Simple approach to the relation between laser frequency noise and laser line shape

Sub-kHz-linewidth broadband-swept fiber laser based on Rayleigh scattering-enabled Brillouin random lasing oscillation with dynamic tunning Brillouin gain spectrum

A sub-kHz-linewidth broadband-swept fiber laser using Rayleigh scattering-based Brillouin random lasing oscillation is proposed and experimentally demonstrated. Benefiting from Brillouin-involved acoustic damping and arbitrary-wavelength distributed Rayleigh feedback, leveraging instantaneously tuning Brillouin gain spectrum induced by a frequency-sweeping pump, a highly coherent random lasing emission with cavity mode elimination as well as frequency noise suppression is achieved in a sweeping manner. Results show that the proposed sweeping Stokes laser with a two-order-magnitude compressed linewidth of 840 Hz and 20 dB frequency noise suppression can unprecedentedly operate over the maximum wavelength range of 16 nm. Dynamic characteristics of the sweeping laser frequency are experimentally investigated, indicating a minimum residual nonlinearity of 0.0001 within the frequency-sweeping range of 126.63 GHz. It is believed that the proposed swept fiber laser may have attractive potential in diverse applications, including sensing and imaging.

High-efficiency, single-frequency, polarized thulium-doped silica fiber lasers

We report on single-frequency, linearly polarized, high-concentration thulium-doped silica fiber-distributed Bragg reflector lasers operating at wavelengths between 1908 and 2050 nm with high efficiencies up to 48% and high powers up to 1 W. Low relative power noise and frequency noise are demonstrated using a low-noise pump diode.

Anneal-free ultra-low loss silicon nitride integrated photonics

Heterogeneous and monolithic integration of the versatile low-loss silicon nitride platform with low-temperature materials such as silicon electronics and photonics, III-V compound semiconductors, lithium niobate, organics, and glasses has been inhibited by the need for high-temperature annealing as well as the need for different process flows for thin and thick waveguides. New techniques are needed to maintain the state-of-the-art losses, nonlinear properties, and CMOS-compatible processes while enabling this next generation of 3D silicon nitride integration. We report a significant advance in silicon nitride integrated photonics, demonstrating the lowest losses to date for an anneal-free process at a maximum temperature 250 °C, with the same deuterated silane based fabrication flow, for nitride and oxide, for an order of magnitude range in nitride thickness without requiring stress mitigation or polishing. We report record low anneal-free losses for both nitride core and oxide cladding, enabling 1.77 dB m-1 loss and 14.9 million Q for 80 nm nitride core waveguides, more than half an order magnitude lower loss than previously reported sub 300 °C process. For 800 nm-thick nitride, we achieve as good as 8.66 dB m-1 loss and 4.03 million Q, the highest reported Q for a low temperature processed resonator with equivalent device area, with a median of loss and Q of 13.9 dB m-1 and 2.59 million each respectively. We demonstrate laser stabilization with over 4 orders of magnitude frequency noise reduction using a thin nitride reference cavity, and using a thick nitride micro-resonator we demonstrate OPO, over two octave supercontinuum generation, and four-wave mixing and parametric gain with the lowest reported optical parametric oscillation threshold per unit resonator length. These results represent a significant step towards a uniform ultra-low loss silicon nitride homogeneous and heterogeneous platform for both thin and thick waveguides capable of linear and nonlinear photonic circuits and integration with low-temperature materials and processes.

Linewidth Measurement of a Narrow-Linewidth Laser: Principles, Methods, and Systems

Narrow-linewidth lasers mainly depend on the development of advanced laser linewidth measurement methods for related technological progress as key devices in satellite laser communications, precision measurements, ultra-high-speed optical communications, and other fields. This manuscript provides a theoretical analysis of linewidth characterization methods based on the beat frequency power spectrum and laser phase noise calculations, and elaborates on existing research of measurement technologies. In addition, to address the technical challenges of complex measurement systems that commonly rely on long optical fibers and significant phase noise jitter in the existing research, a short-delay self-heterodyne method based on coherent envelope spectrum demodulation was discussed in depth to reduce the phase jitter caused by 1/f noise. We assessed the performance parameters and testing conditions of different lasers, as well as the corresponding linewidth characterization methods, and analyzed the measurement accuracy and error sources of various methods.

A self-referenced optical phase noise analyzer for quantum technologies

Second generation quantum technologies aim to outperform classical alternatives by utilizing engineered quantum systems. Maintaining the coherence required to enable any quantum advantage requires detailed knowledge and control over the noise that the hosting system is subjected to. Characterizing noise processes via their power spectral density is routinely done throughout science and technology and can be a demanding task. Determining the phase noise power spectrum in leading quantum technology platforms, for example, can be either outside the reach of many phase noise analyzers or prohibitively expensive. In this work, we present and characterize a low-complexity, low-cost optical phase noise analyzer based on the short-delay optical self-heterodyne measurements for quantum technology applications. Using this setup, we compare two ≈1 Hz linewidth ultra-stable oscillators near 729 nm. Their measurements are used as a baseline to determine and discuss the noise floor achieved in this measurement apparatus with a focus on limitations and their tradeoffs. The achieved noise floor in this all-stock-component implementation of an optical phase noise analyzer compares favorably with commercial offerings. This setup can be used particularly without a more stable reference or operational quantum system as a sensor as would be the case for many component manufacturers.

10 W super-wideband ultra-low-intensity-noise single-frequency fiber laser at 1 µm

A 10 W super-wideband ultra-low-intensity-noise single-frequency fiber laser (SFFL) at 1 µm is experimentally demonstrated, based on dual gain saturation effects from semiconductors and optical fibers, together with an analog-digital hybrid optoelectronic feedback loop. Three intensity-noise-inhibited units synergistically work, which actualizes a connection of effective bandwidth and enhancement of noise-suppressing amplitude. With the cascade action of the semiconductor optical amplifier and optical fiber amplifier, the laser power is remarkably boosted. Eventually, an SFFL with an output power of 10.8 W and a relative intensity noise (RIN) below -150 dB/Hz at the frequency range over 1 Hz is realized. More meaningfully, within the total frequency range of 10 Hz to 10 GHz exceeding 29 octaves, the RIN is controlled to below -160 dB/Hz, approaching the shot-noise limit (SNL) level. To the best of our knowledge, this is the lowest RIN result of SFFL within such an extensive frequency range, and this is the highest output power of the near-SNL super-wideband SFFL. Furthermore, a linewidth of less than 0.8 kHz, a long-term stable polarization extinction ratio of 20 dB, and an optical signal-to-noise ratio of over 60 dB are obtained simultaneously. This start-of-the-art SFFL has provided a systematic solution for high-power and low-noise light sources, which is competitive for sophisticated applications, such as free-space laser communication, space-based gravitational wave detection, and super-long-distance space coherent velocity measurement and ranging.

Narrow-linewidth and low RIN Tm/Ho co-doped fiber laser based on self-injection locking

A narrow-linewidth and low relative intensity noise (RIN) Tm/Ho co-doped fiber laser based on a saturable absorber and self-injection locking was demonstrated for the first time. Utilizing self-injection locking technology, the frequency noise power spectral density is remarkably reduced by more than 17.1 dB from 1.21 × 106 Hz2/Hz to 7.30 × 103 Hz2/Hz when the frequency is approximately 1 kHz. Furthermore, a laser with a linewidth compressed to a quarter of the original linewidth from 44.386 kHz to 2.850 kHz, a RIN of less than -127.74 dB/Hz, and an optical signal-to-noise ratio of more than 71.6 dB can be obtained. Using a delay fiber, the relaxation oscillation peak frequencies move to lower frequencies, from 27.9 kHz to 15.8 kHz. The proposed laser is highly competitive in advanced coherent light detection fields, including coherent Doppler wind lidar, high-speed coherent optical communication, and precise absolute distance coherent measurement.

Narrow laser linewidth measurement with the optimal demodulated Lorentzian spectrum

A method called the optimal demodulated Lorentzian spectrum is employed to precisely quantify the narrowness of a laser's linewidth. This technique relies on the coherent envelope demodulation of a spectrum obtained through short delayed self-heterodyne interferometry. Specifically, we exploit the periodic features within the coherence envelope spectrum to ascertain the delay time of the optical fiber. Furthermore, the disparity in contrast within the coherence envelope spectrum serves as a basis for estimating the laser's linewidth. By creating a plot of the coefficient of determination for the demodulated Lorentzian spectrum fitting in relation to the estimated linewidth values, we identify the existence of an optimal Lorentzian spectrum. The corresponding laser linewidth found closest to the true value is deemed optimal. This method holds particular significance for accurately measuring the linewidth of lasers characterized as narrow or ultranarrow.

Modulation-free laser stabilization technique using integrated cavity-coupled Mach-Zehnder interferometer

Stable lasers play a significant role in precision optical systems where an electro-optic laser frequency stabilization system, such as the Pound-Drever-Hall technique, measures laser frequency and actively stabilizes it by comparing it to a frequency reference. Despite their excellent performance, there has been a trade-off between complexity, scalability, and noise measurement sensitivity. Here, we propose and experimentally demonstrate a modulation-free laser stabilization method using an integrated cavity-coupled Mach-Zehnder interferometer as a frequency noise discriminator. The proposed architecture maintains the sensitivity of the Pound-Drever-Hall architecture without the need for any modulation. This significantly simplifies the architecture and makes miniaturization into an integrated photonic platform easier. The implemented chip suppresses the frequency noise of a semiconductor laser by 4 orders-of-magnitude using an on-chip silicon microresonator with a quality factor of 2.5 × 106. The implemented passive photonic chip occupies an area of 0.456 mm2 and is integrated on AIM Photonics 100 nm silicon-on-insulator process.

Laser frequency noise characterization using high-finesse plano-concave optical microresonators

Characterizing laser frequency noise is essential for applications including optical sensing and coherent optical communications. Accurate measurement of ultra-narrow linewidth lasers over a wide frequency range using existing methods is still challenging. Here we present a method for characterizing the frequency noise of lasers using a high-finesse plano-concave optical microresonator (PCMR) acting as a frequency discriminator. To enable noise measurements at a wide range of laser frequencies, an array of PCMRs was produced with slight variations of thickness resulting in a series of discriminators operating at a series of periodical frequencies. This method enables measuring the frequency noise over a wide linewidth range (15 Hz to <100 MHz) over the 1440-1630 nm wavelength range. To assess the performance of the method, four different lasers were characterized, and the results were compared to the estimations of a commercial frequency noise analyzer.

Broadband phase noise measurement of single-frequency lasers by the short-fiber recirculating delayed self-heterodyne method

Characterization of single-frequency lasers (SFLs) requires a precise measurement of their phase noise. However, there exists a contradiction between the frequency range and laser phase noise measurement sensitivity in the delay self-heterodyne method. Achieving a broadband and highly sensitive phase noise measurement often requires overlapping the results obtained from different delay lengths. In this study, we present a precisely designed short-fiber recirculating delayed self-heterodyne (SF-RDSH) method that enables the broadband and highly sensitive laser phase noise measurement in a compact setup. By designing the length of the delay fiber based on a theoretical model, the RDSH technique with a shortest delay length of 200 m enables a highly sensitive laser phase noise measurement from 1 Hz to 1 MHz for the first time, to our knowledge. In the experiment, we demonstrate the broadband phase noise measurement of an SFL by analyzing the 1st and 10th beat notes.

Near thermal noise limit, 5W single frequency fiber laser base on the ring cavity configuration

In this study, we present an ultralow noise single-frequency fiber laser operating at 1550 nm, utilizing a traveling-wave ring cavity configuration. The frequency noise of the laser approaches the thermal noise limit, achieving a white noise level of 0.025 Hz2/Hz, resulting in an instantaneous linewidth of 0.08 Hz. After amplification, the output power reaches 4.94 W while maintaining the same low white noise level as the laser oscillator. The integration linewidths of the laser oscillator and amplifier are 221 Hz and 665 Hz, respectively, with both exhibiting relative intensity noises that approach the quantum shot noise limit. To the best of our knowledge, this work shows the lowest frequency noise combined with relatively high power for this type of ring cavity fiber laser.

Powerful 1-µm 1-GHz optical frequency comb

A self-referenced optical frequency comb is presented based on Kerr-lens mode-locking of ytterbium-doped CALGO. The robust source delivers 3.5 W average power in 44 fs-long pulses at 1 GHz repetition rate. The residual root-mean-square timing jitter of the emitted pulse-train is 146 fs and the residual integrated phase noise of the carrier-envelope offset frequency is 107 mrad, both in a span from 1 Hz to 10 MHz. After stabilization, 2.7 W average power remains for direct application. This work represents the first multi-mode pumped Kerr-lens mode-locked optical frequency comb at gigahertz-level repetition rate.

Monolithic VECSEL for stable kHz linewidth

Vertical-external-cavity surface-emitting semiconductor lasers (VECSELs) are of increasing interest for applications requiring ultra-coherence and/or low noise at novel wavelengths; performance that is currently achieved via high-Q, air-spaced resonators to achieve long intra-cavity photon lifetimes (for the so-called class-A low noise regime), power scaling and high beam quality. Here, we report on the development of a compact, electronically tunable, monolithic-cavity, class-A VECSEL (monolithic VECSEL) for ultra-narrow free-running linewidths. A multi-quantum-well, resonant periodic gain structure with integrated distributed Bragg reflector (DBR) was optically-bonded to an air-gap-free laser resonator created inside a right-angle fused-silica prism to suppress the influence of environmental noise on the external laser oscillation, thus achieving high stability. Mode-hop-free wavelength tuning is performed via the stabilized temperature; or electronically, and with low latency, via a shear piezo-electric transducer mounted on the top of the prism. The free-running linewidth, estimated via the frequency power spectral density (PSD), is sub-kHz over ms timescales and <1.9 kHz for time sampling as long as 1s, demonstrating at least two orders-of-magnitude improvement in noise performance compared to previously reported single frequency VECSELs. The stable, total internal reflection resonator concept is akin to the prevalent monolithic non-planar ring oscillator (NPRO), however the monolithic VECSEL has several important advantages: tailored emission wavelength (via semiconductor bandgap engineering), no relaxation oscillations, no applied magnetic field, and low requirements on the pump beam quality. This approach is power-scalable in principle and could be applied to VECSELs at any of the wavelengths from the visible to the mid-infrared at which they are already available, to create a range of robust, ultra-coherent laser systems with reduced bulkiness and complexity. This is of particular interest for remote metrology and the translation of quantum technologies, such as optical clocks, from research laboratories into real world applications.

Quantum noise and its evasion in feedback oscillators

Feedback oscillators, consisting of an amplifier whose output is partially fed back to its input, provide stable references for standardization and synchronization. Notably, the laser is such an oscillator whose performance can be limited by quantum fluctuations. The resulting frequency instability, quantified by the Schawlow-Townes formula, sets a limit to laser linewidth. Here, we show that the Schawlow-Townes formula applies universally to feedback oscillators beyond lasers. This is because it arises from quantum noise added by the amplifier and out-coupler in the feedback loop. Tracing the precise origin of quantum noise in an oscillator informs techniques to systematically evade it: we show how squeezing and entanglement can enable sub-Schawlow-Townes linewidth feedback oscillators. Our analysis clarifies the quantum limits to the stability of feedback oscillators in general, derives a standard quantum limit (SQL) for all such devices, and quantifies the efficacy of quantum strategies in realizing sub-SQL oscillators.

Stabilized single-frequency sub-kHz linewidth Brillouin fiber laser cavity operating at 1 µm

We experimentally demonstrate a stabilized single-frequency Brillouin fiber laser operating at 1.06 µm by means of a passive highly nonlinear fiber (HNLF) ring cavity combined with a phase-locking loop scheme. The stimulated Brillouin scattering efficiency is first investigated in distinct single-mode germanosilicate core fibers with increasing G e O 2 content. The most suitable fiber, namely, 21 mol.% G e O 2 core fiber, is used as the Brillouin gain medium in the laser cavity made with a 15-m-long segment. A Stokes lasing threshold of 140 mW is reported. We also show significant linewidth narrowing (below 1 kHz) as well as frequency noise reduction compared to that of the initial pump in our mode-hop free Brillouin fiber laser.

Low phase noise operation of a cavity-stabilized 698 nm AlGaInP-based VECSEL

We report for the first time a high performance, single frequency AlGaInP-based VECSEL (vertical-external-cavity surface-emitting-laser) with emission at 698 nm, targeting the clock transition of neutral strontium atoms. Furthermore, we present comprehensive noise characterization of this class-A semiconductor laser, including the residual fast phase noise in addition to the frequency and relative intensity noise. The low noise VECSEL has output power at around 135 mW with an estimated linewidth of 115 Hz when frequency stabilized via the Pound-Drever-Hall (PDH) technique to a high finesse reference cavity, without intermediate stabilization. The phase noise is measured to be below -126 dBc/Hz for frequencies between 10 kHz and 15 MHz with a total integrated phase noise of 3.2 mrad, suitable not only for ultra-cold neutral strontium-based quantum technologies, such as optical clocks, but also with potential for atom-interferometry applications.

High density lithium niobate photonic integrated circuits

Photonic integrated circuits have the potential to pervade into multiple applications traditionally limited to bulk optics. Of particular interest for new applications are ferroelectrics such as Lithium Niobate, which exhibit a large Pockels effect, but are difficult to process via dry etching. Here we demonstrate that diamond-like carbon (DLC) is a superior material for the manufacturing of photonic integrated circuits based on ferroelectrics, specifically LiNbO3. Using DLC as a hard mask, we demonstrate the fabrication of deeply etched, tightly confining, low loss waveguides with losses as low as 4 dB/m. In contrast to widely employed ridge waveguides, this approach benefits from a more than one order of magnitude higher area integration density while maintaining efficient electro-optical modulation, low loss, and offering a route for efficient optical fiber interfaces. As a proof of concept, we demonstrate a III-V/LiNbO3 based laser with sub-kHz intrinsic linewidth and tuning rate of 0.7 PHz/s with excellent linearity and CMOS-compatible driving voltage. We also demonstrated a MZM modulator with a 1.73 cm length and a halfwave voltage of 1.94 V.

Red narrow-linewidth lasing and frequency comb from gain-switched self-injection-locked Fabry-Pérot laser diode

Narrow-linewidth lasers are in extensive demand for numerous cutting-edge applications. Such lasers operating at the visible range are of particular interest. Self-injection locking of a laser diode frequency to a high-Q whispering gallery mode is an effective and universal way to achieve superior laser performance. We demonstrate ultranarrow lasing with less than 10 Hz instantaneous linewidth for 20 [Formula: see text]s averaging time at 638 nm using a Fabry-Pérot laser diode locked to a crystalline MgF[Formula: see text] microresonator. The linewidth measured with a [Formula: see text]-separation line technique that characterizes 10 ms stability is as low as 1.4 kHz. Output power exceeds 80 mW. Demonstrated results are among the best for visible-range lasers in terms of linewidth combined with solid output power. We additionally report the first demonstration of a gain-switched regime for such stabilized Fabry-Pérot laser diode showing a high-contrast visible frequency comb generation. Tunable linespacing from 10 MHz to 3.8 GHz is observed. We demonstrated that the beatnote between the lines has sub-Hz linewidth and experiences spectral purification in the self-injection locking regime. This result might be of special importance for spectroscopy in the visible range.

Single-frequency violet and blue laser emission from AlGaInN photonic integrated circuit chips

Chip-based, single-frequency and low phase-noise integrated photonic laser diodes emitting in the violet (412 nm) and blue (461 nm) regime are demonstrated. The GaN-based edge-emitting laser diodes were coupled to high-quality on-chip micro-resonators for optical feedback and mode selection resulting in laser self-injection locking with narrow emission linewidth. Multiple group III-nitride (III-N) based photonic integrated circuit chips with different waveguide designs including single-crystalline AlN, AlGaN, and GaN were developed and characterized. Single-frequency laser operation was demonstrated for all studied waveguide core materials. The best side-mode suppression ratio was determined to be ∼36 dB at 412 nm with a single-frequency laser emission linewidth of only 3.8 MHz at 461 nm. The performance metrics of this novel, to the best of our knowledge, type of laser suggest potential implementation in next-generation, portable quantum systems.

Field-programmable-gate-array-based digital frequency stabilization of low-phase-noise diode lasers

We present the comparison of a field-programmable-gate-array (FPGA) based digital servo module with an analog counterpart for the purpose of laser frequency stabilization to a high-finesse optical cavity. The transfer functions of both the digital and analog modules for proportional-integral-derivative control are measured. For the lasers stabilized to the cavity, we measure the singe-sideband power spectral density of fast phase noise by means of an optical beat with filtered light transmitted through the cavity. The comparison between the digital and analog modules is performed for two low-phase-noise diode lasers at 1120 and 665 nm wavelengths. The performance of the digital servo module compares well to the analog one for the lowest attained levels of 30 mrad for the integrated phase noise and 10-3 for the relative noise power. The laser linewidth is determined to be in the sub-kHz regime, only limited by the high-finesse cavity. Our work exploits the versatility of the FPGA-based servo module (STEMlab) when used with open-source software and hardware modifications. We demonstrated that such modules are suitable candidates for remote-controlled low-phase-noise applications in the fields of laser spectroscopy and atomic, molecular, and optical physics.

Over 250 W low noise core-pumped single-frequency all-fiber amplifier

A high-power linearly-polarized all-fiber single-frequency amplifier at 1 µm based on tandem core-pumping is demonstrated by using a large-mode-area Ytterbium-doped fiber with a core diameter of 20 µm, which nicely balances the stimulated Brillouin scattering effect, thermal load, and output beam quality. A maximum output power of more than 250 W with a corresponding slope efficiency of >85% is achieved at the operating wavelength of 1064 nm without being constrained by the saturation and nonlinear effects. Meanwhile, a comparable amplification performance is realized with a lower injection signal power of the wavelength near the peak gain of the Yb-doped fiber. The polarization extinction ratio and the M² factor of the amplifier are respectively measured to be >17 dB and 1.15 under the maximal output power. In addition, by virtue of the single-mode 1018 nm pump laser, the intensity noise of the amplifier under maximal output power is measured to be comparable to that of the single-frequency seed laser at frequencies higher than 2 kHz, except for the emergence of parasitic peaks that can be eliminated by optimizing the driving electronics of the pump lasers, while the deterioration of the amplification process to the frequency noise and linewidth of the laser is negligible. To the best of our knowledge, this is the highest output power of a single-frequency all-fiber amplifier based on the core-pumping scheme.

Ultrafast tunable lasers using lithium niobate integrated photonics

Early works1 and recent advances in thin-film lithium niobate (LiNbO3) on insulator have enabled low-loss photonic integrated circuits2,3, modulators with improved half-wave voltage4,5, electro-optic frequency combs6 and on-chip electro-optic devices, with applications ranging from microwave photonics to microwave-to-optical quantum interfaces7. Although recent advances have demonstrated tunable integrated lasers based on LiNbO3 (refs. 8,9), the full potential of this platform to demonstrate frequency-agile, narrow-linewidth integrated lasers has not been achieved. Here we report such a laser with a fast tuning rate based on a hybrid silicon nitride (Si3N4)-LiNbO3 photonic platform and demonstrate its use for coherent laser ranging. Our platform is based on heterogeneous integration of ultralow-loss Si3N4 photonic integrated circuits with thin-film LiNbO3 through direct bonding at the wafer level, in contrast to previously demonstrated chiplet-level integration10, featuring low propagation loss of 8.5 decibels per metre, enabling narrow-linewidth lasing (intrinsic linewidth of 3 kilohertz) by self-injection locking to a laser diode. The hybrid mode of the resonator allows electro-optic laser frequency tuning at a speed of 12 × 1015 hertz per second with high linearity and low hysteresis while retaining the narrow linewidth. Using a hybrid integrated laser, we perform a proof-of-concept coherent optical ranging (FMCW LiDAR) experiment. Endowing Si3N4 photonic integrated circuits with LiNbO3 creates a platform that combines the individual advantages of thin-film LiNbO3 with those of Si3N4, which show precise lithographic control, mature manufacturing and ultralow loss11,12.

Coherently averaged dual-comb spectroscopy with a low-noise and high-power free-running gigahertz dual-comb laser

We present a new type of dual optical frequency comb source capable of scaling applications to high measurement speeds while combining high average power, ultra-low noise operation, and a compact setup. Our approach is based on a diode-pumped solid-state laser cavity which includes an intracavity biprism operated at Brewster angle to generate two spatially-separated modes with highly correlated properties. The 15-cm-long cavity uses an Yb:CALGO crystal and a semiconductor saturable absorber mirror as an end mirror to generate more than 3 W average power per comb, below 80 fs pulse duration, a repetition rate of 1.03 GHz, and a continuously tunable repetition rate difference up to 27 kHz. We carefully investigate the coherence properties of the dual-comb by a series of heterodyne measurements, revealing several important features: (1) ultra-low jitter on the uncorrelated part of the timing noise; (2) the radio frequency comb lines of the interferograms are fully resolved in free-running operation; (3) we validate that through a simple measurement of the interferograms we can determine the fluctuations of the phase of all the radio frequency comb lines; (4) this phase information is used in a post-processing routine to perform coherently averaged dual-comb spectroscopy of acetylene (C₂H₂) over long timescales. Our results represent a powerful and general approach to dual-comb applications by combining low noise and high power operation directly from a highly compact laser oscillator.

Free-running Yb:KYW dual-comb oscillator in a MOPA architecture

Single-cavity dual-combs comprise a rapidly emerging technology platform suitable for a wide range of applications like optical ranging, equivalent time sampling, and spectroscopy. However, it remains a challenging task to develop a dual-comb system that exhibits low relative frequency fluctuations to allow for comb line resolved measurements, while simultaneously offering high average power and short pulse durations. Here we combine a passively cooled and compact dual-comb solid-state oscillator with a pair of core-pumped Yb-fiber-based amplifiers in a master-oscillator power-amplifier (MOPA) architecture. The Yb:KYW oscillator operates at 250 MHz and uses polarization multiplexing for dual-comb generation. To the best of our knowledge, this is the first demonstration of a single-cavity dual-comb based on this gain material. As the pulse timing characteristics inherent to the oscillator are preserved in the amplification process, the proposed hybrid approach leverages the benefit of both the ultra-low noise solid-state laser and the advantages inherent to fiber amplifier systems such as straight-forward power scaling. The amplifier is optimized for minimal pulse broadening while still providing significant amplification and spectral broadening. We obtain around 1 W of power per output beam with pulses then compressed down to sub-90 fs using a simple grating compressor, while no pre-chirping or other dispersion management is needed. The full-width half-maximum (FWHM) of the radio-frequency comb teeth is 700 Hz for a measurement duration of 100 ms, which is much less than the typical repetition rate difference, making this passively stable source well-suited for indefinite coherent signal averaging via computational phase tracking.

Comparison of Different Linewidth Measuring Methods for Narrow Linewidth Laser

We experimentally demonstrate a fiber laser with different linewidths based on self-injection locking (SIL) and the stimulated Brillouin scattering effect. Based on the homemade fiber laser, the error origin, resolution, and applicable range of delayed self-heterodyne interferometry (DSHI), self-correlation envelope linewidth detection (SCELD) and Voigt fitting are investigated numerically and experimentally. The selection of the linewidth measuring method should meet the following conclusions: an approximately Lorentzian self-heterodyne spectrum without the pedestal and high-intensity sinusoidal jitter is a prerequisite for DSHI; the SCELD needs a suitable length of delay fiber for eliminating flicker noise and dark noise of the electrical spectrum analyzer; a non-Lorentzian self-heterodyne spectrum without a pedestal is an indispensable element for Voigt fitting. According to the experimental results, the laser Lorentzian linewidth of SIL changes from 1.7 kHz to 587 Hz under different injection powers. When the Brillouin erbium fiber laser is utilized, the Lorentzian linewidth is measured to be 60 ± 5 Hz.

A 1-μm-Band Injection-Locked Semiconductor Laser with a High Side-Mode Suppression Ratio and Narrow Linewidth

We demonstrate a narrow-linewidth, high side-mode suppression ratio (SMSR) semiconductor laser based on the external optical feedback injection locking technology of a femtosecond-apodized (Fs-apodized) fiber Bragg grating (FBG). A single frequency output is achieved by coupling and integrating a wide-gain quantum dot (QD) gain chip with a Fs-apodized FBG in a 1-μm band. We propose this low-cost and high-integration scheme for the preparation of a series of single-frequency seed sources in this wavelength range by characterizing the performance of 1030 nm and 1080 nm lasers. The lasers have a maximum SMSR of 66.3 dB and maximum output power of 134.6 mW. Additionally, the lasers have minimum Lorentzian linewidths that are measured to be 260.5 kHz; however, a minimum integral linewidth less than 180.4 kHz is observed by testing and analyzing the power spectra of the frequency noise values of the lasers.

Feed-forward stabilization of a single-frequency, diode-pumped Pr:YLF-Cr:LiCAF laser operating at 813.42 nm

We introduce a simple and compact diode-pumped Pr:YLF-Cr:LiCAF laser, operating at 813.42 nm and providing a 130-mW, single-frequency output tunable over a 3-GHz range. The laser has a short-term intrinsic linewidth estimated to be 700 Hz (β-separation method), while exhibiting a free-running wavelength stability of below 1 pm in one hour. Using a feed-forward technique we demonstrate the integration of the laser output into a fully stabilized, 1-GHz Ti:sapphire laser frequency comb, resulting in a heterodyne beat note between the laser and the comb with a bandwidth of 65 kHz. Combining feed-forward control with a low-bandwidth servo feedback loop permits stable long-term locking with an rms beat note variation of 15 kHz over 2 minutes. This performance makes the laser a potential candidate for the lattice laser in a ⁸⁷Sr optical lattice clock.

Chip-based laser with 1-hertz integrated linewidth

Lasers with hertz linewidths at time scales of seconds are critical for metrology, timekeeping, and manipulation of quantum systems. Such frequency stability relies on bulk-optic lasers and reference cavities, where increased size is leveraged to reduce noise but with the trade-off of cost, hand assembly, and limited applications. Alternatively, planar waveguide-based lasers enjoy complementary metal-oxide semiconductor scalability yet are fundamentally limited from achieving hertz linewidths by stochastic noise and thermal sensitivity. In this work, we demonstrate a laser system with a 1-s linewidth of 1.1 Hz and fractional frequency instability below 10^-14 to 1 s. This low-noise performance leverages integrated lasers together with an 8-ml vacuum-gap cavity using microfabricated mirrors. All critical components are lithographically defined on planar substrates, holding potential for high-volume manufacturing. Consequently, this work provides an important advance toward compact lasers with hertz linewidths for portable optical clocks, radio frequency photonic oscillators, and related communication and navigation systems.

Collinear opto-optical loss modulation for carrier-envelope offset stabilization of a fiber frequency comb

Opto-optical loss modulation (OOM) for stabilization of the carrier-envelope offset (CEO) frequency of a femtosecond all-fiber laser is performed using a collinear geometry. Amplitude-modulated 1064 nm light is fiber coupled into an end-pumped semiconductor saturable absorber mirror (SESAM)-mode-locked all-polarization-maintaining erbium fiber femtosecond laser, where it optically modulates the loss of the SESAM resulting in modulation of the CEO frequency. A noise rejection bandwidth of 150 kHz is achieved when OOM and optical gain modulation are combined in a hybrid analog/digital loop. Collinear OOM provides a simple, all-fiber, high-bandwidth method for improving the CEO frequency stability of SESAM mode-locked fiber lasers.

Impact of finite bandwidth on PRBS-modulated optical spectra

Applying a pseudo-random binary sequence (PRBS) to phase modulators is a recent development in the broadening of optical spectra of laser sources to defeat stimulated Brillouin scattering (SBS). The theoretical underpinning of this method relies on alternating the phase of the optical signal between its native value and an out-of-phase value (i.e., imposing a binary phase shift of 0 or π in a pseudo random manner) to prevent coherent buildup of the SBS acoustic grating. In real physical systems, realizing such a binary shift is impossible due to the finite response times of the electronics and electro-optic components. The influence of these effects is investigated in this work, specifically the finite bandwidth of the electronic PRBS generator and the frequency-dependent response of the phase modulator, on the resultant temporal waveforms of the PRBS signal and its RF optical spectra. It is found that the optimal SBS suppression in real systems is achieved when the phase modulator is driven at a voltage beyond V _π, even though driving at V _π has been deemed as ideal. Moreover, both the SBS suppression and spectral broadening are always weaker than what is predicted by analytical results since any degradation of the sharp edges of the PRBS signal result in loss of high-frequency content in the RF spectrum of the PRBS signal. Lastly, it is noticed that the typical ways of measuring spectral width are not relevant when applied to the complex PRBS RF optical spectrum. An 'equivalent spectral width' is defined to accurately quantify the correlation between spectral width an SBS suppression.

Tens of hertz ultra-narrow linewidth fiber ring laser based on external weak distributed feedback

We suggest and demonstrate a single-frequency fiber ring laser with an ultra-narrow linewidth based on an external weak distributed feedback. A π phase-shifted fiber Bragg grating (PSFBG) is used to improve mode selection and enable single-longitudinal mode (SLM) laser operation. The linewidth is then further strongly compressed using a signal generated by a weak distributed feedback structure (WDFS) and injected into the main laser cavity to suppress spontaneous emission. The resulting ultra-narrow linewidth fiber ring laser achieves a side-mode suppression ratio (SMSR) of ∼72 dB, and low white frequency noise of ∼10.3 Hz²/Hz, which correspond to an instantaneous linewidth of ∼32.3 Hz in the normal operating condition of the laser. Our linewidth compression mechanism not only solves the problems associated with deep linewidth compression in long-cavity fiber laser, but also fosters the development of practical and reliable all-fiber structures. Our laser source is characterized by low cost, high coherence, and low noise, which are highly desirable features in coherent optical detection, high-resolution spectrometers, microwave photonics, and optical sensing.

Fundamental linewidth of an AlN microcavity Raman laser

Raman lasing can be a promising way to generate highly coherent chip-based lasers, especially in high-quality (high-Q) crystalline microcavities. Here, we measure the fundamental linewidth of a stimulated Raman laser in an aluminum nitride (AlN)-on-sapphire microcavity with a record Q-factor up to 3.7 million. An inverse relationship between fundamental linewidth and emission power is observed. A limit of the fundamental linewidth, independent of Q-factor, due to Raman-pump-induced Kerr parametric oscillation is derived.

Low-noise frequency-agile photonic integrated lasers for coherent ranging

Frequency modulated continuous wave laser ranging (FMCW LiDAR) enables distance mapping with simultaneous position and velocity information, is immune to stray light, can achieve long range, operate in the eye-safe region of 1550 nm and achieve high sensitivity. Despite its advantages, it is compounded by the simultaneous requirement of both narrow linewidth low noise lasers that can be precisely chirped. While integrated silicon-based lasers, compatible with wafer scale manufacturing in large volumes at low cost, have experienced major advances and are now employed on a commercial scale in data centers, and impressive progress has led to integrated lasers with (ultra) narrow sub-100 Hz-level intrinsic linewidth based on optical feedback from photonic circuits, these lasers presently lack fast nonthermal tuning, i.e. frequency agility as required for coherent ranging. Here, we demonstrate a hybrid photonic integrated laser that exhibits very narrow intrinsic linewidth of 25 Hz while offering linear, hysteresis-free, and mode-hop-free-tuning beyond 1 GHz with up to megahertz actuation bandwidth constituting 1.6 × 10¹⁵ Hz/s tuning speed. Our approach uses foundry-based technologies - ultralow-loss (1 dB/m) Si₃N₄ photonic microresonators, combined with aluminium nitride (AlN) or lead zirconium titanate (PZT) microelectromechanical systems (MEMS) based stress-optic actuation. Electrically driven low-phase-noise lasing is attained by self-injection locking of an Indium Phosphide (InP) laser chip and only limited by fundamental thermo-refractive noise at mid-range offsets. By utilizing difference-drive and apodization of the photonic chip to suppress mechanical vibrations of the chip, a flat actuation response up to 10 MHz is achieved. We leverage this capability to demonstrate a compact coherent LiDAR engine that can generate up to 800 kHz FMCW triangular optical chirp signals, requiring neither any active linearization nor predistortion compensation, and perform a 10 m optical ranging experiment, with a resolution of 12.5 cm. Our results constitute a photonic integrated laser system for scenarios where high compactness, fast frequency actuation, and high spectral purity are required.

Stable and tunable integrated lasers are fundamental building blocks for applications from spectroscopy to imaging and communication. Here the authors present a narrow linewidth hybrid photonic integrated laser with low frequency noise and fast linear wavelength tuning. They then provide an efficient FMCW LIDAR demonstration.

Heterodyne spectrometer sensitivity limit for quantum networking

Optical heterodyne detection-based spectrometers are attractive due to their relatively simple construction and ultrahigh resolution. Here we demonstrate a proof-of-principle single-mode optical-fiber-based heterodyne spectrometer that has picometer resolution and quantum-limited sensitivity around 1550 nm. Moreover, we report a generalized quantum limit of detecting broadband multispectral-temporal-mode light using heterodyne detection, which provides a sensitivity limit on a heterodyne detection-based optical spectrometer. We then compare this sensitivity limit to several spectrometer types and dim light sources of interest such as spontaneous parametric downconversion, Raman scattering, and spontaneous four-wave mixing. We calculate that the heterodyne spectrometer is significantly less sensitive than a single-photon detector and is unable to detect these dim light sources, except for the brightest and narrowest-bandwidth examples.

Optical linewidth of soliton microcombs

Soliton microcombs provide a versatile platform for realizing fundamental studies and technological applications. To be utilized as frequency rulers for precision metrology, soliton microcombs must display broadband phase coherence, a parameter characterized by the optical phase or frequency noise of the comb lines and their corresponding optical linewidths. Here, we analyse the optical phase-noise dynamics in soliton microcombs generated in silicon nitride high-Q microresonators and show that, because of the Raman self-frequency shift or dispersive-wave recoil, the Lorentzian linewidth of some of the comb lines can, surprisingly, be narrower than that of the pump laser. This work elucidates information about the physical limits in phase coherence of soliton microcombs and illustrates a new strategy for the generation of spectrally coherent light on chip.

Dual-comb optical parametric oscillator in the mid-infrared based on a single free-running cavity

We demonstrate a free-running single-cavity dual-comb optical parametric oscillator (OPO) pumped by a single-cavity dual-comb solid-state laser. The OPO ring cavity contains a single periodically-poled MgO-doped LiNbO₃ (PPLN) crystal. Each idler beam has more than 245-mW average power at 3550 nm and 3579 nm center wavelengths (bandwidth 130 nm). The signal beams are simultaneously outcoupled with more than 220 mW per beam at 1499 nm and 1496 nm center wavelength. The nominal repetition rate is 80 MHz, while the repetition rate difference is tunable and set to 34 Hz. To evaluate the feasibility of using this type of source for dual-comb applications, we characterize the noise and coherence properties of the OPO signal beams. We find ultra-low relative intensity noise (RIN) below -158 dBc/Hz at offset frequencies above 1 MHz. A heterodyne beat note measurement with a continuous wave (cw) laser is performed to determine the linewidth of a radio-frequency (RF) comb line. We find a full-width half-maximum (FWHM) linewidth of around 400 Hz. Moreover, the interferometric measurement between the two signal beams reveals a surprising property: the center of the corresponding RF spectrum is always near zero frequency, even when tuning the pump repetition rate difference or the OPO cavity length. We explain this effect theoretically and discuss its implications for generating stable low-noise idler combs suitable for high-sensitivity mid-infrared dual-comb spectroscopy (DCS).

Line shape of a delayed self-heterodyne varied with noise types and delays

The delayed self-heterodyne and self-homodyne (DSH) method is widely used for measuring the line shapes of high coherent lasers. This method results in an autocorrelation of a laser line under the condition of a delay that is much larger than its coherent time. In practice, the delay is often not so long, especially for very narrow linewidth lasers, resulting in errors in rebuilding the laser's line shape from the DSH line. Many papers were devoted to the topic, but most of them are based on the formula for white noise. Analytical formulas of phase variance for 1/f noises are presented in this paper; the DSH line shapes for different noise types and different delay lengths are simulated based on the formulas. Some experimental data of the DSH line, combined with the power spectral density of frequency noise, are processed, showing good agreement with the theoretical analysis. It is indicated that the DSH line shape shows complicated behaviors varied with the delay, with noise types, and with the measurement duration. Such effects are to be compensated for in retrieving the laser's linewidth from the DSH data.

A 10-kHz intrinsic linewidth coupled extended-cavity DBR laser monolithically integrated on an InP platform

We report a monolithically integrated coupled extended-cavity distributed Bragg reflector laser with, to our knowledge, the lowest reported intrinsic linewidth of ∼10 kHz, which is extracted from a corresponding frequency-noise level of ∼3200 Hz²/Hz, realized on an InP generic foundry platform. Using the delayed self-heterodyne method, the experimentally measured linewidth was 45 kHz. The laser has an on-chip optical output power of 18 mW around 1550 nm at an injection current of 95 mA. The laser operates in a single-mode regime with a side-mode suppression ratio of 54 dB. Our monolithic approach paves the way toward further integration, such as integrated quantum key distribution transceivers.

Single-polarization single-frequency Brillouin fiber laser that emits almost 5 W of power at 1 µm

We demonstrate a high-power single-polarization single-frequency 1064 nm Brillouin fiber laser (BFL) that is constructed with polarization-maintaining germanium-doped fiber with a core/cladding diameter of 20/400 µm. A maximum output power of 4.9 W is achieved with a slope efficiency of 68% and an optical signal-to-noise ratio of 65 dB. To the best of our knowledge, this is the highest power output from a single-frequency fiber laser. The polarization extinction ratio is over 18.7 dB and the BFL output presents a good transverse mode. The BFL shows a significant reduction (10-15 dB) in both the relative intensity noise and frequency noise of the pump source, while the estimated linewidth is 170 kHz with a measurement time of 2 ms at the maximum output power. It is believed that the high power output in combination with the decreased relative intensity and frequency noise renders the proposed BFL an important candidate for applications in optical sensing and high-purity microwave signal synthesis.

Timing jitter characterization of free-running dual-comb laser with sub-attosecond resolution using optical heterodyne detection

Pulse trains emitted from dual-comb systems are designed to have low relative timing jitter, making them useful for many optical measurement techniques such as optical ranging and spectroscopy. However, the characterization of low-jitter dual-comb systems is challenging because it requires measurement techniques with high sensitivity. Motivated by this challenge, we developed a technique based on an optical heterodyne detection approach for measuring the relative timing jitter of two pulse trains. The method is suitable for dual-comb systems with essentially any repetition rate difference. Furthermore, the proposed approach allows for continuous and precise tracking of the sampling rate. To demonstrate the technique, we perform a detailed characterization of a single-mode-diode pumped Yb:CaF₂ dual-comb laser from a free-running polarization-multiplexed cavity. This new laser produces 115-fs pulses at 160 MHz repetition rate, with 130 mW of average power in each comb. The detection noise floor for the relative timing jitter between the two pulse trains reaches 8.0 × 10^-7 fs²/Hz (∼ 896 zs/Hz), and the relative root mean square (rms) timing jitter is 13 fs when integrating from 100 Hz to 1 MHz. This performance indicates that the demonstrated laser is highly compatible with practical dual-comb spectroscopy, ranging, and sampling applications. Furthermore, our results show that the relative timing noise measurement technique can characterize dual-comb systems operating in free-running mode or with finite repetition rate differences while providing a sub-attosecond resolution, which was not feasible with any other approach before.

High-power low-noise 2-GHz femtosecond laser oscillator at 2.4 µm

Femtosecond lasers with high repetition rates are attractive for spectroscopic applications with high sampling rates, high power per comb line, and resolvable lines. However, at long wavelengths beyond 2 µm, current laser sources are either limited to low output power or repetition rates below 1 GHz. Here we present an ultrafast laser oscillator operating with high output power at multi-GHz repetition rate. The laser produces transform-limited 155-fs pulses at a repetition rate of 2 GHz, and an average power of 0.8 W, reaching up to 0.7 mW per comb line at the center wavelength of 2.38 µm. We have achieved this milestone via a Cr²⁺-doped ZnS solid-state laser modelocked with an InGaSb/GaSb SESAM. The laser is stable over several hours of operation. The integrated relative intensity noise is 0.15% rms for [10 Hz, 100 MHz], and the laser becomes shot noise limited (-160 dBc/Hz) at frequencies above 10 MHz. Our timing jitter measurements reveal contributions from pump laser noise and relaxation oscillations, with a timing jitter of 100 fs integrated over [3 kHz, 100 MHz]. These results open up a path towards fast and sensitive spectroscopy directly above 2 µm.

Compact fiber-ring resonator for blue external cavity diode laser stabilization

We demonstrate a compact and low-cost all-fiber-based locking setup for frequency-noise suppression of a 420 nm external-cavity diode laser. Frequency noise reduction in the 100 Hz to 800 kHz range is demonstrated up to 40 dB associated with a linewidth narrowing from 850 kHz to 20 kHz for 10 ms integration time. This simple locking scheme might be implemented for a large range of wavelengths and can be integrated on a small footprint for embedded applications requiring narrow linewidth blue laser diodes.

Carrier-envelope offset frequency dynamics of a 10-GHz modelocked laser based on cascaded quadratic nonlinearities

Cascaded quadratic nonlinearities from phase-mismatched second-harmonic generation build the foundation for robust soliton modelocking in straight-cavity laser configurations by providing a tunable and self-defocusing nonlinearity. The frequency dependence of the loss-related part of the corresponding nonlinear response function causes a power-dependent self-frequency shift (SFS). In this paper, we develop a simple analytical model for the SFS-induced changes on the carrier-envelope offset frequency (f_CEO) and experimentally investigate the static and dynamic f_CEO dependence on pump power. We find good agreement with the measured dependence of f_CEO on laser output power, showing a broad f_CEO tuning capability from zero up to the pulse repetition rate. Moreover, we stabilize the relative intensity noise to the -157 dBc/Hz level leading to a tenfold reduction in f_CEO-linewidth.

High-performance, compact optical standard

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8×10^-13τ^-1/2 for times less than 100 s and a flicker noise floor of 1×10^-14 out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the ac Stark shift. The retrace was measured to 5.7×10^-13 after 30 h of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser.

Watt-level blue light for precision spectroscopy, laser cooling and trapping of strontium and cadmium atoms

High-power and narrow-linewidth laser light is a vital tool for atomic physics, being used for example in laser cooling and trapping and precision spectroscopy. Here we produce Watt-level laser radiation at 457.75 nm and 460.86 nm of respective relevance for the cooling transitions of cadmium and strontium atoms. This is achieved via the frequency doubling of a kHz-linewidth vertical-external-cavity surface-emitting laser (VECSEL), which is based on a novel gain chip design enabling lasing at > 2 W in the 915-928 nm region. Following an additional doubling stage, spectroscopy of the ¹S₀ → ¹P₁ cadmium transition at 228.87 nm is performed on an atomic beam, with all the transitions from all eight natural isotopes observed in a single continuous sweep of more than 4 GHz in the deep ultraviolet. The absolute value of the transition frequency of ¹¹⁴Cd and the isotope shifts relative to this transition are determined, with values for some of these shifts provided for the first time.

Narrow-linewidth single-polarization fiber laser using non-polarization optics

Single longitudinal mode and single polarization are basic requirements of high performance fiber lasers, while their realizations are nontrivial, owing to the long laser cavity and lack of polarization selection of ordinary optical fibers. Here, we demonstrate an all-fiber narrow-linewidth laser realized on an external high-Q fiber ring, with combined functions of single-longitude-mode selection and linewidth reduction. A single-longitude-mode laser with a high polarization extinction ratio of ∼40dB and low white frequency noise at 0.3Hz²/Hz is achieved, corresponding to a fundamental linewidth of ∼0.92Hz. Using all non-polarization fiber components and ordinary gain fiber, our scheme shows the realization of narrow-linewidth single-polarization fiber lasers in a simple and cost-effective way, promising for broadband applications.

Frequency stabilization of a quantum cascade laser by weak resonant feedback from a Fabry-Perot cavity

Frequency-stabilized mid-infrared lasers are valuable tools for precision molecular spectroscopy. However, their implementation remains limited by complicated stabilization schemes. Here we achieve optical self-locking of a quantum cascade laser to the resonant leak-out field of a highly mode-matched two-mirror cavity. The result is a simple approach to achieving stable frequencies from high-powered mid-infrared lasers. For short time scales (<0.1ms), we report a linewidth reduction factor of 3×10^-6 to a linewidth of 12 Hz. Furthermore, we demonstrate two-photon cavity-enhanced absorption spectroscopy of an N₂O overtone transition near a wavelength of 4.53 µm.

On-chip ultra-narrow-linewidth single-mode microlaser on lithium niobate on insulator

We report an on-chip single-mode microlaser with a low threshold fabricated on erbium doped lithium-niobate-on-insulator (LNOI). The single-mode laser emission at 1550.5 nm wavelength is generated in a coupled microdisk via the inverse Vernier effect at room temperature, when pumping the resonator at 977.7 nm wavelength. A threshold pump power as low as 200 μW is demonstrated due to the high quality factor above 10⁶. Moreover, the measured linewidth of the microlaser reaches 348 kHz without discounting the broadening caused by the utilization of optical amplifiers, which is, to our knowledge, the best result in LNOI microlasers. Such a single-mode microlaser lithographically fabricated on chip is in high demand by the photonics community.