects from a high-power state to a low-power state and vice versa. In the optical spectrum, dark pulses exhibit rapid power drops near the central part, followed by flat “wings” away from the center^[264]. Typically, the optical bandwidth of dark pulses is narrower compared to bright solitons, while it can cover over 300 nm under relatively weak second-order dispersion factors^[264].

4.1.2.

Dispersion engineering for microcombs

As discussed above, the core aspect of designing the spectrum is dispersion engineering, a long-standing topic in the field of microcombs^[179], as summarized in Table 6. In earlier research, dispersion engineering was primarily based on tuning the waveguide structure, such as the height and width of the waveguide^[225]. In addition, complex waveguide structures are proposed to meet specific dispersion design requirements^[259]. For example, a concentric microring^[61] is designed to provide wideband anomalous dispersion, as depicted in Fig. 24(a). In addition, the waveguide structure of the microcavity can be tapered^[64] to tune the dispersion of the whole cavity.

Table 6

Design Methods for Dispersion Engineering

Fig. 24

Different dispersion engineering methods. (a) Concentric microring^[61]. (b) Coupled rings for single-point dispersion changing^[78]. (c) Coupled rings for wideband dispersion changing^[68]. (d) PhCR for single-point dispersion changing^[65]. (e) PhCR for multiple-point dispersion changing^[265].

For flexible dispersion design, inter-mode interaction^[132,266] is utilized for dispersion engineering. As the microcavity supports multiple mode families, anti-crossing resonance splitting caused by inter-mode coupling can be employed for dispersion engineering. When the group velocity difference between two modes is large, inter-mode coupling induces localized dispersion changes as the resonant frequencies converge^[266]. These localized changes can introduce effective anomalous dispersion in a normal dispersion cavity, providing modulation instability (MI) gain for microcomb generation with the forward sweeping process. In 2014, researchers demonstrated microcomb generation in normal dispersion cavities assisted by coupling between different modes^[58]. In 2015, dark pulse microcombs were demonstrated^[72]. These dispersion changes can also introduce dispersion waves in bright soliton microcombs within anomalous dispersion cavities^[74]. In another scenario, where the group velocity difference is quite small and the coupling between different modes is strong, wideband dispersion changes are possible^[267]. Such properties have been used to generate bright solitons in normal dispersion cavities. However, this method requires the existence and inter-mode coupling of multiple modes, which is undesired for high-Q operation. In addition, the design for wideband dispersion changing is challenging for integrated platforms. The robust design and tunability challenges remain significant obstacles.

Similarly, the coupled ring scheme can function as two modes for dispersion engineering^[59,78], illustrated in Figs. 24(b) and 24(c). The coupling can be distinctly induced by the interaction between different rings, and the coupling state can be tuned by adjusting the resonant frequency difference between the rings. When a microring is coupled with a microring with a large FSR difference, localized dispersion changes can be induced^[59,67], similar to the coupling between different mode families in a single cavity. This scheme has been used for the tunable generation of dark pulses in normal dispersion cavities^[59,268] and the controllable dispersion wave of bright solitons in anomalous dispersion cavities^[269]. When the two microrings feature closely matched FSRs and strong intra-cavity coupling, wideband dispersion changes are induced^[270,271]. Tunable nonlinear processes including soliton generation and Brillouin lasers have been demonstrated^[68].

Recently, advancements in fabrication have enabled the coupling between forward-backward fields within a single microring using intracavity gratings, known as photonic crystal microrings [PhCRs, shown in Fig. 24(d)]^[272,273], for flexible dispersion profile design. In the design of the intracavity grating, the periodic structure is usually positioned on the inner side of the waveguide to reduce the interaction of the optical field with the etched side. When both the resonant condition and the Bragg condition are satisfied, the corresponding resonance splits into two due to the coupling between the forward and backward fields^[273]. The split frequency is determined by the coupling coefficient, which is designed based on the grating shape. Using PhCRs, the continuous evolution of dark pulses in normal dispersion cavities^[264] and self-excitation of bright solitons in anomalous dispersion cavities^[65] have been illustrated. Theoretically, if the grating structure is synthesized from periodic structures with different periods, as shown in Fig. 24(e), it is possible to separately regulate multiple resonances within a single ring^[265,274]. This has been proven in recent works. Researchers propose a reverse design method where the grating structure can be produced according to the required spectrum shape. For demonstration verification, a flat microcomb is generated using a dispersion-engineered PhCR^[69].

Beyond dispersion engineering, new intracavity dynamics are also being researched. For wideband spectra, it is possible to cover different bands by injecting another pump laser to excite and coherently combine the generated microcombs^[275,276]. For flat spectra, a new type of soliton, the Nyquist soliton, has been proposed to produce flat microcombs driven by the bandpass response^[116].

In conclusion, the development of microcombs with tailored spectra involves delicate dispersion engineering processes. Each approach has its unique challenges and advantages, and ongoing research continues to refine these methods. The integration of these advanced techniques into scalable platforms will be crucial for applications such as telecommunications, spectroscopy, and metrology.

4.3.1.

Noise source

The noise in microcombs can be attributed to the following factors.

Technical noise: this includes various environmental factors such as temperature fluctuations, mechanical vibrations, and acoustic noise. For example, when coupling the pump laser from a fiber to the microcomb chip, relative vibration between the fiber and the chip can cause pump fluctuations on the chip, inducing noise in the output microcomb.

Pump laser noise: since the microcomb is excited by the pump laser, the noise of the pump directly affects the noise of the generated microcomb. The impact of the pump laser’s intensity noise and phase noise on the microcomb can be studied separately to understand their contributions.

Thermal noise: according to thermodynamics, there will be random fluctuations in temperature-related variables, which contribute to noise. Due to the thermo-optical effect and thermal expansion, the cavity is affected by temperature changes, leading to vibrations in the resonant frequency. These vibrations contribute to the noise in the generated microcomb.

Quantum noise: fundamental quantum fluctuations, such as shot noise and spontaneous emission noise, also contribute to the noise in microcombs. These are particularly relevant in low-power regimes where quantum effects become significant.

Similar to the pump laser, the noise of the microcomb can be divided into intensity noise and frequency noise. In most cases, the research on microcomb noise is focused on the frequency noise or phase noise. According to the numerical relationship, phase noise and frequency noise can be converted into each other:

Thus, the frequency noise of comb lines will increase apart from the pump mode. As shown in Fig. 26(a), the intrinsic linewidth $\mathrm{\Delta }{f}_m$ of each comb line can be given by^[288]

Fig. 26

Noise sources and suppression methods. (a) Different noise sources for the intrinsic linewidth of comb lines^[288]. (b) The influence of thermal noise^[289]. (c) Intrinsic (top) and effective (bottom) linewidth distribution of comb lines^[288]. (d) Self-injection locking for high-coherence lasers^[140]. (e) Reduced thermal-optical effect under low temperature^[290]. (f) Suppressed thermal noise with laser cooling^[289]. (g) Low-noise soliton microcomb operating at the quiet point^[176]. Top: spectrum; bottom: phase noise of the repetition rate. (h) KIS for reducing the repetition rate fluctuation^[80].

Aside from pump noise, the thermal noise [shown in Fig. 26(b)] of the cavity imposes a limitation on the noise of the microcomb. The thermal noise of a variable $X$ can be expressed as

Due to the thermal noise, the effective linewidth will increase as the comb line apart from the pump mode, depicted in Fig. 26(c). This feature has been widely observed in experiments^[287,289]. In conclusion, the phase noise $S_{f_{\mathrm{rep}}}^{\varphi }$ of the repetition rate can be written as^[229]

4.3.2.

Noise suppression method

Different methods have been proposed to suppress different noise sources for high-coherence optical microcombs. The most straightforward method to enhance the coherence is to reduce the noise of the pump laser. Different laser sources exhibit different noise levels. For example, fiber lasers^[292] typically have lower noise compared to semiconductor lasers^[293]. In addition, locking schemes such as the well-known Pound-Drever-Hall (PDH) locking loop^[294] can be used to suppress the noise of the pump laser. With the detection of $f_{\mathrm{ceo}}$ and $f_{\mathrm{rep}}$, the noise of microcombs can be greatly reduced by locking these two essential frequencies^[45,295]. The intensity noise of the pump laser can also be suppressed by employing the power control devices with feedback loops^[296]. Despite the high coherence achieved through these locking processes, the overall systems are too complex and challenging to integrate. Recently, the self-injection locking methods have been proposed to provide high coherence with integrated lasers, illustrated in Fig. 26(d). By locking the semiconductor laser to the high-Q microcavity, the phase noise of the hybrid laser can be suppressed to the level of advanced fiber lasers^[140]. Combining the turnkey operation of self-injection locking with heterogeneous integration, fully on-chip high-coherence microcombs can be achieved^[86].

In addition, it is feasible to enhance the coherence by reducing thermal noise. As expressed in Eq. (24), cavity thermal noise is related to the cavity volume. Thus, thermal noise can be reduced using large cavities. A large cavity requires high pump power. The large cavity size and high pump power requirement contradicts the need for integration. Also, the cavity size is usually determined by the desired $f_{\mathrm{rep}}$ of the microcomb. Since the influence of cavity thermal noise on the microcomb is partially from the thermal-optical effect^[289], reducing the thermo-optical coefficient can mitigate this influence. Composite waveguide structures with positive and negative thermo-optical coefficients are proposed^[297]. However, such waveguides require costly multiple depositions of different thin film materials. The quality factor is too low at present steps, obstructing mode-locking comb generation. High pump laser power may also increase thermal noise due to heating by the pump laser. The thermal-optical coefficient can be reduced by decreasing the temperature. For instance, researchers from NIST have proposed thermal effect suppression at cryogenic temperatures^[290], as depicted in Fig. 26(e). However, low-temperature environments require expensive cooling and temperature control equipment. As mentioned in the comb generation section, an assistance laser could be used to balance intracavity temperature changes during the transition from chaotic to soliton states. Similarly, an assistance laser can be injected into the cavity to cool the cavity after carefully tuning the frequency of the assistance laser [Fig. 26(f)]^[289]. A lower effective temperature can be obtained with higher assistance laser power within a reasonable pump power range.

Except for directly suppressing pump laser noise and cavity thermal noise, the phase noise of microcombs can be reduced by leveraging the nature of mode-locked microcombs. As shown in Eq. (20), both the Raman effect and the dispersion wave can cause the shift of $f_{\mathrm{rep}}$ with the detuning. In certain cases, the shift directions are opposite, leading to the reduced fluctuation in $f_{\mathrm{rep}}$^[298]. Ideally, these two shifts can be completely canceled out at a working condition known as the quiet point^[291], resulting in suppressed noise. Operating at the quiet point can reduce the phase noise of $f_{\mathrm{rep}}$ by 20 dB^[176], as depicted in Fig. 26(g). However, this scheme requires the proper position of the dispersion wave. The dual-ring scheme has been proposed to introduce the controllable dispersion wave^[299]. As for dark pulses, recent research indicates a lower noise floor limited by the shot noise compared with the bright solitons^[300].

In most cases, the mode-locked microcombs are generated with a single continuous wave pump. Recent studies reveal that the mode-locked microcomb can be locked to the background field induced by additional fields^[107]. By modulating the pump with a radio frequency close to the FSR of the microcavity, deterministic single-soliton generation can be achieved^[131]. The modulated wave can also lock the generated soliton. In the optical spectral domain, the modulated pump can be viewed as the injection of two or more continuous waves with spacing equal to the cavity FSR^[301,302]. The injection of another laser far away from the pump is also demonstrated to lock mode-locked pulses. In 2023, a laser locked to the Rb reference was directly injected into the microcavity, resulting in the stabilization of the soliton^[80]. Such injection locking process is called Kerr-induced synchronization (KIS), shown in Fig. 26(h). With KIS, the full-width-half-max of $f_{\mathrm{rep}}$ is reduced from 160 to 11 kHz. Combined the locking of $f_{\mathrm{ceo}}$ with f-2f self-referencing, the FWHM of $f_{\mathrm{rep}}$ is locked to 3 Hz. On platforms with electro-optical effects, a microwave signal with a frequency close to $f_{\mathrm{rep}}$ of solitons can be directly applied to the microcavity. The generated solitons will be locked to the applied microwave signal^[207]. Besides the injection from an external source, the self-injection of one comb line can also stabilize the microcomb^[303]. Viewed as an oscillator, the phase noise of the self-injected comb line can be suppressed by 30 dB.

Suppressing noise in microcombs is crucial for their performance in various high-precision applications. By employing methods such as reducing pump laser noise, managing thermal noise, leveraging the intrinsic properties of mode-locked microcombs, and using advanced locking techniques, researchers continue to improve the coherence and stability of microcombs. These advancements pave the way for more reliable and integrated microcomb systems, expanding their potential in scientific and technological applications.

5.1.1.

Frequency standard

With strictly equal-distant frequency spacing, optical frequency combs serve as the clockwork of an optical atomic clock, which is analogous to a gear set, transferring stability between optical and radio frequencies. Such systems leverage stable atomic transitions as a reference, providing a set of referenced optical lines covering tens to hundreds of THz bandwidth while offering precise and accurate optical or microwave standards with the aid of phase-coherent multiplication or optical frequency division (OFD) techniques. An optical frequency synthesizer refers to a phase-coherent microwave-to-optical link that transfers the stability of a microwave oscillator to a referenced laser and vice versa to an optical clock.

Fig. 27

Microcomb-based frequency standard. The stabilization of the microcomb could be achieved by locking (a) one optical mode and repetition frequency^[67], (b) two separate optical modes^[42], and (c) repetition frequency and CEO frequency via the f-2f technique^[304]. First demonstrations of octave-spanning microcomb on (d) SiN^[225], (e) AlN^[206], and (f) 4H-SiC^[305] platforms. The highly integrated (g) optical clock^[34] and (h) optical frequency synthesizer^[46] based on dual-comb frequency clockwork.

In order to construct a reliable bridge across the entire electromagnetic spectrum, the “optical frequency ruler” must be fully stabilized. This process requires accessing two parameters: the frequency spacing of the comb lines $f_{\mathrm{rep}}$ and the CEO frequency $f_{\mathrm{ceo}}$. As introduced in Sec. 2, the absolute frequency of each comb line can be described as $f_m=f_{\mathrm{ceo}}+m{f}_{\mathrm{rep}}$ ($m$ is the mode number). Among $f_m$, $f_{\mathrm{ceo}}$, and $f_{\mathrm{rep}}$ one frequency parameter could be determined or stabilized once the other two are known or locked to the reference. The repetition rate could be directly accessed from the beat note of the adjacent comb line, while the CEO frequency stabilization usually relies on the well-known f-2f self-reference technique.

Here we briefly introduce relative works, as illustrated in Fig. 27. The stabilization techniques of microcombs at early stages mainly focus on the locking of mode spacing and one of the comb modes. In contrast to mode-locked lasers, the pump mode can be directly accessed since it is part of the microcomb itself. Thus, the power and frequency detuning of the pump laser provides two degrees of freedom for stabilization. Specifically, $f_{\mathrm{rep}}$ can be tuned through the power-dependent refractive index change of the microresonator. In this way, Del’Haye et al. perform a complete microcomb stabilization in fused silica toroids with 86 GHz mode spacing^[306]. All-optical stabilization could be realized by locking two comb lines to separate laser references. A microcomb generated from a silica disk resonator is stabilized to two distributed feedback (DFB) lasers^[42], as shown in Fig. 27(b), which are frequency-doubled and stabilized to D1 and D2 Rb transitions, respectively. The synthesized microwave output at a precise subdivision of the Rb reference performs a $5\times {10}^{-9}$ Allan deviation for 1 s averaging, which is improved by a factor of $\sim 100$ over the DFB lasers determined by the fluctuations of the Rb reference.

Moreover, the demonstration of a self-referenced microcomb system is of particular importance since it provides a direct microwave-to-optical link by measuring and controlling the offset frequency of the microcomb. Direct octave-spanning broadband coherent microcomb generation necessitates rigorous dispersion engineering and relatively large mode spacing. One way to broaden the microcomb spectrum in the dielectric platform is supercontinuum generation by injection of the soliton pulse into the highly nonlinear fiber. A spectrum exceeding two-thirds of an octave is realized in a ${\mathrm{MgF}}_2$ microresonator with this solution^[304], as shown in Fig. 27(c). With a 2f-3f self-reference interferometer, the system phase coherently links a 190 THz optical carrier directly to a 14 GHz microwave frequency. Direct f-2f referencing was demonstrated in a fused-silica microdisk resonator at a repetition rate of 16.4 GHz^[45]. The CEO frequency is stabilized to a sub-hertz level, and the absolute pump laser stability has a standard deviation of 620 Hz at a 100 ms gate time. To further simplify the self-referencing system, an external broadening-free microcomb spanning two-thirds of an octave was demonstrated in a SiN microresonator at a repetition rate of $\sim 190\mathrm{GHz}$, using temporal DKS formation and soliton Cherenkov radiation^[307]. The stabilized pump laser exhibits a 172 Hz distribution shift for the 160 s measurement. So far, octave-spanning microcombs have been realized on SiN, SiC, and AlN platforms^{[144,206,225,305,308]}, with their free spectral ranges set at 1 THz or sub-THz levels, as shown in Figs. 27(d)–27(f).

The large repetition rate in octave-spanning microcombs leads to challenges in $f_{\mathrm{rep}}$ and $f_{\mathrm{ceo}}$ detection since those frequencies are too large for direction with present electric equipment. Two solutions are proposed to overcome this challenge. In one way, a second microcomb with detectable microwave repetition is employed to serve as the frequency gearbox between THz and microwave signals^[34]. Another approach is frequency down-mixing by electro-optic modulation. Through the electro-optic modulation, modulated sidebands are generated around the original comb teeth, with the spacing equal to the applied microwave frequency. In this way, a terahertz signal with 0.01 mHz accuracy and precision^[309] resulting from the perfect division of an optical reference is presented, with the absolute frequency noise to one part in ${10}^{17}$.

For the next-generation optical clockwork system, integration level has always been a hot topic. The integrated architectures for both optical frequency synthesizers and optical atomic clocks have been proposed^[34,46], as shown in Figs. 27(g) and 27(h), respectively. The highly integrated synthesizer shows the combination of a heterogeneously III–V/silicon laser whose frequency is stabilized to a microwave standard, guided by a cascaded frequency chain enabled by separated microcombs. The output laser can be programmed by a microwave clock across 4 THz with 1 Hz resolution^[46], with a synthesis error of $7.7\times {10}^{-15}$. As for the optical clock, a pair of interlocked microcombs helps the stability transition from a locked semiconductor laser to its repetition rate. The generated 22 GHz electrical clock shows a fractional frequency instability of one part in ${10}^{13}$. Although the performance needs to be further optimized, the hybrid system, with several silicon-chip devices playing the core function, has already shown its advantages in cost, size, and power consumptions^[34].

More recently, a novel method for high-frequency $f_{\mathrm{ceo}}$ and $f_{\mathrm{rep}}$ detection has been proposed by a pair of Vernier microcombs with slightly different repetition rates^[310]. Such a strategy offers the ability to simultaneously detect 900 GHz repetition rate and 97 GHz CEO frequency, indicating its large potential in self-referencing techniques and optical clock applications.

5.1.2.

Spectroscopy

Frequency comb technology has revolutionized precision measurements in spectroscopy since its first application in the 1970s^[315]. When it comes to microcomb-based spectroscopy, it mainly focuses on molecular fingerprinting measurement^[316]. With the efficient optical nonlinear process, microcombs can span a broader range of frequencies compared to other integrated counterparts like integrated mode-locked lasers and electro-optical combs. This capability allows microcombs to cover a richer spectrum of spectral information. By injecting the frequency comb into the environment to be detected, the spectral information is loaded on the comb in different manners, such as absorption. Two different methods have been proposed to extract the loaded spectral information: direct frequency comb spectroscopy and dual-comb spectroscopy, as illustrated in Fig. 28.

Fig. 28

Microcomb-based spectroscopy. The direct frequency comb spectroscopy (DFCS) utilizes a single frequency comb for molecular fingerprint recognition, which can measure (a) atomic transition^[311] and (b) gas phase^[312]. (c) The plasmonic-enhanced DFCS systems^[313]. Dual-frequency spectroscopy (DCS) is enabled by a pair of microcombs, which can be generated simultaneously by (d) separately pumping^[36], (e) counterpropagating stimulation, and (f) single-pump driving^[314]. (g) The microcomb densification via iDFG scheme^[50].

Direct frequency comb spectroscopy (DFCS) is the simplest approach. By directly detecting the loaded information, the spectral information of the environment is obtained. A pump-laser-free scheme is utilized to directly perform the gas-phase spectroscopy^[312], where the microcomb is generated with a dual-resonance configuration^[317]. To measure broadband molecular absorption spectra of acetylene, the microcomb is tuned by the on-chip micro heater for spectra interleaving. More concisely, to achieve megahertz-linewidth molecular spectroscopy, Stern et al. decouple the control of repetition frequency and offset frequency with a phase modulation scheme^[318], therefore allowing substantial scanning and stabilization. The DFCS of the cascaded transition of around 10 MHz linewidth atomic transition in Rb at 1529.37 nm is demonstrated, indicating absolute optical frequency fluctuations at the kilohertz level over a few seconds and $<1\mathrm{MHz}$ day-to-day accuracy. Moreover, by coupling microcombs with plasmonic systems, Zano et al. recently proposed a plasmonic-cavity-enhanced platform for high sensitivity and multidimensionality spectroscopy^[313]. By projecting the microcomb to a water-cladded prism-based plasmonic resonator, the approach offers insights into the analyte’s concentration, dispersion, and resonance characteristics.

Dual-comb spectroscopy (DCS) offers a non-invasive method for Fourier transform interferometry without moving parts^[319]. It works by mapping an optical comb into radio frequency by multiheterodyne beat with a second comb featuring a slightly different repetition rate. For microcomb-based DCS compared with previous mode-locked lasers, it holds the advantage of a higher FSR, which allows a higher $\delta f_{\mathrm{rep}}$ between the two combs, requiring a shorter minimum acquisition time to resolve the beat notes. In 2016, Suh et al. demonstrated the first microcomb-based DCS^[36], where a microcomb pair with frequency repetition of approximately 22 GHz and $\delta f_{\mathrm{rep}}$ of 2.6 MHz was employed. The microcombs used here were pumped separately with different lasers; thus, the coherence and stability of the heterodyne beats were limited. To further enhance the coherence time, highly coherent dual-comb pairs were generated monolithically. Dutt et al. proposed a single-laser-pumped DCS system on the SiN platform^[320], leading to a long mutual coherence time of 100 µs via on-chip micro-heater tuning. Absorption spectroscopy of dichloromethane was obtained, spanning a 170 nm wavelength range over a fast acquisition time of 20 ms. Meanwhile, by utilizing a dual-locked counterpropagating soliton generated from a single microresonator, Yang et al. demonstrated a Vernier spectrometer^[314]. The counterpropagating microcomb is inherently phase-locked at two spectral points, which offers an exceptionally stable radio-frequency grid^[321]. To extend the spectral detection range, a silicon-chip-based DCS system was proposed^[322], with a single-laser-pumped dual-comb configuration spanning across 2.6 to 4.1 µm. Absorption DCS in the liquid phase is realized by acquiring spectra of acetone spanning from 2900 to 3100 nm at 127 GHz resolution. To further densify the comb lines in mid-infrared, Bao et al. proposed an architecture for GHz microcomb DCS using interleaved difference-frequency-generation (iDFG)^[50]. Four combs consisting of two counterpropagating microcombs at 1550 nm and two EO combs at 1064 nm are generated in a highly locked form, where the repetition frequency of the EO comb is driven and divided from the repetition rates of the microcombs. With the iDFG process, a pair of mid-IR combs with dense spectra could be generated. Meanwhile, the common-mode fluctuations can be canceled out during the multiheterodyne DCS detection process, leading to a normalized DCS precision as high as $1.0\mathrm{ppm}·\mathrm{m}·{\mathrm{s}}^{1/2}$. With highly inherent coherence and multidimensional tunability, the microcomb-based DCS holds great potential for integrated spectroscopy with high signal-to-noise ratios and fast acquisition rates.

5.1.3.

Light detection and ranging

LiDAR has been extensively studied and commercially equipped for various applications such as geology, atmospheric physics, and autonomous navigations^[325]. Primarily, there are two types of LiDAR detection schemes: time-of-flight (ToF) and frequency-modulated continuous wave (FMCW). ToF measures distance by directly calculating the time it takes for a light signal to travel to the target and back, while FMCW LiDAR measures distance and velocity by analyzing frequency shifts of the beating signal between the reflected signal and the emitted signal. The former scheme requires a pulsed light source, and the latter one needs a frequency-tunable laser. By replacing conventional laser sources with microcombs (shown in Fig. 29), a microcomb-based LiDAR system can achieve faster and more accurate ranging with a compact form^[326]. This improvement stems from the parallel characteristics and inherent inter-channel consistency of microcombs.

Fig. 29

Microcomb based LiDAR. Two kinds of LiDAR schemes, ToF and FMCW, are implemented in microcomb-based LiDAR systems. (a) A pair of separated microcombs^[35] and (b) a pair of counter-propagating microcombs^[323] are employed for ToF schemes. (c) Microcomb-based dispersive interferometry^[324] for accurate ranging under long distances. (d) Principle of parallel FMCW LiDAR^[49].

For the ToF scheme, a dual-comb configuration is employed, which utilizes multi-heterodyne detection between a pair of coherent soliton combs with a slight difference in repetition frequency. This setup combines delay-time measurement with coherent interference, enhancing the precision and accuracy of distance measurements by leveraging the stability and coherence of the soliton combs. In Ref. [35], dual-comb distance measurements have been demonstrated with impressive precision, achieving Allan deviations as low as 12 nm at averaging times of just 13 µs. This high degree of accuracy enables ultrafast ranging with acquisition rates up to 100 MHz. Such capabilities are particularly useful in dynamic environments, allowing for the in-flight sampling of fast-moving objects like gun projectiles traveling at speeds around 150 m per second. In the meantime, Suh et al. performed dual-comb measurements by generating clockwise and counterclockwise soliton microcombs within a single microresonator^[323]. With a more compact system configuration, 200 nm precision with a range ambiguity of 16 mm was demonstrated, with an extendable range ambiguity of 26 km by means of the Vernier effect^[327]. More recently, a dual-comb with a shared pump has been generated for extended ambiguity distance, which enhances the coherence without additional control^[328]. To further exploit the spectrum information, microcomb-based dispersive interferometry was demonstrated^[324], where the distance information is demodulated from the interference spectrum envelope. Utilizing a high-repetition-rate microcomb matched well with a linear array image sensor, a long distance of 1179 m is real-time measured in an actual outdoor baseline field, with a minimum Allan deviation of 27 nm at an average time of 1.8 s.

The massively parallel characteristic of microcombs could also benefit the acquisition speed of the LiDAR, which is of great importance in terms of coherent ranging. A microcomb provides a simplified parallel FMCW generator with a single-frequency-chirped pump laser, with great consistency. In Ref. [49], a microcomb-based coherent LiDAR was demonstrated with 30-channel distance and velocity measurement at an equivalent rate of 3 megapixels per second. With the optimized dual-comb configuration, a hardware-efficient microcomb-based FMCW LiDAR is demonstrated by multiheterodyne two synchronously frequency-modulated microcombs^[329]. Information for all individual ranging channels can be extracted on a single receiver, which further simplifies the system for individual separation, detection, and digitization.

Range ambiguity, a common limitation in both ToF and FMCW LiDAR systems, restricts the maximum detectable distance. Recently, a novel parallel LiDAR system utilizing a chaotic microcomb has gained extensive attention. This system circumvents traditional interference issues by emitting parallel physical random light, effectively removing the typical range limitations imposed by the period of the light signal. In Sec. 5.3, we will introduce this special LiDAR system in more detail.

5.1.4.

Optical tomography

Fourier-domain optical coherence tomography (FD-OCT) provides noninvasive optical imaging for medical diagnosis and art conservation with micron-level resolution and millimeters of imaging depth. Conventionally, a commercial super-luminescent diode with continuous spectrum is employed as the light source for the FD-OCT system, in which a wider light spectrum is preferred since the axial resolution in air $\delta z$ is defined by its spectral bandwidth $\mathrm{\Delta }{\lambda }_{\mathrm{FWHM}}$^[298]:

Fig. 30

Microcomb-based OCT. (a) Chaotic microcomb^[48] and (b) soliton-microcomb^[330] -based OCT setups and their scan results.

Although it is commercially mature, the FD-OCT, especially spectral-domain OCT (SD-OCT), still suffers limitations from the depth-dependent sensitivity drop together with mirror-conjugate images, which reduces the total image range and results in performance decay^[331]. Interestingly, the optical frequency comb effectively reduces the depth-dependent drop of sensitivity, meanwhile allowing reduced interpixel crosstalk due to its discrete frequency characteristic^[332]. The chip-based frequency comb source for SD-OCT has been demonstrated recently, both in chaotic^[48] and soliton^[330] microcomb states, as separately illustrated in Figs. 30(a) and 30(b). Ji et al. demonstrate a SiN-based SD-OCT chaotic microcomb source, pumped at around 1310 nm with a 120 nm comb spanning bandwidth^[48]. The FSR is set at 38 GHz to avoid artifacts. The system could horizontally cover a range of 4 and 2.52 mm in depth, with an axial resolution of 16.3 µm. A soliton-state microcomb-driven SD-OCT system is proposed to further mitigate the performance impact of relatively intense noise from the light source^[330]. The chaotic nature results in a 20 dB increase factor for relative intensity noise, lowering its ultimate performance limit. The highly correlated RIN between comb lines in the soliton state is verified to have a limited effect on the background signal-to-noise ratio and imaging dynamic range. The system, therefore, exhibits a residual intensity noise floor at a high offset with 3 dB lower than the traditional incoherent OCT source, showing an axial resolution of 6 µm. By taking multiple scans and average tomograms together, the effects of individual comb line fluctuations can be nearly eliminated. In Ref. [333], 10 scans per tomogram are taken. After the software data process, the axial resolution is 5.65 µm, which is already comparable to that in a soliton microcomb.

Despite the aforementioned progress, frequency-comb-based OCT systems still face a major limitation due to the trade-off between axial resolution and imaging depth, which, until now, can only be addressed by reconstructing the data^[334]. Nonetheless, this chip-based OCT source holds promise for portable clinical devices in low-resource settings, enabling flexible diagnostics by replacing bulky and power-consuming components.

5.1.5.

Astrocomb

A microcomb could provide a precise spectral reference for exoplanet searching via radial velocity (RV) shift. The radial velocity method, also known as Doppler spectroscopy, determines the presence of exoplanets by measuring the Doppler shift in a star’s spectral lines^[337]. This technique calculates the component of the star’s velocity along the line of sight to the observer. Variations in the radial velocity over time, indicative of periodic shifts towards the red and blue ends of the spectrum, suggest the gravitational influence of an orbiting planet. By analyzing the amplitude and periodicity of these velocity changes, the existence, mass, and orbital characteristics of the exoplanet can be inferred with a high degree of precision. For terrestrial planet exploration, the precision must reach 10 cm/s level. Although the mode-locked laser has achieved ultrahigh velocity precision^[335], the relatively dense spectral line down to several hundreds of MHz level is not resolvable by astronomical spectrographs. Extra spectral filters are required to coarsen the line spacing to 10–30 GHz, which adds system complexity. The chip-based microcomb coincidently fits well with this mode spacing due to its compact resonance diameter, therefore holding promise for a small footprint and low-cost system.

Fig. 31

Microphotonic astrocomb. (a) Silica microcomb applied to Keck II telescope^[335]. (b) SiN soliton microcomb adapted to calibrate GIANO-B high-resolution spectrometer^[336].

Two proof-of-concept works have been demonstrated for calibration of astronomical spectrographs, with either silica [Fig. 31(a)] or SiN microcombs [Fig. 31(b)], respectively. A silica micro-resonator with 22.1 GHz soliton comb line spacing is employed, with its repetition rate and one comb line locked to the Rb clock and hydrogen cyanide absorption line. This comb exhibits a frequency imprecision of 1 MHz, equivalent to about 1 m/s of RV imprecision. Eight echelle orders ranging from 1471 to 1731 nm within the astronomical H band are measured, and an actual 3–5 m/s precision is obtained^[336]. Another SiN-based astrocomb is adapted to calibrate the GIANO-B high-resolution spectrometer at the Telecopio Nazionale Galileo. To stabilize the comb, the CW pump laser was locked to a self-referenced mode-locked laser stabilized to a GPS-disciplined rubidium atomic clock. Meanwhile, the repetition rate is microwave injection-locked by referenced electro-optical modulation^[47]. Ideally, this astrocomb can support an RV precision of 1 cm/s with exposure times longer than 1 s. Compared with a traditional calibration light source, the uranium-neon (U–Ne) hollow cathode lamp, the microcomb provides a much denser grid of calibration lines with only 10 s, which is much quicker than 120 s exposure in U-Ne standard due to its stability. The calculated wavelength solution is around 25 cm/s, which is mainly limited by fundamental photon noise resulting from the analog-to-digital conversion.

Although significant progress has been made in the miniaturization of astronomical calibration standards, further research is required to optimize astrocombs for critical applications. Specifically, challenges remain in achieving astrocombs that can span the visible spectrum and offer wavelength resolution precision below 1 cm/s. Nonetheless, the microcomb, as a new class of astronomical calibration tool, offers promising opportunities for lightweight solutions, particularly in space-borne astronomical applications.

5.2.1.

Data transmission

The parallel characteristics, combined with its compact footprint, enable the microcomb to serve as a stable multi-wavelength light source, which is crucial for scaling data transmission capacity. The microcomb integrates seamlessly with modern fiber-based WDM techniques for several key reasons:

Table 8

Comparative Analysis of Parallel Data Transmission in Microcomb Systems

Firstly, the mode spacing of a chip-scale microcomb naturally falls within several tens of GHz or larger, which aligns well with the current dense wavelength division multiplexing (DWDM) channel spacing standards, therefore supporting the high-capacity data transmission. Additionally, compared to commercial laser banks, the frequency spacing between optical carriers in a microcomb is significantly more stable, with deviations typically below 1%. This enhanced stability allows for more efficient use of the spectral resources (at least 10% increased bandwidth) by reducing the need for guard bands, which are usually employed to prevent inter-channel crosstalk. More importantly, the simplicity of the system is greatly enhanced by advanced microcomb generation techniques or heterogeneous integration with a pump laser. These innovations eliminate the need for external feedback control circuits for laser arrays, significantly reducing power consumption and enabling a more compact design. This streamlined configuration not only conserves power but also paves the way for fully integrated systems, further advancing the miniaturization and efficiency of photonic devices.

A microcomb for ultrahigh data capacity, particularly for coherent communications, has been studied for over a decade, as listed in Table 8. The first demonstration for data transmission utilizing microcombs was performed in 2014^[37], where 20-channel QPSK signals at a symbol rate of 18 Gbaud were transmitted through a fiber link up to 300 km. The comb noise at this stage was reduced by a pump-controlled feedback loop. The high coherence and wide spectrum of a DKS state could further boost the data capacity. Afterward, data transmission using different coherent states of microcombs^[338–341] was intensively studied. In Ref. [338], two interleaved DKS state combs are employed to transmit an aggregate data rate of over 50 Tbps. A total of 179 channels across the entire telecommunication C- and L-bands are used at a channel symbol rate of 40 Gbaud in 16-QAM format. More interestingly, no additional penalty is observed in this case for the soliton microcomb when compared with the high-quality ECL, resulting from its highly coherent behavior. The dark-pulse soliton, characterized by a pump-to-signal conversion efficiency that is several times higher than that of a bright soliton, offers significant advantages in data encoding. Its relatively high carrier-to-noise ratio makes it particularly well-suited for encoding data in more complex formats. A high modulation format, 64-QAM, was therefore first demonstrated in a dark-pulse microcomb, which enables a transmitted OSNR above 33 dB^[339]. In this 80 km data transmission configuration, 20 channels with an aggregate data rate of 4.4 Tbps is demonstrated. Moreover, by utilizing frequency comb distillation techniques^[343] for wideband noise reduction, the required optical signal-to-noise ratio could also be reduced. To fully utilize spectrum resources in a soliton crystal microcomb, the initial 80 comb lines with 49 GHz FSR were doubled to 160 using a single-sideband modulation scheme^[340]. The dense channels therefore carried high-order-format 64-QAM signals at a 23 Gbaud symbol rate, resulting in a total data capacity of 44.2 Tbps and an ultrahigh spectrum efficiency of 10.4 bits/s/Hz. More recently, a record-breaking high microcomb parallel data transmission was demonstrated, achieving an aggregate data rate of 1.84 Pbps^[341]. This remarkable feat was accomplished using both WDM and space division multiplexing (SDM). The system employed 223 wavelength channels across a 37-core fiber, showcasing the immense potential of microcomb technologies in scaling up data transmission capacities in optical communication networks.

In addition to increasing capacity, parallelized data transmission in systems utilizing microcombs imposes a significant burden on the receiving end due to the substantial amount of digital signal processing (DSP) required for coherent communications. This complexity arises because each of the numerous parallel channels must be individually processed, decoded, and synchronized, which demands extensive computational resources. As the number of channels and the data rate per channel increase, the DSP tasks become more challenging, potentially leading to higher latency and power consumption at the receiver. The synchronization of two individual microcombs^[75] could alleviate such resource deficiency by means of cloning a microcomb for local oscillation, which is highly coherent with the carrier-microcomb. By coupling a small fraction of one microcomb to the input of the other microresonator, two silicon nitride microcombs on separate chips could be synchronized. Therefore, DSP-based electrical frequency offset estimation (FOE) and carrier phase estimation (CPE) can be significantly simplified during coherent data retrieval. Such a scheme enabled three orders of magnitude lower CPE rate than the free-running independent carrier and LO lasers within a proof-of-concept 1.68 Tbps data transmission system^[344]. More recently, by utilizing a self-injection locking scheme in an ultra-low-loss 100 nm SiN resonator, Zhang et al. achieved an over 60 Tbps data transmission with nearly no CPE expenditure^[56].

Microcomb sources can also drive advancements in free space optical (FSO) communications and wireless communications. A Tbps-level parallel FSO communication system was demonstrated using 102 comb lines modulated by 10 Gbps DQPSK signals over a 1 km straight-line air transmission^[52]. Besides, using a microcomb for carrier generation in wireless communications could benefit from its inherent low noise. With both data stream and LO wirelessly transferred, a wireless communication link at 300 GHz was demonstrated. The transfer rate is 60 Gbps under 15 Gbaud 16-QAM modulation format^[342]. These applications demonstrate the versatility of microcombs in various communication platforms beyond traditional fiber optics.

5.2.2.

Optical computing

Optical computing, compared with its electronic counterpart, holds the promise of “compute as it propagates”, which breaks the bottleneck of operation speed limited by capacitance meanwhile providing considerable parallelism capabilities^[347]. Very recently, optical neural networks (ONNs) have attracted significant attention due to their high throughput and energy efficiency in neuromorphic computing tasks^[348,349]. One of the natural advantages of performing matrix operation in the optical domain is the ultra-large frequency bandwidth. Wavelength, as a new degree of freedom for parallel computing, isolates different channels by its intrinsic orthogonality so that each individual comb line could serve as an element in the matrix. Using traditional multi-wavelength laser arrays, small-scale ONNs have been demonstrated^[350,351]. However, further increasing the number of individual lasers significantly adds to the power consumption and system complexity. Interestingly, the massively parallel nature of microcombs can be leveraged to handle the complexity of large models in optical neural networks, making them well-suited for scaling up.

Fig. 32

Microcomb-based optical computing. (a) A SiN soliton microcomb combined with a phase-change material attached to an on-chip waveguide array for tensor core operation^[345]. (b) A time-stretch strategy for both the convolution layer and fully connected layer in the optical neural network^[51]. (c) Silicon-photonic-assisted highly integrated optical computing processor based on a microcomb^[346].

To verify this, two proof-of-concept demonstrations have been proposed, as shown in Figs. 32(a) and 32(b). A “photonic tensor core” consists of a silicon nitride microcomb and a phase-change material (PCM) attached to waveguide networks^[345]. This processor implements parallel MVM operation using multiple wavelengths, while the $16\times 16$ PCM cell matrix serves as a weight vector, attenuating matrix elements based on their phase configurations. Both sequential and parallel MVM operations are performed to accelerate the image edge highlighting, including more than 63000 inner-product operations with the entire convolution processed at a speed of 1 kHz. Also, a CNN digital recognition task is performed to sort 10000 test images with an accuracy of 95.3%. At the same time, another microcomb-based convolutional accelerator was realized by employing a time-stretch scheme^[51], where a fiber-based dispersion delay line was used to align the multiplication results at different wavelengths. This setup enabled the completion of a full multiply-accumulate (MAC) operation within the proper sampling interval. Thanks to the large optical bandwidth and quick electro-optical conversion, the vector computing speed can be as high as 11.3 TOPS. Serving as the building block of a convolutional ONN, such a processor accelerates calculations both in convolutional and fully connected layers for a handwritten digit recognition benchmark, showing an accuracy of 88%.

More recently, a highly integrated photonic processor has been proposed for the aforementioned time-stretch optical convolution operation by employing a microcomb and a silicon photonic processing unit, as illustrated in Fig. 32(c). Key functions such as the input vector loading, weight bank loading, and the true time delay are all integrated monolithically on a silicon chip, therefore greatly simplifying the system size^[346]. Based on this system, a high compute density of over $1\mathrm{TOPS}/{\mathrm{mm}}^2$ is demonstrated, accelerating both image edge detection and handwritten digit recognition tasks. Demonstrating the highest level of integration in a microcomb-based optical computing system, this work has shown great promise for achieving high packing density and scalability in integrated optical computing.

5.2.3.

Microwave photonics

The utilization of the optical domain for microwave generation, manipulation, and measurement, which is known as microwave photonics, has attracted extensive research interests due to the inherent abundance of bandwidth optical devices^[352]. Microcomb-based microwave photonic applications mainly focus on two functions: low noise microwave generation and multi-tap signal processing.

1) Low-noise microwave generation

Table 9

Low-Noise Radio Frequency Generation Based on Microcombs

By direct detection of a free-running microcomb, a high-purity microwave can be generated from a soliton pulse. Such pure-optical solution has been demonstrated in several platforms, with the repetition rate ranging from tens to hundreds of GHz level^[44,229,353], as shown in Table 9. Despite the absence of a locking regime, these high-Q microresonators enable a low-noise microwave generation with absolute single-sideband (SSB) phase noise power spectra density lower than $-110\mathrm{dBc}/\mathrm{Hz}$ at 10 kHz. On top of that, Yi et al. find that the nonlinear behavior of single-mode dispersive waves can be used to further suppress the repetition rate noise^[74]. With adequate pump detuning, the coupling of pump-laser frequency noise into the repetition rate could be minimized.

Achieving a low-noise microwave oscillation with higher performance requires external active feedback for thermal drift and actuation correction. Approaches including microwave injection locking^[301], optical self-injection locking^[140], fiber-photonic stabilization^[295], Kerr-induced synchronization^[80], and optical frequency division (OFD)^[42,354] are proposed for the microwave purification. Microwave injection locking is adapted in a 14 GHz-MgF2 microcomb to discipline the soliton by creating an intracavity potential gradient^[301]. The self-purifying mechanism in a soliton pulse reduces the RF tone phase noise by nearly 30 dB at 10 kHz offset frequency. A mode-locked Kerr comb in an ultra-low-loss 5 GHz SiN microresonator exhibits phase noise of $-114\mathrm{dBc}/\mathrm{Hz}$^[140]. A DFB laser is injection-locked to this high-Q ($>{10}^8$) resonator, resulting in an extraordinarily narrowed linewidth. This leads to generating a dark-pulse-shaped coherent comb generated with excellent stability. Repetition rate stabilization could also be achieved by fiber photonics. The generation of a low-phase-noise 22 GHz microwave signal is demonstrated using a kilometers-long fiber delay line as a timing reference^[295]. The phase noise PSD of this fiber-stabilized microcomb is around $-125\mathrm{dBc}/\mathrm{Hz}$, which shows one of the best noise performances without atomic locking.

With the optical frequency division technique, the stability of an ultra-low-noise laser could be transferred to the repetition rate. Recently, such an approach has been adopted in soliton microcombs, with the division operation performed in either the electrical^[354] or optical^[42] domain. A simplified OFD on a microcomb is performed via electrically canceling the comb phase noise and providing division of the ultrastable pump laser frequency to the microwave domain, with an adequate manipulation and combination of signals^[354]. The phase noise of the 14 GHz repetition rate output is below $-135\mathrm{dBc}/\mathrm{Hz}$ at 10 kHz Fourier frequency. A more common approach to achieve optical frequency division is locking two comb lines to precise optical references and reading out the output frequency from the repetition rate beat note^[42,355]. In Ref. [42], two comb lines, including the pump laser, are stabilized to rubidium frequency references separated by 3.5 THz, with a division factor of 108. More recently, microcomb OFD in highly integrated form has been demonstrated^[355,356]. Employing a 4 mm long ultra-low-loss SiN coil cavity as an optical reference, two lasers are stabilized and thereafter locked to a SiN soliton microcomb. Optically-electrically converted by a high-speed flip-chip bonded charge-compensated modified uni-travelling carrier photodiode, a record low 100 GHz phase noise of $-114\mathrm{dBc}/\mathrm{Hz}$ at 10 kHz offset frequency has been reached^[355]. In the meantime, stabilized self-injection-locked integrated lasers are used to lock the dark soliton microcomb in thin-film SiN. Such a system achieved a purified 20 GHz microwave with unprecedented absolute phase noise of $-135\mathrm{dBc}/\mathrm{Hz}$ at 10 kHz offset in integrated photonics^[355]. To reduce the system cost and complexity, a single-laser-based all-optical OFD is proposed by synchronizing two distinct nonlinear states, optical parameter oscillator (OPO) and soliton microcomb^[357]. The inherent stability of OPO is therefore transferred to a microwave state with $-114$ and $-128\mathrm{dBc}/\mathrm{Hz}$ at 10 kHz offset for the 227 and 16 GHz. These works, co-published recently, show the state-of-the-art performance in integrated-photonics-assisted microwave generation.

Moreover, Kerr-induced synchronization offers passive and electronics-free stabilization of a microcomb soliton to an external reference laser^[80]. The joint injection of the pump and reference laser leads to an optically captured comb line during the Kerr nonlinear dynamic so that the repetition rate can be tuned and its stability can be inherited from the reference through the OFD process. This novel approach marks an important step toward achieving power-efficient and architecturally simplified ultra-stable microwave generation.

2) Multi-tap signal processing

In addition to microwave generation, the parallel nature of microcombs allows for multi-tap signal processing, also known as the transversal filtering method, and relevant research has been initiated in various areas. These include signal integration^[363], differentiation^[362], Hilbert transformation^[361,365], arbitrary waveform generation^[364,366], channelizing^[359,367], reconfigurable filtering^{[43,53,358,368]}, beam forming^[360,369], and frequency conversion^[370], as shown in Fig. 33. Each application takes advantage of the microcomb’s ability to process wideband RF signals simultaneously, thereafter processing each carrier’s intensity, phase, or time delay for a specific function, opening up possibilities for more complex and versatile signal processing architectures.

Fig. 33

Microcomb-based microwave processing. (a) Reconfigurable filter^[358]. (b) Channelizer^[359]. (c) Beam former^[360]. (d) Hilbert transformer^[361]. (e) Differentiator^[362]. (f) Integrator^[363]. (g) Arbitrary waveform generator^[364].

One of the earliest demonstrations of microwave photonic processing using a microcomb involved the implementation of radio-frequency filters. In 2014, Xue et al. conducted a study on a programmable microwave photonic filter using a multi-tap delay line scheme^[43], where the RF signal is replicated across each comb-based optical carrier and subsequently manipulated in both the frequency and time domains to achieve the desired frequency response. Using a silicon nitride (SiN) microcomb paired with a commercial Waveshaper for spectral shaping, the optical carriers with a 230 GHz channel spacing are programmatically adjusted. This setup results in an RF transfer function that offers flexible frequency tunability and a flat-top characteristic, enhancing the performance and adaptability of the system for various applications. A tighter FSR can provide more taps, with a Hydex microcomb achieving up to 80 taps within the C-band. This configuration has demonstrated a high out-of-band rejection of up to 48.9 dB, featuring a tunable center frequency and 3 dB bandwidth^[358]. With advanced silicon photonic techniques, it is possible to implement not only microcombs but also other essential components such as modulators, true-time delay lines, and line-by-line shapers monolithically^[53]. This integration demonstrates the potential for achieving a high level of integration in RF processing for complex signal manipulation. Besides, one alternative for line-by-line shaping-free RF filters can be achieved by directly controlling the soliton state of the microcomb^[368]. By adjusting the pump power and frequency detuning, the mode spacing and spectral profile of the microcomb can be altered. This adjustment results in a tunable filter with variable frequency repetition and center frequency.

Mathematical operations can also be realized in this multi-tap delay line configuration, since its transfer function is given by

Therefore, any arbitrary desired operation can be tailored by setting the appropriate time delay $T$ and tap coefficients $h(n)$, enabling precise customization of signal processing tasks. For signal integration, the operation can be imitated via a discrete time-spectrum convolution operation between the RF input and the flattened microcomb^[363]. A large integration time window of 6.8 ns with time resolution as fast as 84 ps is realized. For the signal differentiator, the corresponding tap coefficient could be calculated based on the Remez algorithm^[362], in which way the first-, second-, and third-order intensity differentiator could be realized. Similarly, a band-limited Hilbert transformer can be realized using a transversal filtering method, where the tap coefficients are set to a hyperbolic function^[365]. Further, a fractional Hilbert transformer with tunable fractional order can be obtained with an operation bandwidth of $\sim 16\mathrm{GHz}$ with root mean square errors (RMSEs) under 3%^[361]. The number of taps, which corresponds to up to 17 usable comb lines, is crucial for the accuracy of the computation results.

Photonic RF arbitrary waveform generation could offer high-bandwidth signals with low noise that are difficult to obtain with pure electronic devices. Utilizing a microcomb, arbitrary waveforms can be synthesized both in time and frequency domains^[364,366]. In Ref. [364], Tan et al. achieved square waveforms with tunable duty cycles from 10% to 90% and a sawtooth waveform with tunable slope ratios from 10% to 90%. The seed signal is an RF pulse signal whose duration time is related to the dispersive time delay between the comb lines. In Ref. [366], Wang et al. demonstrated a microcomb-based Fourier synthesis AWG. The frequency domain of the desired signal is imitated at the optical domain and then down-converted to the baseband via a dual-comb photo mixing configuration. The system is more portable to be integrated since there is no need for the deployment of a long dispersive delay line, which is lossy on-chip.

Microwave beamforming interferes with electromagnetic waves from multi-paths to control the beam patterns in free space, where microcombs are promising candidates. A microcomb acts as the multiwavelength source in a true time delay technique of beamforming, where a dispersive medium offers a time delay between adjacent channels. Therefore, beam steering could be achieved either by changing the physical length of the dispersive medium^[369] or just by selecting the specific channels with a separation index of $m$^[360]. Both of the solutions have been demonstrated. With over 80 comb lines available, the $m$ is able to vary from 1 to 15. Therefore, a large tuning range from $-69.7°$ to 72.9° can be achieved^[360]. In Ref. [369], a programmable dispersion element is built with commercial $2\times 2$ optical switches and standard single-mode fibers. Within 21 comb lines, a 16-step dispersive delay line could offer a beam scanning range of $\pm 60°$. Such a delay scheme is also free of the beam-squint problem within tens of GHz operation bandwidth, where the system holds a consistent beam direction.

RF channelization splits broadband microwave signals into narrow slices for parallel baseband processing. In Ref. [359], a microcomb-based RF channelizer consists of an active microcomb generator and a passive microring filter connected serially. The mode difference between the two devices, namely, the Vernier effect, determines the sequential frequency shift of each channel. A spectral slice resolution of 1.04 GHz was experimentally demonstrated with about 19 GHz operation bandwidth. Moreover, by utilizing dual-polarization states, the channelized spectral segments and the RF instantaneous bandwidth could be doubled^[367].

Besides, a microwave frequency converter could be performed by utilizing the frequency relationship between microcomb mode spacing and the applied RF frequency:

Such configuration achieves a ratio of $-6.8\mathrm{dB}$ between output radio-frequency power and intermediate frequency power and a spurious suppression ratio of $>43.5\mathrm{dB}$^[370], showing the ability to realize a low-cost, compact footprint frequency converter.