Advances in Soliton Crystal Microcombs

Abstract

Soliton crystal microcombs, as a new type of Kerr frequency comb, offer advantages such as higher energy conversion efficiency and a simpler generation mechanism compared to those of traditional soliton microcombs. They have a wide range of applications in fields like microwave photonics, ultra-high-speed optical communication, and photonic neural networks. In this review, we discuss the recent developments regarding soliton crystal microcombs and analyze the advantages and disadvantages of generating soliton crystal microcombs utilizing different mechanisms. First, we briefly introduce the numerical model of optical frequency combs. Then, we introduce the generation schemes for soliton crystal microcombs based on various mechanisms, such as utilizing an avoided mode crossing, harmonic modulation, bi-chromatic pumping, and the use of saturable absorbers. Finally, we discuss the progress of research on soliton crystal microcombs in the fields of microwave photonics, optical communication, and photonic neural networks. We also discuss the challenges and perspectives regarding soliton crystal microcombs.

1. Introduction

Over the last twenty years, advancements in photonic nanofabrication technology have given rise to a variety of sophisticated integrated microcomb devices, providing considerable benefits regarding compactness, reduced weight, lower power consumption, and economic efficiency [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. Microcombs, a special type of light source, exhibit a series of coherent spectral lines, with uniform spacing in the frequency domain. This pattern manifests in the time domain as optical pulses that occur at regular intervals [15]. Thanks to their high coherence and stability, soliton microcombs exhibit great potential in applications such as spectroscopy [16,17,18,19], optical clocks [20,21], astronomical detection [22,23], communications [24,25,26,27,28,29], frequency synthesis [30,31,32,33], range measurement [34,35], and photonic neural networks [36,37,38,39,40]. Additionally, soliton microcombs provide a novel physical platform for studying interactions between light and matter [41,42].

Dissipative Kerr solitons (DKSs) are self-sustaining waves that can be produced in nonlinear optical microresonators. The study of DKSs originated in 2004 with the initial experimental observation of several discrete comb lines in high-quality factor silica microcavities [43]. The cascaded four-wave mixing in a silica toroid microcavity was reported in 2007, creating a broadband optical frequency comb with uniformly spaced lines in the frequency domain. This pioneering research achievement marks the official birth of microcavity optical frequency comb technology [44]. In 2010, back-to-back reports on optical frequency combs based on high-index doped silica [45] and silicon nitride (SiN) [46] platforms were published, marking the first on-chip integration of microcavities with coupled waveguides and pioneering the field of integrated on-chip microcombs. In 2014, the formation of mode-locked DKSs was first observed within a magnesium fluoride crystal cavity, displaying anomalous dispersion [47]. These solitons are the combined effects of optical loss, gain, nonlinearity, and dispersion within the microresonator. This discovery opened up a new field of research for soliton microcomb. Compared to previous microcavity optical frequency combs, soliton microcombs eliminate the effects of modulation instability (MI), thus offering the advantages of high coherence and stability.

During the last ten years, soliton microcombs have seen considerable advancements in both their theoretical foundations and applications, becoming one of the important research directions in the field of photonics. However, there are still some challenges regarding the generation of soliton microcombs that need to be urgently addressed. The generation of DKSs requires adjusting the pumping wavelength from the short-wavelength region to the long-wavelength region of the resonance mode. However, the accumulation of thermal effects during this transition impedes the microcomb’s shift from an MI state to single-soliton state stability [47,48,49], which necessitates a complex pump laser control mechanism for the generation of DKSs. In order to overcome the thermal effects during the generation process of DKSs, researchers have adopted a variety of strategies, such as the power-kicking method [50], the thermal tuning method [51], the auxiliary laser thermal stabilization method [52,53,54], and the photorefractive effect in lithium niobate microresonators [55]. Moreover, the efficiency of transforming the energy of the pump light into the optical comb within traditional DKS is approximately 1%.

Soliton crystals (SC) are composed of a series of closely spaced solitons arranged in a well-ordered, crystal-like formation, exhibiting a highly organized spectral pattern [56]. When transitioning from the MI state to the SC state, the solitons are closely packed within the microcavity, and the intracavity optical power is very close to the spatiotemporal chaos that precedes its formation in the experimental setup, encompassing the entire angular domain of the resonator [56]. Therefore, the generation of SC microcombs does not require complex wavelength control mechanisms and can be produced by slowly tuning the laser wavelength. Up until now, leveraging sophisticated experimental techniques, soliton crystal microcombs have been successfully demonstrated across a variety of material platforms [42,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73], such as yttria-stabilized zirconia (YSZ) microdisks [57], aluminum gallium arsenide (AlGaAs) microrings [58], silica microdisks and microrods [56,59,60], graphene–nitride heterogeneous microrings [61], SiN_x microrings [42,62,63,64,65,66,67], lithium niobate (LN) microrings [68], aluminum nitride (AlN) microrings [69], and high-index doped silica microrings [70,71,72,73].

Table 1. Typical specifications for reported SC microcombs.

Material Platform	Structure	FSR (GHz)	Wavelength Range (nm)	Crystal Types	Refs.
YSZ	microdisk	~74.5	1530–1580	PSC 1	[57]
AlGaAs	microring	~1018	1400–1700	PSC	[58]
SiO2	microrod	~25.6	1535–1565	Defected SC	[59]
SiO2	microdisk	~26	1530–1570	Multiple SC	[56]
SiO2	microrod	~60.7	1500–1600	PSC	[60]
Graphene–Nitride	microring	~90	1400–1900	PSC	[61]
SiNx	microring	~200	1400–1800	PSC	[62]
LN	microring	~199.7	1480–1640	PSC	[68]
AlN	microring	~374	1150–2300	PSC	[69]
High-Index Doped Silica	microring	~49	1500–1650	PSC	[70]
High-Index Doped Silica	microring	~48.9	1450–1650	Flat Spectral SC	[71]
High-Index Doped Silica	microring	~48.9	1500–1600	Multiple SC	[72]

¹ Perfect soliton crystals.

provides a concise summary of some typical SC microcombs realized on various material platforms, each with its unique cavity characteristics. Additionally, mode-locked lasers have become a critical technology for generating soliton crystals due to their ability to produce stable ultrashort pulse sequences and coherent optical frequency combs [74,75,76,77,78,79,80,81,82,83]. By precisely controlling the dispersion, nonlinearity, and gain/loss mechanisms within the cavity, they enable the efficient generation of soliton crystals. Adjusting the parameters of the mode-locked lasers allows for flexible control over the properties of soliton crystals, catering to various application needs.

In this paper, we provide an overview of the latest advancements in SC microcombs and present the outlook for the future perspectives of soliton crystal microcombs. The subsequent sections of this paper are arranged in the following manner: Section 2 briefly introduces the fundamental principles of optical frequency combs. Section 3 summarizes several methods for generating SC. Section 4 presents the applications of SC microcombs in the fields of microwave photonics, optical communication, and photonic neural networks. The challenges and perspectives regarding SC microcombs are discussed in Section 5. Section 6 discusses the automatic generation and adjustability of SC microcombs. Finally, the conclusions are provided in Section 7.

2. Numerical Model of Soliton Microcombs

The nonlinear dynamics of soliton microcombs involve the decay, dispersion, continuous optical pumping, and third-order nonlinear effects experienced by each comb tooth. This nonlinear process can be articulated through mathematical formulations in the frequency domain or the time domain. In the frequency domain, a differential equation can be formulated for each tooth of the microcomb optical frequency comb, with the various differential equations coupled together through four-wave mixing terms. This set of differential equations is collectively referred to as the coupled mode equations (CMEs) [84,85]. When describing the nonlinear dynamics of microcombs using the CMEs, the frequency dependence of various parameters can be fully taken into account, leading to more accurate results. When conducting coupled mode analysis, it is assumed that the optical field of each comb line is $A_j$, with the corresponding resonant frequency of ${\omega }_j$. The optical field of the pump mode is $A_{j0}$, and the resonant frequency of the pump mode is ${\omega }_p$. Since microcombs are typically centered around the pump light and extend bilaterally in the frequency domain, the relative mode number $\mu =j-j_0$ is introduced, with the pump mode’s relative mode number being 0. The dynamical equation for the optical field $A_{\mu }$ can be expressed as follows:

$${\displaystyle \frac{d{A}_{\mu }}{dt}}=-\left(i{\omega }_{\mu }+\kappa /2\right)A_{\mu }+{\delta }_{0,\mu }\sqrt{{\displaystyle \frac{{\kappa }_{\mathrm{ext} }{P}_{\mathrm{in} }}{\hslash {\omega }_0}}}{e}^{-i{\omega }_{p}t}+ig\sum _{{\mu }_1,{\mu }_2,{\mu }_3}{A}_{{\mu }_1}{A}_{{\mu }_2}{A}_{{\mu }_3}^{*}$$

(1)

where ${\omega }_{\mu }={\omega }_0+D_1\mu +D_2{\mu }^2/2!+D_3{\mu }^3/3!+\cdots$, and $\kappa$ represents the overall decay rate of the cavity, which encompasses both the intrinsic decay rate and the rate due to coupling losses ${\kappa }_{ext}$. $P_{in}$ represents the pump power. The nonlinear coupling coefficient $g=\mathrm{\hslash }{\omega }_0^{2}c{n}_2/n_0^2{V}_{eff}$, where $n_0$ and $n_2$ denote the linear and nonlinear refractive indices, respectively. $V_{eff}$ represents the cavity’s effective modal volume, while $\mathrm{c}$ denotes the speed of light under vacuum, and $\mathrm{\hslash }$ signifies the reduced Planck constant.

The CMEs illustrate the intricate nonlinear behavior of microcombs in the frequency domain. By applying a discrete Fourier transform, these equations can be reinterpreted in the time domain, resulting in the formulation of the Lugiato–Lefever equation (LLE). When performing numerical simulations of steady-state SC microcombs, it is common to introduce a local dispersion shift in the LLE to model mode coupling, which can be described in the frequency domain by the following equation [56,86,87,88]:

$$\begin{array}{c}{\displaystyle \frac{d{A}_{\mu }}{dt}}=-\left({\displaystyle \frac{\kappa }{2}}+i\delta \omega \right)A_{\mu }+i{D}_{\mathrm{int}}^{\mathrm{AMX}}\left(\mu \right)A_{\mu }+ig\mathcal{F}{\left[|A{|}^{2}A\right]}_{\mu }+\sqrt{{\displaystyle \frac{{\kappa }_{\mathrm{ext} }{P}_{\mathrm{in} }}{\hslash {\omega }_0}}}{\delta }_{0\mu }\\ D_{\mathrm{int}}^{\mathrm{AMX}}\left(\mu \right)=D_{\mathrm{int}}\left(\mu \right)-{\delta }_{\mu {\mu }_0}\Delta {\omega }_{\mathrm{AMX}}\end{array}$$

(2)

3. Generating Schemes for Soliton Crystal Microcombs

Various schemes for generating SC microcombs have been developed, such as utilizing avoided mode crossings (AMXs), harmonic modulation, bi-chromatic pumping, and saturable absorbers. In this section, we offer an exhaustive summary of these cutting-edge approaches.

3.1. Avoided Mode Crossing

The formation of SC is observed to correlate with the expanded background wave, resulting from the interference between the mode that gains surplus power due to mode crossing and the pump laser. Enough solitons coexist in the microcavity for the total intracavity energy to approach the level of chaotic MI states. Typical SC steps appear at the top of the intracavity power curve and exhibit excellent thermal interference resistance. The fluctuations of temperature within the cavity are comparatively minor, having a minimal impact on the resonance frequency, thus allowing for the stable formation of SC utilizing a slow-speed adjusting method without the need for complex methods to overcome thermo-optic effects.

Figure 1a illustrates several typical material platforms for generating soliton crystal microcombs utilizing AMXs. The dispersion curve on the top right of Figure 1a contains an obvious AMX point. Figure 1b shows that we classified the typical SC microcombs listed in Ref. [56]. We can roughly divide them into the following categories: PSCs, solitons with vacancies, solitons with a shifted pulse, solitons with irregular spacings, and solitons with periodicity over multiple scales (superstructure). PSCs, representing a distinctive state of SC, feature solitons uniformly distributed within the cavity, resulting in comb lines spaced by integer multiples of the free spectral range (FSR). The comb repetition rate of PSCs is related to the number of solitons, which depends on the spacing between the pump wavelength and the AMXs. When there are a larger number of solitons within the cavity, PSCs can increase the FSR to above THz. Furthermore, the generation of PSCs does not require excessively high power. A pump power threshold has been identified below which photonic soliton crystals can be generated deterministically [62]. An SC with a single vacancy exhibits a spectrum that is a superposition of a single soliton microcomb and a PSC microcomb. An SC with two vacancies exhibits a frequency domain that is a superposition of two-soliton microcombs and a PSC, with spectral characteristics related to the number of solitons between the two vacancies. Crystals that exhibit a superstructure, also known as “palm-like” SCs, feature a large number of solitons within the cavity, with a power level nearly equivalent to that of the MI state, and their spectral characteristics display a single FSR. Compared to traditional single-soliton microcombs, palm-like SC microcombs exhibit a higher energy conversion efficiency, are less susceptible to thermal effects, and are easier to generate.

3.2. Harmonic Modulation

Single-soliton microcombs have been successfully generated by employing the sub-harmonic phase-modulation scheme (SPS) [89]. In 2020, the method of achieving PSCs using SPS was numerically explored [90]. The interaction between side bands and cavity modes was meticulously adjusted through modulation to generate PSC microcombs. The modulation frequency was meticulously designed and optimized to achieve the desired outcome. The results demonstrate that adjustable repetition frequencies ranging from approximately 50 to 200 GHz can be achieved using a doped silica microcavity with an FSR of 10 GHz. In this scheme, the repetition frequencies of the PSC microcombs are controlled by phase-modulating the pump laser through an electro-optic modulator (EOM). Conceptually, for the formation of an N-soliton PSC, the modulation frequency ought to correspond to a ratio of n/m of the microcavity’s FSR. Consistent with the resonant criteria [91], interferometric enhancement within the microcavity occurs exclusively for those modulated comb lines that match the cavity resonance modes. As a result, the effective pump signal for creating an N-soliton PSC has a frequency spacing of n times the FSR. They realized PSC microcombs with soliton counts between 5 and 20 through numerical simulation, accomplishing this by fine-tuning the pump power.

3.3. Bi-Chromatic Pumping

The bi-chromatic pumping method is widely used to counteract the effects of thermo-optics in single-soliton microcombs [52,53,54]. The principle is as follows: Initially, the auxiliary light is tuned to the blue detuning region of the resonance peak, and then the pump light is tuned to the red detuning direction by coupling into the microring resonator (MRR) in the opposite direction. As the pump light is tuned beyond the MI state, the auxiliary laser offsets the drop in intracavity power, maintaining the cavity’s resonant state. Thus, transitioning from the MI state to the soliton states becomes feasible without the need for a particular tuning rate.

The bi-chromatic pumping technique for deterministic PSC synthesis operates via a distinct mechanism compared to those of the previously mentioned approaches. Figure 2a shows a typical experimental setup, with control and pump lasers propagating in opposite directions through a high-index doped silica microresonator [70]. Figure 2b depicts the concept of deterministic SC synthesis. In this approach, an additional laser acts as a control beam. A fraction of the control light is reflected opposite to the pump, forming a modulated background field. This modulated background is used to regulate the generation of PSC microcombs. The period of the potential field corresponds to the difference in the number of modes between the pump and the control lasers. As illustrated in Figure 2c, by adjusting the spacing between the two lasers, a comprehensive set of PSC microcombs with repetition rates spanning from 1 × FSR to 32 × FSR of the microcavity can be deterministically generated, with a high degree of reproducibility.

3.4. Saturable Absorber

PSCs can be deterministic and can be produced within a system incorporating a saturable absorber (SA) [92]. In previous schemes [93], it has been proven that the structure with carbon nanotubes deposited on a silica microresonator, as shown in Figure 3a, can achieve the saturable absorption effect. Figure 3b demonstrates the principle of achieving PSCs using the SA effect, in which the system transitions directly from the Turing state to the PSC state, skipping the chaotic state. This happens as the nonlinear absorption curbs the development of sub-pulses and noise, maintaining a stable waveform. Furthermore, the SA effect enhances the modulation depth of the Turing patterns. Consequently, the system transitions directly from the Turing patterns to the DKS state, bypassing the chaotic phase [92]. This can also be interpreted as the presence of the SA effect being instrumental in creating the periodic potential wells necessary for the formation of PSC [92]. Figure 4 presents the relevant numerical simulation results. As shown in Figure 4a–d, without the introduction of the SA effect, the system successively experiences the Turing state, the chaotic state, and ultimately enters the DKS state. When the SA effect is introduced (Figure 4e–h), the system bypasses the chaotic state and directly enters the PSC state.

4. Applications

Compared to the traditional single-soliton state Kerr microcomb, the SC microcomb displays the advantages of high-power conversion efficiency and a simple generation mechanism. Thanks to these, SC microcombs are widely applied in various fields such as microwave photonics [94,95,96,97,98], optical communication [99,100], and photonic neural networks [101,102]. In this section, we summarize the applications realized by the palm-like SC microcomb generated from the doped silica microresonator, as shown in Figure 5. This palm-shaped SC microcomb can be generated simply by slowly adjusting the swept laser, and its relatively flat central spectrum is very conducive to spectral shaping.

4.1. Microwave Photonics

SC microcombs can supply numerous wavelength sources for microwave photonics, enabling diverse processing capabilities. In particular, SC microcombs have the advantage of low-phase noise, and a great deal of research focuses on the application of microwave photonics based on SC microcombs.

In 2020, Tan M. et al. proposed an arbitrary fractional order differentiator ranging from 0.15 to 0.90 utilizing SC [94]. The experimental setup and results are shown in Figure 6a and Figure 7, respectively. Firstly, a palm-shaped SC microcomb was produced by tuning the pump wavelength, and the lines of the comb were smoothed by the first waveshaper (WS). Subsequently, the comb lines were modulated by the input RF signal, which was then distributed across the wavelength channels to create duplicates. The RF duplicates were transmitted via conventional optical fiber, achieving a cumulative time delay of 29.2 ps between neighboring wavelengths. The second WS fine-tunes the coefficients by controlling the power of the comb lines, and the outcome is then measured by the balanced photodetector, yielding the aggregate of both positive and negative coefficients. By adjusting the power of the comb lines following the calculated tap coefficients, it is possible to achieve any desired fractional order.

The working principle of the fractional-order differentiator is based on processing the input RF signal in the optical domain, using photonic technology to simulate the mathematical operations of fractional-order differentiation. The foundation lies in utilizing the multiple equally spaced wavelength channels produced by the microcomb, which serve as “taps” for signal processing, with each tap corresponding to a specific point in time within the signal processing. By precisely controlling the weights of these taps (i.e., the power of the comb lines), arbitrary fractional-order differentiation of the input signal can be achieved. This weight adjustment is accomplished by a waveform shaper, which adjusts the power distribution of the comb lines according to the desired fractional differentiation characteristics. Ultimately, the signals that have been delayed in time and adjusted in power are combined at the photodetector, realizing the fractional-order differentiation of the RF signal. This method not only provides precise control over the signal processing process but also, due to the high bandwidth and high-speed characteristics of photonics, confers the fractional-order differentiator with potential advantages in dealing with ultra-wideband RF signals.

In 2021, Tan M. et al. demonstrated three kinds of fractional-order Hilbert transformers utilizing SC microcombs within the identical experimental setup (Figure 6a) [95], such as lowpass Hilbert transformers and bandpass Hilbert transformers with phase shifts of 90 and 45 degrees, respectively. The fractional-order Hilbert transformer is an extension of the traditional Hilbert transformer, which is a linear time-invariant system that provides a phase shift of 90 degrees to the input signal, effectively transforming it into its analytical signal representation. Fractional-order systems, in contrast, offer a variable phase shift, denoted by the fractional order $P$, which allows for more flexible manipulation of the signal’s phase spectrum. In the experiment of this scheme, a WS is used to spectrally shape the palm-like microcomb, and then an electro-optic modulator is used to replicate the RF signal onto all wavelength channels. The modulated optical signals are transmitted through a dispersive medium to introduce wavelength-dependent delays, and are finally combined on a photodetector and converted back to the RF domain. By adjusting the weights of the comb lines, Hilbert transformers with different bandwidths and center frequencies can be achieved. Figure 8a presents the optical spectra of these fractional-order Hilbert transformers, both as designed and as measured. Figure 8b–d shows the simulated and experimental results of these fractional-order Hilbert transformers. The results show that the bandwidth of the lowpass Hilbert transformer, 45-degree phase shift bandpass Hilbert transformer, and 90-degree phase shift bandpass Hilbert transformer can be adjusted in 1.2–7.1 GHz, 3.5–15.2 GHz, and 3.4–15.3 GHz, respectively. This flexibility enables a wide range of signal processing functions, including frequency discrimination, signal differentiation, and complex modulation schemes.

Except for the microwave photonic filter, SC microcombs have the potential to achieve an RF arbitrary waveform generator using the experimental systems shown in Figure 6a. In 2020, by utilizing SC microcombs, Tan M. et al. provided over 80 channels and successfully achieved various arbitrary waveform shapes [96]. As depicted in Figure 9, they created square waves with adjustable duty cycles from 10% to 90%, sawtooth waves with adjustable slope ratios between 0.2 and 1, and symmetric concave quadratic chirp signals in the sub-GHz frequency range. That same year, utilizing up to 60 wavelength channels from the microcomb, Xu X. et al. obtained a substantial pulse compression ratio, peaking at 30 [97]. Figure 10 illustrates the working principle of phase encoding and the test results of reconfigurable phase encoding rates. By altering the duration of each phase encoding, adjustments can be made between 1.98 to 5.95 Gb/s.

In phased array antenna applications [98], as illustrated in Figure 6b, the SC microcomb is used as a premium source of multi-wavelength light for the true time delay line, modulating the microwave signal across various wavelengths, followed by dispersion introduction through a single-mode fiber (SMF), thereby creating a delay difference between the adjacent channels. Subsequently, a waveform shaper is employed to weight the individual channels, with each channel being separated by a wavelength division multiplexer. Following photoelectric detection, microwave signals with diverse time delays are input into the antenna array. Finally, as shown in Figure 11, the essential performance metrics for the phased array antenna utilizing the device have been determined.

4.2. Optical Communication

Emerging technologies such as 5G-A/6G, big data, and artificial intelligence are experiencing exponential growth in the demand for transmission capacity, posing unprecedented challenges to existing optical communication technologies. Wavelength division multiplexing technology can significantly enhance data transmission efficiency, requiring a large number of equally spaced frequency parallel laser sources as optical carriers. By leveraging advanced encoding techniques to precisely modulate their amplitude and phase, high-speed information transmission can be achieved. Thanks to the large number of parallel wavelength channels provided by the palm-like SC microcombs, several milestones have been achieved, including ultra-high data transmission over 75 km of standard optical fiber and the implementation of a broadband RF channelizer.

The system setup for ultra-high bandwidth optical communication is shown in Figure 12a [99]. Corcoran B. et al. selected 80 comb lines from the SC microcomb within the C-band using a WS, and by employing single-sideband modulation, they increased the comb line count to 160, resulting in a 24.5 GHz line spacing and an improved spectral efficiency. The implementation of 64 QAM across the entire comb spectrum was achieved at 23 gigabauds, efficiently utilizing 94% of the available spectrum. They conducted a load test on the network using a 76.6 km optical fiber installed in Melbourne, Australia, achieving a rate of 39 terabits s⁻¹. Figure 12b–d shows the SC microcomb spectra following flattening, modulation, and passage through either 75 km of lab fiber or the field trial connection. Figure 12e presents constellation diagrams of the received signals under different conditions, including back-to-back (directly connecting the transmitter to the receiver), through 75 km of in-lab fiber, and through the 76.6 km field trial link. These constellation diagrams reveal the signal quality under various transmission conditions, including parameters such as bit error rate (BER) and signal quality (Q²). The results demonstrate that the system can maintain a low BER and exhibit good transmission performance even after long-distance transmission. Additionally, in this scheme, due to the bandwidth limitations of commercial WS, the relevant experiments are confined to the C-band (1535–1565 nm). Furthermore, to fully leverage the advantage of wide spectral bandwidth, through adjustments in pump wavelength and power, manipulation of dispersion properties, and other techniques, soliton crystal microcombs may have the capability to span both C and L bands. By substituting a wider bandwidth spectrum shaper and increasing the number of wavelength channels, there is potential to achieve over 80 Tb/s, or even higher transmission rates, through a single integrated light source device.

The commercial prospects for SC microcomb technology in the field of optical communication are promising. In terms of cost, SC microcomb technology, through the implementation of integrated photonic circuits, has the potential to reduce the complexity and costs associated with traditional multiwavelength light source systems. Regarding energy consumption, due to its high efficiency in energy conversion and compact design, SC microcomb technology can reduce power usage, which is particularly important for data centers and high-speed communication networks. In terms of market potential, with the growing demand for high-speed data transmission, especially in the areas of 5G/6G and data center interconnects, SC microcomb technology can provide higher spectral efficiency and data transmission rates, meeting the market’s urgent need for bandwidth. Therefore, as the technology matures and production scales up, SC microcomb technology is expected to play a significant role in the optical communication market, driving the industry towards higher speeds and lower energy consumption.

The setup for the broadband RF channelizer, depicted in Figure 13a, incorporates two MRRs, with closely aligned FSRs of around 49 GHz [100]. The active MRR generates an SC microcomb that provides up to 92 comb lines in the operating band, while the other MRR acts as an intensity modulator. Xu X. et al. utilized the Vernier effect between the two to segment the broadband RF spectrum, with a high resolution of 121.4 MHz, thereby achieving continuous channelization at a rate of 87.5 MHz per channel. As shown in Figure 13b,c, their experiments confirmed an instantaneous RF operating bandwidth of 8.08 GHz.

4.3. Photonic Neural Network

With the development of big data, network convergence, and the Internet of things, artificial intelligence has attracted widespread attention worldwide, achieving significant results in fields such as computer vision, medical diagnosis, molecular and materials science, and speech recognition. Against this backdrop, the world generates massive amounts of data at an exponential growth rate, necessitating faster and more efficient processing methods. However, traditional electronic neural networks face a series of technical bottlenecks, including long latency and high power consumption. With its advantages of high speed, high bandwidth, and low crosstalk, photonic technology can significantly enhance computational speed by introducing optical processing mechanisms to construct photonic neural networks.

In 2021, Xu X. et al. proposed a microcomb-based photonic convolutional accelerator [101], which utilizes time, wavelength, and spatial interleaving technology to achieve a photonic neural network with a computing speed of 11.3 TOPS (tera operations per second). As shown in Figure 14, the convolutional kernel is unfolded into a weight vector $W$, and each element of the weight vector is mapped onto lines of the SC microcomb by a WS. Next, the image data matrix is one-dimensionalized and unfolded into a one-dimensional vector, where each pixel of the image is transformed into a part of a time-sequence digital signal. The symbols correspond one-to-one with the vector elements, with each symbol lasting for a duration of $\tau$. Subsequently, this digital signal is modulated onto the microcomb by an electro-optic Mach–Zehnder modulator, and then it is input into a single-mode fiber, where a fixed time delay is introduced. Eventually, the delayed optical signal is detected by a photodetector, and the time-domain signal sequence is collected on an oscilloscope. During the photoelectric detection process, the detector sums the optical power of all frequency components, which is essentially a convolution process for the weight matrix and the input data. Under the same experimental conditions, a photonic convolutional neural network containing ten output neurons was constructed in sequence, and this network achieved an accuracy rate as high as 88% in the task of recognizing handwritten digital images, which is very close to the 90% numerical result calculated on an electronic digital computer. This achievement not only demonstrates the potential for optical convolutional neural networks in the field of image recognition but also proves the scalability and trainability of the method, which is expected to be applied to scenarios with more stringent requirements, such as autonomous driving, high-speed big data processing, medical image analysis, radar image recognition, etc.

In 2023, Tan M. et al. designed a photonic processor for video processing utilizing the time-wavelength convolutional accelerator [102]. This system achieves ultra-high-speed performance, reaching 17 terabits per second (Tbs/s), simultaneously processing approximately 399,061 video signals and performing up to 34 different image processing functions on each signal. Figure 15 illustrates the working principle of the photonic signal processor based on an SC microcomb, which includes the following key steps: (1) The creation of the SC microcomb is achieved by utilizing a microring resonator made with a doped silica platform, with the comb lines of the microcomb acting as signal processing carriers. (2) The shaping of the optical signal produced by the microcomb using a WS to form the required weights. (3) The modulation of the shaped optical signal through an EOM, which is driven by the analog input film signal, encoding the information of the film signal into the optical signal. (4) The utilization of SMF to introduce a group delay dispersion for various wavelength channels. These controlled delays are essential for performing signal processing operations, including convolution. (5) The processed optical signal is detected by a photodetector, transforming it back into an electrical signal. (6) The detected electrical signal undergoes resampling and digital conversion to rebuild the digital video frames, constituting the system’s digital output signal.

Although the performance of the two SC microcomb-based schemes mentioned above cannot yet compete with that of the most advanced electronic processors [103,104,105], their performance can be further extended through various methods. Firstly, by extending the operating wavelength range to the S-band (1460–1530 nm), C-band (1530–1565 nm), and L-band (1565–1625 nm), the number of available wavelength channels can be significantly increased. This extension enables the use of a broader optical bandwidth, thereby increasing the parallel processing of the data streams and enhancing the system’s computational capacity and data transfer rate. Secondly, by introducing polarization-sensitive components and devices, it is possible to utilize the two orthogonal polarization states of light, thereby doubling the data transmission rate without the need for additional wavelength channels. Lastly, employing spatial-division multiplexing technology and using devices such as waveshapers or passive filters to add extra transmission paths in the spatial domain offers great potential to improve the system’s scalability and parallel processing capabilities.

The advancement of nanofabrication technology will significantly promote the development of photonic neural network chips, giving them broad application prospects. The current fabrication process for microcomb source chips is very mature and compatible with the CMOS (complementary metal–oxide–semiconductor) platform, making it suitable for large-scale integration [45,46,58,62,68,69]. In recent years, with the development of integrated processes, other components such as on-chip integrated lasers [106,107,108,109,110], optical spectral shapers [111], modulators [112,113,114,115,116,117,118,119,120,121], dispersive media [122], and photodetectors [123,124,125,126,127,128,129] have all been realized in integrated forms. Therefore, it can be optimistically assumed that optical neural network chips will eventually display broad market prospects in areas such as medical diagnosis, autonomous driving, big data, and artificial intelligence.

5. Challenges and Perspectives

Over the past few years, the study of SC microcombs has rapidly advanced, with enhancements in their performance and an expansion of their application scope. In this section, we discuss the current challenges and prospects faced in the generation and applications of SC microcombs.

Despite numerous studies having achieved the deterministic generation and switching of PSC microcombs [58,59,60,61,62,63,64,65,66,67,68,69,70], their application is still limited due to the large FSR of the PSC microcombs, which results in a smaller number of available wavelength channels within specific bands, especially the communication C-band. For single FSR palm-like SC microcombs, their generation is limited by the position and intensity of the AMX. This poses a challenge because variations in fabrication can influence the positioning and intensity of AMXs in microresonators.

AMXs arise from the interactions between distinct mode families and are prevalent in rings with anomalous dispersion. Waveguides exhibiting anomalous dispersion typically feature a larger cross-sectional area and often facilitate the coexistence of multiple modes, leading to the possibility of intermodal crossings. The dispersion characteristics of the mode family undergo significant alterations in the vicinity of the AMX. For devices without cladding, their dispersion and AMXs can be tuned after fabrication [130], but for integrated single-resonator devices, the dispersion and AMXs are difficult to tune over large ranges. For instance, experimental results in Ref. [131] indicated that in two high-index doped silica microrings, by altering the temperature, the position of the AMX shifted by 0.88 and 0.55 resonances within the 10–40 °C range, respectively. Furthermore, a study in Ref. [65] experimentally demonstrated that as the pump power increases, both the fundamental and higher-order modes undergo a redshift with differing shifts, decreasing the frequency gap and inducing minor alterations in the AMX’s location and intensity. For dual-ring devices, the auxiliary ring, acting as a source of additional modes, can facilitate the occurrence of mode crossings [132,133,134,135,136]. The AMX can be tuned across an extensive range by independently tuning two microrings with on-chip heaters. Therefore, the dual-ring structure has the potential to generate palm-like SC microcombs with arbitrary tuning of the pump wavelength.

In the applications mentioned in Section 4, the spectral control of the SC microcombs is exclusively achieved by using non-integrated devices (such as commercial programmable optical processors). The bulky volume of these devices limits their use in subsequent applications, thus urgently requiring their miniaturization and integration. Fortunately, a variety of innovative on-chip spectral shaping devices [137,138,139,140,141] have recently emerged, offering significant potential for the miniaturization essential for compact device applications. For example, PICs composed of MZI coupler arrays and linearly incremental delay lines can be programmed to perform various signal processing functions as needed [137]. PICs based on MRR arrays [138,139,140,141] can also process input signals. By independently controlling each MRR with thermos-optic phase shifters, these PICs can achieve high precision in regards to optical power control. Additionally, with the advancements in photonic nanofabrication and heterogeneous integration technologies, in the future, it will be possible to achieve the co-integration of MRRs with other on-chip active and passive devices, such as integrated lasers [142], high-performance modulators [143,144,145], photodetectors [146,147], etc., to achieve the monolithic integration of diverse systems.

6. Discussion

Integrated microcombs still face some technical challenges that must be overcome for their practical applications in the future, such as the automatic generation and adjustability of microcombs. This section mainly discusses the progress of SC microcombs in these areas.

The automated generation technology for soliton microcombs is crucial in practical applications. The traditional generation of soliton microcombs faces the challenge of microcavity thermal effects and still requires complex pumping and feedback mechanisms [47,48,49]. With the development of SC microcombs, the aforementioned issues can be effectively resolved. Because the intracavity power of the SC state is very close to that of the chaotic state, there will be no significant change in the cavity temperature while transitioning from the chaotic state to the SC state [56]. This temperature stability is crucial for achieving automated generation, as it reduces the risk of soliton state instability caused by thermal effects. This advantage greatly simplifies the generation process for SC microcombs, allowing for the automated generation of SC microcombs by programming a simple unidirectional scanning routine to control the pump laser detuning. Additionally, the automated generation of SC can be achieved through the thermal tuning method. Unlike in the frequency sweeping method, the pump laser wavelength is fixed, and the temperature is lowered to gradually bring the pump laser into the red detuning region of the resonance peak. Both methods can achieve the automated generation of SC microcombs. It is worth noting that the movement of the resonance peak due to temperature decrease is less sensitive compared to that for tuning the pump laser wavelength, which can effectively prevent excessive detuning that might cause the laser to overshoot the red detuning region.

Regarding the adjustability of SC microcombs, there are two types: one is repetition rate adjustability, and the other is pump wavelength adjustability. The tunability of the repetition rate is mainly aimed at PSC microcombs. For instance, in the harmonic modulation method [90] introduced earlier in this paper, by controlling the modulation frequency to correspond to a specific ratio of the microcavity’s FSR, it is possible to generate PSCs with an adjustable FSR ranging from 5 to 20. In the bi-chromatic pumping method [70], an auxiliary laser is introduced to form a modulated background field. By changing the spacing between this background field and the pump laser wavelength, FSRs of the PSC microcomb can be controlled between 1 and 32. Additionally, by using a dual-coupled microresonator [67], it is also possible to achieve PSC microcombs with tunable soliton numbers. The tunability of the pump wavelength in SC microcombs mainly depends on whether the position of the AMX is adjustable. For instance, in a dual-coupled structure, by changing the temperature of the auxiliary ring, the position of the AMX can be controlled [136]. Furthermore, by using an external temperature control device to change the microcavity temperature, the frequency of the pump laser can also be fine-tuned. According to the measurement results in Ref. [131], the offset is 1.7 GHz/°C.

7. Conclusions

In this article, we examined the recent developments for soliton crystal microcombs. Firstly, we briefly introduced the numerical model of the Kerr optical frequency comb. Secondly, we introduced several typical schemes for generating soliton crystals. Then, we summarized the applications of palm soliton crystal microcombs in the fields of microwave photonics, optical communication, and photonic neural networks. Ultimately, we analyzed the current challenges and prospects faced by SC microcombs.