Stabilized high-power laser system for the gravitational wave detector advanced LIGO

Continuous adiabatic frequency conversion for FMCW-LiDAR

Continuous tuning of the frequency of laser light serves as the fundamental basis for a myriad of applications spanning basic scientific research to industrial settings. These applications encompass endeavors such as the detection of gravitational waves, the development of precise optical clocks, environmental monitoring for health and ecological purposes, as well as distance measurement techniques. However, achieving a broad tuning range exceeding 100 GHz along with sub-microsecond tuning times, inherent linearity in tuning, and coherence lengths beyond 10 m presents significant challenges. Here, we demonstrate that electro-optically driven adiabatic frequency converters utilizing high-Q microresonators fabricated from lithium niobate possess the capability to convert arbitrary voltage signals into frequency chirps with temporal resolutions below 1 µs. The temporal evolution of the frequency correlates accurately with the applied voltage signal. We have achieved to generate 200-ns-long frequency chirps with deviations of less than 1 % from perfect linearity without requiring supplementary measures. The coefficient of determination isR 2 > 0.999 . Moreover, the coherence length of the emitted light exceeds 20 m. To validate these findings, we employ the linear frequency sweeps for Frequency-Modulated Continuous Wave (FMCW) LiDAR covering distances ranging from 0.5 to 10 m. Leveraging the demonstrated nanosecond-level tuning capabilities, coupled with the potential to tune the eigenfrequency of lithium-niobate-based resonators by several hundred GHz, our results show that electro-optically driven adiabatic frequency converters can be used in applications that require ultrafast and flexible continuous frequency tuning characterized by inherent linearity and substantial coherence length.

Multi-frequency self-injection locking of a FSR-tunable multimode laser diode

This study presents the controllable multi-frequency self-injection locking regimes realization with an original experimental setup composed of a reflective semiconductor optical amplifier, an external feedback mirror, and a high-Q chip-scale Si3N4 ring microresonator. Our findings demonstrate the conditions of multiple modes' simultaneous locking being analogous to Vernier effect. We varied the free spectral range of the external-cavity laser by its length tuning, enabling the robust generations from 1 to 4 self-injection locked narrow lines on demand, that is important for optical telecommunications, and photonic-based microwave and THz sources.

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.

A scalable scanning transfer cavity laser stabilization scheme based on the Red Pitaya STEMlab platform

Many experiments in atomic and molecular physics require simultaneous frequency stabilization of multiple lasers. We present a stabilization scheme based on a scanning transfer cavity lock that is simple, stable, and easily scalable to many lasers at minimal cost. The scheme is based on the Red Pitaya STEMlab platform, with custom software developed and implemented to achieve up to 100 Hz bandwidth. As an example demonstration, we realize simultaneous stabilization of up to four lasers and a reduction of long-term drifts to well below 1 MHz/h. This meets typical requirements, e.g., for experiments on laser cooling of molecules.

Multiple beam coherent combination via an optical ring resonator

Future gravitational wave detectors (GWDs) require low noise, single frequency, continuous wave lasers with excellent beam quality and powers in excess of 500 W. Low noise laser amplifiers with high spatial purity have been demonstrated up to 300 W. For higher powers, coherent beam combination can overcome scaling limitations. In this Letter we introduce a new, to the best of our knowledge, combination scheme that uses a bow-tie resonator to combine three laser beams with simultaneous spatial filtering performance.

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.

Continuously and widely tunable frequency-stabilized laser based on an optical frequency comb

Continuously and widely tunable lasers, actively stabilized on a frequency reference, are broadly employed in atomic, molecular, and optical (AMO) physics. The frequency-stabilized optical frequency comb (OFC) provides a novel optical frequency reference, with a broadband spectrum that meets the requirement of laser frequency stabilization. Therefore, we demonstrate a frequency-stabilized and precisely tunable laser system based on it. In this scheme, the laser frequency locked to the OFC is driven to jump over the ambiguity zones, which blocks the wide tuning of the locked laser, and tuned until the mode hopping happens with the always-activated feedback loop. Meanwhile, we compensate the gap of the frequency jump with a synchronized acoustic optical modulator to ensure the continuity. This scheme is applied to an external cavity diode laser (ECDL), and we achieve tuning at a rate of about 7 GHz/s, with some readily available commercial electronics. Furthermore, we tune the frequency-stabilized laser only with the feedback of diode current, and its average tuning speed can exceed 100 GHz/s. Due to the resource-efficient configuration and the simplicity of completion, this scheme can be referenced and can find wide applications in AMO experiments.

Effective linewidth compression of a single-longitudinal-mode fiber laser with randomly distributed high scattering centers in the fiber induced by femtosecond laser pulses

Femtosecond lasers can be used to create many functional devices in silica optical fibers with high designability. In this work, a femtosecond laser-induced high scattering fiber (HSF) with randomly distributed high scattering centers is used to effectively compress the linewidth of a fiber laser for the first time. A dual-wavelength, single-longitudinal-mode (SLM) erbium-doped fiber laser (EDFL) is constructed for the demonstration, which is capable of switching among two single-wavelength operations and one dual-wavelength operation. We find that the delayed self-heterodyne beating linewidth of the laser can be reduced from >1 kHz to <150 Hz when the length of the HSF in the laser cavity increases from 0 m to 20 m. We also find that the intrinsic Lorentzian linewidth of the laser can be compressed to several Hz using the HSF. The efficiency and effectiveness of linewidth reduction are also validated for the case that the laser operates in simultaneous dual-wavelength lasing mode. In addition to the linewidth compression, the EDFL shows outstanding overall performance after the HSF is incorporated. In particular, the optical spectrum and SLM lasing state are stable over long periods of time. The relative intensity noise is as low as <-150 dB/Hz@>3 MHz, which is very close to the shot noise limit. The optical signal-to-noise ratios of >85 dB for single-wavelength operation and >83 dB for dual-wavelength operation are unprecedented over numerous SLM fiber lasers reported previously. This novel method for laser linewidth reduction is applicable across gain-medium-type fiber lasers, which enables low-cost, high-performance, ultra-narrow linewidth fiber laser sources for many applications.

Modulation depth and bandwidth analysis of planar thermo-optic diamond actuators

Thermo-optic actuators based on bulk materials are considered too slow in applications such as laser frequency control. The availability of high-quality optical materials that have extremely fast thermal response times, such as diamond, present an opportunity for increasing performance. Here, diamond thermal actuators are investigated for configurations that use a planar thermal resistive layer applied to a heat-sinked rectangular prism. A general analytical formulation is obtained which simplifies substantially for high thermal conductivity such as diamond. Expressions for modulation depth, bandwidth and power requirements are obtained as functions of modulator dimensions and heat-transfer coefficients. For a 1 mm × 1 mm cross-section diamond at wavelength of 1 μm, around 450 W of applied heat power is needed to achieve a π phase shift at a modulation frequency of 2 kHz.

Frequency noise stabilisation of a 1550 nm external cavity diode laser with hybrid feedback for next generation gravitational wave interferometry

Longer wavelength lasers will be needed for future gravitational wave detectors that use cryogenic cooling of silicon based test-mass optics. Diode lasers with a 1550 nm wavelength output are potential seed light sources for such a detector, however diode laser devices have a different spectral profile and higher frequency noise than the solid state lasers used in current detectors. We present a frequency stabilisation system for a 1550 nm external cavity diode laser capable of reducing the laser frequency noise to a level of 0.1HzHz up to 1 kHz with a unity gain frequency of 535 kHz using a hybrid analogue-digital servo with in-loop cancellation of resonant features. In addition, a method of high speed digital filter optimisation and automated design is demonstrated.

Modulation-free portable laser frequency and power stabilization system

The performance of laser-based instruments heavily depends on the stability of their laser source. Some instruments, such as the Cs-⁴He magnetometer, even require the frequency stabilization and the power stabilization at the same time. In this work, we design a double-locking system with a fiber-coupled output on a small bread board and apply it to the pump laser of a Cs-⁴He magnetometer. By carefully choosing the stabilization methods, we significantly improve the long-term simultaneous stability of frequency and power of the pump laser. The laser frequency drifts in 2 h are reduced from 100 to 10 MHz. For 10 h continuous measurements, their Allan deviation obtains about two orders of magnitude improvement for the averaging time larger than 200 s and reaches σ(τ) = 1.57 × 10^-9 with a 200 s averaging time. The laser power stability for 1.8 h also obtains two orders of magnitude improvement from 3.22% to 0.031%, and its power noise reaches a level that is very close to the electronic noise of the detector. Applying this stabilization system to the pump laser of a fiber-coupled Cs-⁴He magnetometer, its magnetic sensor noise is significantly reduced from 0.158 to 0.009 nT, which is a reasonable noise for magnetic field detection. With this on-board design of the laser stabilization system, it is more convenient to transform the magnetometer into an outdoor device.

Research Facilities for Europe’s Next Generation Gravitational-Wave Detector Einstein Telescope

The Einstein Telescope is Europe’s next generation gravitational-wave detector. To develop all necessary technology, four research facilities have emerged across Europe: The Amaldi Research Center (ARC) in Rome (Italy), ETpathfinder in Maastricht (The Netherlands), SarGrav in the Sos Enattos mines on Sardinia (Italy) and E-TEST in Liége (Belgium) and its surroundings. The ARC pursues the investigation of a large cryostat, equipped with dedicated low-vibration cooling lines, to test full-scale cryogenic payloads. The installation will be gradual and interlaced with the payload development. ETpathfinder aims to provide a low-noise facility that allows the testing of full interferometer configurations and the interplay of their subsystems in an ET-like environment. ETpathfinder will focus amongst others on cryogenic technologies, silicon mirrors, lasers and optics at 1550 and 2090 nm and advanced quantum noise reduction schemes. The SarGrav laboratory has a surface lab and an underground operation. On the surface, the Archimedes experiment investigates the interaction of vacuum fluctuations with gravity and is developing (tilt) sensor technology for the Einstein Telescope. In an underground laboratory, seismic characterisation campaigns are undertaken for the Sardinian site characterisation. Lastly, the Einstein Telecope Euregio meuse-rhine Site & Technology (E-TEST) is a single cryogenic suspension of an ET-sized silicon mirror. Additionally, E-TEST investigates the Belgian–Dutch–German border region that is the other candidate site for Einstein Telescope using boreholes and seismic arrays and hydrogeological characterisation. In this article, we describe the Einstein Telescope, the low-frequency part of its science case and the four research facilities.

Prompt Frequency Stabilization of Ultra-Stable Laser via Improved Mean Shift Algorithm

In many scientific fields, the continuous operation of ultra-stable lasers is crucial for applications. To speed up the frequency stabilization process in case of the occurence of unexpected interruptions, a prompt frequency stabilization approach based on an improved mean shift algorithm is proposed and verified with a homemade laser system. We developed a double-loop feedback controller to steer the laser frequency with fast and slow channels, respectively. In this study, an improved mean shift algorithm is utilized to intelligently search for the transmission signal, which involves adaptively updating the sliding window radius and incorporating a Gaussian kernel function to update the shift vector. The number of lock points on the left and right sides of the central point determines the scanning direction to search for the transmission signal quickly. The laser is intentionally interrupted 306 times within 10,000 s to evaluate the relocking performance. The median auto-locking time of the laser is improved from 16 s to 4 s. By beating with another ultra-stable laser system, the laser frequency instability is measured to be less than 2.1×10−14 and the linewidth is 5 Hz. This work improves the adaptation and relocking ability of the ultra-stable laser in a complex environment.

Review of the Advanced LIGO Gravitational Wave Observatories Leading to Observing Run Four

Gravitational waves from binary black hole and neutron star mergers are being regularly detected. As of 2021, 90 confident gravitational wave detections have been made by the LIGO and Virgo detectors. Work is ongoing to further increase the sensitivity of the detectors for the fourth observing run, including installing some of the A+ upgrades designed to lower the fundamental noise that limits the sensitivity to gravitational waves. In this review, we will provide an overview of the LIGO detectors optical configuration and lock acquisition procedure, discuss the detectors’ fundamental and technical noise limits, show the current measured sensitivity, and explore the A+ upgrades currently being installed in the detectors.

48 -cm-long room-temperature cavities in vertical and horizontal orientations for Sr optical clock

The development of an optical clock with ultimate accuracy and stability requires lasers with very narrow linewidths. We present two ultrastable laser systems based on 48-cm-long Fabry-Perot cavities made of ultralow expansion glass in horizontal and vertical configurations operating at 698 nm. Fractional frequency instability of the beat signal between the two lasers reaches 1.6×10^-15 at the averaging time of 1 s. We experimentally characterized the contribution of the different noise sources (power fluctuations, residual amplitude modulation, the Doppler noise, and sensitivity to the shock impact) and found that in our case the laser frequency instability to a large extent is determined by an optoelectronic feedback loop. Although the vertical configuration was easier to manufacture and transport, it is much more sensitive to acoustics and horizontal accelerations compared to the horizontal one. Both laser systems were transported over a 60 km distance from the Lebedev Physical Institute to the All-Russian Scientific Research Institute for Physical-Engineering and Radiotechnical Metrology (VNIIFTRI), where they serve as local oscillators for spectroscopy of the clock transition in the recently developed strontium optical clock.

Improving laser power stability with a photosensitive lens

We propose a method to improve relative laser power stability using a passive photosensitive sunglass lens, which is a commercially available off-the-shelf product. We present a theoretical analysis and identify factors that affect the optimal working state of the lens. A relative laser power stability of 3.3 × 10^-5 at 1 s is experimentally achieved, which is more than three times that of 1.2 × 10^-4 at 1 s, acquired without power stabilization. This method does not require any active driving device, thereby significantly reducing the complexity and cost of the system, making it suitable for broad applications.

Low noise 400 W coherently combined single frequency laser beam for next generation gravitational wave detectors

Design studies for the next generation of interferometric gravitational wave detectors propose the use of low-noise single-frequency high power laser sources at 1064 nm. Fiber amplifiers are a promising design option because of their high output power and excellent optical beam properties. We performed filled-aperture coherent beam combining with independently amplified beams from two low-noise high-power single-frequency fiber amplifiers to further scale the available optical power. An optical power of approximately 400 W with a combining efficiency of more than 93% was achieved. The combined beam contained 370 W of linearly polarized TEM₀₀-mode and was characterized with respect to the application requirements of low relative power noise, relative beam pointing noise, and frequency noise. The noise performance of the combined beam is comparable to the single amplifier noise. This represents, to our knowledge, the highest measured power in the TEM₀₀-mode of single frequency signals that fulfills the low noise requirements of gravitational wave detectors.

Advanced LIGO Laser Systems for O3 and Future Observation Runs

The advanced LIGO gravitational wave detectors need high power laser sources with excellent beam quality and low-noise behavior. We present a pre-stabilized laser system with 70 W of output power that was used in the third observing run of the advanced LIGO detectors. Furthermore, the prototype of a 140 W pre-stabilized laser system for future use in the LIGO observatories is described and characterized.

Gravitational-Wave Burst Signals Denoising Based on the Adaptive Modification of the Intersection of Confidence Intervals Rule

Gravitational-wave data (discovered first in 2015 by the Advanced LIGO interferometers and awarded by the Nobel Prize in 2017) are characterized by non-Gaussian and non-stationary noise. The ever-increasing amount of acquired data requires the development of efficient denoising algorithms that will enable the detection of gravitational-wave events embedded in low signal-to-noise-ratio (SNR) environments. In this paper, an algorithm based on the local polynomial approximation (LPA) combined with the relative intersection of confidence intervals (RICI) rule for the filter support selection is proposed to denoise the gravitational-wave burst signals from core collapse supernovae. The LPA-RICI denoising method's performance is tested on three different burst signals, numerically generated and injected into the real-life noise data collected by the Advanced LIGO detector. The analysis of the experimental results obtained by several case studies (conducted at different signal source distances corresponding to the different SNR values) indicates that the LPA-RICI method efficiently removes the noise and simultaneously preserves the morphology of the gravitational-wave burst signals. The technique offers reliable denoising performance even at the very low SNR values. Moreover, the analysis shows that the LPA-RICI method outperforms the approach combining LPA and the original intersection of confidence intervals (ICI) rule, total-variation (TV) based method, the method based on the neighboring thresholding in the short-time Fourier transform (STFT) domain, and three wavelet-based denoising techniques by increasing the improvement in the SNR by up to 118.94% and the peak SNR by up to 138.52%, as well as by reducing the root mean squared error by up to 64.59%, the mean absolute error by up to 55.60%, and the maximum absolute error by up to 84.79%.

Reduction of laser intensity noise over 1 MHz band for single atom trapping

We reduce the intensity noise of laser light by using an electro-optic modulator and acousto-optic modulator in series. The electro-optic modulator reduces noise at high frequency (10 kHz to 1 MHz), while the acousto-optic modulator sets the average power of the light and reduces noise at low frequency (up to 10 kHz). The light is then used to trap single sodium atoms in an optical tweezer, where the lifetime of the atoms is limited by parametric heating due to laser noise at twice the trapping frequency. With our noise eater, the noise is reduced by up to 15 dB at these frequencies and the lifetime of the atom in the optical tweezer is increased by an order of magnitude to around 6 seconds. Our technique is general and acts directly on the laser beam, expanding laser options for sensitive optical trapping applications.

Intensity-noise suppression in 1950-nm single-frequency fiber laser by bidirectional amplifier configuration

In this Letter, a bidirectional amplifier configuration suppressing the relative intensity noise in a 1950-nm linearly polarized single-frequency fiber laser (SFFL) is proposed. The scheme to amplify the signal in a nonlinear saturated amplification regime with low gain distribution for suppressing the RIN is theoretically analyzed. By optimizing the input power level and reflectivity of the bidirectional power-amplifier, the RIN is decreased maximally by >24dB within the frequency range of 200 kHz. A stable output power of over 5.16 W with a polarization extinction ratio of 21.2 dB is obtained. Additionally, the amplified signal maintains a linewidth of 7.1 kHz nearly identical with that of the seed, both with a signal-to-noise ratio of more than 60 dB. This all-optical technique on noise suppression applied to the fiber amplifier paves the way to realize low-noise SFFL with power improvement.

Sequential high power laser amplifiers for gravitational wave detection

Advanced gravitational wave detectors require highly stable, single mode, single frequency and linear polarized laser systems. They have to deliver an output power of ∼200 W and need to provide suitable actuators for further stabilization via fast, low noise feedback control systems. We present such a laser system based on sequential Nd:YVO₄ amplifiers and its integration into a typical laser stabilization environment. We demonstrate robust low noise operation of the stabilized amplifier system at 195 W, which makes it a viable candidate for use in gravitational wave detectors.

5 W ultra-low-noise 2 µm single-frequency fiber laser for next-generation gravitational wave detectors

We demonstrated an ultra-low-noise polarization-maintaining (PM) single-frequency fiber laser at 2 µm. Both relative intensity noise (RIN) and frequency noise were improved by suppressing the pump source RIN using feedback control. After a two-stage Tm³⁺-doped PM fiber amplifier, the output power reached about 5 W, and the amplifier did not introduce any observable extra frequency noise. The frequency noise was less than 100Hz/Hz above 13 Hz, which is comparable to the frequency noise of a typical seed laser of the Advanced LIGO high-power laser. The central wavelength was measured to be 1990.25 nm, with a polarization extinction ratio above 24 dB.

Ultra-low intensity noise, all fiber 365 W linearly polarized single frequency laser at 1064 nm

We demonstrate a robust linearly polarized 365 W, very low amplitude noise, single frequency master oscillator power amplifier at 1064 nm. Power scaling was done through a custom large mode area fiber with a mode field diameter of 30 µm. No evidence of stimulated Brillouin scattering or modal instabilities are observed. The relative intensity noise is reduced down to -160 dBc/Hz between 2 kHz and 10 kHz via a wide band servo loop (1 MHz bandwidth). We achieve 350 W of isolated power, with a power stability < 0.7% RMS over 1100 hours of continuous operation and a near diffraction limited beam (M² < 1.1).

Demonstration of a Timescale Based on a Stable Optical Carrier

We report on the first timescale based entirely on optical technology. Existing timescales, including those incorporating optical frequency standards, rely exclusively on microwave local oscillators owing to the lack of an optical oscillator with the required frequency predictability and stability for reliable steering. We combine a cryogenic silicon cavity exhibiting improved long-term stability and an accurate ^{87}Sr lattice clock to form a timescale that outperforms them all. Our timescale accumulates an estimated time error of only 48±94  ps over 34 days of operation. Our analysis indicates that this timescale is capable of reaching a stability below 1×10^{-17} after a few months of averaging, making timekeeping at the 10^{-18} level a realistic prospect.

Simplified phase-stable dual-comb interferometer for short dynamic range distance measurement

A simplified phase-stable dual-comb interferometer for absolute distance measurement within a short dynamic range is proposed in this paper. The experimental results demonstrate that stable phase-difference information and lower timing jitter can be obtained within a time delay of 2000 ns between the reference interference signal and measurement interference signal. Using the proposed technique, the time-of-flight (TOF) result can link directly to the carrier-wave interferometric (CWI) result in an average time of 20 ms and can reach 2 nm precision in 0.5 s averaging time. Millimeter-scale measurement dynamic range and nanometer-level precision can thus be achieved without additional noise suppression. This method can also be applied at different stand-off distances.

Narrow-linewidth fiber amplifier for gravitational-wave detectors

We report on the design and noise performance of a narrow-linewidth Yb-doped fiber amplifier emitting up to 178 W at 1064 nm for possible use in gravitational-wave (GW) interferometric detectors. The novel design utilizes a specialty large-mode-area gain fiber with confined-core doping and depressed cladding, followed by a smaller-core passive fiber to improve output beam quality. We show that the free-running noise of the system is equal to or better than current Advanced LIGO noise requirements. Finally, we discuss potential improvements for long-term use in GW detectors.

Implementation of a stable, high-power optical lattice for quantum gas microscopy

We describe the design and implementation of a stable high-power 1064 nm laser system to generate optical lattices for experiments with ultracold quantum gases. The system is based on a low-noise laser amplified by an array of four heavily modified, high-power fiber amplifiers. The beam intensity is stabilized and controlled with a nonlinear feedback loop. Using real-time monitoring of the resulting optical lattice, we find the stability of the lattice site positions to be well below the lattice spacing over the course of hours. The position of the harmonic trap produced by the Gaussian envelope of the lattice beams is stable to about one lattice spacing and the long-term (six-month) relative root-mean-square stability of the lattice spacing itself is 0.5%.

Nd:YVO4 high-power master oscillator power amplifier laser system for second-generation gravitational wave detectors

Ultrastable high-power laser systems are essential components of the long baseline interferometers that detected the first gravitational waves from merging black holes and neutron stars. One way to further increase the sensitivity of current generation gravitational wave detectors (GWDs) is to increase the laser power injected into the interferometers. In this Letter, we describe and characterize a 72 W and a 114 W linearly polarized, single-frequency laser system at a wavelength of 1064 nm, each based on single-pass Nd:YVO₄ power amplifiers. Both systems have low power and frequency noise and very high spatial purity with less than 10.7% and 2.9% higher order mode content, respectively. We demonstrate the simple integration of these amplifiers into the laser stabilization environment of operating GWDs and show stable low-noise operation of one of the amplifier systems in such an environment for more than 45 days.

Laser systems stabilized to cryogenic silicon cavities for precision measurements

We consider laser systems stabilized to external Fabry-Perot silicon cavities operated at cryogenic temperatures. In order to characterize frequency stability two identical systems were created. Fractional frequency instability of individual system reached 6×10-15 at 1 s. Different sources of noises were studied, and the dominant one now is the fluctuations of residual amplitude modulation.

Squeezed vacuum states of light for gravitational wave detectors

A century after Einstein's formulation of general relativity, the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves. This historic achievement was the culmination of a world-wide effort and decades of instrument research. While sufficient for this monumental discovery, the current generation of gravitational-wave detectors represent the least sensitive devices necessary for the task; improved detectors will be required to fully exploit this new window on the Universe. In this paper, we review the application of squeezed vacuum states of light to gravitational-wave detectors as a way to reduce quantum noise, which currently limits their performance in much of the detection band.

Power stabilization of a diode laser with an acousto-optic modulator

Laser power fluctuations can significantly reduce the device performances in various applications. High frequency fluctuations impact the signal-to-noise ratio, while slow variations can reduce the device repeatability or accuracy. Here we report experimental investigations on the power stabilization of a diode laser with an acousto-optic modulator. In the frequency domain, the relative power noise is reduced at the level of 2.2 × 10^-8 Hz^-1/2 in the range 1-100 kHz. The slow variations are studied in the time domain. The relative Allan standard deviation is measured at the level of 6 × 10^-7 at 100 s averaging time. Above 100 s, the instability increases and reaches 2 × 10^-6 at 10 000 s.

Investigation about the influence of longitudinal-mode structure of the laser on the relative intensity noise properties

The influence of the longitudinal-mode structure (LMS) of the laser on the relative intensity noise (RIN) properties was investigated in this paper after an all-solid-state continuous-wave (CW) single-frequency 1064 nm laser with output power of 50.3 W was achieved. The LMS of the laser was manipulated by controlling the temperature of the nonlinear lithium triborate (LBO) crystal deliberately introduced to the resonator. When the laser worked with single-longitudinal-mode (SLM) operation, the stable RIN spectrum was observed and measured. Moreover, with the decrease of the nonlinear conversion efficiency (NCE), the frequency and amplitude of the resonant-relaxation oscillation (RRO) peak regularly shifted to the higher frequencies and increased, respectively. However, with further decrease of the NCE, the laser began to work with the multi-longitudinal-mode (MLM) or mode-hopping operation and the unstable RIN spectra of the laser were both observed not only at low frequencies but also at high frequencies. Once the NCE was moved away, the MLM or mode-hopping can only enhance the fluctuation of the laser RIN spectrum at the low frequencies (lower than the frequency of RRO). The experimental results directly revealed the relationship between the LMS of the laser and the RIN spectra, and confirmed definitely that the key to achieve a stable high power laser with low intensity noise was to realize single-frequency operation of the laser with free MLM and mode-hopping.

Active intensity noise suppression for a broadband mid-infrared laser source

Excess relative intensity noise (RIN) constitutes one of the major limitations of most spectroscopic methods involving lasers. Here, we present an active RIN suppression scheme for a coherent mid-infrared (MIR) light source (8.4-11 µm), based on intra-pulse difference frequency generation (DFG). Three different stabilization concepts that rely on modulating the intensity of the driving near-infrared (NIR) pulse train with an acousto-optic modulator are investigated and compared. By using the wings of the NIR spectrum to generate the error signal, a RIN suppression of the MIR pulse train of up to a factor of 20 was achieved in the band between 1 Hz and 100 kHz, resulting in a total integrated RIN of 0.07%.

High-power and near-shot-noise-limited intensity noise all-fiber single-frequency 1.5 μm MOPA laser

An all-fiber high-power and broad-frequency-band near-shot-noise-limited kHz-linewidth (Δν ~1.7 kHz) single-frequency master-oscillator power amplifier (MOPA) laser at 1.5 μm is demonstrated. To significantly suppress the intensity noise of seed laser and mitigate the detrimental effects of amplified spontaneous emission and stimulated Brillouin scattering in fiber amplifiers, more than 23 W of a stable low noise single-frequency laser output is achieved with a relative intensity noise of < -150 dB/Hz @0.5 mW (near to the shot-noise limit: -152.9 dB/Hz) in the frequency band from 0.1 to 50 MHz. It is believed that the achieved laser performance of ultra-low intensity noise and high-power output make the laser source become a promising candidate in further applications, such as cold atom optical lattice, quantum key distribution, and gravitational wave detection.

Interferometer techniques for gravitational-wave detection

Several km-scale gravitational-wave detectors have been constructed worldwide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review, we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.

Higher-order Laguerre-Gauss modes in (non-) planar four-mirror cavities for future gravitational wave detectors

One of the limiting noise sources in the current generation of gravitational wave detectors, such as the advanced laser interferometer gravitational wave observatory (aLIGO), is the thermal noise in the interferometer's test mass coatings. One proposed method to reduce the coupling of this noise source to the gravitational wave readout is using a laser beam in the higher-order spatial LG₃₃ mode within the interferometer. Here we show that the current four-mirror cavities of aLIGO are not compatible with Laguerre-Gauss modes due to astigmatism. A non-degeneracy of modes of the same order could be observed in experiment and simulation. We demonstrate that a non-planar cavity could be used instead as it compensates for the astigmatism and transmits the LG₃₃ mode undisturbed.

Gain dynamics of clad-pumped Yb-fiber amplifier and intensity noise control

Gain dynamics study provides an attractive method to understand the intensity noise behavior in fiber amplifiers. Here, the gain dynamics of a medium power (5 W) clad-pumped Yb-fiber amplifier is experimentally evaluated by measuring the frequency domain transfer functions for the input seed and pump lasers from 10 Hz to 1 MHz. We study gain dynamic behavior of the fiber amplifier in the presence of significant residual pump power (compared to the seed power), showing that the seed transfer function is strongly saturated at low Fourier frequencies while the pump power modulation transfer function is nearly unaffected. The characterization of relative intensity noise (RIN) of the fiber amplifier is well explained by the gain dynamics analysis. Finally, a 600 kHz bandwidth feedback loop using an acoustic-optical modulator (AOM) controlling the seed intensity is successfully demonstrated to suppress the broadband laser intensity noise. A maximum noise reduction of about 30 dB is achieved leading to a RIN of -152 dBc/Hz (~1 kHz-10 MHz) at 2.5 W output power.

Coherently combined master oscillator fiber power amplifiers for Advanced Virgo

Stable low-noise high-power lasers are indispensable in advancing the strain sensitivity of interferometric gravitational wave detectors. Advanced LIGO and Advanced Virgo are currently under commissioning and require about 200 W of single-frequency laser power, while the future detector design may require up to the order of 500 W. In this Letter, we present the design and, to the best of our knowledge, the first experimental demonstration of the laser system for Advanced Virgo that is based on coherently combined fiber laser amplifiers. We show the long-term performance of two 40 W fiber laser amplifiers, as well as their characterization in terms of beam quality, power noise, phase noise, and beam pointing. Moreover, a simple and compact setup utilizing fibered modulators and actuators for the coherent beam combination of these two fiber laser amplifiers is reported. A combination efficiency of about 96% was achieved, and no spurious noise was observed.

Distributed state machine supervision for long-baseline gravitational-wave detectors

The Laser Interferometer Gravitational-wave Observatory (LIGO) consists of two identical yet independent, widely separated, long-baseline gravitational-wave detectors. Each Advanced LIGO detector consists of complex optical-mechanical systems isolated from the ground by multiple layers of active seismic isolation, all controlled by hundreds of fast, digital, feedback control systems. This article describes a novel state machine-based automation platform developed to handle the automation and supervisory control challenges of these detectors. The platform, called Guardian, consists of distributed, independent, state machine automaton nodes organized hierarchically for full detector control. User code is written in standard Python and the platform is designed to facilitate the fast-paced development process associated with commissioning the complicated Advanced LIGO instruments. While developed specifically for the Advanced LIGO detectors, Guardian is a generic state machine automation platform that is useful for experimental control at all levels, from simple table-top setups to large-scale multi-million dollar facilities.

GW150914: First results from the search for binary black hole coalescence with Advanced LIGO

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) simultaneously observed the binary black hole merger GW150914. We report the results of a matched-filter search using relativistic models of compact-object binaries that recovered GW150914 as the most significant event during the coincident observations between the two LIGO detectors from September 12 to October 20, 2015. GW150914 was observed with a matched filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203000 years, equivalent to a significance greater than 5.1 σ.

GW150914: The Advanced LIGO Detectors in the Era of First Discoveries

Following a major upgrade, the two advanced detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) held their first observation run between September 2015 and January 2016. With a strain sensitivity of 10^{-23}/sqrt[Hz] at 100 Hz, the product of observable volume and measurement time exceeded that of all previous runs within the first 16 days of coincident observation. On September 14, 2015, the Advanced LIGO detectors observed a transient gravitational-wave signal determined to be the coalescence of two black holes [B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016)], launching the era of gravitational-wave astronomy. The event, GW150914, was observed with a combined signal-to-noise ratio of 24 in coincidence by the two detectors. Here, we present the main features of the detectors that enabled this observation. At full sensitivity, the Advanced LIGO detectors are designed to deliver another factor of 3 improvement in the signal-to-noise ratio for binary black hole systems similar in mass to GW150914.

Observation of Gravitational Waves from a Binary Black Hole Merger

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

The advanced LIGO input optics

The advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics subsystem is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article, we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.

Monitoring and analysis of thermal deformation waves with a high-speed phase measurement system

Thermal effects in optical substrates are vitally important in determining laser damage resistance in long-pulse and continuous-wave laser systems. Thermal deformation waves in a soda-lime-silica glass substrate have been measured using high-speed interferometry during a series of laser pulses incident on the surface. Two-dimensional images of the thermal waves were captured at a rate of up to six frames per thermal event using a quantitative phase measurement method. The system comprised a Mach-Zehnder interferometer, along with a high-speed camera capable of up to 20,000 frames-per-second. The sample was placed in the interferometer and irradiated with 100 ns, 2 kHz Q-switched pulses from a high-power Nd:YAG laser operating at 1064 nm. Phase measurements were converted to temperature using known values of thermal expansion and temperature-dependent refractive index for glass. The thermal decay at the center of the thermal wave was fit to a function derived from first principles with excellent agreement. Additionally, the spread of the thermal distribution over time was fit to the same function. Both the temporal decay fit and the spatial fit produced a thermal diffusivity of 5×10^-7  m²/s.

Novel technique for thermal lens measurement in commonly used optical components

The absorption of light in transmissive optics cause a thermally induced effect known as thermal lensing. This effect provokes an often undesired change of a laser beam transmitted by the optic. In this paper we present a measurement method that allows us to determine thermal lensing in commonly used optical components. The beam influenced by the thermal lens is expanded into the eigenmodes of an optical cavity, and its modal content is analyzed in the eigenbasis of the cavity. The measured quantity depends neither on beam parameters nor on the position of the optical component under investigation. This method allows, to our knowledge, for the first time the direct measurement of the mode conversion coefficient |ε(2)| of the thermal lens.

Advanced technologies for future ground-based, laser-interferometric gravitational wave detectors

We present a review of modern optical techniques being used and developed for the field of gravitational wave detection. We describe the current state-of-the-art of gravitational waves detector technologies with regard to optical layouts, suspensions and test masses. We discuss the dominant sources and noise in each of these subsystems and the developments that will help mitigate them for future generations of detectors. We very briefly summarise some of the novel astrophysics that will be possible with these upgraded detectors.

Generation of high-purity higher-order Laguerre-Gauss beams at high laser power

We have investigated the generation of highly pure higher-order Laguerre-Gauss (LG) beams at high laser power of order 100 W, the same regime that will be used by second-generation gravitational wave interferometers such as Advanced LIGO. We report on the generation of a helical-type LG33 mode with a purity of order 97% at a power of 83 W, the highest power ever reported in literature for a higher-order LG mode. This is a fundamental step in proving technical readiness for use of LG beams in gravitational wave interferometers of future generations.

High power single frequency solid state master oscillator power amplifier for gravitational wave detection

High power single frequency, single mode, linearly polarized laser output at the 1 μm regime is in demand for the interferometric gravitational wave detectors (GWDs). A robust single frequency solid state master oscillator power amplifier (MOPA) is a promising candidate for such applications. We present a single frequency solid state multistage MOPA system delivering 177 W of linearly polarized output power at 1 μm with 83.5% TEM(00) mode content.