Mark Dong, Matthew W. Day, Herbert G. Winful, Steven T. Cundiff
We demonstrate simple optical frequency combs based on semiconductor quantum well laser diodes. The frequency comb spectrum can be tailored by choice of material properties and quantum-well widths, providing spectral flexibility. Finally, we demonstrate the mutual coherence of these devices by using two frequency combs on the same device to generate a radio-frequency dual comb spectrum.
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We present an InP-based epitaxially regrown photonic crystal surface emitting laser diode, lasing in quasi- CW conditions at 1523nm.
Highly efficient collective coupling between laser diode array and lensed fibre ribbon
提出一种基于光纤带切割与熔接的低成本集体制造带透镜光纤新概念，实现激光二极管阵列与光纤带的高效耦合。
Electrically pumped AlGaN edge-emitting UV-B laser diodes grown by molecular beam epitaxy
本研究展示了一种基于AlGaN的电泵紫外B激光二极管，通过分子束外延技术实现，工作波长为298.5nm，具有低阈值电流密度和窄谱线宽度。
Soliton microcombs offer the prospect of advanced optical metrology and timing systems in compact form factors. In these applications, pumping of microcombs directly from a semiconductor laser without amplification or triggering components is desirable for reduced power operation and to simplify system design. At the same time, low repetition rate microcombs are required in many comb applications for interface to detectors and electronics, but their increased mode volume makes them challenging to pump at low power. Here, 10 GHz repetition rate soliton microcombs are directly pumped by low-powe…
Generation of incoherent light from a laser diode based on the injection of an emission from a superluminescent diode
本研究通过向激光二极管注入超辐射二极管的非相干光，实现了高功率宽谱非相干光输出，探明了模式转变过程中的光学特性，该系统兼具非相干光放大与相干度可调光源功能。
An all optical set-reset flip flop is presented that is based on two coupled identical laser diodes. The lasers are coupled so that when one of the lasers lases it quenches lasing in the other laser. The state of the flip flop is determined by which laser is currently lasing. Rate equations are used to model the flip flop and obtain steady state characteristics. The flip flop is experimentally demonstrated by use of antireflection coated laser diodes and free space optics.
Generating visible light with wide tunability and high coherence based on photonic integrated circuits is of high interest for applications in biophotonics, precision metrology and quantum technology. Here we present the first demonstration of a hybrid-integrated diode laser in the visible spectral range. Using an AlGaInP optical amplifier coupled to a low-loss Si3N4 feedback circuit based on microring resonators, we obtain a spectral coverage of 10.8 nm around 684.4 nm wavelength with up to 4.8 mW output power. The measured intrinsic linewidth is 2.3$\pm$0.2 kHz.
A Schottky diode integrated into a terahertz quantum cascade laser waveguide couples directly to the internal laser fields. In a multimode laser, the diode response is correlated with both the instantaneous power and the coupling strength to the diode of each lasing mode. Measurements of the rectified response of diodes integrated in two quantum cascade laser cavities at different locations indicate that the relative diode position strongly influences the laser-diode coupling.
Spectra of laser diodes
本文介绍半导体激光二极管的理论，重点探讨其噪声特性，作为教材补充章节，参考书中相关方程。
We report the realization of the continuous wave laser emission in the orange at 607 nm from a Pr:BaY2F8 (Pr:BYF) crystal pumped by a blue GaN laser diode. A maximal output power of 78 mW is obtained in a quasi single transverse mode beam. The effect of reabsorption losses at the laser wavelength is also evidenced
The frequency of a 700mW monolithic non-planar Nd:YAG ring laser (NPRO) depends with a large coupling coefficient (some MHz/mW) on the power of its laser-diode pump source. Using this effect we demonstrate the frequency stabilization of an NPRO to a frequency reference by feeding back to the current of its pump diodes. We achieved an error point frequency noise smaller than 1mHz/sqrt(Hz), and simultaneously a reduction of the power noise of the NPRO by 10dB without an additional power stabilization feed-back system.
Injection locking of diode lasers is commonly used to amplify low power laser light, but is extremely sensitive to perturbations in the laser current and temperature. To counter such perturbations, active stabilization is often applied to the current of the injection locked diode. We observe that the diode laser's polarization extinction ratio (PER) greatly increases when injection locked, and therefore the PER provides a measure of injection lock quality. We report robust active stabilization of a diode laser injection lock based on the PER, demonstrating the technique at 399 nm wavelength wh…
We report on the generation of 500 mW of spectrally pure laser light at the 460.86 nm transition used for laser cooling of strontium atoms. To this end we inject a high power single mode laser diode with light from a stabilized extended cavity diode laser. To optimize and monitor the injection status and the spectral purity of the slave diode we developed a novel technique that uses a single passive optical element. A narrow band interference filter generates a suitable monitoring signal without any additional electronics for post processing of the data. Our method greatly simplifies the daily…
We describe passive phase-locking architectures based on external-cavity setups to improve the brightness of diode laser bars. Volume Bragg gratings are used to stabilize the lase line. Numerical modelling and experimental results will be presented.
We demonstrate yellow laser emission using silicate glass fiber as the gain medium. By employing core pumping using widely available GaN diode lasers with emission at 445 nm, we show that Dy3+-doped aluminosilicate glass fiber can be readily excited creating sufficient gain at 581 nm. In this proof of concept demonstration, the maximum output power generated was 3 mW with a slope efficiency approximately 1.8% with respect to injected pump.
Detailed polarization properties have been examined in laser-diode-pumped (LD-pumped) micro-grained ceramic Nd:YAG lasers in different microchip cavity configurations. Stable linearly-polarized single-frequency oscillations, whose polarization direction coincide with that of an LD pump light, were observed in an external cavity scheme. While, in the case of a thin-slice laser scheme with coated reflective ends, elliptically-polarized single-frequency operations took place in the low pump-power regime and dynamic instabilities appeared, featuring self-induced antiphase modulations among counter…
We report ultra-stable locking of a commercially available extended cavity diode laser to a vibration-insensitive high finesse Fabry-Perot cavity. A servo bandwidth of 2 MHz is demonstrated. The absolute stability of the diode laser after locking is measured with a three-cornered-hat method. The resulting Allan deviation reaches a level of $2.95\times10^{-15}$ at 1 s, corresponding to only 0.93 Hz linewidth, even without vibration isolation of the reference cavity.
We characterized the DC transport response of a diode embedded in a THz quantum cascade laser as the laser current was changed. The overall response is described by parallel contributions from the rectification of the laser field due to the non-linearity of the diode I-V and from thermally activated transport. Sudden jumps in the diode response when the laser changes from single mode to multi-mode operation, with no corresponding jumps in output power, suggest that the coupling between the diode and laser field depends on the spatial distribution of internal fields. The results demonstrate con…
Frequency comb assisted diode laser spectroscopy, employing both the accuracy of an optical frequency comb and the broad wavelength tuning range of a tunable diode laser, has been widely used in many applications. In this letter we present a novel method using cascaded frequency agile diode lasers, which allows extending the measurement bandwidth to 37.4 THz (1355 to 1630 nm) at MHz resolution with scanning speeds above 1 THz/s. It is demonstrated as a useful tool to characterize a broadband spectrum for molecular spectroscopy and in particular it enables to characterize the dispersion of inte…
We show the abundance of Exceptional Points in the generic asymmetric configuration of two coupled diode lasers, under nonzero optical detuning and differential pumping. We pinpoint the location of these points with respect to the stability domains and the Hopf bifurcation points, in the solution space as well as in the space of experimentally controlled parameters.
We studied complex lasing pattern formations in a thin-slice solid-state laser with wide-aperture laser-diode end-pumping. Radial and rectangular vortex arrays were found to be formed in a controlled fashion with symmetric and asymmetric pump beam profiles, respectively. Most of these vortices exhibited single-frequency oscillations arising from a spontaneous process of transverse mode locking of nearly degenerate modes assisted by the laser nonlinearity. Single-frequency rectangular array beams consisting of a large number of vortices, e.g., closely packed 36 or 46 vortex pixels, were generat…
A semiconductor diode laser having a modified Littrow external resonator is described. An additional output coupling mirror in a V-shape configuration of the resonator makes the system more efficient and convenient to operate.
High-power, diffraction-limited organic solid-state laser operation has been achieved in a vertical external cavity surface-emitting organic laser (VECSOL), pumped by a low-cost compact blue laser diode. The diode-pumped VECSOLs were demonstrated with various dyes in a polymer matrix, leading to laser emissions from 540 nm to 660 nm. Optimization of both the pump pulse duration and output coupling leads to a pump slope efficiency of 11% for a DCM based VECSOLs. We report output pulse energy up to 280 nJ with 100 ns long pump pulses, leading to a peak power of 3.5 W in a circularly symmetric, d…
We demonstrate a simple, compact, and cost-effective laser noise reduction method for stabilizing an extended cavity diode laser to a 3x105 finesse mirror Fabry-Pérot (F-P) cavity corresponding to resonance linewidth of 10 kHz using a crystalline MgF2 whispering gallery mode microresonator (WGMR). The laser linewidth is reduced to sub-kHz such that a stable Pound-Drever-Hall (PDH) error signal is built up. The wavelength of the pre-stabilized laser is tunable within a large bandwidth covering the high reflection mirror coating of a F-P supercavity.
We report on a methodology for the evaluation of the DC characteristics, small-signal frequency response and large-signal dynamic response of carrier and photon density responses in semiconductor laser diodes. A single mode laser is considered and described with a pair of rate equations containing a novel non-linear gain compensation term depending on a single parameter that can be chosen arbitrarily. This approach can be applied to any type of solid-state laser as long as it is described by a set of rate equations.
We realize a fiber Bragg grating InGaN based laser diode emitting at 400 nm and demonstrate its high coherency. Thanks to the fabrication of a narrow band fiber Bragg grating in the near-UV, we can reach single-mode and single-frequency regimes for the self-injection locked diode. The device exhibits 44 dB side-mode-suppression-ratio and mW output power. Detailed frequency noise analysis reveals sub-MHz integrated linewidth and 16 kHz intrinsic linewidth. Such a narrow linewidth laser diode in the near-UV domain with a compact and low-cost design could find applications whenever coherency and …
We present and investigate different external cavity diode laser (ECDL) configurations for the manipulation of neutrals atoms, wavelength-stabilized by a narrow-band high transmission interference filter. A novel diode laser, providing high output power of more than 1 W, with a linewidth of less than 200 kHz, based on a self-seeded tapered amplifier chip has been developed. Additionally, we compare the optical and spectral properties of two laser systems based on common laser diodes, differing in their coating, as well as one, based on a distributed-feedback (DFB) diode. The linear cavity setu…
We report on the spectral properties of a diode laser with a tunable external cavity in integrated optics. Even though the external cavity is short compared to other small-bandwidth external cavity lasers, the spectral bandwidth of this tunable laser is as small as 25 kHz (FWHM), at a side-mode suppression ratio (SMSR) of 50 dB. Our laser is also able to access preset wavelengths in as little as 200 us and able to tune over the full telecom C-band (1530 nm - 1565 nm).
Active control of a diode laser with injection locking
本研究提出一种基于注入锁定的二极管激光器主动稳定方法，借助窄线宽激光滤波器增强的光电探测与主动反馈，无需大型设备即可同时实现高光谱纯度与低强度噪声，可简化其在集成光学系统中的应用。
We describe the operation of two GaN-based diode lasers for the laser spectroscopy of gallium at 403 nm and 417 nm. Their use in an external cavity configuration enabled the investigation of absorption spectroscopy in a gallium hollow cathode. We have analyzed the Doppler broadened profiles accounting for hyperfine and isotope structure and extracting both the temperature and densities of the neutral atomic sample produced in the glow discharge. We have also built a setup to produce a thermal atomic beam of gallium. Using the GaN-based diode lasers we have studied the laser induced fluorescenc…
We demonstrate passive harmonic mode-locking of a quantum well laser diode designed to support a discrete comb of Fabry-Perot modes. Spectral filtering of the mode spectrum was achieved using a non-periodic patterning of the cavity effective index. By selecting six modes spaced at twice the fundamental mode spacing, near-transform limited pulsed output with 2 ps pulse duration was obtained at a repetition rate of 100 GHz.
Continuous frequency tuning of an external cavity diode laser significantly beyond the free spectral range by sweeping the injection current
本研究针对外腔二极管激光器的频率调谐问题，通过使用带增透膜的激光二极管并仅扫描注入电流，实现了远超自由光谱范围的连续调谐，结合理论分析揭示了增透膜对拓宽调谐范围的作用。
Narrow linewidth lasers and optical frequency combs generated with mode-locked lasers revolutionized optical frequency metrology. The advent of soliton Kerr frequency combs in compact crystalline or integrated ring optical microresonators opens new horizons for applications. These combs, as was naturally assumed, however, require narrow-linewidth single-frequency pump lasers. We demonstrate that a regular multi-frequency Fabry-Perot laser diode self-injection locked to an optical whispering gallery mode (WGM) microresonator can be first efficiently transformed to a single-frequency ultra-narro…
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number g…
We developed a high-power laser system at a wavelength of 399 nm for laser cooling of ytterbium atoms with ultraviolet laser diodes. The system is composed of an external cavity laser diode providing frequency stabilized output at a power of 40 mW and another laser diode for amplifying the laser power up to 220 mW by injection locking. The systematic method for optimization of our injection locking can also be applied to high power light sources at any other wavelengths. Our system, which does not depend on complex nonlinear frequency-doubling, has great importance for implementing transportab…
Advances in high-resolution laser spectroscopy have enabled many scientific breakthroughs in physics, chemistry, biology and astronomy. Optical frequency combs have pushed measurement limits with ultrahigh-frequency accuracy and fast-measurement speed while tunable diode laser spectroscopy is used in scenarios that require high power and continuous spectral coverage. Despite these advantages of tunable diode laser spectroscopy, it is challenging to precisely determine the instantaneous frequency of the laser because of fluctuations in the scan speed. Here we demonstrate a simple spectroscopy s…
We demonstrate a technique for locking the frequency of a tunable diode laser to a ring-cavity resonator. The resonator is stabilized to a diode laser which is in turn locked to an atomic transition, thus giving it absolute frequency calibration. The ring-cavity design has the principal advantage that there is no feedback destabilization of the laser. The cavity has a free-spectral range of 1.3 GHz and $Q$ of about 35, which gives robust locking of the laser. The locked laser is able to track large scans of the cavity.
1.1 kW, 100 Hz room-temperature diode-pumped nanosecond laser by water immersion cooling
该研究通过水浸冷却实现了1.1千瓦、100赫兹室温二极管泵浦纳秒激光器，输出11焦耳脉冲能量，束质量因子为衍射极限的2.6倍，展示了室温纳秒激光器的高性能表现。
We probe the physical mechanism behind the known phenomenon of power synchronization of two diode lasers that are mutually coupled via their delayed optical fields. In a diode laser, the amplitude and the phase of the optical field are coupled by the so-called linewidth enhancement factor, $α$. In this work, we explore the role of optical phases of the electric fields in amplitude (and hence power) synchronization through $α$ in such mutually delay-coupled diode laser systems. Our numerical results show that the synchronization of optical phases drives the powers of lasers to synchronized deat…
Continuous-wave mode-locked femtosecond 2 um solid-state laser with a c-cut Tm:CaYAlO4 as gain medium was experimentally demonstrated. The mode locked laser generated stable pulses with average output power as high as 531 mW, pulse duration of 496 fs, and repetition rate of 97 MHz at 1975 nm. The research results show that Tm:CaYAlO4 is an excellent gain medium for femtosecond pulse generation at 2um wavelength.
Stable 30 fs pulses centered at 1068 nm (less than 10 optical cycles) are demonstrated in a diode pumped Yb:CaYAlO4 laser by using high-quality chemical vapor deposited monolayer graphene as the saturable absorber. The mode locked 8.43 optical-cycle pulses have a spectral bandwidth of ~ 50 nm and a pulse repetition frequency of ~ 113.5 MHz. To our knowledge, this is the shortest pulse ever reported for graphene mode-locked lasers and mode-locked Yb-doped bulk lasers. Our experimental results demonstrate that graphene mode locking is a very promising practical technique to generate few-cycle op…
We report the design and performance of a Littrow-type 671 nm External Cavity Diode Laser (ECDL) that delivers output power greater than 150 mW and features enhanced passive stability. The main body of the ECDL is constructed using titanium to minimize temperature related frequency drifts. The laser diode is mounted in a cylindrical mount that allows vertical adjustments while maintaining thermal contact with the temperature stabilized base plate. The wavelength tuning is achieved by horizontal displacement of the diffraction grating about an optimal pivot point. The compact design increases t…
An extended cavity diode laser operating in the Littrow configuration emitting near 657 nm is stabilized via its injection current to a reference cavity with a finesse of more than 10^5 and a corresponding resonance linewidth of 14 kHz. The laser linewidth is reduced from a few MHz to a value below 30 Hz. The compact and robust setup appears ideal for a portable optical frequency standard using the Calcium intercombination line.
We report on an interference-filter-stabilized external cavity diode laser using a gallium-nitride-based violet laser diode. Surface-activated-bonded glass substrates were employed as cat's eye output couplers in order to suppress power degradation due to optical damage. From the results of a long-term frequency-stabilization test, mode-hop-free operation for about one week was demonstrated. After a continuous operation of about three weeks, the power degradation was less than 10$\%$. The results show the potential of such interference-filter-stabilized external cavity diode lasers for practic…
Pulse duration retrieval using a commercial laser diode with a monitor photodiode
本文利用商用InGaAsP激光二极管及其集成监测光电二极管作为室温双光子吸收探测器，通过非线性与线性信号实现无移动部件的飞秒脉冲宽度反演，并在2 μW平均光功率下验证了该方法的可行性。
A phase modulated RF current source is applied to an injection locked diode laser operating at $780\unit{nm}$. This produces tunable phase modulated sidebands of the laser suitable for stabilizing the length of an optical transfer cavity using the Pound-Drever-Hall technique. The Pound-Drever-Hall signal is anti-symmetric about the lock point, despite the presence of significant diode laser amplitude modulation. The stabilized optical transfer cavity is used to frequency stabilize a 776 nm external cavity diode laser. The stability and tunability of this transfer cavity locked laser is establi…
We describe an efficient laser emission from a directly grown Er3+:YAG single-crystal fiber that is resonantly pumped using a continuous-wave (CW) laser diode at 1532 nm. In a longitudinal pumping, it emits 12.5 W at 1645 nm with a slope efficiency of 32%, which is the highest ever reported for a directly grown Er:YAG single-crystal fiber laser. Using an off-axis pumping scheme, CW output powers up to 7.3 W can be reached and in Q-switched operation, the laser produces 2 mJ pulses with a duration of 38 ns at the repetition rate of 1 kHz with an M^{2} factor below 1.8. To our knowledge this is …
An external-cavity diode laser is reported with ultralow noise, high power coupled to a fiber, and fast tunability. These characteristics enable the generation of an optical frequency comb in a silica micro-resonator with a single-soliton state. Neither an optical modulator nor an amplifier was used in the experiment. This demonstration greatly simplifies the soliton generation setup and represents a significant step forward to a fully integrated soliton comb system.
The intensity fluctuations of laser light are derived from photon number rate equations. In the limit of short times, the photon statistics for small laser devices such as typical semiconductor laser diodes show thermal characteristics even above threshold. In the limit of long time averages represented by the low frequency component of the noise, the same devices exhibit squeezing. It is shown that squeezing and thermal noise can coexist in the multi-mode output field of laser diodes. This result implies that the squeezed light generated by regularly pumped semiconductor laser diodes is quali…
It is demonstrated that RF current modulation of a frequency stabilized injection-locked diode laser allows the stabilization of an optical cavity to adjustable lengths, by variation of the RF frequency. This transfer cavity may be used to stabilize another laser at an arbitrary wavelength, in the absence of atomic or molecular transitions suitable for stabilization. Implementation involves equipment and techniques commonly used in laser cooling and trapping laboratories, and does not require electro- or acousto-optic modulators. With this technique we stabilize a transfer cavity using a RF cu…
Frequency combs, broadband light sources whose spectra consist of coherent, discrete modes, have become essential in many fields. Miniaturizing frequency combs would be a significant advance in these fields, enabling the deployment of frequency-comb based devices for diverse measurement and spectroscopy applications. We demonstrate diode-laser based frequency comb generators. These laser diodes are simple, electrically pumped, inexpensive and readily manufactured. Each chip contains several dozen diode-laser combs. We measure the time-domain output of a diode frequency comb to reveal the under…
Diode-pumped 88-fs SESAM mode-locked Tm,Ho:CLNGG laser at 2090 nm
报道了首台2.1 μm波段经济型二极管抽运亚100 fs被动锁模Tm,Ho:CLNGG激光器，利用无序增益材料的宽平滑增益曲线和GaSb基SESAM，在2090 nm实现了88 fs脉冲和120 mW平均功率的稳定自启动锁模运转。
We demonstrated a 967 nm diode end-pumped Er:GSGG laser operated at 2.794 Micrometer with spectrum width 3.6 nm in the continuous wave(CW) mode. The maximum output power of 440 mW is obtained at an incident pumping power of 3.4 W, which corresponds to an optical-to-optical efficiency of 13% and slope efficiency of 13.2%. The results suggest that short cavity and efficient cooling setup for crystal are advantageous to improve laser performance.
We report on a device to electronically stabilize the optical injection lock of a semiconductor diode laser. Our technique uses as discriminator the peak height of the laser's transmission signal on a scanning Fabry-Perot cavity and feeds back to the diode current, thereby maintaining maximum optical power in the injected mode. A two-component feedback algorithm provides constant optimization of the injection lock, keeping it robust to slow thermal drifts and allowing fast recovery from sudden failures such as temporary occlusion of the injection beam. We demonstrate the successful performance…
We present a current-modulation technique for diode-laser systems that is specifically designed for high-bandwidth laser-frequency stabilization and wideband frequency modulation with a flat transfer function. It consists of a dedicated current source and an impedance-matching circuit both placed close to the laser diode. The transfer behaviour of the system is analysed under realistic conditions employing an external-cavity diode laser (ECDL) system. We achieve a phase lag less than 90$°$ up to 25 MHz and a gain flatness of $\pm$ 3 dB in the frequency range of DC to 100 MHz while the passive …
Broad area laser diodes are attractive for the high optical power they can produce. Unfortunately, this high power normally comes at the cost of severely reduced spatial coherence since the wide area of the semiconductor wave-guide is inherently spatially multi-mode (in the slow axis). We demonstrate a method to majorly improve the spatial coherence of a high-power broad-area diode laser by placing it in an external cavity that is mode selective. We design the cavity, such that the diode aperture acts as its own spatial filter, obviating the need for an intra-cavity slit-filter, and optimally …
We have developed external-cavity diode lasers, where the wavelength selection is assured by a low loss interference filter instead of the common diffraction grating. The filter allows a linear cavity design reducing the sensitivity of the wavelength and the external cavity feedback against misalignment. By separating the feedback and wavelength selection functions, both can be optimized independently leading to an increased tunability of the laser. The design is employed for the generation of laser light at 698, 780 and 852 nm. Its characteristics make it a well suited candidate for space-bor…
We present a traveling wave model for a semiconductor diode laser based on quantum wells. The gain model is carefully derived from first principles and implemented with as few phenomeno- logical constants as possible. The transverse energies of the quantum well confined electrons are discretized to automatically capture the effects of spectral and spatial hole burning, gain asym- metry, and the linewidth enhancement factor. We apply this model to semiconductor optical amplifiers and single-section phase-locked lasers. We are able to reproduce the experimental re- sults. The calculated frequenc…
We present a method for remote interrogation of passive fiber Bragg grating Fabry-Perot resonators, employing current modulation of the diode laser source. With the presence of both RF amplitude and frequency modulation, it is a variant of the ultra-sensitive Pound-Drever-Hall laser frequency locking technique. We demonstrate that current modulation and interferometric demodulation removes the need for a phase modulator in the sensing architecture.
We present a simple method for narrowing the intrinsic Lorentzian linewidth of a commercial ultraviolet grating extended-cavity diode laser (TOPTICA DL Pro) using weak optical feedback from a long external cavity. We achieve a suppression in frequency noise spectral density of 20 dB measured at frequencies around 1 MHz, corresponding to the narrowing of the intrinsic Lorentzian linewidth from 200 kHz to 2 kHz. The system is suitable for experiments requiring a tunable ultraviolet laser with narrow linewidth and low high-frequency noise, such as precision spectroscopy, optical clocks, and quant…
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