High-energy low-repetition broadband ultrafast lasers empowered by hollow-core fiber

Abstract

Low-repetition-rate ultrafast lasers with high peak power and broadband spectrum are critical for applications such as industrial processing, lidar, imaging and spectroscopy, but a key missing element is a low-nonlinearity, low-dispersion single-mode waveguide suitable for mass production. Here we show that inserting a homemade anti-resonant hollow-core fiber with nonlinear coefficient 1.97×10⁻⁷ W⁻¹m⁻¹ and single transverse mode low-loss transmission into a simple compact mode-locked cavity yields a turn-key single-pulse all-fiber laser at 2.63 MHz repetition, 103 kW peak power, and 35 nm bandwidth. The stable phase across wavelengths generates highly coherent swept signals with frequency noise of 97 Hz²/Hz via time stretching, which is useful for coherent detection, and enables swept-source optical coherence tomography with 1.6 m range and MHz frame rate, vibration sensing up to 113.2 kHz, and dispersive Fourier transform spectrometry at 1.54 pm resolution. Our scheme provides a perspective for developing high-performance low-repetition-rate mode-locked lasers and applications.

This work demonstrates a hollow-core-fiber-enabled high-energy low-repetition ultrafast laser that provides broadband coherent swept sources for high-speed optical imaging, dynamic spectral characterization, and precision vibration sensing.

Introduction

Ultrafast lasers have attracted great attention in recent years due to their unique advantages in applications, such as material processing¹, biomedical imaging², and fast spectral analysis³. From the point of energy, a low repetition rate ultrafast laser with high energy is preferred for high precision micromachining process and nonlinear-microscopy-based biomedical imaging, as it can mitigate the thermal accumulation^4,5. From the point of spectrum, a broadband low repetition rate mode-locked laser with MHz-level can be time stretched to generate a highly coherent swept laser. Current swept lasers, such as short cavity laser⁶, MEMS-VCSEL⁷, and Fourier domain mode locked laser⁸, have been proposed to achieve MHz-level sweep rate. However, they all suffer from instability and low coherence length due to the weak phase relationship between the laser signals at different wavelengths in the full sweep range. Mode-locked laser pulses have strong, predictable phase relationships with high coherence, which can be applied to generate a swept signal by time stretching technology with proper dispersion modules^9–11. Many researchers have demonstrated tens to hundreds of megahertz swept signal by time stretching mode locked lasers and their applications in swept source optical coherence tomography (SS-OCT)^12–16 and precision measurement^17–21. However, limited by the bandwidth of the photodetector, a sweep rate of tens to hundreds of MHz affects the spectral resolution for spectroscopy and the detection range for metrology. To simultaneously realize high speed, high resolution, and long-range detection, a highly coherent swept laser with a broadband sweep range and MHz sweep rate is desirable. Therefore, achieving stable low repetition rate operation while maintaining high energy and wide bandwidth remains a challenging but critical direction for research.

The general methods for reducing the pulse repetition rate of a fiber laser are to use an external pulse picker^14,22 and to increase the length of the mode-locked fiber cavity^23–25. The output power is attenuated around ~20 dB, and the system is too complex. The major difficulties encountered in long cavity mode-locked fiber lasers are the accumulated nonlinearity and higher-order dispersion distortions, which limit the pulse spectral bandwidth, highest energy and time lower limit^26–28. Traditional mode-locked fiber lasers are challenging to surpass the 100-kW peak power when operating at MHz-level repetition rate^29–32. The Mamyshev oscillator, as a new type of mode-locked fiber laser, has a large tolerance to the accumulation of nonlinear phase shifts^33,34. This design can directly increase the maximum single-pulse energy of the oscillator, and it also has a wider spectrum and a narrower pulse duration (<50 fs)^35,36. However, the Mamyshev oscillator has inherently inevitable large noise and low coherence, which hinders its further application and development^37,38. How to overcome current bottlenecks for low repetition mode-locked lasers is challenging, which deserves further investigation to simultaneously obtain high energy, broad bandwidth, low noise and high coherence.

Low dispersion and low nonlinearity fibers, such as anti-resonant hollow core fibers (AR-HCFs), can be adopted in the laser cavity to mitigate the deleterious effect of nonlinearity. Multiple breakthroughs have been achieved in the development of HCFs in the last decade. Recently, AR-HCFs have demonstrated a transmission loss of ~0.1 dB/km in a broad spectral window^39–42. The connection loss between AR-HCFs and silica fibers could also be engineered to <0.2 dB⁴³. The first major advantage of HCF is the ultra-low nonlinearity, which is ~3–4 orders of magnitude lower than that in single-mode silica fibers⁴⁴. The dispersion of most demonstrated AR-HCFs are only 1–3 ps/nm/km in a very broad spectral range with very low high-order dispersions^45,46. AR-HCFs have been used in the mode-locked laser or Mamyshev oscillator to realize low repetition rate working at 1.0 μm wavelength window^47,48. However, there are still some remaining problems that limit the coherence and stability of the mode locking. Firstly, the AR-HCF is prone to excite higher-order modes due to its larger mode field, disrupting the phase synchronization of mode locking. Besides, the relative position of the quartz capillary is easily compromised by external forces, leading to drift in the output polarization state. Furthermore, the broadband transmission leads to significant fluctuations in the group velocity dispersion (GVD) curve, which cannot meet the requirements for pulse compression and broadening in mode-locking.

In this work, we demonstrate a low-repetition-rate broadband ultrafast fiber laser enabled by a 6-tube AR-HCF. The fabricated AR-HCF exhibits low transmission loss (0.53 dB/km), a low nonlinear coefficient (1.97 × 10⁻⁷ W⁻¹ m⁻¹), and single-mode transmission characteristics. By incorporating this fiber into a mode-locked cavity, we realize a 2.63 MHz repetition-rate ultrafast laser at 1550 nm with a 35 nm bandwidth, 100 fs pulse duration and 103 kW peak power. The generated coherent pulses are further time-stretched to produce MHz-level swept signals, enabling SS-OCT with meter-scale imaging range, vibration sensing and high-resolution dispersive Fourier transform (DFT) spectroscopy.

Results

Generation of a low-repetition-rate single pulse

Increasing the cavity length to reduce the repetition rate will benefit energy accumulation, thereby increasing the single-pulse energy. The key factor for preventing the pulse from splitting is that the accumulated nonlinear phase shift should not exceed the limit phase (π)¹⁰. This phase is proportional to the total nonlinear coefficient and the pulse peak power in the cavity. Besides, compensating the net dispersion in the cavity to a nearly zero region can significantly enhance the pulse energy threshold. The intracavity breathing mechanism causes the pulse to be periodically broadened and compressed. Then the nonlinear and dispersion effects are dynamically balanced, thereby avoiding pulse splitting caused by excessive nonlinearity. The numerical simulation can be found in Supplementary Note S2. Therefore, to generate high energy single pulse, low dispersion and low nonlinearity are preferred and achieved by AR-HCF. The concept of high-energy single pulse propagation in single-mode fiber (SMF) and AR-HCF is portrayed in Fig. 1a. Due to the accumulation of dispersion and nonlinearity in the long SMF, a single high-energy pulse will split into multiple pulses. However, AR-HCF can support high energy pulses, benefitting from its low dispersion as shown in Fig. 1c and low nonlinearity as shown in Fig. 1e. The dispersion parameter (D) is 2.09 ps/nm/km, which is around ten times smaller than SMF. The dispersion of AR-HCF is abnormal dispersion at the 1550 nm wavelength band. Compared with SMF, the nonlinearity coefficient is 5.4 × 10³ times lower. Another key factor is the low loss of AR-HCF with 0.53 dB/km (Fig. 1d), which makes it possible to build up long mode locked laser cavity. The cross-sectional structure of AR-HCF is shown in inset i, and single-mode transmission is shown in inset ii. More parameters and performance of the AR-HCF can be found in the Supplementary Note S2. The 110 m self-made 6-tube AR-HCFs are inserted inside the mode locked laser cavity to generate low repetition rate and high energy single pulse as shown in Fig. 1b. Even though the dispersion of AR-HCF is smaller, more than 100 m AR-HCF and other components such as PC, EDF, TI-WDM will still accumulate some dispersion. A section of DCF is used to compensate for the dispersion to broaden the spectrum. The obtained low-repetition-rate pulses with high energy and broadband spectrum are then time-stretched to achieve highly coherent swept signals using a large dispersion component. Self-built optical amplifier is used to compensate for the loss induced by the dispersion component.

Fig. 1. Conceptual design and operation of the low-repetition-rate ultrafast all-fiber laser.

a Conceptual diagram of the propagation and evolution of high-energy pulses in single-mode fiber (SMF-28e) and AR-HCF, respectively. b Left: schematic of the mode-locked laser that consists of 110 m anti-resonant hollow-core fiber (AR-HCF). EDF erbium-doped fiber, TI-WDM tap-isolator wavelength division multiplexer, PS polarization sensitive, PC polarization controller, DCF dispersion compensation fiber. Inset: i transmission electron microscope (TEM) image of the cross-section of the AR-HCF. ii Transverse mode field profile distribution. Right: time stretching and optical amplification. ISO isolator, CIR circulator, CFBG chirped fiber Bragg grating, EDFC EDF optimized for C-band region, WDM wavelength division multiplexer. c Simulated dispersion curve of the AR-HCF. d Simulated various loss curves of AR-HCF. e Nonlinear curves of AR-HCF and SMF-28e.

The nonlinear polarization rotation (NPR) mode locking scheme is easy to realize high power compared with using SESAMs. Taking advantage of the anti-polarization sensitivity characteristic of self-made AR-HCF, the NPR mode-locking mechanism with a simple configuration is chosen. By adjusting the polarization state of light in the laser cavity, multiple states of mode locking are observed, as shown in Fig. 2a, due to two main factors. Firstly, when light with different polarization states are propagated through the fiber, their orthogonal components (such as horizontal and vertical polarization) undergo different nonlinear phase shifts due to intensity-dependent self-phase modulation and cross-phase modulation (XPM) effects^49,50. Hence, when the polarization state is changed (P₁ to P₂), the polarization-dependent loss in the cavity selectively suppresses the gain of a specific wavelength and shifts the wavelength to meet the low-loss condition. A series of spectra with different shapes and center wavelengths can be generated by continuously changing the intracavity polarization state. Figure 2a shows two typical states (P₁ to P₂) with different spectral characteristics to illustrate the influence of polarization state on laser output. Here, the generated mode-locked pulses are based on dissipative solitons, and their spectral shapes typically have a flat top and sharp edges or a bimodal structure. Our target is to realize a single high-energy pulse. By precisely adjusting the polarization state, a mode-locked laser with a 10 dB spectral bandwidth of 35 nm is obtained, as shown in Fig. 2a by the pink curve. Figure 2b shows the time-domain pulse sequence of the laser output with 379.6421 ns time interval, which corresponds to a 2.63 MHz repetition rate. The signal-to-noise ratio (SNR) measured at a resolution of 1 Hz and within a frequency range of 7 kHz is as high as 85.8 dB, as shown in Fig. 2c, indicating a stable mode-locking operation. The inset in Fig. 2c shows the high-order harmonics with a resolution of 1 kHz and a range of 50 MHz. The frequency components appear periodically in the radio frequency (RF) spectrum without noise spikes, indicating that the laser is working at the stable single pulse operation.

Fig. 2. Experimental study of basic laser output characteristics.

a Optical spectra of a laser in different polarization states (P₁and P₂). b Time-domain pulse sequence. c Measured RF spectrum at 1 Hz resolution. Inset: higher-order harmonics in the frequency domain. d, e Two-dimensional pseudo-color images plot of optical spectra and time-domain pulses evolution with pump power (300–600 mW). f, g Optical spectra and temporal pulse train at some specific pump powers (468, 570, and 600 mW). h Output power of the constructed mode-locked laser at different pump powers. i Intensity autocorrelation function (ACF) trace and the Sech fitting curve.

Soliton operation states are dependent on the intracavity energy and demonstrated as shown in Fig. 2d, e, where two-dimensional (2D) pseudo-color images of the evolution of the spectrum and time-domain pulse sequence with different pump powers are measured. By increasing the pump power, the pulse energy is also increased. The spectrum will be periodically broadened, and the pluses will be evolved continuously. The laser evolution dynamics includes six operation stages as the pump power increases, which are spontaneous emission amplification (ASE: 300–372 mW), continuous wave (CW: 373–419 mW), single pulse (SP: 420–468 mW), dual multi-pulse (DP: 469–569 mW), noise-like (NL: 570–576 mW), and soliton molecule (SM: 577–600 mW). To study the evolution, we further show the optical spectra and time domain pulses with special pump powers as shown in Fig. 2f, g. When the pump power is 468 mW, to maintain single-pulse operation of the laser, the excess energy will be transferred to the CW to stabilize the single-soliton mode locking. As a result, a direct current (DC) peak, as shown by the pink curve, will appear in the spectrum. When the pump power is increased to 570 mW, the balance between the nonlinearity and dispersion is disrupted, resulting in a noise peak as shown by the light green curve in the spectrum. The laser enters a NL mode-locking state, where the corresponding time domain pulse still operates as a single pulse. Continue to increase the pump power to 600 mW, and the interference pattern shown by the light purple curve will appear in the spectrum, and the spacing between the time domain sub-pulses will increase with the pump power. Figure 2h shows the laser output power with different pump powers. The output power of the laser ranges from 13.9 to 27 mW during single-pulse operation. The experimentally measured autocorrelation function (ACF) of the pulse is shown in Fig. 2i. The full width at half maximum of the ACF is 155 fs. The actual pulse width is estimated to be 100 fs assuming a Sech shape. The highest single pulse energy achieved in the SP state can reach 10.3 nJ, corresponding to a peak pulse energy of 103 kW. These results demonstrate that the introduction of a long AR-HCF into the mode-locked cavity effectively reduces the nonlinear phase shift and enables high-performance low-repetition-rate mode-locked laser output.

Self-starting and long-term stability

The dynamics of the single-pulse mode-locking operation is studied using a single-shot DFT technique to demonstrate the self-starting property. Figure 3a shows the evolution of the low-repetition-rate mode-locking process, including spontaneous emission, relaxation oscillation, and stable mode locking operation. The spontaneous emission lasts for 3.7 ms, and the oscillations lasts for ~15.6 ms. Subsequently, the oscillation becomes intense until a stable single-pulse operation is achieved. This is similar to the previous studies on the real-time dynamic behaviour of dispersion-managed solitons in long-cavity fiber lasers, where the spectrum broadening is observed due to the evolution of the Q-switched multi-pulse spectrum⁵¹. Figure 3b shows the intensity integration of a single-frame spectrum. The laser intensity remains stable during spontaneous emission and single-pulse operation, while the energy fluctuates significantly during the relaxation oscillation stage. The complex single-shot spectrum and energy evolution dynamics are related to the long-term population inversion in the gain medium⁵². The above results indicate that the laser can automatically enter a stable SP mode-locked state and achieve self-starting operation. The optical spectrum and RF spectrum are continuously observed within 240 min to study the long-term stability at single-pulse operation, which is under free-running state and natural environment. Spectral shape fluctuations are small, as shown in Fig. 3c. Figure 3d shows the evolution of the corresponding central wavelength and output power. The standard deviation (SD) of the central wavelength is 0.0321 nm, and the SD of the output power fluctuation is 0.0257 mW. Figure 3e shows the temporal evolution of the RF spectrum, where no significant fundamental frequency changes are observed. Figure 3f presents the repetition rate and SNR over time, with SDs of 9.9 Hz and 0.031 dB, respectively. The above results indicate that the constructed low-repetition-rate long-cavity mode-locked laser maintains excellent long-term stability.

Fig. 3. Real-time measurement of the self-starting process and long-term stability.

a Real-time experimental observation of the build-up dynamics of the stretched SP over 63,289 consecutive roundtrips. b Corresponding intensity evolution during the laser start-up process. Robustness of the laser single-pulse operation over a period of 240 min. c Continuous monitoring of the output optical spectrum. d Fluctuation and standard deviation (SD) analysis of central wavelength and output power. e Temporal evolution of the measured RF spectrum. f Stability performance of the laser repetition rate and the signal-to-noise ratio (SNR).

Short-term stability with DFT technology

To investigate the short-term stability of the proposed MHz repetition rate mode-locked laser, DFT technology is used to obtain the single-shot spectrum. A section of CFBG with large dispersion is used to time stretch the pulse as shown in Fig. 1b. To compensate for the loss after the time stretching process, the laser signal is optically amplified (see Supplementary Note S3 for details). The evolution of the transient spectrum of a single pulse with round trips is shown in Fig. 4a. To compare the repeatability of the shot-to-shot spectra in detail, single-frame spectra of different round trips (1-st, 4000-th, and 8000-th) are also measured as shown in Fig. 4b. Here, no obvious fluctuation is observed in the single-frame spectrum, indicating that the laser operation has good repeatability. The energy stability of a single-frame spectrum is an important indicator to evaluate the short-term stability. We calculated the normalized spectral energy distribution under different laser operation periods, as shown in Fig. 4c. The energy fluctuation of the obtained single-frame spectrum is between 0.9734 and 0.9812, with a fluctuation range of 0.9%, indicating that the proposed laser has high periodic repeatability and short-term stability. The energy fluctuations of 8000 transient spectra are further analysed by histogram statistics as shown in Fig. 4d. The spectral energy spreads outwards around ~0.97722, and the ratio of the standard deviation to the mean, i.e., the coefficient of variation (std/mean), is 0.12%. By fitting the histogram, the energy fluctuation follows a normal distribution, indicating that the laser has relatively small energy fluctuations. To assess the noise level of the laser, the relative intensity noise (RIN) is further calculated, as shown in Fig. 4e. The RIN is a noise level that describes the random fluctuations in laser output power and is one of the key indicators for measuring laser stability. The high-frequency RIN measured at frequency offsets above 1 MHz is −127 dB/Hz, and low-frequency noise is also suppressed.

Fig. 4. Excellent short-term stability and spectral statistical cross-correlation.

a Two-dimensional pseudo-color map of single-shot spectral evolution recorded by DFT over 8000 consecutive roundtrips. b Comparison of single-frame spectra for specific round trips (1-st, 4000-th, and 8000-th). c Transient spectral energy evolution with round trip. d Statistical histogram of the single-frame spectral energy for 8000 round trips. e Relative intensity noise (RIN) of the low-repetition-rate laser after power amplification. f Evolution of the cross-correlation values of full single-shot spectra within 8000 round trips. g Cross-correlation coefficient curves plotted for the round-trip offset range of 0–8000. h Statistical histogram showing the counts distribution of each cross-correlation coefficient.

To further verify the correlation of single-shot spectra between different round trips, a 2D pseudo-color map of the full-spectrum cross-correlation coefficient is calculated^53,54, as shown in Fig. 4f. The 45° diagonal line represents the cross-correlation coefficient of the single-shot spectrum itself, where the correlation coefficient is 1. The measured correlation coefficient is close to 1, indicating that the spectra have high similarity between different round trips. To explore the evolution law of the cross-correlation coefficient, the spectral cross-correlation curve with round-trip offset is calculated in Fig. 4g. The cross-correlation coefficients of different round trips vary from 0.997693 to 0.998035, which indicates that the laser signals generated in different roundtrips are consistent. Figure 4h presents a histogram of the cross-correlation coefficient distribution of single-frame spectra corresponding to different round trips, where the values are roughly distributed around ~0.997885. Consequently, the calculated value of the coefficient of variation is only 0.0047%. The spectra between different roundtrips have high similarity, verifying that the low-repetition-rate mode-locked laser by AR-HCF has high short-term stability and low noise level.

Coherent detection and fast spectrum characterization

There is a trade-off between the sweep rate and detection range in the SS-OCT system due to the limited bandwidth of the photodetector⁵⁴. Reducing the sweep rate from hundreds of MHz to MHz will increase the detection range. The ultralong detection range SS-OCT system is shown in Fig. 5a-i, where the proposed low repetition rate mode-locked laser is time stretched to generate a swept source. The performance of the SS-OCT system is characterized using an interferometer whose signal arm can be extended and retracted by a reflective mirror. The fringes obtained by the interferometric system are non-uniform, as shown in Fig. 5b. To achieve k-space linearization, the original interference signal needs to be phase-calibrated through frequency-domain resampling. The accuracy of this process directly depends on the phase stability and RIN of the swept source. In this experiment, the low-phase-noise swept source exhibits excellent long-time and short-time stability with small timing jitter, so there is no need to repeatedly calibrate the starting point of the sampling period. The mapping relationship between each wavelength and its corresponding time position is shown in Fig. 5c. By fitting the sweep trace with a quadratic polynomial, we successfully extracted the total dispersion parameter (−9354 ps/nm) and the second-order dispersion coefficient (1.698 ps/nm²), which are consistent with the expected dispersion of CFBG. Here, the frequency noise of the time-stretched swept source is measured using a coherent detection system (inset i of Fig. 5d). The high-frequency white noise is 97 Hz²/Hz, and the corresponding intrinsic linewidth is approximately ~305 Hz. Here, this low noise and narrow linewidth are determined by the low repetition rate and high output power of the laser (see Supplementary Note S4 for details). Then, by performing a fast Fourier transform (FFT) on the resampled interference signal, the point spread function (PSF) that characterizes the detection range of the imaging system can be obtained. The PSF is used to describe the intensity distribution of an image formed by an ideal point light source. The main panel of Fig. 5d presents the comparison results of the measured distance and the actual distance, and the fitting linearity is close to ~1. By adjusting the distance between the reflective mirror and the collimator, we have demonstrated the PSF at some specific positions (insets ii-viii in Fig. 5d, more PSFs, see supplementary Fig. S5), with a highest SNR reaching up to 52 dB (typically 40 dB). Inset ix in Fig. 5d shows 41 μm axial resolution of the SS-OCT system. The imaging range reaches up to 1.3 and 1.6 m, and the corresponding sensitivity roll-off is 6 and 9.2 dB (inset ⅹ of Fig. 5d), respectively. As far as we know, meter-level detection range with MHz imaging speed is a world record for the SS-OCT system. The SS-OCT images clearly distinguish the reflection signals of each layer of tape, and its Fresnel reflection bands at the air/adhesive interface, as shown in inset ⅹi of Fig. 5d. This demonstrates that the system can accurately distinguish multilayer material interfaces within the longitudinal detection range.

Fig. 5. Coherent detection and fast spectra characterization with a self-developed MHz-level swept laser.

a Experimental setups of the i coherent detection and ii spectra characterization. OC optical coupler, CIR circulator, Col. Collimator, PZT piezoelectric transducer, BPD balanced photodetector, OSC oscilloscope, FFP-TF fiber Fabry–Pérot tunable filter, AWG arbitrary waveform generator, PD photodetector, OSA optical spectrum analyzer. b Real-time interferogram generated by single-shot scanning. c Swept trace of wavelength and time mapping, fitted by a quadratic polynomial from 1526 to 1565. d Comparison of measured distance and actual distance at various mirror locations. Insets: i frequency noise power spectral density (PSD) of the swept laser, ii–viii point spread functions (PSFs) in logarithmic coordinates for different target distances (horizontal axis has been converted to distance values for easier visual display), ix axial resolution measured in air, x peak amplitude of the PSFs at different measured distances, and xi SS-OCT imaging of a multilayer tape sample. Single-shot spectral characterization of the FFP-TF under the driving frequencies of e 42.4 kHz and f 113.2 kHz. g Comparison of the average spectra obtained by dispersive Fourier transform (DFT) and OSA at a driving frequency of 42.4 kHz. h Single-shot spectra of the 15-th, 246-th, and 480-th round trips at a driving frequency of 113.2 kHz.

The SS-OCT system is one application of coherent detection by the swept laser. Another key application of the swept laser is fast spectrum characterization. MHz-level swept laser with ~305 Hz intrinsic linewidth can be applied to realize ultra-high-resolution and fast spectral characterization, as shown in Fig. 5a-ii. DFT spectrometer by a high-speed photodetector achieves a resolution of 1.54 pm (see the “Methods” section for details), fully capable of dynamic detection of ultra-narrowband optical devices. More details about the fast spectra characterization are described in Supplementary Note S6. Here, the electronically controlled fiber Fabry–Pérot tunable filter (FFP-TF) serves as the passive device under test. Figure 5e, f show the spectral evolution of 500 round trips when the FFP-TF is driven by an 8 Vpp sinusoidal signal at driving frequencies of 42.4 and 113.2 kHz, respectively. The sweep trajectory of the FFP-TF transmission spectrum is clearly observed, presenting a sinusoidal waveform consistent with the driving signal. Here, the periods of the sinusoidal waveforms driving the FFP-TF are 23.5824 and 8.83392 μs, respectively, and the corresponding frequencies are exactly 42.4 and 113.2 kHz. This indicates that the FFP-TF exhibits excellent responsivity, further demonstrating the ultra-high repeatability and stability of the constructed mode-locked laser. To verify the accuracy of the DFT spectrometer measurements, the transient spectra measured are averaged and compared with those obtained by the OSA, as presented in Fig. 5g. The average spectrum measured by the DFT method overlaps well with all OSA measurements. Therefore, the correctness and practicality of the constructed DFT system are verified. Figure 5h depicts single-shot spectra at the 15-th, 246-th, and 480-th round trips, where the transmission spectrum exhibits no sidelobes in each scan cycle. The inset shows a magnified single-shot spectrum, demonstrating that the FFP-TF maintains a well-defined Lorentzian line shape even during fast scanning. Furthermore, the dynamic filtering bandwidth is as low as 45 pm, maintaining narrow filtering characteristics during the scanning process.

Discussion

Compared with other swept lasers based on tunable filters whose phases of different wavelengths are not locked, a stable phase relationship among the various frequency components of mode-locked pulses enables a highly coherent and highly stable swept signal by time stretching technology. Time-stretched swept laser based on mode locked laser is promising for coherent detection and applications. We have demonstrated the SS-OCT system with meter level imaging range by performing a FFT on the resampled interference signal. Moreover, a detection system with a larger bandwidth can be used to enable a longer imaging range ¹⁶. Another method is to demodulate the phase of the interference signal to achieve precise measurement, benefitting from the low noise and high coherence of the mode-locked laser. Our proposed 2.63 MHz repetition rate mode-locked laser enables 2.63 MHz high sweep rate, which determines the sampling rate of the dynamic spectrum in the coherent detection system, thereby facilitating the detection of vibration signals with bandwidths on the order of megahertz. Another advantage is broadband spectrum, which overcomes the limitation in operating within a linear region. Based on this, the weak vibration signal in the coherent detection system is analyzed, and the relevant principle and experimental details are described in Supplementary Note S7.

Another key application of time-stretched swept laser is spectroscopy, which has been widely applied for the study of laser dynamics. However, previous spectrum resolution is typically around ~0.2 nm, which cannot exceed the level of traditional spectrometers (~0.02 nm). The resolution is determined by the dispersion of the stretched pulse, the detection bandwidth, and the sampling rate. Currently, high-speed photodetectors and sampling rates are no longer the limitations. Therefore, to improve the resolution of spectral detection, it is necessary to apply a sufficiently large dispersion⁵⁵. However, the existing mode-locked lasers have a high repetition rate (tens of MHz and above) and cannot tolerate large dispersion (easily cause spectral aliasing). Even if a MHz-level low-repetition-rate laser is realized, large-scale spectral detection cannot be achieved due to insufficient spectral bandwidth. Here, we have utilized the low-repetition-rate broadband mode-locked laser constructed with AR-HCF to achieve a spectrometer with a resolution of 1.54 pm and a speed of 2.63 MHz through a large dispersion of CFBG as demonstrated above. However, the large dispersion CFBG will introduce significant insertion loss. Its higher loss at longer wavelengths causes spectral response asymmetry, compressing the effective scanning bandwidth and restricting broadband spectroscopy applications.

As the discussion above, a low repetition rate mode-locked laser with a broadband spectrum is desirable for coherent detection and spectroscopy. Table 1 shows a comprehensive comparison of low-repetition-rate mode-locked fiber lasers operating at 1550 nm, which includes carbon nanotube (CNT), figure-8 nonlinear optical loop mirror (NOLM), figure-8 nonlinear amplifying loop mirror (NALM), figure-9 NALM, and nonlinear polarization rotation (NPR) mode-locking mechanisms. Our proposed low-repetition-rate mode-locked fiber laser has superior performance, including output power, pulse duration and spectral bandwidth. The laser samples demonstrated are far from reaching the limits of low-repetition-rate mode-locking technology and can be further improved. Based on the principle, if AR-HCF with superior transmission performances are achieved, the spectral bandwidth and single pulse energy can be further improved, and the repetition rate of mode-locked laser can be further decreased. However, the manufacturing process of this 6-tube AR-HCF is quite complex and is not suitable for large-scale mass production in the traditional sense. But it has entered the stage of small-batch, high-value, and customized mass production, which is the early stage of industrialization of high-end special optical fibers.

Table 1.

Parameter comparison of 1550 nm low repetition rate mode-locked fiber lasers

Mechanism	Repetition rate (MHz)	Output power (mW)	Pulse duration (ps)	Bandwidth (nm)	Refs. no.
CNT	0.154	0.15	6.2	0.65	23
	9.8	335	12.7	12.1	58
NOLM (figure-8)	3.63	10.1	0.53	7.4	59
NALM (figure-8)	7.9	0.85	0.5	8.7	60
	1.96	7.84	2.5	5.5	61
NALM (figure-9)	3.57	0.13	3.9	<5	62
	5.2	16.58	0.934	6.5	63
NPR	3.9	0.1	1.25	2.32	64
	1.2	0.768	34	15	65
	5.76	0.5	1.259	6.1	16
	2.63	27.1	0.1	35	This work

In conclusion, we have proposed a low repetition rate mode-locked laser working at 1550 nm by inserting low dispersion and low nonlinearity AR-HCF inside the laser cavity, which has a self-starting property, high long-term and short-term stability, broadband spectrum and high pulse energy. The laser has a repetition rate of 2.63 MHz, a pulse duration of 100 fs, an output power of 27 mW, and a bandwidth of 35 nm. The proposed mode-locked laser is used to generate a time-stretched swept source, achieving a high-frequency noise of 97 Hz²/Hz, corresponding to an intrinsic linewidth of 304 Hz. The swept laser has km-level coherence length, one-button startup capability, and excellent long- and short-term stability. Therefore, by applying it to the coherent detection system, it is demonstrated that the imaging depth of SS-OCT can be extended to an exaggerated 1.6 m at a MHz-level scanning rate, and weak vibration signals of hundreds of kHz can also be detected. Besides, the resolution of the DFT spectrometer is improved to 1.54 pm. Exploiting the potential of AR-HCF could lead to transformative insights into the operation of low-repetition mode-locked fiber lasers and pave the way for performance and applications.

Methods

Fabrication of AR-HCF

The high-performance 6-tube AR-HCF is fabricated using an improved stack-and-draw method⁵⁶. Cladding-nested capillaries, consisting of six outer silica tubes each containing a nested inner tube, are meticulously stacked to achieve the target geometry and fused within a jacket tube before being drawn into intermediate canes. This process requires stringent control of material purity and dimensional tolerances to minimize material loss during subsequent drawing. The canes are further reduced to fiber dimensions via a conventional cane-in-tube method. Upon solidification, the molten material formed an anti-resonant nested-tube cladding microstructure with an air core and periodic cladding structure. Uncontrolled distortions are mitigated by employing a relatively low furnace temperature and high drawing tension. The thicknesses of the inner and outer tubes are precisely controlled by maintaining differential pressure to satisfy anti-resonance conditions at 1550 nm.

Simulation of AR-HCF

The transmission mode field, dispersion curve and various transmission losses of AR-HCF are numerically simulated using the finite element solver (COMSOL Multiphysics). The geometric parameters of the optical fiber are obtained through scanning electron microscopy imaging technology and systematically calibrated by the measurement error analysis. The nonlinear coefficient is calculated using the following formula⁵⁷:

$$\gamma =\frac{2\pi n_0}{\lambda A_{eff}}$$ 1

where n₀ is the nonlinear refractive index of the material, λ is the working wavelength, c is the speed of light in vacuum, and A_eff is the effective mode field area. The n₂ values for AR-HCF and SMF are 3 × 10⁻²³ m²/W and 2 × 10⁻²⁰ m²/W, respectively. The A_eff values for AR-HCF and SMF are 6.16 × 10⁻¹⁰ m² and 7.54 × 10⁻¹¹ m², respectively.

Details of the laser experimental setup

The technical details of the low repetition rate mode-locked fiber laser based on AR-HCF are shown in Fig. 1b. Compared with other mode-locking technologies, nonlinear polarization rotation (NPR) exhibits advantages such as high damage threshold, self-starting capability, and broadband spectrum. A 0.7 m erbium-doped fiber (EDF, Liekki Er80-8/125) with high doping level is used as the gain, and the transmission window in the C+L band is negative dispersion (16.14 ps/nm/km@1550 nm). A multifunctional integrated device including a tap, isolator and wavelength division multiplexer (TI-WDM), simplifies the laser system and reduces the overall nonlinearity. The TI-WDM is polarization-sensitive (PS) and functions as a polarizer. The EDF is pumped by a 980 nm laser diode (LD). To reduce the repetition rate of the laser, a self-made low-nonlinear AR-HCF with a length of about ~110 m is introduced. In addition, a 1.5 m dispersion-compensating fiber (DCF) with a dispersion of −166.1 ps/nm/km at 1550 nm is used to compensate for the total dispersion in the laser cavity to near zero, thereby broadening the spectrum. Therefore, the net intracavity dispersion can be calculated as −0.00037 ps/nm. The NPR mode locking is achieved by carefully adjusting the polarization controller (PC1) to control the intra-cavity polarization state. An isolator (ISO) is configured behind the output port with a 20% splitting ratio to effectively block the influence of external reflected light on the seed source. Here, the CFBG combined with the circulator (CIR) is used to time stretch the mode-locked laser to generate a swept signal. A self-built EDFA consisting of a low-doped EDF (Nufern EDFC-980-HP), a WDM, and a 980 nm pump (Pump2) is used to compensate for the 12 dB loss induced by the CFBG.

Details of the measurement system

The optical spectrum is measured by an optical spectrum analyzer (OSA, Yokogawa, AQ6374). The RF spectrum is detected by a photodetector (PD, Max-ray Photonics) with a bandwidth of 3 GHz and an electro-spectrum analyzer (ESA, N9020A, KEYSIGHT). Figure 5a-i shows the schematic of the high-speed coherent detection system. The swept signal is split into two paths through a 10:90 coupler (OC1). Ninety percent of the light is injected into the collimator (Col.) via a circulator (CIR). A mirror adjusts the length of the signal arm, and a piezoelectric transducer (PZT) provides the vibration signal to be tested. The reflected light is injected into the CIR and is combined with 10% of the light from OC1 via 50:50 OC2. The above optical system forms a Michelson interferometer. Ultimately, the time domain signals of the swept source and the interferometric signal are detected by a balanced photodetector (BPD) with a bandwidth of 70 GHz and acquired by a real-time oscilloscope (OSC, Tektronix, DPO77002SX ATI) with a bandwidth of 70 GHz and a sampling rate of 200 GSa/s. Figure 5a-ii shows the schematic of the fast spectra characterization system. Here, the fiber Fabry–Pérot tunable filter (FFP-TF) serves as the device under test. An arbitrary waveform generator (AWG, Keysight, 33600A) generates electrical signals of different frequencies and amplitudes to drive the FFP-TF. A 50:50 optical coupler (OC) splits the output signal into two paths, allowing simultaneous detection by an OSA and a real-time OSC. The photodetector (PD) has a bandwidth of 70 GHz. The OSC is synchronously triggered by the scan electrical signal of the AWG.

Resolution of the DFT spectrometer

DFT is a technique that uses a strongly dispersive medium to spread light of different wavelengths over time. The key parameters of the DFT technique include spectral resolution, scanning rate, and spectral data points, which present a multi-dimensional constraint relationship⁵⁵. The scanning rate R is determined by the laser repetition rate. The wavelength-time relationship by the dispersion process satisfies the physical law ∆τ = |D|∆λ, where D represents the total GVD of the medium (unit: ps/nm). To avoid the overlap of adjacent pulses, the stretched pulse ∆τ should satisfy the condition ∆τ < R⁻¹. The number of time domain sampling points N = S|D|∆λ, S is the sampling rate of analog-to-digital converter (ADC), and the optical spectral resolution δλ_S = (S|D|)⁻¹. The detection system analog bandwidth B forms another limitation through δλ_B = (B|D|)⁻¹. In the ideal optimum, S = 2B (Nyquist sampling theorem), while in actual operation, B < S/2. The actual spectral resolution is determined by three factors: digital sampling capability, dispersion characteristics, and system bandwidth, which is described as:

$$\mathrm{\delta }\lambda =max\left(\mathrm{\delta }{\lambda }_S,\mathrm{\delta }{\lambda }_B,\mathrm{\delta }{\lambda }_D\right)$$ 2

Therefore, it can be concluded that lower repetition rate, larger detection bandwidth and larger dispersion will achieve higher resolution by the DFT spectrometer.

Author contributions

L.D. and D.H. conceived the idea of the experiment. X.Z. and P.W. designed, fabricated and tested the anti-resonance hollow-core fiber. L.D., X.Z., and Y.Z. carried out the numerical simulation. D.H., F.L., and P.W. provide guidance and support. Measurements were performed by L.D., with assistance from Y.Z., W.Z., S.Z., and Y.S. Analysis of the results was conducted by L.D., X.Z., Y.Z, D.H., and P.W. The manuscript was written by L.D. and D.H. All authors contributed to the discussion and revision of the manuscript.

Peer review

Peer review information

Nature Communications thanks Danheng Gao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by the Research Grants Council, University Grants Committee of Hong Kong SAR (PolyU 15206023); Innovation and Technology Fund – Guangdong-Hong Kong Technology Cooperation Funding Scheme (ITF-TCFS, GHP/096/22SZ); the Science Foundation of the Fujian Province, China (2025J01312).

Data availability

Data supporting the key findings of this study are available within the article and Supplementary Information files. Source data underlying the figures are provided with this paper. The complete raw datasets generated during this study are not deposited in a public repository due to their exceptionally large size and associated storage requirements. These data are available from the corresponding author for academic research purposes. Requests for access should be directed to the corresponding author.

Code availability

The custom code used for data analysis and visualization in this study is available from the corresponding author for academic research purposes. Requests for access should be directed to the corresponding author.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains Supplementary Material available at https://doi.org/10.1038/s41467-026-78141-4.