Laser Frequency Stabilization Research Articles

Research on Brownian Thermal Noise Limit of a Cylindrical Ultra-Stable Cavity with Support Pads

Brownian thermal noise (TN) of ultra-stable cavities (USCs) imposes a fundamental limitation on the frequency stability of ultra-narrow linewidth lasers. This work investigates the TN in cylindrical USCs with the four support pads in detail through theoretical estimation and simulation. To evaluate the performance of state-of-the-art ultra-narrow linewidth lasers, we derive an expression of the TN for a cylindrical spacer according to the fluctuation–dissipation theorem, which takes into account the front face area of the spacer. This estimation is more suitable for the TN of the cylindrical USC than the previous one. Meanwhile, we perform detailed studies of the influence of the four support pads on the TN in cylindrical USCs for the first time by numerical simulations. For a 400 mm long cylindrical USC with an ultra-low expansion spacer and fused silica substrates, the displacement noise contributed from the four support pads is roughly four times that of the substrates and the GaAs/AlGaAs crystalline coating. The results show that the four support pads are the primary TN contributors under some materials and geometries of USCs.

Optical Phase/Frequency Demodulation Using Polarization-Maintaining Fiber Bragg Gratings

Conventional techniques for demodulating phase/frequency-modulated (PM/FM) optical signals either require a sophisticated frequency-stable laser or employ a discriminator with poor characteristics. Here, we present a simple, compact, and robust technique featuring high linearity over a wide bandwidth and low background noise. Our technique exploits the reflection characteristics of fiber Bragg gratings written in polarization-maintaining fibers to create a frequency discriminator, which is able to convert PM/FM signals into intensity-modulated (IM) signals. A simple theoretical analysis is presented to highlight the advantages of the scheme. Experimentally, the transfer characteristics of the demodulator are characterized, yielding a linear FM-to-IM conversion slope of 1.238 mV/Hz in a 0.2-nm (∼25 GHz) bandwidth. Highly linear operation up to an FM-modulation index of 1.2 has been achieved. Background-free operation is shown by demonstrating negligible carrier leakage and a 10-dB IM rejection. Finally, high fidelity in demodulating arbitrary PM/FM optical signals is demonstrated with a correlation coefficient of 0.99 and a confidence of almost 100%. This simple yet efficient technique can potentially find applications in optical communications, microwave photonics and radar/lidar technologies.

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

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

Compact Michelson Interferometers with Subpicometer Sensitivity

The network of interferometric gravitational-wave observatories has successfully detected tens of astrophysical signals since 2015. In this paper, we experimentally investigate compact sensors that have the potential to improve the sensitivity of gravitational-wave detectors to intermediate-mass black holes. We use only commercial components, such as sensing heads and lasers, to assemble the setup and demonstrate its subpicometer precision. The setup consists of a pair of Michelson interferferometers that use deep frequency modulation techniques to obtain a linear, relative displacement readout over multiple interference fringes. We implement a laser-frequency stabilisation scheme to achieve a sensitivity of 0.3\,$\text{pm} / \sqrt{\text{Hz}}$ above 0.1\,Hz. The device has also the potential to improve other experiments, such as torsion balances and commercial seismometers.

Mirror coating-thermal-noise mitigation using multi-spatial-mode cavity readout

We present an approach to mitigating coating thermal noise in optical cavities by using multiple transverse electromagnetic (TEM) spatial modes to read out and stabilize laser frequency. With optimal weightings we synthesize a wider sampling of mirror surfaces, improving the averaging of Brownian thermal fluctuations. We show a thermal noise improvement factor of 1.57, comparable to a mesa beam of a nominal 12 m prototype cavity, and a factor 1.61 improvement over the ${\text{TEM}}_{00}$ using three modes in a 0.1 m cavity for a practical laboratory experiment, equivalent to cooling mirrors to 120 K from room temperature.

Fundamental thermal noise in antiresonant hollow-core fibers

To understand the effect of fundamental thermal noise in hollow-core optical fibers, the authors propose an adapted noise model and compare it to careful measurements. They find that the use of evacuated hollow cores could allow for an order-of-magnitude improvement in phase sensitivity with respect to standard fiber, enabling better precision in interferometric applications such as fiber gyroscopes and laser frequency stabilization.

Frequency stabilization of multiple wavelength lasers based on a broadband spectrum

We report on frequency stabilization of multiple wavelength lasers operating at 1389 and 1695 nm simultaneously on a broadband spectrum. These lasers are implemented in ytterbium optical lattice clock experiments, which need to have a narrow enough linewidth and maintain high long-term frequency stability. A 1560 nm femtosecond mode-locked laser with a narrow mode spacing of 250 MHz is used as a master laser, which is referenced to a local ultrastable optical cavity with the instability better than 1 × 10−15 at 1 s averaging time. Through the combination of erbium-doped fiber amplifier and high nonlinear fiber, the spectral width of the maser laser is broadened from 10 nm to more than 300 nm. The range of the broadened spectrum can cover 1389 and 1695 nm. Meanwhile, the spectral intensity at the corresponding wavelength can ensure that the signal-to-noise ratio of the beat signals between the two lasers and the broadened spectrum is about 30 dB at a resolution bandwidth (RBW) of 100 kHz. After phase locking the 1389 and 1695 nm lasers on the broadband spectrum, the residual linewidths are obtained to be about 0.8 Hz at 1 Hz RBW, and the stabilities are 3.5 × 10−16 and 4.7 × 10−16 at 1 s averaging time respectively, improving about six orders of magnitude. Our result can be conducive to obtaining the stabilized laser sources for the atomic optical clock, and will be of great significance for simplifying and miniaturizing the optical clock system.

Reducing frequency fluctuation in a Brillouin random fiber laser by a random fiber grating ring resonator.

Frequency fluctuation is a major problem in high-precision metrology as real-time optical frequency measurement is not available with commercial photodetectors; alternatively, frequency-stabilized lasers as a reference are also not accessible in most laboratories. In this study, we propose and demonstrate a polarization-maintaining random fiber grating ring (PM-RFGR) resonator in a PM Brillouin random fiber laser (BRFL) to achieve sub-MHz frequency drift, which is measured by the optical beat of the random laser and the pump laser. Experimental results show that longitudinal modes are suppressed in the BRFL owing to the feedback of the RFGR resonating with one longitudinal mode of the random laser. The BRFL shows mode-hopping-free operation over 14.9 s due to the self-adjustment of random modes with small frequency difference to thermal and acoustic variations and self-injection locking through RFGR. As a result, a small frequency drift of ∼340 kHz with single-longitudinal mode is achieved in the BRFL enabled by the RFGR, which offers an all optical locking mechanism for optical frequency stabilization.

High stability multiple-frequency cavity locking based on Doppler-free optogalvanic Calcium ion spectroscopy.

Doppler-free spectroscopy of 40Ca+ on the transition 3D3/2 → 4P1/2 known as the frequency standard for repumping beam of Calcium ion trap was performed by means of optogalvanic detection. This reference signal was applied to measure the frequency stability of laser locked to the resonance of an ultra-low expansion (ULE) glass made cavity. Lamb dip spectrum fitting of this Calcium ion spectra revealed that the long-term drift of our laser system is below 2 MHz per hour. A simple setup for frequency locking of dual colour of lasers at 866 nm and 780 nm was also demonstrated. Consistencies of the frequency difference between these two lasers were measured less than 2 MHz in a hour after stabilizing both lasers to the cavity.

Enhanced magneto-optical rotation of probe field in thermal medium via spontaneous generated coherence

A four-level double lambda closed atomic configuration is considered to study the polarization plane rotation of the probe beam through cold as well as thermal Rb^{87} atomic medium by varying the spontaneously generated coherence (SGC). Magnetic field and strong coupling field are applied to the atomic configuration. The light-matter interaction leads to enhanced the magneto-optical rotation. The intensity of the applied fields plays promising role in the generation and enhancement of birefringence. It ultimately enhances the polarization plane rotation of the probe beam in the Doppler medium. In the presence of both SGC and Doppler broadening effects, the optical rotation and transmission of the weak light beam are modified and controlled as well, which have potential applications in magnetometery and laser frequency stabilization.

Absolute Frequency Readout of Cavity against Atomic Reference

Future space-based geodesy missions such as the Mass Change Mission and the Next Generation Gravity Mission are expected to rely on laser ranging as their primary instrument. Short-term laser frequency stability has previously been achieved on the GRACE Follow On mission by stabilizing the lasers to an optical cavity. The development of a technique to provide long-term laser frequency stability is expected to be required. We have previously demonstrated a technique to track long-term frequency changes by using measurements of the optical cavity’s free spectral range. In this paper, we calibrate this technique to absolute frequency by using an atomic reference. We have also validated an approach for on-ground calibration to allow the absolute frequency to be determined whilst in orbit.

Wideband current modulation of diode lasers for frequency stabilization.

We present a current modulation technique for diode laser systems, which 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 behavior of the system is analyzed under realistic conditions employing an external cavity diode laser (ECDL) system. We achieve a phase lag smaller than 90° up to 25 MHz and a gain flatness of ±3 dB in the frequency range of DC to 100 MHz, while the passive stability of the laser system is not impaired. The potential of the current modulation scheme is demonstrated in an optical phase-locked loop between two ECDL systems with a phase noise of 42 mradrms. The design files are available as an open-source project.

Linien: A versatile, user-friendly, open-source FPGA-based tool for frequency stabilization and spectroscopy parameter optimization.

We present a user-friendly and versatile tool for laser frequency stabilization. Its main focus is spectroscopy locking, but the software is suitable for lock-in techniques in general as well as bare proportional-integral-derivative (PID) operation. Besides allowing for sinusoidal modulation (up to 50MHz), triangular ramp scanning, in-phase and quadrature demodulation (1-5 f), infinite impulse response, and PID filtering, Linien features two different algorithms for automatic lock point selection; one of them performs time-critical tasks completely on field-programmable gate arrays. Linien is capable of autonomously optimizing spectroscopy parameters by means of machine learning and can measure the error signal's power spectral density. The software is built in a modular way, providing both a graphical user interface as well as a Python scripting interface. It is based on the RedPitaya STEMLab platform but may be ported to different systems.

Design and analysis of Pound-Drever-Hall-based free-space and fiber-based frequency discriminators: A comparison

Lasers with high coherence and low frequency and amplitude noise are essential for applications requiring high-precision measurement. Laser frequency stabilization is therefore a critical component of lasers used in these applications. In this work, we investigate the frequency stability characteristics of a laser system utilizing Pound-Drever-Hall (PDH) frequency locking and two different frequency discrimination systems, one based on a free-space Fabry-Pérot (F-P) cavity and another based on fiber Bragg gratings (FBGs). The result shows that F-P-based systems offer better performance than FBG-based systems, with each system showing frequency drifts of 83 MHz and 197 MHz respectively over a period of 30 min. The advantages and limitations of both approaches are discussed.

Ultrastable laser referenced on velocity-grating atom interferometry

A laser with superb frequency stability plays an important role in fundamental physics research and advanced technologies. Frequency references are usually utilized to stabilize the laser, such as high-finesse cavities and atomic ensembles, of which thermal atomic beams are attractive because of their balanced performance between simplicity and stability. However, due to the transverse-velocity distribution in the thermal atomic beams, most atoms (generally $>99%$) are wasted when interacting with the laser. Here, we propose a laser referenced on a version of velocity-grating Ramsey-Bord\'e atom interferometry with greatly improved atom utilization and thus superior laser frequency stability. Compared with a conventional atomic interferometry applied to stabilize the laser, the proposed system in principle generates optical Ramsey fringes with the amplitude enhanced by 1000-fold or more. Such a configuration has promising applications in diverse areas, including precision measurements and quantum metrology.

High-power, frequency-quadrupled UV laser source resonant with the 1S0-3P1 narrow intercombination transition of cadmium at 326.2 nm.

We present a novel high-power, frequency-stabilized UV laser source at 326.2 nm, resonant with the Cd 1S0-3P1 narrow intercombination transition. We achieve a maximum produced power of 1 W at 326.2 nm by two successive frequency doubling stages of a narrow-linewidth (<1 kHz) seed laser at 1304.8 nm. Approximately 3.4 W of optical power at 652.4 nm is produced by a visible Raman fiber amplifier (VRFA) that amplifies and generates the second harmonic of the infrared radiation. The visible light is subsequently frequency-doubled down to 326.2 nm in a nonlinear bow-tie cavity using a Brewster-cut beta-barium-borate (BBO) crystal, with a maximum conversion efficiency of approximately 40% for 2.5 W of coupled red power. Full characterization of the laser source, together with spectroscopy signals of all Cd isotopes, spanning more than 4 GHz in the UV, are shown.

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.

The Variation of the Linewidths and Amplitudes of Sub-Doppler Resonances of 87Rb D2 Line with Laser Beam Intensity

The sub-Doppler resonances linewidths and amplitudes depend on the laser beam intensity. The effect of laser beam intensity on the resonance linewidths and amplitudes obtained from different energy transitions of atoms varies from resonance to resonance. The effect of laser beam intensity on resonance linewidths and amplitudes is of great importance for diode laser frequency stability applications. It needs to be determined by measuring. The effect of the laser beam intensity on the linewidths and amplitudes of sub-Doppler resonances were measured by laser heterodyne spectroscopy using the linearly polarized frequency stabilized extended cavity diode lasers. The measurements are compatible with the theory and the uncertainty of the measurements are fewer than 1.6 MHz and 0.3 mV for linewidths and amplitudes, respectively.

Narrow linewidth semiconductor laser with a multi-period-delayed feedback photonic circuit.

A multi-period-delayed feedback (MPDF) photonic circuit constructed by a Sagnac ring and two coupled rings was designed. By coupling a distributed feedback (DFB) laser diode (LD) with the MPDF, a narrow linewidth semiconductor laser was demonstrated. The linewidth of the DFB-LD with MPDF was narrowed to be around 2 kHz, which is reduced by three orders of magnitude, and the linewidth reduction capability could be maintained when the wavelength of the DFB-LD was tuned in a range wider than 3 nm. The laser frequency stability can also be improved using the proposed technique, and the frequency fluctuation was reduced for nearly 8 times in comparison with the DFB-LD.

Frequency-stabilized Faraday laser with 10−14 short-term instability for atomic clocks

In this Letter, stabilizing a Faraday laser frequency to the atomic transition is proposed and experimentally demonstrated, where the Faraday laser can work at single- or dual-frequency modes. High-resolution spectroscopy of a cesium atom induced by a Faraday laser is obtained. By stabilizing a Faraday laser with atomic spectroscopy, the frequency fluctuations of the Faraday laser are suppressed without the need of a high-cost Pound–Drever–Hall system. The fractional frequency Allan deviation of the residual error signal is 3 × 10−14/τ at the single-frequency mode. While at the dual-frequency mode, the linewidth of the beat-note spectra between the two modes of the Faraday laser after locking is narrowed to be 85 Hz, which is an order of magnitude better than the free-running linewidth. It can be used for microwave atomic clocks and may have the potential to be used in the application of optical microwave generation when the performance is further improved.