Advances in soliton microcomb generation Download: 1829次
1 Introduction
Optical microcavities, which emerged from the rapid development of modern micro/nanofabrication technologies, have grown to be revolutionary devices that light the way toward several fantastic applications, including advanced light sources, ultrafast optical signal processing, and ultrasensitive sensors, benefitting from their unprecedented small size and high buildup of energy inside the resonators.1 The resonant optical field can be strongly enhanced in a high-quality (
Technically speaking, the character of microcomb mainly depends on microresonator properties as well as the pumping parameters (e.g., pump power and frequency detuning). The
Until now, based on advanced experimental techniques, SMCs have been realized in an
Table 1. Typical parameters of reported SMCs.
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Fig. 2. Typical spectral coverage of SMCs on various material platforms using different approaches.
In this review, we summarize recent experimental achievements with a perspective on the potential and challenges. The remainder of this paper is organized as follows. Sec.
2 Physics and Numerical Models for Microcombs
The generation of microcombs arises from parametric frequency conversion through the FWM effect that generates a pair of photons (a signal and an idler) that are equally spaced to the pump. The photonic interaction can be expressed as
The CMEs have been successfully used to determine the threshold and explain the role of dispersion as well as other mechanisms in the microcomb formation. However, the amount of computation increases dramatically with increases in the mode number. Through considering the total intracavity field an entirety
Based on the LLE, mode-locked microcombs have been predicted and rich physical phenomena have been explained, including the single soliton with dispersion wave,12 soliton crystals by taking into account of perturbation,46 and dark pulse states with a modified form to involve mode interaction.23 Raman self-frequency shift was also precisely simulated by adding the Raman response item
3 Experimental Schemes for Single SMC Generation
It has been found that SMC can be spontaneously formed while a CW pump stabilizes in the red-detuned regime of a dissipative nonlinear microcavity. However, the soliton existing range exhibits thermal instabibility for microcavities with negative temperature coefficients, which blinded SMC observation for more than 6 years since the first microcomb realization.8,10 Therefore, the major challenge for SMC generation has been how to stabilize a pump in the red-detuned regime of a microcavity. An intuitive thought is preventing the cavity from heating up before the pump sweeping to the soliton existing range, such as the frequency scanning method for SMC realization in a low thermal-optic coefficient
3.1 Frequency-Scanning Method
The basic idea of the frequency-scanning method is sweeping the pump to the red-detuned regime before the microcavity is heated up by the thermo-optic effect. Generally, the frequency-scanning speed is determined by the thermo-optic response time,
Fig. 3. Experimental demonstration of stable temporal solitons in a high- microresonator using the frequency-scanning method. (a) Experimental setup for stable temporal soliton generation. (b) Optical transmission power trace when the pump scans over a resonance. The discrete steps in the red-detuned regime (green shading) indicate existence of cavity solitons. (c) Optical spectral evolution while the pump sweeps in the blue-detuned regime. (d) Optical spectra for SMCs with 1, 2, and 5 solitons. OSA, optical spectrum analyzer; ESA, electrical spectrum analyzer; PD, photodetector; LO, local oscillator; FPC, fiber polarization controller; EDFA, erbium-doped fiber amplifier. Images are adapted with permission from Ref. 10.
The pump frequency-scanning method is a fundamental and intuitional approach for SMC generation. The success of this method relies on the control of the pump frequency sweeping speed and accuracy. The laser scanning time should be comparable to the cavity lifetime and thermal lifetime of the microresonator, which has a very high
For some special cases, SMCs can also be generated with relatively slow scanning speeds once the thermal dynamics during soliton formation can be stabilized by other approaches. For example, a partial overlapping mode can be used to compensate for the thermal dissipation when the pump tunes to the red-detuning regime. By taking advantage of an adjacent mode family in a specific
3.2 Power-Kicking Scheme
For microresonators with a high thermal-optic effect, the durations of soliton steps are so short that stopping the laser frequency exactly within these steps is technically difficult.63 As shown in
Fig. 4. SMC generation based on power-kicking scheme. (a) Experimental setup of power-kicking scheme. The microresonator is pumped by an external cavity diode laser that is amplified and modulated by an AOM and an EOM. (b) Typical triangular shape of the transmission power while the pump sweeps across a resonance. (c)–(e) Soliton steps of microcavities with repetition rates of 38, 70, and 190 GHz, respectively. (f) Measured optical spectrum of single SMC covering over 2/3 octave bandwidth. AFG, arbitrary function generator; EDFA, erbium-doped fiber amplifier; FPC, fiber polarization controller; OM, optical modulator; RF, radio frequency; TLF, tapered-lensed fiber. Images are adapted with permission from Ref. 12.
A typical experimental setup is shown in
Fig. 5. Schematic and timing sequences of the power-kicking scheme. (a) Setup used to bring very short-lived soliton states to a steady state, including two modulators to adjust the pump power. (b) Timing sequences of the pump scanning, the fast and slow power modulation, and the converted light power. (c) Initial timing of the fast modulation with respect to the thermal triangle and slow power modulation. (d) The fast power modulation induced soliton steps. (e) Combined effect of the fast and slow modulation. Images are adapted with permission from Ref. 63.
For cases with long enough soliton steps (e.g., longer than several microseconds), a single AOM can provide enough modulation speed for SMC generation. Additionally, the pump parameters can be adjusted with an active feedback loop to realize active capture and stabilization of temporal solitons.64 The power-kicking scheme has been widely used in some proof-of-concept applications such as DCS38 and microcomb-based range measurement.65 However, additional modulators and the precision control circuit complicate the SMC system, which increases the technical difficulties for miniaturized integration. Therefore, more compact SMC generation approaches, such as the thermal-tuning method and self-injected locked scheme, have been developed and are discussed next.
3.3 Thermal-Tuning Method
An equivalent approach for SMC generation is shifting the resonances of a microresonator through a thermal-tuning method rather than tuning the pump frequency. As shown in
Fig. 6. SMC generation based on thermal-tuning method. (a) Experimental setup of thermally controlled SMC generation in a microresonator. (b) Transmission optical power trace of the generated microcomb. Steps marked by arrows indicate transitions between different multisoliton states. Images are adapted with permission from Ref. 14.
In principle, the thermal-tuning method can be regarded as a variant of the pump frequency-scanning method. Compared with tunable lasers, fixed frequency lasers usually have much narrower linewidth and lower noise. So it is attractive for soliton generation using a fixed frequency laser to improve the microcomb performance. Meanwhile, a fixed frequency laser has a smaller footprint and the integration technique of current source is rather mature, so the thermal-tuning method has the potential to realize a fully integrated microcomb.52
3.4 Auxiliary-Laser-Based Method
Because the challenges of SMC generation mainly arise from the thermal instability of the soliton existing range, it is reasonable to imagine that the thermal effect can be solved by maintaining the intracavity optical power at a similar level during SMC generation. It is noted that microresonators exhibit contrary thermal characters when pumps are located at the blue- and red-detuned regimes. As a result, the dramatic decrease of intracavity heat when a pump laser tunes into a soliton existing range can be effectively compensated for by an auxiliary laser located at the blue-detuned regime. This principle has been verified recently,15,16,28,29,34 and the requirement for a rigid tuning time (on the order of thermal lifetime) can be relaxed using the auxiliary-laser-assisted approach.
A typical experimental setup is shown in
Fig. 7. SMC generation by the auxiliary-laser-based method. (a) Experimental setup. (b) Schematic of the counter-coupled auxiliary-laser-assisted thermal response control method. (c) The pump and auxiliary laser counter-balance thermal influences on the microcavity. (d) Optical spectrum of single SMC. Images are adapted with permission from Refs. 16 and 66.
Based on the auxiliary-laser-assistant thermal-balance approach, a new SMC regime is discovered in which the soliton power exhibits a negative slope versus pump frequency detuning. It is distinct from the traditional soliton existence regime with a positive slope that is accessible via thermal locking by thermal-avoided methods. The negative slope implies that the increase of average comb power is less than the decrease of pump background, resulting in the total intracavity power decreasing with the increasing of detuning. In another experiment, it is proved that the durations of soliton steps can be extended by two orders of magnitude under the assistance of a codirectional-coupled
All of these experimental results suggest that using an auxiliary laser can contribute to intracavity thermal equilibrium. It is regarded as an effective and universal method for stable SMC generation. Further, the auxiliary laser provides an additional degree of freedom for microcomb dynamic research. For example, the frequency spacing of the auxiliary and pump lasers has a significant impact on the microcomb states, and the beating between the auxiliary and pump lasers provides an optical lattice for soliton capture, which would be helpful for soliton crystal generation. This method can also provide a feasible approach to realizing spectral extension and synchronization of a microcomb in a single microresonator.67
3.5 Photorefractive Effect for Stable SMC Generation
Because of the negative temperature coefficient of microresonators, the soliton existing range exhibits thermal instability, which results in complex pump tuning techniques for SMC generation. By contrast, if the refractive index of a microresonator decreases with increasing intracavity optical power, the pump can enter the red-detuned regime stably for SMC generation, just like the MI comb generation in a negative temperature coefficient microresonator. It has been discovered that the photorefractive effect in a Z-cut
Fig. 8. Bichromatic SMC generation in a microresonator. (a) Schematic for influences of optical Kerr and photorefraction effects. The inset is the measured optical power traces when a pump sweeps across a resonance from the red-detuned side. (b) Comb power trace versus scanning time when the pump slowly sweeps forward and backward in the red-detuned regime. (c) Comb power trace versus scanning time when the pump rapidly sweeps from the red- to blue-detuned regimes. The power spikes are caused by the relatively slower response speed of the photorefraction effect. (d) and (e) Optical spectra of SMCs in near-infrared and visible bands, respectively. Images are adapted with permission from Ref. 31.
Because of the photorefractive effect, the thermal instability of the soliton existing range is completely compensated for. Therefore, SMC can be stably generated by coupling a pump into the resonance from the red-detuned side, and the pump can freely tune forward and backward for soliton switching. Meanwhile, the thermal stability of the soliton existing range can contribute to simplification of control circuits for SMC generation, which is crucial for miniaturized integration and practical applications. More interestingly, the
3.6 Forward and Backward Tuning Method
Due to the inherently stochastic intracavity dynamics, it remains a challenge to realize repeatable soliton switching and deterministic single SMC generation if using the aforementioned strategies. For example,
Fig. 9. (a) Scheme of the forward frequency-tuning method. (b) 200 overlaid experimental traces of the output comb light in the pump forward tuning, revealing the formation of a predominant soliton number of . (c) Scheme of the laser forward and backward tuning. (d) Experimental traces of the forward tuning (in yellow) and backward tuning (in white) for soliton switching and deterministic single SMC generation. (e) Measured absolute soliton existing range of a microring. The lower boundary presents staircase pattern that can be stably accessed step by step using backward-scanning method. (f) Optical spectrum of single SMC in a 100-GHz microresonator. Images are adapted with permission from Ref. 69.
After the frequency-scanning method was proposed, a forward and backward frequency-sweeping technique was introduced for deterministic single SMC generation.69 Briefly, the forward frequency tuning is first applied for multiple-SMC generation. In the next stage, the pump sweeps backward with a slow scanning speed, leading to successive reduction of the soliton number. The cavity dynamics comparison of forward and backward frequency tuning methods is shown in
A parallel progress on deterministic single SMC generation was fulfilled in a high-index doped silica glass microring through the forward and backward thermal-tuning method.15 The high-
Fig. 10. Deterministic single SMC generation using thermal-tuning method.15 (a) Power traces when just decreasing the operation temperature. (b) Power traces using forward and backward operation temperature tuning method. (c) Optical spectra for soliton number of 4, 3, 2, and 1 in a 49-GHz high-index doped silica glass microring. Images are adapted with permission from Ref. 15.
3.7 Self-Injection Locking
One of the ultimate goals for the microcomb field is fully integrated SMC sources. A common feature of all methods mentioned above is reliance on external narrow-linewidth pumps, which introduces great challenge for miniaturized integration. Benefitting from the advanced micro/nanofabrication technologies, ultra-high-
Fig. 11. Self-injection locking and spectral narrowing of a multifrequency laser diode coupled to an ultrahigh- WGM microresonator. (a) Experimental setup. (b)–(d) Spectrum and (e)–(g) the corresponding beat note signal for the free-running multifrequency diode laser, laser stabilized by the microcavity, and single SMC in the self-injection locking regime, respectively.45
A key factor of this technique is the
3.8 Pulse-Pumped Single-Soliton Generation
In addition to the narrow-linewidth CW lasers, temporally structured light sources can also be used as a pump for SMC generation.11,76,77 The merits of pulse-pumped schemes are reduction of the pump power and improvement in the conversion efficiency. Meanwhile, the generated soliton pulses are copropagating with pump pulses, which results in the synchronization of repetition rates. The principle for this scheme is depicted in
Fig. 12. Principle and experimental scheme for SMC generation driven by optical pulses.76 (a) For the CW-driven case, solitons propagate with a resonantly enhanced CW background. (b) For the pulse-driven case, pump pulses with repetition rate periodically drive the solitons. (c) Resonator transmission trace as the central driving mode scans across a resonance for an optimized repetition rate. (d) Contour plot of the resonator transmission showing soliton steps can exist for a wide (100 kHz) spanning interval of . Images are adapted with permission from Ref. 76.
Following the pulse-pumped cavity soliton generation in fiber and Fabry–Pérot cavities,78,79 generation has also been realized in a chip-based SiN microring, which can provide a spurious-free spectrum of resolvable calibration lines in the demonstration of a proof-of-concept microphotonic astrocomb.77 Importantly, locking cavity solitons to the external driving pulse (or soliton self-synchronization) enables direct, all-optical control of both the repetition rate and carrier-envelope offset frequency for the microcomb. Through stabilizing the subharmonically (i.e., the soliton repetition rate is twice that of the EOM frequency) driven astrocomb to a frequency standard, the absolute calibration with a precision of
Physically, a pulse pump can break the symmetry of a microcavity, which induces optical lattice for soliton capture. The soliton quantity is determined by the repetition rate, width of the pump pulse, and intrinsic properties of the microresonator (dispersion,
4 Extraordinary Soliton Microcombs
Different soliton forms in microcavities besides typical single or multisolitons, such as the soliton crystals, Stokes solitons, breather solitons, soliton molecules, laser cavity solitons, and dark pulses (solitons), also exist. They present distinct behaviors in both frequency and time domains, as well as enrich soliton dynamics and physics for microcomb research. In this section, the generation of these extraordinary solitons and their unique characteristics are reviewed.
4.1 Soliton Crystals
Soliton crystals defined as spontaneously and collectively ordered ensembles of copropagating solitons that are regularly distributed in a microcavity were recently discovered in silica WGM,46
Fig. 13. (I) Soliton crystals in a silica disk resonator.46 Left panel: measured (in black) and simulated (in color) optical spectra. Right panel: schematic depictions of the corresponding soliton distribution in the resonator with major ticks indicating (expected) soliton location and minor ticks indicating peaks of extended background wave due to mode crossing. (II) Soliton crystals in a high-index doped silica glass microring.19 Left panel: measured (in red) and simulated (blue solid circles) optical spectra. Right panel: simulated temporal traces exhibiting (expected) soliton distributions of the corresponding soliton crystals. Images are adapted with permission from Refs. 19 and 46.
A special state of soliton crystals, i.e., the perfect soliton crystals (PSCs), is defined as all solitons are evenly distributed in a cavity and experimentally observed recently.82,83 In a certain sense, such PSCs could be regarded as single SMC in a microresonator with larger FSR and thus, be capable of boosting the repetition rate to beyond THz level and breaking the limitation of bending loss for extremely small microresonators. Meanwhile, compared with single SMC in a same microresonator, the power of each comb line is multiplied by
Soliton crystals introduce a new regime of soliton physics and act as a test bed for the research of soliton interaction. The extreme degeneracy of the configuration space of soliton crystals suggests its capability in on-chip optical buffers.46 Meanwhile, benefitting from a tiny intracavity energy change, the easy accessibility and excellent stability of soliton crystals could facilitate SMCs toward a portable and adjustable system for out of laboratory applications.
4.2 Stokes Soliton
Stokes soliton is a special type of soliton that arises from Kerr-effect trapping and Raman amplification when a first soliton (primary soliton) is present.17
Fig. 14. Stokes soliton in a high- silica microdisk.17 (a) Stokes soliton (red) is overlapped with primary soliton (blue) in time and space, which introduces maximum Raman gain. Stokes soliton is trapped by optical potential well induced by Kerr effect, which locks the repetition rate to the primary soliton. (b) Measured FSRs of different mode families versus wavelength of a 3-mm silica microdisk cavity. (c) Beating RF spectra of isolated Stokes and primary soliton, indicating the repetition rate of Stokes soliton is locked to primary comb. (d) Measured optical spectrum of Stokes soliton. The inset shows the high-resolution spectrum of the overlapping range, which confirms that the Stokes soliton is formed in a different mode family. Images are adapted with permission from Ref. 17.
The central wavelength of the Stokes soliton relies on the FSR matching of distinct mode families, which offers a potential approach for controllable multicolor soliton generation through advanced-dispersion engineering techniques.84 Thus, it contributes to the SMC generation even in the spectrum range where anomalous-dispersion or high-power pump is not achievable.
4.3 Breather Solitons
Distinct from the stationary soliton states mentioned above, breather solitons show periodic oscillation in both pulse amplitude and duration20,51,85
Fig. 15. Breather soliton in a microresonator. (a) Schematic of soliton “breathing” behavior in a microcavity. (b) Recorded power trace of breather solitons. (c) Operating regimes of microcombs. Breathers are generated at relatively small detuning and high pump power through three steps (illustrated by I, II, and III). (d) Simulated transmission power trace. States 1 to 4 correspond to the primary comb, unstable MI, breather solitons, and stationary soliton state, respectively. (e) Averaged spectrum of the breather soliton in a microresonator. (f) RF spectrum of breather soliton. Images are adapted with permission from Refs. 20 and 51.
The breather soliton state also can be triggered by avoided mode crossings (regarded as the intermode breather soliton), which is a ubiquitous phenomenon in multimode microresonators as illustrated in
Fig. 16. Intermode breather solitons in microcavities. (a) Simulated intracavity power trace over the laser detuning in the absence of intermode interactions. The intermode breather soliton exists in the region where stationary soliton is expected (orange area). (b) Simulated power trace based on the coupled LLEs, showing a hysteretic power transition (gray area) and an oscillatory behavior (orange area). (c), (d) Measured optical spectra for intermode breather solitons in (c) an crystalline microresonator and (d) a SiN microring, which exhibits spikes that result from intermode interactions. Images are adapted with permission from Ref. 85.
4.4 Soliton Molecules
Soliton molecules are balanced states in which attractive force caused by group velocity dispersion (GVD) of bound solitons is counteracted by the intersoliton repulsive force induced by the XPM effect.22
Fig. 17. Heteronuclear soliton molecule generation using two discrete pumps. (a) Principle of bound solitons where attractive force and repulsive force are balanced. (b) Calculated repulsive force versus the temporal separation of solitons. (c) The experimental setup for soliton molecule generation. (d) Measured transmission power trace while the pumps sweep across a cavity resonance. The red-shaded area is the comb power of the major pump, while the comb power of the minor pump is indicated by the blue-shaded area. (e) Optical spectrum of soliton molecules of two bound solitons, which corresponds to a linear superposition of optical spectra of the major soliton (f) and minor soliton (g). Images are adapted with permission from Ref. 22.
Concerning experimental realization, discrete pumps are obtained by modulating a CW laser using an EOM. The frequency separation of discrete pumps is controlled by the driven RF signal. An example work is implemented in an
Soliton molecules in microcavities go beyond the frame of their predecessors in fiber lasers, which enriches the soliton physics. In terms of applications, soliton molecules might contribute to comb-based sensing and metrology by providing an additional coherent comb, as well as optical telecommunications if storing and buffering soliton-molecule-based data come true.22
4.5 Laser Cavity Solitons
SMCs can also be generated in a nested laser cavity in which a Kerr microresonator is embedded into a gain fiber cavity.21 The principle of laser cavity soliton is demonstrated in
Fig. 18. Laser cavity solitons. (a) Principle of cavity soliton formation. The microresonator is nested into a gain fiber cavity. (b) Mode relationship of the nonlinear microresonator and gain fiber cavity. (c) Typical optical spectrum of laser cavity soliton, which includes two equidistant solitons per round-trip. Images are adapted with permission from Ref. 21.
Comparatively, the laser cavity soliton is background-free, which is beneficial for improving the energy conversion efficiency. According to the LLE, the energy conversion efficiency is limited to 5% for CW laser pumped single soliton. However, the conversion efficiency of laser cavity soliton can be boosted to 96% in theory, and 75% is experimentally obtained.21 Furthermore, as the lasing modes are the common modes of nested cavities, the repetition rate of cavity soliton can be simply tuned through changing the fiber cavity length (e.g., using a high-precision delay line), providing a new approach for the realization of SMC frequency locking. Meanwhile, the generation of laser cavity solitons mainly relies on the modes relationship of nested cavities, so they exhibit high robustness against environment fluctuations.
4.6 Dark Soliton Generation in the Normal-Dispersion Regime
Dark solitons (or dark pulses) are generally understood as intensity dips on a constant background, which demonstrate some unique advantages (e.g., less sensitivity to the system loss than bright solitons and more stability against the Gordon–Haus jitter in long communication lines) and have attracted increasing interest in many areas. Based on the mean-field LLE in the context of ring cavities or Fabry–Pérot interferometer with transverse spatial extent, it is found that in the time domain the dark solitons manifest themselves as low-intensity dips embedded in a high-intensity homogeneous background with a complex temporal structure, as being a particular type of solitons appearing in dissipative systems.92,93 Although the original nonlinear Schrödinger equation admits a solution in the form of bright solitons in the anomalous-dispersion regime, dark solitons are in the normal-dispersion regime.94,95 It is worth noting that mode-locking transitions do not necessarily correspond to dark or bright pulse (soliton) generation in microresontors with normal dispersion.96,97 This is in contrast to the situations for the negative-dispersion regime where all soliton forms are actually “bright solitons.” Actually, in the field of traditional mode-locked fiber lasers, it has been proved that different types of bright pulses can emit from a laser cavity in the normal-dispersion regime, including dissipative solitons with rectangular spectrum (Gaussian in time domain), Gaussian spectrum (flat-topped pulses), broadband spectrum (wave-breaking-free pulses), and noise-like pulses (low-coherence pulse clusters).98 Or even, bright and dark solitons can coexist in the same fiber laser cavity with strong normal dispersion.94 A similar phenomenon is also theoretically revealed in normal-dispersion microresonators.95 In other words, it can be considered that there does not exist a rigid “barrier” to distinguish the two states (depending on the pulse duration and duty cycle). Since rich phenomena have been discovered exhibiting distinct features from different aspects and with rather complicated excitation dynamics, there have been various prediction and explanations related to the physical origin of the observed temporal behaviors for microcombs with normal dispersion in the literature, such as “platicons” (flat-topped bright solitonic pulses),99 dark pulses,23,92 and dark solitons93,95,96 or just normal-dispersion microcombs.97 In this part, we mainly focus on the mode-locked character, rather than a strict physical clarification for this kind of pulse. For simplicity, these localized reduction structures with an intense CW background in microcavites are all referred to as “dark solitons.”
An obvious difference between the two opposite-dispersion regimes is that the anomalous region usually favors ultrashort pulse emission with time-bandwidth-product limited (chirp-free or nearly chirp-free) durations, while for the normal-dispersion regime it prefers strongly chirped waves that are far from the Fourier-transform limitation with the absence of intrinsic balancing between the nonlinearity and negative dispersion. Thus intuitively, the route to DS generation as well as its excitation dynamics will deviate from those for bright solitons in anomalous-dispersion microresonators. During the past years, several experiments with normal-dispersion resonators on diverse material platforms, including
Fig. 19. Frequency comb generation in normal-dispersion microcavities. (a) Experiment setup using a semiconductor laser self-injection locked to an WGM resonator, wherein the spectral envelope shows three distinct maxima. (b) Numerically simulated envelope of intracavity optical pulses in terms of normalized amplitude (blue) and the pulse formed by only a limited number of modes with no pump frequency included (red).101 (c) Example comb spectrum spanning more than 200 nm obtained in a SiN microring (inset: an optical micrograph of the microring). (d) Square optical pulses directly generated under special conditions at high pump power.102 (e) Spectrum for the mode-locked state using dual-coupled SiN microrings in normal-dispersion regime.97 Insets: microscope image of microrings (upper left) and transmission spectra versus heater power showing the resonances can be selectively split (upper right). (f) Comb intensity noise corresponding to (e) measurement by an electrical spectrum analyzer (top) and autocorrelation of the transform-limited pulse after line-by-line shaping (bottom).
All of this progress demonstrates that the mode-locking mechanism for normal-dispersion microcavities might have analogies to, but surely is not identical to, that in anomalous-dispersion regimes. One of the most obvious differences, compared with bright solitons observed in negative-dispersion microcavities, is that the soliton regime now favors the blue-detuned region instead of the red-shifted regime, which leads to the intracavity pump field staying on the upper branch of the bistability curve where modulational instability is generally absent.103,104 A representative work is shown in
Fig. 20. DS generation in a normal-dispersion SiN microring using (a) and (b) the thermal-tuning method23 and (c)–(e) second-harmonic-assisted approach.93 (a) Drop-port power transmission when one mode is pumped. (b) Comb spectra (left panel) and intensity noise (right panel) corresponding to different stages in (a). (c) Experimental setup for the second-harmonic-assisted comb generation. Inset: microscope image of the microring with second-harmonic radiation. (d) Transition curves of the through port (top) and drop port (bottom) when the pump laser scans across the resonance from shorter to longer wavelengths. (e) Reconstructed waveforms at through port (top) and drop port (bottom), showing bright and dark pulses, respectively (inst. freq.: instantaneous frequency). Images (a) and (b) are adapted with permission from Ref. 23 and images (c)–(e) are adapted with permission from Ref. 104.
Looking back on the research of extraordinary SMCs related to rich physical phenomena (including soliton crystals, Stokes solitons, breathers, molecules, and cavity solitons, as well as dark solitons), all of these encouraging discoveries have revealed deeper insight into the dynamics and properties of this new category of laser sources for integrated photonics. As a comparison, the developing route is, interestingly and legitimately, mimicking the evolution roadmap of the mode-locked fiber lasers of previous pioneers in nonlinear optics in the last few decades (and still continuously yielding cutting-edge progresses at present105). Actually, a lot of unusual phenomena in microcombs have already been predicted or verified in a similar manner to some degree. That is, although different in material platforms and generation mechanisms, classic fiber nonlinearities can still offer a guidance or reference for microcombs, especially regarding unexplored temporal and spectral behaviors (e.g., vector solitons,106,107 wave-breaking-free pulses,108,109 optical bullets,110 or even rouge waves111,112). Meanwhile, they can inspire new fundamental research on intrinsic soliton features that are not yet considered in this area, such as the chirp parameter (or time-bandwidth-product),113 which is crucial in traditional fiber lasers for dedicated control on pulse shaping qualities114 and contributes significantly to further system optimization.
5 Applications
To date, various proof-of-concept experiments concerning extensive applications of SMCs have been demonstrated (
5.1 Coherent Optical Communications
Future demand in “big data” interconnection leads to optical communication systems with terabits to petabits per second data rates in a single fiber with hundreds of parallel wavelength-division multiplexing channels. The SMC can act as a promising candidate of multiwavelength carriers due to its favorable characteristics of frequency stability, broad band, suitable mode spacing, and narrow linewidth. Even based on a nonsoliton-state microcomb with an imperfect spectrum, Pefeifle et al.115 demonstrated coherent transmission of
5.2 Spectroscopy
The DCS, which is similar to Fourier transform spectroscopy, provides an excellent method for gas composition detection with outstanding features of shorter sampling time, higher optical spectrum resolution, and multicomposition detection capability. Two SMCs in the telecommunication band with slightly different repetition rates that were generated in two separate
5.3 Distance Measurement
OFCs are promising as excellent coherent sources for light detection and ranging (LIDAR) systems to fulfill fast and accurate distance measurements. Using a setup similar to the DCS system, dual-comb ranging systems have been carried out recently, which opens the door to low-SWaP LIDAR systems. For example, by employing the dual counter-propagating SMCs within a single silica wedge resonator, a dual-comb laser ranging system substantiates the time-of-flight measurement with 200-nm accuracy at an averaging time of 500 ms and within a range ambiguity of 16 mm.65 Another parallel progress is achieved on a SiN dual-microcomb LIDAR system, demonstrating ultrafast distance measurements with a precision of 12 nm at averaging times of
5.4 RF Related
SMCs are promising candidates for microwave-related applications including optical atomic clocks, ultrastable microwave generation, and microwave signal processing. Early attempts of photonic-microwave links include locking a nonsoliton state microcomb to atomic Rb transitions124 and a self-referenced microcomb with a broadened spectrum locked to an atomic clock.125 Recently, more compact schemes with fully stabilized SMCs have been reported, taking a big step toward photonic integration of optical-frequency synthesis40,126 and optical atomic clocks.127 The proposed optical frequency synthesizer was verified to be capable of transferring the stability from a 10-MHz microwave clock to laser frequency within an uncertainty of
5.5 Quantum Optics
Benefitting from the significant cavity enhancement, microresonators can offer attractive integrated platforms for single photon or entangled quantum state generation.136 Broadband quantum frequency comb has been realized in a high-refractive-index glass microring resonator via a high-efficiency spontaneous FWM effect at a relatively low pump power.137 Based on the quantum microcomb technique, more breakthroughs have been achieved, including the first integrated multiphoton entanglement137 and high-dimensional entangled quantum states.138 Compared with the quantum microcomb relying on the spontaneous parametric process, SMCs generated through the stimulated FWM effect can also play important roles in quantum optics. For example, a novel quantum key distribution system by demultiplexing the coherent microcomb lines was proposed very recently, showing the potential of the Gbps secret key rate.139 Considering other progress made in this field by ultilizing microcombs,140
6 Summary and Outlook
The experimental realization of SMCs represents the successful convergence of materials science, physics, and engineering techniques. SMCs have been regarded as an outstanding candidate in the exploration of next generation of optical sources due to the unprecedented advantages of lower SWaP (size, weight, and power), higher repetition rate as well as high coherence across the spectral coverage.147 Until now, the challenge of SMC generation has been gradually overcome using a variety of advanced experimental techniques, from the universal power-kicking method to the “forward and backward tuning” scheme for deterministic single SMC generation. Meanwhile, the dynamics of cavity soliton physics are substantially understood along with discovery of various extraordinary solitons and the rich nonlinear effects of dispersive waves, mode-crossing effect, and Raman self-frequency shift.
Although SMC-based applications present unprecedented performance improvements in many fields, generally they are still at the stage of proof-of-concept in laboratories at present. Considering engineering applications, the developments of SMCs (should) favor the tendency toward automatic generation, as well as higher integration density and higher energy conversion efficiency. The main challenge of automatic or programmable-controlled SMC generation comes from the ultrashort thermal lifetime of a microresonator, which is beyond the capacity of practical instruments for timely judgment on the soliton state through spectrum recognition. Fortunately, some advanced tuning speed independent schemes (e.g., the auxiliary-laser-assistant method and photorefractive effect in
It should be noted that a majority of reported SMCs are operating at communication bands. However, there are still great challenges for the generation of visible and mid-infrared SMCs, which would enable broad applications in molecular spectroscopy and chemical/biological sensing. The bandwidth of visible SMC28 is rather limited, and no mid-infrared single-SMC has yet been reported. Therefore, more efforts to improve the performance of SMCs on existing platforms and explore new materials are expected for vastly extending the spectral coverage to reach their full potential.153,154 Furthermore, microcavities are yet to be thoroughly developed and recognized by revealing more characteristics in the space and time domains, so as to identify their intrinsic essences and ultimate capabilities.155
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Article Outline
Weiqiang Wang, Leiran Wang, Wenfu Zhang. Advances in soliton microcomb generation[J]. Advanced Photonics, 2020, 2(3): 034001.