High-bandwidth laser frequency stabilization to a fiber-optic delay line

Arm locking using laser frequency comb

The space-borne gravitational wave (GW) detectors, e.g., LISA, TaiJi, and TianQin, will open the window in the low-frequency regime (0.1 mHz to 1 Hz) to study the highly energetic cosmic events, such as coalescences and mergers of binary black holes and neutron stars. For the sake of successful observatory of GWs, the required strain sensitivity of the detector is approximately 10^-21/Hz^1/2 in the science band, 7 orders of magnitude better than the state of the art of the ultra-stable laser. Arm locking is therefore proposed to reduce the laser phase noise by a few orders of magnitude to relax the burden of time delay interferometry. During the past two decades, various schemes have been demonstrated by using single or dual arms between the spacecraft, with consideration of the gain, the nulls in the science band, and the frequency pulling characteristics, etc. In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. When the laser source is pre-stabilized to a Fabry-Perot cavity or a Mach-Zehnder interferometer, the noise can reach the floor determined by the clock noise, the spacecraft motion, and the shot noise. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only does our method allow the suppression of the peaks, the high gain, and low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We then discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Finally, the time-series simulations in Simulink have been carried out, and the results indicate a good agreement with the theory, showing that the presented method is reasonable and feasible. Our work could provide a back-up strategy for the arm locking in the future space-borne GW detectors.

Double Rayleigh scattering in a digitally enhanced, all-fiber optical frequency reference

We demonstrate a passive, all-optical fiber frequency reference using a digitally enhanced homodyne interferometric phase readout. We model the noise contributions from fiber thermal noise and the coupling of double Rayleigh scattering in a digitally enhanced homodyne interferometer. A system frequency stability of 0.1 Hz/Hz is achieved above 100 Hz, which coincides with the double Rayleigh scattering estimate and is approximately a factor of five above the thermo-dynamic noise limit.

High-frequency broadband laser phase noise cancellation using a delay line

Laser phase noise remains a limiting factor in many experimental settings, including metrology, time-keeping, as well as quantum optics. Hitherto this issue was addressed at low frequencies ranging from well below 1 Hz to maximally 100 kHz. However, a wide range of experiments, such as, e.g., those involving nanomechanical membrane resonators, are highly sensitive to noise at higher frequencies in the range of 100 kHz to 10 MHz, such as nanomechanical membrane resonators. Here we employ a fiber-loop delay line interferometer optimized to cancel laser phase noise at frequencies around 1.5 MHz. We achieve noise reduction in 300 kHz-wide bands with a peak reduction of more than 10 dB at desired frequencies, reaching phase noise of less than -160 dB(rad²/Hz) with a Ti:Al₂O₃ laser. These results provide a convenient noise reduction technique to achieve deep ground-state cooling of mechanical motion.

Infrasonic performance of a passively stabilized, all-fiber, optical frequency reference

We report the infrasonic performance of a fiber optic laser frequency reference with potential application to space-based gravitational wave detectors, such as the Laser Interferometer Space Antenna. We determine the optimum cross-over frequency between an optical frequency comb stabilized to a Rubidium atomic reference and two passive, all-fiber interferometers interrogated using digitally enhanced homodyne interferometery. By measuring the relative stability between the three independent optical frequency references, we find the optimum cross-over frequency to occur at 1.5 mHz, indicating that our passive fiber frequency reference is superior to the optical frequency comb at all higher frequencies. In addition, we find our fiber interferometers achieve a stability of 20 kHz/Hz at 1.5 mHz, improving to a stability of 4 Hz/Hz above 3 Hz. These results represent an independent characterization of digitally enhanced fiber references over long time scales and provide an estimate of thermal effects on these passively isolated systems, informing future reference architectures.

10 kHz linewidth mid-infrared quantum cascade laser by stabilization to an optical delay line

We present a mid-infrared quantum cascade laser (QCL) with a sub-10 kHz full width at half-maximum linewidth (at 1 s integration time) achieved by stabilization to a free-space optical delay line. The linear range in the center of a fringe detected at the output of an imbalanced Mach-Zehnder interferometer implemented with a short free-space pathlength difference of only 1 m is used as a frequency discriminator to detect the frequency fluctuations of the QCL. Feedback is applied to the QCL current to lock the laser frequency to the delay line. The application of this method in the mid-infrared is reported for the first time, to the best of our knowledge. By implementing it in a simple self-homodyne configuration, we have been able to reduce the frequency noise power spectral density of the QCL by almost 40 dB below 10 kHz Fourier frequency, leading to a linewidth reduction by a factor of almost 60 compared to the free-running laser. The present limits of the setup are assessed and discussed.

Self-stabilization of an optical frequency comb using a short-path-length interferometer

We stabilized the repetition rate of an optical frequency comb using a self-referenced phase-locked loop. The phase-locked loop generated its error signal with a fiber-optic delay-line interferometer that had a path-length difference of 8 m. We used the stabilized repetition rate to generate a 10 GHz signal with a single-sideband phase noise that was limited by environmental noise to -120  dBc/Hz at an offset frequency of 1 kHz. Modeling results indicate that thermoconductive noise sets a fundamental phase noise limit for an 8 m interferometer of -152  dBc/Hz at a 1 kHz offset frequency. The short length of the interferometer indicates that it could be realized as a photonic integrated circuit, which may lead to a chip-scale stabilized optical frequency comb with an ultralow-phase-noise repetition rate.

Efficient laser noise reduction method via actively stabilized optical delay line

We report a fiber laser noise reduction method by locking it to an actively stabilized optical delay line, specifically a fiber-based Mach-Zehnder interferometer with a 10 km optical fiber spool. The fiber spool is used to achieve large arm imbalance. The heterodyne signal of the two arms converts the laser noise from the optical domain to several megahertz, and it is used in laser noise reduction by a phase-locked loop. An additional phase-locked loop is induced in the system to compensate the phase noise due to environmentally induced length fluctuations of the optical fiber spool. A major advantage of this structure is the efficient reduction of out-of-loop frequency noise, particularly at low Fourier frequency. The frequency noise reaches -30 dBc/Hz at 1 Hz, which is reduced by more than 90 dB compared with that of the laser in its free-running state.

Fourier transform-limited optical frequency-modulated continuous-wave interferometry over several tens of laser coherence lengths

We report on a versatile optical frequency-modulated continuous-wave interferometry technique that exploits wideband phase locking for generating highly coherent linear laser frequency chirps. This technique is based on an ultra-short delay-unbalanced interferometer, which leads to a large bandwidth, short lock time, and robust operation even in the absence of any isolation from environmental perturbations. In combination with a digital delay-matched phase error compensation, this permits the achievement of a range window about 60 times larger than the intrinsic laser coherence length with a 1.25 mm Fourier transform-limited spatial resolution. The demonstrated configuration can be easily applied to virtually any semiconductor laser.

All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave

High-impact frequency comb applications that are critically dependent on precise pulse timing (i.e., repetition rate) have recently emerged and include the synchronization of X-ray free-electron lasers, photonic analogue-to-digital conversion and photonic radar systems. These applications have used attosecond-level timing jitter of free-running mode-locked lasers on a fast time scale within ~100 μs. Maintaining attosecond-level absolute jitter over a significantly longer time scale can dramatically improve many high-precision comb applications. To date, ultrahigh quality-factor (Q) optical resonators have been used to achieve the highest-level repetition-rate stabilization of mode-locked lasers. However, ultrahigh-Q optical-resonator-based methods are often fragile, alignment sensitive and complex, which limits their widespread use. Here we demonstrate a fibre-delay line-based repetition-rate stabilization method that enables the all-fibre photonic generation of optical pulse trains with 980-as (20-fs) absolute r.m.s. timing jitter accumulated over 0.01 s (1 s). This simple approach is based on standard off-the-shelf fibre components and can therefore be readily used in various comb applications that require ultra-stable microwave frequency and attosecond optical timing.

Frequency noise suppression of a single mode laser with an unbalanced fiber interferometer for subnanometer interferometry

We present a method of noise suppression of laser diodes by an unbalanced Michelson fiber interferometer. The unstabilized laser source is represented by compact planar waveguide external cavity laser module, ORION^TM (Redfern Integrated Optics, Inc.), working at 1540.57 nm with a 1.5-kHz linewidth. We built up the unbalanced Michelson interferometer with a 2.09 km-long arm based on the standard telecommunication single-mode fiber (SMF-28) spool to suppress the frequency noise by the servo-loop control by 20 dB to 40 dB within the Fourier frequency range, remaining the tuning range of the laser frequency.

Distribution of high-stability 10 GHz local oscillator over 100 km optical fiber with accurate phase-correction system

We have developed a radio-frequency local oscillator remote distribution system, which transfers a phase-stabilized 10.03 GHz signal over 100 km optical fiber. The phase noise of the remote signal caused by temperature and mechanical stress variations on the fiber is compensated by a high-precision phase-correction system, which is achieved using a single sideband modulator to transfer the phase correction from intermediate frequency to radio frequency, thus enabling accurate phase control of the 10 GHz signal. The residual phase noise of the remote 10.03 GHz signal is measured to be -70  dBc/Hz at 1 Hz offset, and long-term stability of less than 1×10⁻¹⁶ at 10,000 s averaging time is achieved. Phase error is less than ±0.03π.

Optical-frequency transfer over a single-span 1840 km fiber link

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of 2×10(-15) for a gate time τ of 1 s reaching 4×10(-19) in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about 3×10(-19). The spectral noise distribution of our fiber link at low Fourier frequencies leads to a τ(-2) slope in the modified Allan deviation, which is also derived theoretically.

Microwave generation with low residual phase noise from a femtosecond fiber laser with an intracavity electro-optic modulator

Low phase-noise microwave generation has previously been demonstrated using self-referenced frequency combs to divide down a low noise optical reference. We demonstrate an approach based on a fs Er-fiber laser that avoids the complexity of self-referenced stabilization of the offset frequency. Instead, the repetition rate of the femtosecond Er-fiber laser is phase locked to two cavity-stabilized cw fiber lasers that span 3.74 THz by use of an intracavity electro-optic modulator with over 2 MHz feedback bandwidth. The fs fiber laser effectively divides the 3.74 THz difference signal to produce microwave signals at harmonics of the repetition rate. Through comparison of two identical dividers, we measure a residual phase noise on a 1.5 GHz carrier of -120 dBc/Hz at 1 Hz offset.

Linewidth reduction of a distributed-feedback diode laser using an all-fiber interferometer with short path imbalance

The linewidth of a distributed-feedback (DFB) diode laser at 1156 nm, of which free-running linewidth was 3 MHz, was reduced to 15 kHz using an all-fiber interferometer with 5-m-long path imbalance. Optical power loss and bandwidth limitation were negligible with this short optical fiber patch cord. This result was achieved without acoustic and vibration isolations, and the frequency lock could be maintained over weeks. In addition to its simplicity, compactness, robustness, and cost-effectiveness, this technique can be applied at any wavelength owing to the availability of DFB diode lasers and fiber-optic components.

An agile laser with ultra-low frequency noise and high sweep linearity

We report on a fiber-stabilized agile laser with ultra-low frequency noise. The frequency noise power spectral density is comparable to that of an ultra-stable cavity stabilized laser at Fourier frequencies higher than 30 Hz. When it is chirped at a constant rate of approximately 40 MHz/s, the max non-linearity frequency error is about 50 Hz peak-to-peak over more than 600 MHz tuning range. The Rayleigh backscattering is found to be a significant frequency noise source dependent on fiber length, chirping rate and the power imbalance of the interferometer arms. We analyze this effect both theoretically and experimentally and put forward techniques to reduce this noise contribution.

Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line

We report the frequency stabilization of an erbium-doped fiber distributed-feedback laser using an all-fiber-based Michelson interferometer of large arm imbalance. The interferometer uses a 1 km SMF-28 optical fiber spool and an acousto-optic modulator allowing heterodyne detection. The frequency-noise power spectral density is reduced by more than 40 dB for Fourier frequencies ranging from 1 Hz to 10 kHz, corresponding to a level well below 1 Hz2/Hz over the entire range; it reaches 10(-2) Hz2/Hz at 1 kHz. Between 40 Hz and 30 kHz, the frequency noise is shown to be comparable to the one obtained by Pound-Drever-Hall locking to a high-finesse Fabry-Perot cavity. Locking to a fiber delay line could consequently represent a reliable, simple, and compact alternative to cavity stabilization for short-term linewidth reduction.

Coherent transfer of an optical carrier over 251 km

We transfer an optical frequency over 251 km of optical fiber with a residual instability of 6x10(-19) at 100 s. This instability and the associated timing jitter are limited fundamentally by the noise on the optical fiber and the link length. We give a simple expression for calculating the achievable instability and jitter over a fiber link. Transfer of optical stability over this long distance requires a highly coherent optical source, provided here by a cw fiber laser locked to a high finesse optical cavity. A sufficient optical carrier signal is delivered to the remote fiber end by incorporating two-way, in-line erbium-doped fiber amplifiers to balance the 62 dB link loss.