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

High-energy, low-repetition broadband ultrafast lasers empowered by hollow-core fiber | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article High-energy, low-repetition broadband ultrafast lasers empowered by hollow-core fiber Dongmei Huang, Laiyang Dang, Xin Zhang, Yinghui Zhuang, Wenhao ZHU, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8215335/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Low-repetition-rate ultrafast lasers with high peak power and broadband spectrum are key components in applications such as industrial processing, lidar, optical imaging, and spectroscopy. To turn these capabilities from concepts into reality, the missing element is a low nonlinearity and low dispersion waveguide with purified transverse mode that can be mass-produced. Here, a self-made anti-resonant hollow-core fiber with a nonlinear coefficient as low as 1.97×10-7 and single transverse mode low-loss transmission is inserted into a nonlinear polarization rotation mode locking cavity with simple and compact configuration to realize high performance ultrafast laser. A turn-key single-pulse mode-locked all-fiber laser with repetition rate as low as 2.63 MHz, peak power up to 103 kW, and bandwidth of 35 nm is demonstrated. The stable phase relationship of the different wavelengths enables highly coherent swept signal with low frequency noise of 97 Hz2/Hz by time stretching technology, which has been demonstrated for coherent detection systems. A 1.6 m detection range with a MHz-level refresh frame rate in swept source optical coherence tomography system is demonstrated. Besides, a fast vibration signal of 113.2 kHz is reconstructed by demodulating the phase of the interference signal. Furthermore, the laser is also used in a dispersive Fourier transform spectrometer to achieve fast spectral monitoring with the highest resolution of 1.54 pm. The proposed scheme provides a new perspective for developing high-performance low-repetition-rate mode-locked lasers and promoting the development of optical applications. Physical sciences/Optics and photonics/Lasers, LEDs and light sources/Ultrafast lasers Physical sciences/Physics/Optical physics/Nonlinear optics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Ultrafast lasers have attracted great attention in recent years due to their unique advantages in applications such as material processing 1 , biomedical imaging 2 , and fast spectral analysis 3 . From the point of energy, 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, broadband low repetition rate mode-locked laser with MHz level can be time stretched to generate highly coherent swept laser. Current swept lasers such as short cavity laser 6 , MEMS-VCSEL 7 , and Fourier domain mode locked (FDML) laser 8 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 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 photodetector, tens to hundreds of sweep rate affect the spectral resolution for spectroscopy and detection range for metrology. To simultaneously realize high speed, high resolution, and long-range detection, a highly coherent swept laser with 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 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, 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 dB 43 . 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 fibers 44 . 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. Here, a self-made 6-tube AR-HCF through the cladding nested design with thinner and more uniform capillary wall has ultra-low transmission loss (0.53 dB/km) and extremely small nonlinear coefficient (1.97×10 − 7 W − 1 m − 1 ), while maintaining excellent single-mode transmission performance. This high- performance AR-HCF is then inserted inside the mode locked laser cavity to achieve 2.63 MHz low repetition-rate, 35 nm broadband pulse with high coherence working at 1.55 µm wavelength. The output power reaches 27 mW, the pulse duration is100 fs, and the peak power is up to 103 kW. High-energy, high coherence and low-repetition broadband ultrafast laser is further time stretched to generate MHz-level frequency-swept signal, which has been applied in SS-OCT system with 1.6 m imaging range as well as in fast spectroscopy with pm-level resolution. To the best of our knowledge, the results reported represent the first demonstration of MHz repetition rate broadband mode locked fiber laser and MHz highly coherent swept laser working at 1.55 µm band, which will boost the advancement of high resolution, high speed, and long-range detection systems including SS-OCT, OFDR, and spectroscopy, as well as benefit medical diagnosis and industrial inspection. Results Generation of 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, 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 1550 nm wavelength band. Compared with SMF, the nonlinearity coefficient is 5.4×10 3 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 S1. 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. Nonlinear polarization rotation (NPR) mode locking scheme is easy to realize high power compared with using SESAMs. Taking advantage of anti-polarization sensitivity characteristic of self-made AR-HCF, NPR mode-locking mechanism with 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 (SPM) and cross-phase modulation (XPM) effects 59 , 50 . In addition, when the polarization state is changed (P 1 to P 2 ), the polarization-dependent loss (PDL) in the cavity selectively suppresses the gain of a specific wavelength and shifts the wavelength to meet the low-loss condition. 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. 2b, indicating a stable mode-locking operation. The inset in Fig. 2b 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. Soliton opration 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 milliwatts), 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 shwon 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, 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 the pump powers. It can be seen that the output power of the laser ranges from 13.9 mW 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 reache 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 single-shot dispersive Fourier transform (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 spectrum 51 . 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 medium 52 . 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 120 minutes 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 0.0463 nm, and the SD of the output power fluctuation is 0.3983 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 standard deviations of 12.1 Hz and 0.034 dB, respectively. The above results indicate that the constructed low-repetition-rate long-cavity mode locked laser maintains excellent long-term stability. 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 th- e 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 high-frequency RIN measured at frequency offsets above 1 MHz is -127 dB/Hz, and low-frequency noise is also suppressed. 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 , 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 photodetector 54 . 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. 5ai, where proposed low repetition rate mode locked laser is time stretched to generate 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 coeffici- ent (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 Hz 2 /Hz, and the corresponding intrinsic linewidth is approximately ~ 305 Hz (see Supplementary Note S4 for details). Then, by performing a fast Fourier transform on the resampled interference signal, the point spread function (PSF) that characterizes the detection range of the imaging system can be obtained. 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 m and 1.6 m, and the corresponding sensitivity roll-off is 6 dB and 9.2 dB (inset ⅹ of Fig. 2d), 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 system is one application of coherent detection by the swept laser. Another key application of swept laser is the 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. 5aii. DFT spectrometer by a high-speed photodetector achieves an unprecedented 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. Figures 5e and f show the spectral evolution of 500 round trips when the FFP-TF is driven by an 8 vp- p sinusoidal signal at driving frequencies of 42.4 kHz 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 µs and 8.83392 µs, respectively, and the corresponding frequencies are exactly 42.4 kHz 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 phase of different wavelengths are not locked, 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 fast Fourier transform on the resampled interference signal. 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 the last subsection of the supplementary information. 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 photodetector and sampling rate are no longer the limitations. Therefore, to improve the resolution of spectral detection, it is necessary to apply a sufficiently large dispersion 55 . 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. As the discussion above, low repetition rate mode locked laser with 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, the repetition rate of mode locked laser can be further decreased. In conclusion, we have proposed a novel 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 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 Hz 2 /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 new low-repetition mode-locked fiber lasers and pave the way for unprecedented performance and applications. Methods Fabrication of AR-HCF . The high-performance 6-tube AR-HCF is fabricated using an improved stack-and-draw method 63 . 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 (SEM) imaging technology and systematically calibrated by the measurement error analysis. The nonlinear coefficient is calculated using the formula in reference 64 . Details of laser experimental setup. The technical details of the low repetition rate mode-locked fiber laser based on AR-HCF are shown in Fig. 1a. 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 tap, isolator and wavelength division multiplexer (TI-WDM), simplifies the laser system and reduces the overall nonlinearity. 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. 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 is used to time stretch the mode locked laser to generate 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 5ai shows the schematic of the high-speed coherent detection system. The swept signal is split into two paths through a 10:90 coupler (OC1). 90% 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 5aii 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 DFT spectrometer. The key parameters of the DFT technique include spectral resolution, scanning rate, and spectral data points, which present a multi-dimensional constraint relationship 55 . 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 group velocity dispersion of the medium (unit: ps/nm). To avoid the overlap of adjant 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 = 2 B (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: Therefore, it can be concluded that lower repetition rate, larger detection bandwidth and larger dispersion will achieve higher resolution by the DFT spectrometer. Declarations Data availability The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Acknowledgments 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). 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. 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1","display":"","copyAsset":false,"role":"figure","size":885557,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eConceptual design and operation of the low-repetition-rate ultrafast all-fiber laser. a \u003c/strong\u003eConceptual diagram of the propagation and evolution of high-energy pulses in single-mode fiber (SMF) and AR-HCF, respectively. \u003cstrong\u003eb \u003c/strong\u003eLeft: 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, 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, CFBG chirped fiber Bragg grating, EDFC EDF optimized for C-band region, WDM wavelength division multiplexer. \u003cstrong\u003ec\u003c/strong\u003e Simulated\u003cstrong\u003e \u003c/strong\u003edispersion curve of the AR-HCF. \u003cstrong\u003ed \u003c/strong\u003eSimulated various loss curves of AR-HCF. \u003cstrong\u003ee\u003c/strong\u003eNonlinear curves of AR-HCF and SMF-28e.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/318c6729197450b110a2c4a5.png"},{"id":98766646,"identity":"ca87cbff-956f-4eab-85dc-539c1cd60504","added_by":"auto","created_at":"2025-12-22 10:18:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1025312,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental study of basic laser output characteristics. a \u003c/strong\u003eOptical spectra of laser in different polarization states (P\u003csub\u003e1\u003c/sub\u003eand P\u003csub\u003e2\u003c/sub\u003e).\u003cstrong\u003e b\u003c/strong\u003e Time-domain pulse sequence. \u003cstrong\u003ec \u003c/strong\u003eMeasured RF spectrum at 1 Hz resolution. Inset: higher-order harmonics in the frequency domain. \u003cstrong\u003ed, e \u003c/strong\u003e2D pseudo-color images plot of optical spectra and time-domain pulses evolution with pump power (300 mW-600 mW). \u003cstrong\u003ef, g\u003c/strong\u003e Optical spectra and temporal pulse train at some specific pump powers (468 mW, 570 mW and 600 mW). \u003cstrong\u003eh\u003c/strong\u003e Output power of the constructed mode-locked laser at different pump powers. \u003cstrong\u003ei \u003c/strong\u003eIntensity autocorrelation function (ACF) trace and the Sech fitting curve.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/d75e7bfacc670e6d3ae7947e.png"},{"id":98766648,"identity":"850a1539-e10f-4290-9092-2071649fb956","added_by":"auto","created_at":"2025-12-22 10:18:59","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1207479,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eReal-time measurement of the self-starting process and long-term stability. a\u003c/strong\u003e Real-time experimental observation of the build-up dynamics of the stretched SP over 63,289 consecutive roundtrips. \u003cstrong\u003eb \u003c/strong\u003eCorresponding intensity evolution during the laser\u003cstrong\u003e \u003c/strong\u003estart-up process. Robustness of the laser single-pulse operation over a period of 120 min. \u003cstrong\u003ec\u003c/strong\u003e Continuous monitoring of the output optical spectrum. \u003cstrong\u003ed \u003c/strong\u003eFluctuation and standard deviation (SD) analysis of central wavelength and output power. \u003cstrong\u003ee \u003c/strong\u003eTemporal evolution of the measured RF spectrum. \u003cstrong\u003ef\u003c/strong\u003e Stability performance of the laser repetition rate and the signal-to-noise ratio (SNR).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/861651b88c1ab061ed0cabc0.png"},{"id":98780419,"identity":"20de1eeb-ea8d-4c7d-aa0f-c08b6f48d16d","added_by":"auto","created_at":"2025-12-22 12:31:20","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1669709,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExcellent short-term stability and spectral statistical\u003c/strong\u003e \u003cstrong\u003ecross-correlation. a\u003c/strong\u003e 2D pseudo-color map of single-shot spectral evolution recorded by DFT over 8000 consecutive roundtrips. \u003cstrong\u003eb \u003c/strong\u003eComparison of single-frame spectra for specific round trips (1-st, 4000-th, 8000-th).\u003cstrong\u003e c\u003c/strong\u003e Transient spectral energy evolution with round trip. \u003cstrong\u003ed\u003c/strong\u003e Statistical histogram of the single-frame spectral energy for 8000 round trips. \u003cstrong\u003ee\u003c/strong\u003e Relative intensity noise (RIN) of the low-repetition-rate laser after power amplification. \u003cstrong\u003ef\u003c/strong\u003e Evolution of the cross-correlation values of full single-shot spectra within 8000 round trips. \u003cstrong\u003eg\u003c/strong\u003eCross-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.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/d8dbae474a3895127cd26d53.png"},{"id":98766649,"identity":"1b300049-e0d3-4adb-84a0-6ccca70e3c42","added_by":"auto","created_at":"2025-12-22 10:18:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1169144,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCoherent detection andfast spectra characterization with self-developed MHz-level swept laser. a\u003c/strong\u003e Experimental setups of the (i) coherent detection and (ii) spectra characterization. \u003cstrong\u003eb\u003c/strong\u003e Real-time interferogram generated by single-shot scanning. \u003cstrong\u003ec \u003c/strong\u003eSwept trace of wavelength and time mapping, fitted by a quadratic polynomial from 1526 to 1565. \u003cstrong\u003ed\u003c/strong\u003e 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, and (x) peak amplitude of the PSFs at different measured distances. Single-shot spectral charaterization of the FFT-TF under the driving frequencies of \u003cstrong\u003ee \u003c/strong\u003e42.4 kHz and \u003cstrong\u003ef \u003c/strong\u003e113.2 kHz. \u003cstrong\u003eg\u003c/strong\u003e R Comparison of the average spectra obtained by DFT and OSA at a driving frequency of 42.4 kHz. \u003cstrong\u003eh\u003c/strong\u003e Single-shot spectra of the 15-th, 246-th and 480-th round trips at a driving frequency of 113.2 kHz.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/b26fd16ca0a5cf0a95de722f.png"},{"id":98786838,"identity":"5d7cbec4-a560-41ee-8d9e-7c333c151316","added_by":"auto","created_at":"2025-12-22 12:43:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6776591,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/e6494cae-753f-46a8-bdc7-c9638345de3c.pdf"},{"id":98780784,"identity":"9fa671e5-63db-448a-a929-039f26c058d8","added_by":"auto","created_at":"2025-12-22 12:31:39","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":16379096,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/9ad4762c960430496dfaac65.docx"},{"id":98780882,"identity":"1cc60fe5-5cd6-458d-91bc-3a5a3702bf15","added_by":"auto","created_at":"2025-12-22 12:31:48","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":119490,"visible":true,"origin":"","legend":"","description":"","filename":"TAB1.docx","url":"https://assets-eu.researchsquare.com/files/rs-8215335/v1/cc467fe8f4fd35694bb482e6.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"High-energy, low-repetition broadband ultrafast lasers empowered by hollow-core fiber","fulltext":[{"header":"Introduction","content":"\u003cp\u003eUltrafast lasers have attracted great attention in recent years due to their unique advantages in applications such as material processing\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, biomedical imaging\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, and fast spectral analysis\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. From the point of energy, 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\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. From the point of spectrum, broadband low repetition rate mode-locked laser with MHz level can be time stretched to generate highly coherent swept laser. Current swept lasers such as short cavity laser\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, MEMS-VCSEL\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, and Fourier domain mode locked (FDML) laser\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e 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 swept signal by time stretching technology with proper dispersion modules\u003csup\u003e\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e–\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. 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)\u003csup\u003e\u003cspan additionalcitationids=\"CR13 CR14 CR15\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e–\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e and precision measurement\u003csup\u003e\u003cspan additionalcitationids=\"CR18 CR19 CR20\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e–\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. However, limited by the bandwidth of photodetector, tens to hundreds of sweep rate affect the spectral resolution for spectroscopy and detection range for metrology. To simultaneously realize high speed, high resolution, and long-range detection, a highly coherent swept laser with 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.\u003c/p\u003e\u003cp\u003eThe general methods for reducing the pulse repetition rate of a fiber laser are to use an external pulse picker\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e and to increase the length of the mode-locked fiber cavity\u003csup\u003e\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e–\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. 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\u003csup\u003e\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e–\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Traditional mode-locked fiber lasers are challenging to surpass the 100-kW peak power when operating at MHz-level repetition rate\u003csup\u003e\u003cspan additionalcitationids=\"CR30 CR31\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e–\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. The Mamyshev oscillator, as a new type of mode-locked fiber laser has large tolerance to the accumulation of nonlinear phase shifts\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. 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 (\u0026lt; 50 fs)\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. However, Mamyshev oscillator has inherently inevitable large noise and low coherence, which hinders its further application and development\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. 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.\u003c/p\u003e\u003cp\u003eLow 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\u003csup\u003e\u003cspan additionalcitationids=\"CR40 CR41\" citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e–\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. The connection loss between AR-HCFs and silica fibers could also be engineered to \u0026lt; 0.2 dB\u003csup\u003e43\u003c/sup\u003e. 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 fibers\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. 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\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. 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\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e,\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. 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.\u003c/p\u003e\u003cp\u003eHere, a self-made 6-tube AR-HCF through the cladding nested design with thinner and more uniform capillary wall has ultra-low transmission loss (0.53 dB/km) and extremely small nonlinear coefficient (1.97×10\u003csup\u003e− 7\u003c/sup\u003e W\u003csup\u003e− 1\u003c/sup\u003em\u003csup\u003e− 1\u003c/sup\u003e), while maintaining excellent single-mode transmission performance. This high- performance AR-HCF is then inserted inside the mode locked laser cavity to achieve 2.63 MHz low repetition-rate, 35 nm broadband pulse with high coherence working at 1.55 µm wavelength. The output power reaches 27 mW, the pulse duration is100 fs, and the peak power is up to 103 kW. High-energy, high coherence and low-repetition broadband ultrafast laser is further time stretched to generate MHz-level frequency-swept signal, which has been applied in SS-OCT system with 1.6 m imaging range as well as in fast spectroscopy with pm-level resolution. To the best of our knowledge, the results reported represent the first demonstration of MHz repetition rate broadband mode locked fiber laser and MHz highly coherent swept laser working at 1.55 µm band, which will boost the advancement of high resolution, high speed, and long-range detection systems including SS-OCT, OFDR, and spectroscopy, as well as benefit medical diagnosis and industrial inspection.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cb\u003eGeneration of low-repetition-rate single pulse\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIncreasing 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)\u003csup\u003e10\u003c/sup\u003e. 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.\u0026nbsp;1a. Due to the accumulation of dispersion and nonlinearity in the long SMF, 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.\u0026nbsp;1c and low nonlinearity as shown in Fig.\u0026nbsp;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 1550 nm wavelength band. Compared with SMF, the nonlinearity coefficient is 5.4×10\u003csup\u003e3\u003c/sup\u003e times lower. Another key factor is the low loss of AR-HCF with 0.53 dB/km (Fig.\u0026nbsp;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 S1. 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.\u0026nbsp;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.\u003c/p\u003e\u003cp\u003eNonlinear polarization rotation (NPR) mode locking scheme is easy to realize high power compared with using SESAMs. Taking advantage of anti-polarization sensitivity characteristic of self-made AR-HCF, NPR mode-locking mechanism with 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.\u0026nbsp;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 (SPM) and cross-phase modulation (XPM) effects\u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e,\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. In addition, when the polarization state is changed (P\u003csub\u003e1\u003c/sub\u003e to P\u003csub\u003e2\u003c/sub\u003e), the polarization-dependent loss (PDL) in the cavity selectively suppresses the gain of a specific wavelength and shifts the wavelength to meet the low-loss condition. 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.\u0026nbsp;2a by the pink curve. Figure\u0026nbsp;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.\u0026nbsp;2b, indicating a stable mode-locking operation. The inset in Fig.\u0026nbsp;2b 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.\u003c/p\u003e\u003cp\u003eSoliton opration states are dependent on the intracavity energy and demonstrated as shown in Fig.\u0026nbsp;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 milliwatts), 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 shwon in Fig.\u0026nbsp;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, 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\u0026nbsp;2h shows the laser output power with different the pump powers. It can be seen that the output power of the laser ranges from 13.9 mW to 27 mW during single-pulse operation. The experimentally measured autocorrelation function (ACF) of the pulse is shown in Fig.\u0026nbsp;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 reache 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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eSelf-starting and long-term stability\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe dynamics of the single-pulse mode-locking operation is studied using single-shot dispersive Fourier transform (DFT) technique to demonstrate the self-starting property. Figure\u0026nbsp;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 spectrum\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. Figure\u0026nbsp;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 medium\u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. 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 120 minutes 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.\u0026nbsp;3c. Figure\u0026nbsp;3d shows the evolution of the corresponding central wavelength and output power. The standard deviation (SD) of the central wavelength is 0.0463 nm, and the SD of the output power fluctuation is 0.3983 mW. Figure\u0026nbsp;3e shows the temporal evolution of the RF spectrum, where no significant fundamental frequency changes are observed. Figure\u0026nbsp;3f presents the repetition rate and SNR over time, with standard deviations of 12.1 Hz and 0.034 dB, respectively. The above results indicate that the constructed low-repetition-rate long-cavity mode locked laser maintains excellent long-term stability.\u003c/p\u003e\u003cp\u003e\u003cb\u003eShort-term stability with DFT technology\u003c/b\u003e\u003c/p\u003e\u003cp\u003eTo 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.\u0026nbsp;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.\u0026nbsp;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.\u0026nbsp;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.\u0026nbsp;4c. The energy fluctuation of th-\u003c/p\u003e\u003cp\u003ee 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.\u0026nbsp;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.\u0026nbsp;4e. The high-frequency RIN measured at frequency offsets above 1 MHz is -127 dB/Hz, and low-frequency noise is also suppressed.\u003c/p\u003e\u003cp\u003eTo 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\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e, as shown in Fig.\u0026nbsp;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.\u0026nbsp;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\u0026nbsp;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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eCoherent detection and fast spectrum characterization\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThere is a trade-off between the sweep rate and detection range in the SS-OCT system due to the limited bandwidth of the photodetector\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. 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.\u0026nbsp;5ai, where proposed low repetition rate mode locked laser is time stretched to generate 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.\u0026nbsp;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.\u0026nbsp;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 coeffici-\u003c/p\u003e\u003cp\u003eent (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.\u0026nbsp;5d). The high-frequency white noise is 97 Hz\u003csup\u003e2\u003c/sup\u003e/Hz, and the corresponding intrinsic linewidth is approximately ~ 305 Hz (see Supplementary Note S4 for details). Then, by performing a fast Fourier transform on the resampled interference signal, the point spread function (PSF) that characterizes the detection range of the imaging system can be obtained. The main panel of Fig.\u0026nbsp;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.\u0026nbsp;5d, more PSFs, see supplementary Fig. S5), with a highest SNR reaching up to 52 dB (typically 40 dB). Inset ix in Fig.\u0026nbsp;5d shows 41 µm axial resolution of the SS-OCT system. The imaging range reaches up to 1.3 m and 1.6 m, and the corresponding sensitivity roll-off is 6 dB and 9.2 dB (inset ⅹ of Fig.\u0026nbsp;2d), respectively. As far as we know, meter-level detection range with MHz imaging speed is a world record for the SS-OCT system.\u003c/p\u003e\u003cp\u003eThe SS-OCT system is one application of coherent detection by the swept laser. Another key application of swept laser is the 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.\u0026nbsp;5aii. DFT spectrometer by a high-speed photodetector achieves an unprecedented 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. Figures\u0026nbsp;5e and f show the spectral evolution of 500 round trips when the FFP-TF is driven by an 8 vp-\u003c/p\u003e\u003cp\u003ep sinusoidal signal at driving frequencies of 42.4 kHz 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 µs and 8.83392 µs, respectively, and the corresponding frequencies are exactly 42.4 kHz 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.\u0026nbsp;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\u0026nbsp;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.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eCompared with other swept lasers based on tunable filters whose phase of different wavelengths are not locked, 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 fast Fourier transform on the resampled interference signal. 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 the last subsection of the supplementary information.\u003c/p\u003e\u003cp\u003eAnother 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 photodetector and sampling rate are no longer the limitations. Therefore, to improve the resolution of spectral detection, it is necessary to apply a sufficiently large dispersion\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. 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.\u003c/p\u003e\u003cp\u003eAs the discussion above, low repetition rate mode locked laser with broadband spectrum is desirable for coherent detection and spectroscopy. Table\u0026nbsp;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, the repetition rate of mode locked laser can be further decreased.\u003c/p\u003e\u003cp\u003eIn conclusion, we have proposed a novel 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 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 Hz\u003csup\u003e2\u003c/sup\u003e/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 new low-repetition mode-locked fiber lasers and pave the way for unprecedented performance and applications.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cb\u003eFabrication of AR-HCF\u003c/b\u003e. The high-performance 6-tube AR-HCF is fabricated using an improved stack-and-draw method\u003csup\u003e\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e. 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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eSimulation of AR-HCF.\u003c/b\u003e 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 (SEM) imaging technology and systematically calibrated by the measurement error analysis. The nonlinear coefficient is calculated using the formula in reference \u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDetails of laser experimental setup.\u003c/b\u003e The technical details of the low repetition rate mode-locked fiber laser based on AR-HCF are shown in Fig.\u0026nbsp;1a. 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 tap, isolator and wavelength division multiplexer (TI-WDM), simplifies the laser system and reduces the overall nonlinearity. 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. 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 is used to time stretch the mode locked laser to generate 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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eDetails of the measurement system.\u003c/b\u003e 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\u0026nbsp;5ai shows the schematic of the high-speed coherent detection system. The swept signal is split into two paths through a 10:90 coupler (OC1). 90% 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\u0026nbsp;5aii 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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eResolution of DFT spectrometer.\u003c/b\u003e The key parameters of the DFT technique include spectral resolution, scanning rate, and spectral data points, which present a multi-dimensional constraint relationship\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. The scanning rate \u003cem\u003eR\u003c/em\u003e is determined by the laser repetition rate. The wavelength-time relationship by the dispersion process satisfies the physical law ∆\u003cem\u003eτ\u003c/em\u003e = |\u003cem\u003eD\u003c/em\u003e|∆\u003cem\u003eλ\u003c/em\u003e, where \u003cem\u003eD\u003c/em\u003e represents the total group velocity dispersion of the medium (unit: ps/nm). To avoid the overlap of adjant pulses, the stretched pulse ∆\u003cem\u003eτ\u003c/em\u003e should satisfy the condition ∆\u003cem\u003eτ\u003c/em\u003e \u0026lt; \u003cem\u003eR\u003c/em\u003e⁻¹. The number of time domain sampling points \u003cem\u003eN\u003c/em\u003e = \u003cem\u003eS\u003c/em\u003e|\u003cem\u003eD\u003c/em\u003e|∆\u003cem\u003eλ\u003c/em\u003e, \u003cem\u003eS\u003c/em\u003e is the sampling rate of analog-to-digital converter (ADC), and the optical spectral resolution \u003cem\u003eδλ\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e = (\u003cem\u003eS\u003c/em\u003e|\u003cem\u003eD\u003c/em\u003e|)\u003csup\u003e−1\u003c/sup\u003e. The detection system analog bandwidth \u003cem\u003eB\u003c/em\u003e forms another limitation through \u003cem\u003eδλ\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e = (\u003cem\u003eB|D\u003c/em\u003e|)\u003csup\u003e−1\u003c/sup\u003e. In the ideal optimum, \u003cem\u003eS\u003c/em\u003e = 2\u003cem\u003eB\u003c/em\u003e (Nyquist sampling theorem), while in actual operation, \u003cem\u003eB\u003c/em\u003e \u0026lt; \u003cem\u003eS\u003c/em\u003e/2. The actual spectral resolution is determined by three factors: digital sampling capability, dispersion characteristics, and system bandwidth, which is described as:\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"183\" height=\"28\"\u003e\u003c/p\u003e\u003cp\u003eTherefore, it can be concluded that lower repetition rate, larger detection bandwidth and larger dispersion will achieve higher resolution by the DFT spectrometer.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis 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).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eL.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.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing competing interests.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMalinauskas M et al (2016) Ultrafast laser processing of materials: from science to industry. 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Infrared Phys Techn 131:104688\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYe G et al (2023) L-band mode-locked fiber laser using all polarization-maintaining nonlinear polarization rotation. Opt Lett 48:4729\u0026ndash;4732\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCai Y et al (2010) Erbium-doped fiber lasers operated in a strong normal dispersion regime at low repetition rate. IEEE Photonics Technol Lett 22:1401\u0026ndash;1403\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAmouzad Mahdiraji G et al (2014) Challenges and solutions in fabrication of silica-based photonic crystal fibers: an experimental study. Fiber Integr Opt 33:85\u0026ndash;104\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJi X et al (2021) Millimeter-scale chip\u0026ndash;based supercontinuum generation for optical coherence tomography. Sci Adv 7:eabg8869\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8215335/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8215335/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Low-repetition-rate ultrafast lasers with high peak power and broadband spectrum are key components in applications such as industrial processing, lidar, optical imaging, and spectroscopy. To turn these capabilities from concepts into reality, the missing element is a low nonlinearity and low dispersion waveguide with purified transverse mode that can be mass-produced. Here, a self-made anti-resonant hollow-core fiber with a nonlinear coefficient as low as 1.97×10-7 and single transverse mode low-loss transmission is inserted into a nonlinear polarization rotation mode locking cavity with simple and compact configuration to realize high performance ultrafast laser. A turn-key single-pulse mode-locked all-fiber laser with repetition rate as low as 2.63 MHz, peak power up to 103 kW, and bandwidth of 35 nm is demonstrated. The stable phase relationship of the different wavelengths enables highly coherent swept signal with low frequency noise of 97 Hz2/Hz by time stretching technology, which has been demonstrated for coherent detection systems. A 1.6 m detection range with a MHz-level refresh frame rate in swept source optical coherence tomography system is demonstrated. Besides, a fast vibration signal of 113.2 kHz is reconstructed by demodulating the phase of the interference signal. Furthermore, the laser is also used in a dispersive Fourier transform spectrometer to achieve fast spectral monitoring with the highest resolution of 1.54 pm. The proposed scheme provides a new perspective for developing high-performance low-repetition-rate mode-locked lasers and promoting the development of optical applications.","manuscriptTitle":"High-energy, low-repetition broadband ultrafast lasers empowered by hollow-core fiber","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-22 10:18:53","doi":"10.21203/rs.3.rs-8215335/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d6117b71-4ce1-41f1-9b20-7dc320cfe465","owner":[],"postedDate":"December 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":59847205,"name":"Physical sciences/Optics and photonics/Lasers, LEDs and light sources/Ultrafast lasers"},{"id":59847206,"name":"Physical sciences/Physics/Optical physics/Nonlinear optics"}],"tags":[],"updatedAt":"2026-03-31T09:20:56+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-22 10:18:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8215335","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8215335","identity":"rs-8215335","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}