1. INTRODUCTION

Over the past few decades, optical frequency combs (OFCs) have revolutionized a broad range of applications at both fundamental and technological levels [1–5], including photonic microwave frequency generation [6–8], optical-clock comparisons [9,10], attosecond science [11,12], precision measurements [13,14], ultrasensitive sensing [15,16], and astronomy [17]. Among various OFC-based applications, dual-comb technology (DCT) has emerged as a powerful tool for precision spectroscopy, distance metrology, and ultrafast detection. Utilizing Fourier-transform interferometry [18–20], DCT offers exceptional spectral resolution, rapid data acquisition, enhanced signal-to-noise ratio (SNR), and scalability. These advantages position DCT as a versatile method for complex spectral analyses across diverse scientific and industrial fields. However, a fundamental requirement for DCT is high mutual coherence between the two combs, as phase noise and frequency instability can severely degrade spectral reconstruction, limiting resolution and dynamic range [21,22]. Moreover, high coherence enhances SNR by suppressing noise artifacts, enabling robust and repeatable measurements even over extended durations.

Microcombs, generated via the Kerr effect in microresonators, offer a promising path toward highly integrated and high-repetition-rate DCT sources [18,23,24]. Their high level of integration and low-power consumption make them well-suited for reducing system complexity while simultaneously enhancing stability and reliability. However, the development of microcombs remains constrained by phase noise and long-term frequency drift, stemming from fundamental quantum noise [25–27], thermal noise, and various technical noise sources. To mitigate these instabilities, additional stabilization techniques such as phase locking [28] and feedback control loop [29,30] are typically employed. While effective, however, these external locking schemes require complex optoelectronic components, complicating the system and hindering full miniaturization. Consequently, the realization of a low-noise, highly compact, and functionalized, microcomb device remains a significant challenge.

Here, we address these challenges through a fiber Fabry–Perot resonator (FFPR) platform that pave a new way for both the photonic architecture and the stabilization paradigm. Previous works have demonstrated the great potential of FFPRs [31–35] in achieving high-Q and low-noise combs. By synergistically integrating (1) large-mode-volume FFPRs with quality factors exceeding  to suppress quantum noise, (2) self-injection locking to intrinsically suppress pump and technical noise without active feedback, and (3) integrated packaging that ensures environmental immunity while maintaining a compact size of . The implemented device exhibits low phase noise of  at 10 kHz,  at 100 kHz, and  at 100 MHz, which is approaching the fundamental quantum limit. And the Allan deviation of the single-soliton repetition rate is measured to be  at 0.02 s averaging time, showing good long-term stability in a fully free-running setup. Crucially, this performance is maintained with a 99% single-soliton yield across  activation cycles.

To validate practical applicability, we implemented two microcomb units in free-running dual-comb configurations for ultrafast distance ranging and molecular spectroscopy. At 51.59 MHz acquisition rate, the ranging system achieved a distance measurement accuracy of approximately 1.61 µm in one-shot detection, while dual-comb spectroscopy of  demonstrated a 0.998% standard deviation in  band absorption spectrum measurement. These results not only confirm the devices’ metrological-grade stability but also establish a new benchmark for fully compact comb systems.

2. CHARACTERIZATIONS OF SELF-INJECTION LOCKING COMB

In this section, we present the compact self-injection locking comb device. Figure  1 (a) illustrates the schematic of the soliton microcomb device and the high-coherent dual-microcomb system. The core of this device consists of an electrically driven distributed feedback (DFB) laser chip and an FFPR, which are integrated into a butterfly packaged device. The generated Kerr comb exhibits sufficient coherence and long-term frequency stability without requiring any external auxiliary locking mechanisms. On the basis of scheme, it is an ideal candidate for practical dual-comb applications. Here, high-precision demonstrations in two representative fields are presented in our works: ultrafast dual-microcomb ranging and near-infrared spectroscopy detection.

Fig. 1. Architecture of compact low-noise microcomb device and its dual-comb applications. (a) Overview of low-noise dual microcomb for high-precision applications. Two individual devices generate a probe comb and a reference comb to achieve precise ranging and spectroscopy via highly coherent dual-comb heterodyne. The fiber Fabry–Perot resonator (FFPR) serves both as the high-Q cavity for self-injection locking and as the primary medium for Kerr optical frequency comb generation. (b) The laser output from the DFB enters a high-Q FFPR, where a portion of the transmitted light is redirected back into the DFB via a compact optical setup, including a half-wave plate (HWP) and a polarizing beam splitter (PBS), which tune the transmitted light to be vertically polarized. And through self-injection locking, the DFB laser can be stabilized and locked in the resonance to generate the Kerr comb. The inset is the picture of internal design. The bottom-left image shows the compact FFPR device in butterfly package. The whole size is , and the FFPR has a length of 0.5 cm (bottom right), with both ends coated with Bragg mirrors that have a reflectivity greater than 99.99%. (c) The ringdown trace is obtained with a scanning speed of 200 GHz/s. The dashed orange line is an exponential fit. According to the relationship , where  is the ringdown time, giving an intrinsic Q factor of . (d) The comparison of frequency noise spectral density of the DFB laser in free-running (blue curve) and self-injection-locked states (red curve). The dashed line marks the baseline linewidth level. Due to the high-Q properties, the linewidth compression factor reaches over .

The device architecture and internal configuration are illustrated in the upper panel of Fig.  1 (b). This system leverages self-injection locking to generate low-noise Kerr frequency combs, where the high- FFPR plays a dual role: it narrows the linewidth of the DFB laser and facilitates soliton formation through the Kerr nonlinearity. The FFPR, measuring 0.5 cm in length [lower right panel, Fig.  1 (b)], achieves a comb repetition rate of . Fabricated from a commercially available few-mode fiber segment designed to support only two transverse modes at 1550 nm, the FFPR features a fundamental mode field area of µ. Both fiber ends are precision-polished and coated with high-reflectivity Bragg mirrors ( reflectivity at 1550 nm). Ringdown measurements [Fig.  1 (c)] reveal a cavity decay time of 253 ns, corresponding to a Q-factor of . Besides, a series of micro-optical components are incorporated to ensure precise optical feedback and isolation. Specifically, a half-wave plate (HWP), a Faraday rotator (FR), and a polarizing beam splitter (PBS) collectively function as an optical circulator, preventing back-reflected light from the FFPR from re-entering the DFB laser cavity. Precise thermo-optic phase control is achieved via a 0.8 mm thick silicon wafer inserted into the feedback path. And reflective mirrors (RMs) are set to build the feedback loop. The whole system is integrated in a butterfly package with temperature regulation managed by a thermoelectric component beneath the baseplate, whose photographs are shown in the lower left panel of Fig.  1 (b).

To validate the self-injection locking effect enabled by the FFPR, we characterized the frequency noise of the DFB laser before and after locking using the correlated delayed self-heterodyne method [36], as shown in Fig.  1 (d). In the locked region, the intrinsic linewidth of the DFB laser is suppressed to 168 mHz, compared to 73.6 kHz in the free-running state, corresponding to a linewidth reduction factor of , which significantly minimizes the comb system’s timing jitter. We further characterized the long-term laser wavelength stability, over an 8 h observation period, wavelength fluctuations remained confined within 5 pm across both low-power (below the Kerr nonlinearity threshold) and high-power (above the threshold) operational regimes (see Supplement 1).

In Fig.  2 , we present the characteristics of the FFPR comb generated through self-injection locking. The optical spectra of distinct soliton states—single soliton, two soliton, and perfect soliton crystal (PSC) are shown in Fig.  2 (a). The single-soliton spectrum exhibits a  profile corresponding to a pulse width of 542 fs (dashed fit). These states are selectively accessed by fine-tuning the laser current or thermo-optic phase, which adjusts the effective pump detuning for precise soliton control. The current applied to the DFB laser is 96.5 mA, corresponding to an output power of . The output power of the soliton comb is 105 µW, thus the conversion efficiency is 0.53%. It should be noted that this result involves coupling loss before and after FFPR, implying that the intrinsic conversion efficiency would be higher. For coherence analysis, the comb output (pump laser at 1549.8 nm attenuated by a bandpass filter) is amplified via an erbium-doped fiber amplifier (EDFA) and detected by a fast photodetector. The resulting radiofrequency (RF) spectrum [Fig.  2 (b)] shows a single-tone beat note at 19.9 GHz with  signal-to-noise ratio, confirming stable mode-locked operation. In Fig.  2 (c), we characterize the repetition rate phase noise of the single-soliton RF beat note by a phase noise analyzer (APPH40G, Anapico). At 10 kHz, 100 kHz, and 100 MHz offset frequencies, the phase noise is , , and , respectively. According to the calculations, the crossing point between the quantum noise limit and the thermorefractive noise limit is observed at an offset frequency of approximately 200 Hz. At lower offset frequencies, thermorefractive noise remains the dominant factor limiting phase noise performance. Our experimental results show good agreement with this analysis. Notably, while thermorefractive noise sets a relatively high limit at low-offset frequencies, it can be significantly suppressed through external feedback locking techniques, enabling improved noise performance at these frequencies. And the measured phase noise nearly approaches the theoretical quantum noise limit (gray dashed line) for offset frequencies from several hundred hertz to 100 kHz. And at larger offset frequencies (), the phase noise is primarily limited by the quantum noise floor, which corresponds to the shot noise level. Because the phase noise is influenced by the transfer from laser amplitude noise in the RF signal through a phase-locking mechanism that is analogous to that in mode-locked lasers. The bump near the 1 MHz offset frequency is primarily related to the locking bandwidth [27,37–39], which is close to the FFPR resonance linewidth.

Fig. 2. Characterization of the microcomb device. (a) Optical spectra of single soliton, two soliton, and perfect soliton crystal states (from left to right). The red dashed curve represents a  fitting. (b) RF spectrum of the soliton repetition rate. (c) Single-sideband (SSB) phase noise spectrum of the 19.9576 GHz soliton repetition rate (red curve). The solid yellow line indicates the thermorefractive noise limit, the dashed gray line shows the calculated quantum noise limit, and the dashed black line represents the shot noise level. Below 100 Hz, the phase noise is primarily limited by thermorefractive fluctuations, while at higher offset frequencies, the quantum noise limit dominates. (d) Soliton repetition rate tuning by periodically linearly tuning the injection current of the DFB laser in a range of 0.9 mA. The resulting tunable range of the repetition rate is . (e) Comb power evolution during seven consecutive turnkey operations in 450 s. Green shaded regions: soliton generation (switch-on to stabilization); yellow: steady-state operation. (f) Success probability across 100 activation attempts. (g) Allan deviation of the repetition rate, measured with 0.01 s gate time. (h) Measured optical comb power of a single-soliton state over 8 h under free-running conditions. Inset: 1 h temporal variations.

The exceptionally low free-running phase noise achieved in our work, compared to other self-injection-locked microcombs, can be attributed to a combination of three key factors: (1) reduced quantum and thermal noise limits, a large-mode area (µ), and a low nonlinear coefficient (), which lead to a low quantum noise limit. At the same time, the thermal noise floor is also significantly reduced due to the large-mode volume. (2) High-Q FFPR () and low pump laser noise, which are essential for achieving a near-quantum-noise-limit Kerr comb. (3) Compact packaging, which greatly enhances passive stability by mitigating environmental perturbations such as temperature fluctuations and mechanical vibrations.

Within the single-soliton region, we observed periodic changes in the soliton repetition rate by applying repeated periodic modulation to the current of the diode laser chip. We periodically linearly tune the injection current of the DFB laser with a tuning range of 0.9 mA (96.1–97.0 mA). In the process, we recorded the repetition rate in real time. This phenomenon highlights the direct correlation between the laser current and the soliton dynamics, providing a controllable approach to fine-tuning the repetition rate for applications requiring precise frequency adjustment and stabilization. In Fig.  2 (d), we show the repetition rate modulation efficiency of 19.7 kHz/mA, and the repetition rate range can be modulated between .

Fig. 3. Dual-comb characterization. (a) Optical spectra with smooth profiles and repetition rates demonstrating narrow RF linewidths for the two independent combs. (b) SSB phase noises and timing jitters of the two combs’ repetition rates. The integrated jitters of comb1 and comb2 are 1.27 and 1.59 fs, respectively. (c) RF beat notes of the dual combs with a frequency spacing of 51.59 MHz. And the extracted RF comb line shows a 20 dB linewidth of 24.7 kHz, which is mainly resulted from the relative frequency instability of the dual combs. (d)  variation during 4 h observation, showing a frequency drift of less than 5 kHz.

The theoretical analysis in Supplement 1 shows that the FFPR soliton generation can be achieved without dynamic tuning [40,41]. Experimentally, the device demonstrates robust turnkey operation through deterministic soliton initiation upon pump current activation. The soliton state can be built once the laser diode current is turned on and remains till the current is turned off. We monitored soliton dynamics in real time by tracking photodetector (PD) electrical signals, with successful activation defined by consistency in spectral and electrical signal level between initial and final states. Actually, the soliton state forms deterministically upon laser diode activation and remains stable until current termination, enabled by active temperature stabilization of both the baseplate and the silicon phase-tuning element. Taking the three soliton states in Fig.  2 (a) as examples, the evolutions of comb power are recorded during seven consecutive switch-on cycles. In Fig.  2 (e), the green-shaded region illustrates the evolution of the soliton from its initial state to shutdown, followed by subsequent regeneration within a single cycle, lasting less than 100 s in total. We observe that the PSC has the shortest recovery time, while the single soliton has the longest. This is mainly due to the different detuning between the soliton crystal and the single-soliton state [42]. The yellow-shaded region indicates that the soliton states remain unchanged with exceptional long-term stability when the laser current is held constant. Notably, we conducted 100 switch-on attempts for each of the three states, achieving nearly 100% turnkey success probability, indicating phase-independent and highly reliable operation [Fig.  2 (f)]. And we also show the real-time evolution of the RF beat-note signal for the single-soliton state with 10 turnkey operations in a time scale of 880 s, confirmed by synchronous monitoring of the comb power and the clean RF beat note of the comb repetition rate (see Supplement 1). Besides, we characterize the repetition rate stability by the Allan deviation measurement using a frequency counter with a 10 MHz Rubidium clock signal as a time base. The results are plotted in Fig.  2 (g). It shows that the measured frequency instability can reach  at 0.02 s averaging time. Furthermore, we measure the power instability of the free-running soliton microcomb. During an operating period of 8 h, the standard deviation of comb power of single soliton is 0.276% [Fig.  2 (h)]. The inset shows the tiny comb power drift within 1 h in detail.

3. FREE-RUNNING DUAL-COMB MEASUREMENTS

The measurement precision and acquisition rates in dual-comb heterodyne detection techniques are fundamentally governed by the stability characteristics of the . Building upon the foundational single-comb stability metrics established in Figs.  1 and 2 , which set the foundation for high-fidelity dual-comb operation. Here, we systematically characterize the free-running dual-comb architecture’s coherent detection capabilities through complementary dimensions.

Figures  3 (a) and 3 (b) present the characteristics of the two optical frequency combs used in our dual-comb system. The two devices share an identical configuration except for a slight difference in FFPR length, resulting in repetition rates of 19.90760 and 19.95919 GHz, respectively, yielding a differential repetition rate of . In the RF spectrum, both combs exhibit narrow linewidths, indicating individual high coherence. Moreover, their phase noise approaches the quantum noise limit, with integrated timing jitters of 1.27 and 1.59 fs at 10 kHz, highlighting their exceptional temporal stability.

To generate and analyze dual-comb interference signals, the free-running two combs are individually filtered, amplified, and directed together to a single photodetector. In Fig.  3 (c), the resulting RF spectrum reveals multiple beat notes between the two combs, spaced by the . A detailed examination of the 4.578 GHz beat note component shows a 20 dB linewidth of 24.7 kHz, limited by the relative jitter of the two combs. Then, two 20 GHz photodetectors are used for generating repetition rate RF signals for two combs, respectively, and they are subsequently mixed in an electrical mixer to produce a repetition rate difference RF signal () for real-time frequency drift measurement. Over a 4 h measurement period, the  in the free-running system exhibits a frequency drift of less than 5 kHz, demonstrating remarkable long-term stability [Fig.  3 (d)]. Besides, as presented in Supplement 1, the measured single-sideband (SSB) phase noise spectral density ( at 10 kHz offset) and the Allan deviation of  ( at 0.04 s averaging time) provide conclusive evidence that our free-running dual-comb system maintains unique stability, even in the absence of active feedback control.

4. DUAL-COMB TOF RANGING

Dual-comb time-of-flight (TOF) ranging exploits the interference between two frequency combs with a slight . This technique maps temporal delays between pulse pairs into phase shifts of RF beat notes, enabling sub-wavelength resolution in distance measurements [20,43,44]. The method capitalizes on the combs’ inherent coherence and broadband spectral coverage to achieve rapid, non-contact measurements with exceptional dynamic range.

In TOF ranging, one comb serves as the reference, while the other is used to probe a target. The two combs with slightly different repetition rates () are combined and detected, generating an RF comb in the electrical domain, with beat frequencies given by . The probe comb reflects off the target, introducing a time delay . Consequently, the distance , where  is light velocity, can be extracted from the interferogram with high precision. Previous works [44,45] have already demonstrated that the asynchronous sampling ranging system based on dual combs can effectively improve time measurement accuracy and achieve high-precision distance measurement. Here, we mainly focus on the impact of comb noise on distance measurement accuracy.

When considering only quantum noise, the pulse sequence of the soliton microcomb exhibits a random motion. The optical pulse period jitter, denoted as , is the deviation between the th pulse and the ()th pulse interval relative to the ideal period, following the white noise distribution . After  pulses, the accumulated time error introduced by the random walk is given by the variance

The variance satisfies . When the pulse sequence with time jitter is sampled by the local oscillator (LO), the sampling process simultaneously amplifies the time scale and timing jitter. Therefore, using two low-noise microcombs will significantly improve the distance measurement accuracy. In fact, the pulses are not rigorously spaced due to amplified spontaneous emission (ASE) noise, SSB phase noise, vibrations from the ranging link, etc. Assuming the time interval between the LO and signal comb pulses is subject to a tiny variation, the sampled pulse train may read a magnified timing variation with a factor of  [46], where . Due to the trade-off between update rate and resolution, an excessively small  can affect the amplification factor and further amplify the errors introduced by jitter. Therefore,  with MHz level is preferred here.

In Fig.  4 (a), the distance measurement process is as depicted by the solid line considering the two sets of comb pulse trains without timing jitter, but, in the real situation, the ranging process is simplified and illustrated as dashed gray lines. Therefore, the error induced by pulse train timing jitter can be divided into  and , both of which follow a Poisson distribution.  represents the timing error in the interval between successive signal pulses and reference pulses.  represents the timing error between adjacent reference pulses after time stretching. Under the influence of various noise sources, the output pulse sequence of the femtosecond laser will deviate from its ideal pulse positions. The pulse flight time error introduced by the oscillator’s pulse time jitter can be expressed as follows [47]:

where  is the repetition rate of the signal comb, and  and  are the deviations of the sampled pulse and the LO pulse, respectively. Assuming that the pulse jitter of the th pulse follows a distribution ,  and  can be expressed as

Fig. 4. Dual-comb ranging measurement. (a) The jitter effect on ranging precision. The pulse actual position (dashed blue) of the LO comb deviates from its theoretical location (solid blue), with the shifted pulse position shown by the gray dashed curve. After asynchronous sampling, the yellow dots represent the theoretical sampled values, while the cyan dots denote the actual values. Within one period,  represents the ranging time error and  represents the reference time error. Both follow Poisson distributions. (b) Within the unambiguous range, the ranging accuracy exhibits a symmetric relationship with timing jitter. Notably, at , the ranging accuracy shows a linear increase with jitter. This symmetric distribution indicates that as timing jitter increases, the precision of distance measurements degrades linearly, particularly around the midpoint of the unambiguous range. (c) Parametric spaces. Both the  and the jitter determine the precision, and in our case, the theory limit can reach to 1.17 µm, according to the calculated quantum limit. (d) Experimental setup. PD, photodetector; PC, polarization controller; EDFA, erbium-doped fiber amplifier; OSC, oscilloscope. Both pumps of combs are filtered. (e) Typical interferogram over two time periods. The higher and lower periodic pulses represent reference peaks and target peaks, respectively. (f) Repeated 20,000 ranging results and their distribution, suggesting a maximum error of µ. (g) Precision of the distance measurement versus averaging time. Allan deviation reaches 16.18 nm with an averaging time of 39.69 µs.

Therefore, we show the numerical simulation results of ranging precision under different jitter conditions within a non-ambiguity range of  [Fig.  4 (b)]. The overall symmetric precision curves indicate that the ranging accuracy is at its lowest at the midpoint of the non-ambiguity range and the ranging precision linearly increases with jitter. In Fig.  4 (c), we map the relationship between , jitter, and ranging precision. The white dot presents the selected parameter in our experiment. According to the calculated quantum limit and the shot noise, given the  and the theory limit jitter of the individual comb = 0.46 fs. The simulated ranging precision limit is approximately 0.58 µm. More calculations are shown in Supplement 1.

In our implementation [Fig.  4 (d)], comb1 is divided into two paths by a 50:50 fiber coupler: one path travels a certain distance before combining with the other path, which we refer to the former as the probe path and the latter as the reference path. Then, comb2 asynchronously samples both signal channels simultaneously. According to the TOF theories [23,48,49], the slightly different repetition rates between two combs enable them to realize a maximum . The Nyquist sampling theorem requires the spectral bandwidth of the probe combs to satisfy the relationship . As a result, the  is enlarged to be , where . In this work, the sampling period , and the sampling step . For a target with a fixed position, the two kinds of interferometric traces of the asynchronous sampling are shown in Fig.  4 (e). The distance can be calculated from  and the . We conducted statistical analysis on 20,000 measured data points [Fig.  4 (f)]. The overall ranging results exhibit a Gaussian distribution, with a root-mean-square error of 594 nm. For single-shot detection, the maximum error is µ, which can be compressed via improving the stability of the fiber links. Besides, it is necessary to use the Hilbert transform to obtain the envelope of each interference pulse, thereby reducing the adverse effects of carrier phase evolution on the calculation results. Figure  4 (g) plots the statistical Allan deviation of our ranging measurements. For single-shot measurement, the typical detection limit can reach to 1.61 µm, which is slightly larger than the theoretical prediction. We attribute it to the degradation caused by high-frequency noise introduced by self-injection locking, as well as additional system jitter under the condition of the dual comb not being fully locked. After 39.69 µs averages, the detection limit approaches 16.18 nm. The results are comparable to those achieved with dual-fiber mode-locked laser ranging systems under locked conditions, while also offering a significantly faster detection rate.

5. DUAL-COMB SPECTROSCOPY

Next, we extend our dual-comb platform to high-resolution molecular spectroscopy. The absorption of the sample alters both the amplitudes and phases of the transmitted comb lines, which are mapped onto the RF domain via coherent heterodyning [50,51]. By analyzing these changes across multiple modes, a broadband absorption or dispersion spectrum can be reconstructed with high accuracy. Among various technical noise sources, such as comb relative intensity noise, detector noise, and thermal noise, the fundamental quantum shot noise remains the dominant source of uncertainty in measuring the amplitudes of comb modes [52]. Notably, our free-running FFPR-based soliton combs maintain sufficient stability in frequency and amplitudes, enabling simultaneous TOF ranging and absorption spectroscopy without requiring active stabilization.

The spectroscopy setup [Fig.  5 (a)] follows a similar dual-comb architecture, as shown in Fig.  4 (d). The amplified combs are split into four paths: LO1 and LO2 (local oscillators), Sig (sample arm), and Ref (reference arm). The Sig arm from comb2 traverses a 48 cm  gas cell (300 Torr pressure, 22 GHz linewidth at 1550 nm) before combining with LO1 from comb1 at the photodetector. Simultaneously, the Ref arm combines directly with LO2 for baseline normalization. To prevent aliasing, we centered the RF spectrum at  through tuning the , achieving an effective RF bandwidth of 4.5–7.5 GHz [Fig.  5 (b)]. To determine the absolute frequency, the experimental spectral lines were cross-referenced with the rotational–vibrational transition lines in the HITRAN database within the 1.55 µm band. The frequency offset of the spectral axis was extracted via least-squares fitting. For detailed operational steps, refer to Supplement 1. This corresponds to an optical coverage of 1543.317–1552.505 nm, verified via wavelength meter calibration (reference: 1548.21 nm at 193.6376 THz).

Fig. 5. Measurement of dual-comb spectroscopy. (a) Experimental setup. The HCN gas cell is 48 cm with 300 Torr. (b) The interferograms before (orange region) and after (blue region) passing through the gas cell. The free induction decay (FID) signal arises on one end of signal part due to molecular absorption. (c) Numerically calculated Fourier transform of a recorded time-domain signal. (d) Overlay of the HITRAN database and the dual-comb spectrum showing line-by-line matching. (e) The residual differences between the two spectra.

It is interesting to note that free induction decay (FID) arises when a light signal interacts with gas molecules through absorption and collision, producing a persistent “echo” signal that lasts several nanoseconds after the initial pulse. This signal results from the gradual dephasing of molecular polarization due to mechanisms like collision broadening, Doppler effects, and spontaneous emission [53,54]. Detecting the FID signal indicates that spectral information necessarily contains absorption dips. And it confirms the high coherence of the dual-comb system, as it demonstrates the ability to maintain phase relationships over time. The presence of a well-resolved FID indicates minimal phase noise and timing jitter, ensuring precise spectral measurements with high resolution and sensitivity [55,56]. We have highlighted this feature with a red arrow in Fig.  5 (b).

In the resulting comb-like RF spectra [Fig.  5 (c)], we observe a reduction in intensity at specific frequency components, corresponding to the absorption features of . The absorption spectrum is extracted by normalizing the signal spectrum against the reference spectrum. To enhance the signal-to-noise ratio (SNR), the results were analyzed after 5000 cycles of coherent averaging (total duration: 96.9 µs). Due to the limitation of sampling depth, we did not perform coherent averaging over a longer duration. During the heterodyne measurement, benefited from the ultrafast sampling rate and the unique individual comb stability, the frequency drift was almost negligible, which is difficult to achieve in dual-comb spectroscopy at the MHz level. Notably, no phase correction was applied during this process, and the sampling duration was constrained by the limited sampling depth of the system, preventing extended acquisition times. The outcomes are presented in the lower panel of Fig.  5 (c). Also, as the measurement time increases, the background spectrum may change due to temperature effects. To assess the accuracy of our measured absorption spectrum, we compared it with theoretical values from the HITRAN database. Within the observed wavelength range of 1543.3–1552.3 nm, we performed a line-by-line overlay of the measured dual-comb spectrum with the HITRAN reference [Fig.  5 (d)] from 1543.1 to 1552.5 nm. The deviation between the measured absorption lines and the HITRAN standard was found to be as small as 0.998% [Fig.  5 (e)], demonstrating excellent agreement. This consistency with the HITRAN database further confirms the high resolution and precision of our dual-comb spectroscopy system.

6. DISCUSSION

We demonstrate a compact Kerr frequency comb integrated in a  butterfly package. This self-injection-locked design eliminates bulky lasers, amplifiers, and high-voltage components while maintaining low system complexity. Using a high-Q () FFPR with a large-mode-field area, we compress the pump linewidth below 200 mHz. This reduces quantum and shot noise by over 10 dB compared to standard chip-scale systems [40,57]. To our knowledge, this work presents the first Kerr comb combining ultra-low noise, turnkey operation, and extreme compactness.

Furthermore, in its free-running state, we validate the device’s coherence in dual-comb applications with high precision. In single-shot ranging measurements, our device demonstrates micrometer-level accuracy. And an error rate of less than 1% in spectral analysis. These results confirm its intrinsic stability and signal-to-noise ratio without external locking mechanisms, significantly simplifying dual-comb implementations. Compared to mode-locked fiber laser dual-comb systems, our FFPR-based Kerr comb offers a much smaller footprint and reduced complexity, while achieving competitive phase noise and coherence performance. And thanks to the exceptionally high quality factor enabled by low fiber propagation loss, our FFPR can maintain ultrahigh  even when the cavity length is extended to achieve repetition rates ranging from hundreds of MHz to several GHz. This fills the performance gap between traditional meter-scale fiber systems and high-repetition-rate chip-scale microcombs, enabling a unique combination of portability, robustness, and precision.

Looking ahead, the spectral span of our FFPR-based microcombs could be further extended through dispersion engineering, for instance, by operating at wavelengths with smaller dispersion (e.g., around 1.3 µm), and employing specially designed fibers with flatter dispersion, or incorporating dispersion compensation via the reflective coating stack. In addition, the use of multimode or photonic crystal fibers offers the possibility of dispersive-wave-assisted mode expansion, providing an effective route to achieve broader spectral coverage [58,59]. Additionally, the integration of multiple microwave frequency bands with high performance—such as the L-band, K-band, and other bands spanning from1 to 50 GHz—is essential for modern wireless communications. These bands support key applications including 5G networks, satellite communications, and radar systems, all of which demand high-speed data transmission and precise object detection. The broad spectral range also underpins emerging technologies such as millimeter-wave imaging and quantum computing interfaces while supporting a diverse array of foundational applications. Notably, the repetition rate is solely determined by the cavity length, making it straightforward to control and optimize.

Additionally, by enabling independent control of the offset frequency and repetition rate through separate control inputs, we aim to achieve fully self-locked operation within an ultra-compact footprint [60]. This innovation paves the way for next-generation optical frequency comb technologies that seamlessly integrate enhanced practicality and superior performance, addressing critical demands in 5G/6G communications, quantum metrology, and scalable quantum computing architectures.