Frequency Stabilization Method Research Articles

A Method of Laser Frequency Stabilization Based on the Effect of Linear Dichroism in Alkali Metal Vapors in a Modulated Transverse Magnetic Field

We present a method of laser frequency stabilization based on the linear dichroism signal in a transverse magnetic field. This method is similar to the DAVLL (Dichroic Atomic Vapor Laser Lock) method. It differs from DAVLL and from its existing modifications primarily by the fact that it uses signals of linearly polarized light caused by alignment, rather than circular refraction caused by orientation, and therefore allows us to obtain error signals at the magnetic field modulation frequency (or its second harmonic) by extremely simple means. The method allows the laser frequency to be stabilized in the vicinity of the low-frequency transition in the D1 line of Cs; it does not require strong magnetic fields or careful shielding of cells containing cesium atoms. Although the absorption line in a gas-filled cell is typically gigahertz wide, the achievable resolution, limited by the signal-to-noise ratio of photon shot noise, can reach units or tens of kilohertz in a one hertz bandwidth.

Robust LFC design using adaptive neuro‐fuzzy inference‐aided optimal fractional‐order PIDA control for perturbed power systems with solar and wind power sources

AbstractMaintaining stability in modern power systems is challenging due to complex structures, rising power demand, and load disturbances. The integration of renewable energy sources further threatens stability by causing imbalances between generation and demand. Conventional load frequency stabilization methods fall short in such scenarios. This paper proposes an optimal fractional‐order proportional‐integral‐derivative‐acceleration (FOPIDA) controller, enhanced by a robust adaptive neuro‐fuzzy inference system (ANFIS), to improve load frequency control and reliability in power systems with wind and solar generators. First, the dynamical model of a multi‐area interconnected power system, including a thermal power plant, wind turbine, and solar photovoltaic generators, is developed. A decentralized ANFIS‐FOPIDA controller is then designed for load frequency control objectives. The gains of this controller are optimized using the whale optimization algorithm (WOA), focusing on frequency deviation and tie‐line power exchange. Simulations on a New England IEEE 10‐generator 39‐bus power system demonstrate the approach's effectiveness under various disturbances, including random load‐generation disturbances and nonlinear generation behaviors. Comparisons with other strategies, such as fractional order (FO) beetle swarm optimization algorithm (FOBSOA)‐FOPIDA, WOA‐PIDA, and WOA‐ANFIS‐PIDA, and recent control approaches highlight the superior performance of the WOA‐ANFIS‐FOPIDA method in enhancing power system stability.

Laser Frequency Stabilization Method Based on Intelligent Identifying Absorption Peaks with Convolutional Neural Network

Laser Frequency Stabilization Method Based on Intelligent Identifying Absorption Peaks with Convolutional Neural Network

Frequency stabilization method of optical phase-locked loop He-Ne laser based on acousto-optic modulator

Frequency stabilization method of optical phase-locked loop He-Ne laser based on acousto-optic modulator

Single-Element Dual-Interferometer for Precision Inertial Sensing: Sub-Picometer Structural Stability and Performance as a Reference for Laser Frequency Stabilization.

Future GRACE-like geodesy missions could benefit from adopting accelerometer technology akin to that of the LISA Pathfinder, which employed laser interferometric readout at the sub-picometer level in addition to the conventional capacitive sensing, which is at best at the level of 100 pm. Improving accelerometer performance holds great potential to enhance the scientific output of forthcoming missions, carrying invaluable implications for research in climate, water resource management, and disaster risk reduction. To reach sub-picometer displacement sensing precision in the millihertz range, laser interferometers rely on suppression of laser-frequency noise by several orders of magnitude. Many optical frequency stabilization methods are available with varying levels of complexity, size, and performance. In this paper, we describe the performance of a Mach-Zehnder interferometer based on a compact monolithic optic. The setup consists of a commercial fiber injector, a custom-designed pentaprism used to split and recombine the laser beam, and two photoreceivers placed at the complementary output ports of the interferometer. The structural stability of the prism is transferred to the laser frequency via amplification, integration, and feedback of the balanced-detection signal, achieving a fractional frequency instability better than 6 parts in 1013, corresponding to an interferometer pathlength stability better than 1pm/Hz. The prism was designed to host a second interferometer to interrogate the position of a test mass. This optical scheme has been dubbed "single-element dual-interferometer" or SEDI.

Optimized cascaded controller for frequency stabilization of marine microgrid system

The trend towards reducing greenhouse gas emissions by dipping the use of traditional sources of energy in marine power grids, as well as the rapid expansion of renewable energy sources (RESs), were the driving forces behind the incorporation of RESs in maritime microgrid systems and enquiry of the ensuing prevalent control mechanism. The frequency stability of a Marine Microgrid System (MMGS) is a critical aspect that directly affects its reliable and efficient operation. This study describes a method for frequency stabilization in independent maritime microgrids consists of diverse renewable energy resources including wind turbine generators, sea wave energy/tidal power generation, solar generation, bio-diesel generator and energy storage systems. This paper aims to develop a new optimal cascaded order proportional integral based proportional derivative for marine load frequency control. Due to the fact that the performance of the controller is highly dependent on the parameters of the controller, optimizing these coefficients can have a significant impact on the output performance of the LFC control. In light of this, this paper presents the sewing training-based optimization (STBO), a new human-based metaheuristic algorithm to optimize the coefficient of the suggested controller. The essential stimulation of STBO is the teaching procedure of sewing to beginner tailors. By utilizing a population of candidate solutions, the algorithm iteratively refines the control parameters to find the optimal set that minimizes frequency deviations and enhances system stability. The responses of the cascaded PI-PD controller are linked to those of the PID and PI controllers in order to demonstrate its superiority. To evaluate the efficiency of STBO, it is compared to well-established recent techniques such as fitness dependent optimization, grey wolf optimization and Jellyfish search optimization. From the results, it is observed that our proposed approach improved the settling time by 25.35%, 45.89%, and 29.35%, reduced peak overshoot by 78.34%, 67.71%, and 78.23%, and similarly reduced undershoot by 81.56%, 56.22% and 76.56% as compared to FDO, GWO and JSO techniques respectively. Finally, the sensitivity analysis is performed under ±50% load variation and ± 40% power system parameters to prove the robustness of the proposed controller.

Laser frequency stabilization in the 10 -14 range via optimized modulation transfer spectroscopy on the 87Rb D2 line.

We present a high-performance laser frequency stabilization method using modulation transfer spectroscopy (MTS) on the rubidium 87D2 transition line. A substantial improvement of the laser frequency stability was achieved by searching for the optimal diameter and intensity settings of the probe and pump beam. The frequency instability measured from the beat frequency of two locked external cavity diode lasers (ECDLs) reached a short-term stability of 4.5×10-14/τ and did not exceed 2 × 10-12 until 105 s, which is the best performance reported thus far with a D2 transition. The long-term stability is limited by the offset fluctuations of the baseline induced by the residual amplitude modulation (RAM), which can be further improved by reducing the current temperature variation of about 0.2 K by means of temperature stabilization or through a further reduction of the RAM.

Novel Frequency-Based Approach to Analyze the Stability of Polynomial Fractional Differential Equations

This paper proposes a novel approach for analyzing the stability of polynomial fractional-order systems using the frequency-distributed fractional integrator model. There are two types of frequency and temporal stabilization methods for fractional-order systems that global and semi-global stability conditions attain using the sum-of-squares (SOS) method. Substantiation conditions of global and asymptotical stability are complicated for fractional polynomial systems. According to recent studies on nonlinear fractional-order systems, this paper concentrates on polynomial fractional-order systems with any degree of nonlinearity. Global stability conditions are obtained for polynomial fractional-order systems (PFD) via the sum-of-squares approach and the frequency technique employed. This method can be effective in nonlinear systems where the linear matrix inequality (LMI) approach is incapable of response. This paper proposes to solve non-convex SOS-designed equations and design framework key ideas to avoid conservative problems. A Lyapunov polynomial function is determined to address the problem of PFD stabilization conditions and stability established using sufficiently expressed conditions. The main goal of this article is to present an analytical method based on the optimization method for fractional order models in the form of frequency response. This method can convert it into an optimization problem, and by changing the solution of the optimization problem, the stability of the fractional-order system can be improved.

Adaptive PDH Frequency Stabilization Method with Large Linear Dynamic Range Based on Two Modulation Depths

Adaptive PDH Frequency Stabilization Method with Large Linear Dynamic Range Based on Two Modulation Depths

Laser frequency locking method for Rydberg atomic sensing

Based on the Rydberg cascade electromagnetically induced transparency, we propose a simultaneous dual-wavelength locking method for Rydberg atomic sensing at room temperature. The simplified frequency-locking configuration uses only one signal generator and one electro-optic modulator, realizing real-time feedback for both lasers. We studied the effect of the different probe and coupling laser powers on the error signal. In addition, the Allan variance and a 10 kHz amplitude-modulated signal are introduced to evaluate the performance of the laser frequency stabilization. In principle, the laser frequency stabilization method presented here can be extended to any cascade Rydberg atomic system.

Prerequisites and Theoretical Foundations of the Statistical Method of Frequency Stabilization in Information and Telecommunication Systems

The article deals with issues related to the manifestation of the properties of synergy and emergence, potentially inherent in systems with the same or similar properties of components. These properties can be used to increase the accuracy of estimates of the frequency of signals in the system of simultaneously and independently functioning oscillators. It makes possible to increase the stability of the frequency of the generated signals. To implement these properties, simultaneous measurement of signal phase values at a number of time intervals with subsequent processing using the likelihood function can be used. It is shown that the manifestation of the synergistic property in a system of simultaneously and independently operating oscillators reduces the error in estimating random fluctuations in the frequency of oscillators. The manifestation of the emergence property allows you to exclude a constant frequency shift from the nominal value. The conditions for obtaining unbiased effective estimates of the frequency of each of the oscillators are formulated. It is noted that from a physical point of view, an increase in the accuracy of estimating the frequency of signals corresponds to multiple non-precision indirect measurements. The results of mathematical modeling are presented.

Study of the Steady-State Operation of a Dual-Longitudinal-Mode and Self-Biasing Laser Gyroscope.

In order to stabilize the self-biasing state of a laser gyroscope, a dual-longitudinal-mode asymmetric frequency stabilization technique was studied. The special frequency stabilization is based on the accurate control of the intensity tuning curve in the prism ring laser. In this study, the effects of the ratio of the Ne isotopes, the inflation pressure, and the frequencies coupling on the intensity tuning curve in a laser gyro were examined. The profiles of the intensity tuning curve were simulated under the mixing ratios of Ne20 and Ne22 of 1:1 and 7:3, and the inflation pressures were 350 Pa, 400 Pa, and 450 Pa. The mixing ratio of Ne20 and Ne27 was dealt with similarly. The method for precisely adjusting the profiles of the intensity tuning curve was analyzed. The profiles were verified by experiments under different isotope ratios and pressures. Finally, based on a prism ring laser with an optical length of 0.47 m, the proposed frequency stabilization method was preliminarily verified.

Enhanced frequency noise suppression for LISA by combining cavity and arm locking control systems

This paper presents a novel method for laser frequency stabilization in the Laser Interferometer Space Antenna (LISA) mission by locking a laser to two stable length references-the arms of the interferometer and an on-board optical cavity. The two references are digitally fused using carefully designed control systems, attempting minimal or no changes to the baseline LISA mission hardware. The interferometer arm(s) provides the most stable reference available in the LISA science band (0.1 mHz--1 Hz), while the cavity sensor's wideband and linear readout enables additional control system gain below and above the LISA band. The main technical issue with this dual sensor approach is the undesirable slow laser frequency pulling which couples into the control system with the imperfect knowledge of the Doppler shift of the light due to relative spacecraft motion along the LISA arm. This paper outlines requirements on the Doppler shift knowledge to maintain the cavity well within the resonance when activating the fused control system. Two Doppler shift estimation methods are presented that use the already on-board measurements, the inter-spacecraft interferometer link (the main science measurement), and the absolute inter-spacecraft laser ranging system. Both methods reach the required precision after a few thousand seconds of measurement integration. The paper demonstrates an approach to initialize and engage the proposed laser stabilization system, starting from free-running laser and ending with the dual sensor frequency control system. The results show that the technique lowers the residual laser frequency noise in the LISA science band by over 3 orders of magnitude: from $30\text{ }\text{ }\mathrm{Hz}/\sqrt{\mathrm{Hz}}$ to as low as $7\text{ }\text{ }\mathrm{mHz}/\sqrt{\mathrm{Hz}}$, potentially allowing the requirements on Time Delay Interferometry (TDI) to be relaxed---possibly to the point where first-generation TDI may be sufficient.

Secondary frequency regulation and stabilization method of islanded droop inverters based on integral leading compensator

The microgrid multi-parallel inverters system with droop control strategy will produce microgrid frequency static error due to the reference power mismatch. In order to eliminate the frequency static error caused by droop control as well as enhance the stability of multi droop inverters system, a secondary frequency regulation and stabilization method for multi-parallel droop inverters system based on island operation of the frequency static error integral lead compensator is proposed. The proposed method includes no communication link among inverters. Through the state space modeling of the multi-parallel drooping inverter microgrid system based on the component connection method (CCM), the state space model of multi parallel inverters is established. Parameter design and analysis are carried out accordingly. The state space model of the load is also established with transfer function-state space mapping method as a comparison. The method proposed in this paper can effectively enhance the small signal stability of the system while realizing the frequency error-free operation of multiple parallel droop inverters. To verify the method proposed in this paper, MATLAB/Simulink simulation is conducted to compare the proposed method with the method based on communication consensus algorithm and proves the effectiveness of the proposed method and at the same time.

Large-tuning-range frequency stabilization of an ultraviolet laser by an open-loop piezoelectric ceramic controlled Fabry-Pérot cavity.

We demonstrate a laser frequency stabilization method with large tuning range to stabilize a UV laser by installing piezoelectric ceramic actuators into a Fabry-Pérot cavity with an ultra-low expansion spacer. To suppress piezoelectric drift, a two-layer symmetrical structure is adopted for the piezoelectric actuator, and a 14.7 GHz tuning range is achieved. The short-term drift of the piezoelectric ceramics caused by temperature and creep is eliminated, and the long-term drift is 0.268 MHz/h when the Fabry-Pérot cavity is sealed in a chamber without a vacuum environment. The long-term frequency drift is mainly caused by stress release and is eliminated by compensating the cavity voltage with an open loop. Without the need for an external reference or a vacuum environment, the laser frequency stabilization system is greatly simplified, and it can be extended to wavelengths ranging from ultraviolet to infrared. Owing to its simplicity, stability, and large tuning range, it is applicable in cold atom and trapped ion experiments.

Design of combine load frequency and voltage control of power system using optimisation algorithm

Engineers' main concern is the stability of nominal frequency and voltage levels in an electric power system. If these two characteristics deteriorate, the performance and life expectancy of the power system's related equipment would suffer. Because of this, control devices must be set up and installed specifically for a given working environment in order to maintain the frequency and terminal voltage magnitude within acceptable ranges. An effort has been made to develop a fractional-order PID (FOPID) controller for combined frequency and voltage control issues, since the system performance may be enhanced by choosing an appropriate controller. Utilizing moth flame optimization method, this study examines the plan and execution of the FOPID controller for simultaneous load frequency and voltage management of the power system. An AVR-based excitation voltage control system is used in the first portion of the study to illustrate the suggested method for frequency stabilization of isolated power systems. Comparison of dynamic responsiveness of the system with PID controllers improved by other intelligent methods reveals the superiority and efficacy of the suggested methodology. Also included in this project are multi-unit two-area power systems. The algorithm's capacity to be tuned is examined in great detail and compared to other algorithms.

Comparison of two low-noise CEO frequency stabilization methods for an all-PM Yb:fiber NALM oscillator

We present a comparison of two low-noise carrier-envelope offset (CEO) frequency stabilization methods studied using an ytterbium (Yb) fiber laser oscillator based on a nonlinear amplifying loop mirror. We first investigate the phase locking performance achieved with cross-gain modulation (XGM) via injection of an auxiliary low-power continuous-wave (CW) laser into the fiber gain medium. Amplification of the injected CW laser light cross-modulates the gain of the oscillator, resulting in an intra-cavity power modulation, thus providing control of the CEO frequency. The XGM method is then compared with the conventional pump-current modulation scheme. Both stabilization methods provide similar locking performances with sub-200-mrad of integrated residual carrier-envelope-phase (CEP) noise (10 Hz to 1 MHz), suitable for high-resolution comb spectroscopy applications.

Spectral filtering of dual lasers with a high-finesse length-tunable cavity for rubidium atom Rydberg excitation* *Project supported by National Key Research and Development Program of China (Grant No. 2016YFA0302800), the National Natural Science Foundation of China (Grant Nos. U20A2074 and 12074391), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 21010100), the Youth Innovation Promotion Association

We propose and demonstrate an alternative method for spectral filtering and frequency stabilization of both 780-nm and 960-nm lasers using a high-finesse length-tunable cavity (HFLTC). Firstly, the length of HFLTC is stabilized to a commercial frequency reference. Then, the two lasers are locked to this HFLTC using the Pound–Drever–Hall (PDH) method which can narrow the linewidths and stabilize the frequencies of both lasers simultaneously. Finally, the transmitted lasers of HFLTC with each power up to about 100 μW, which act as seed lasers, are amplified using the injection locking method for single-atom Rydberg excitation. The linewidths of obtained lasers are narrowed to be less than 1 kHz, meanwhile the obtained lasers’ phase noise around 750 kHz are suppressed about 30 dB. With the spectrally filtered lasers, we demonstrate a Rabi oscillation between the ground state and Rydberg state of single-atoms in an optical trap tweezer with a decay time of (67 ± 37) μs, which is almost not affected by laser phase noise. We found that the maximum short-term laser frequency fluctuation of a single excitation lasers is at ∼3.3 kHz and the maximum long-term laser frequency drift of a single laser is ∼46 kHz during one month. Our work develops a stable and repeatable method to provide multiple laser sources of ultra-low phase noise, narrow linewidth, and excellent frequency stability, which is essential for high precision atomic experiments, such as neutral atom quantum computing, quantum simulation, quantum metrology, and so on.

Метод оценивания частотно-временных параметров сигналов в системе одновременно и независимо функционирующих генераторов.

The issues of assessing the current frequency of each of the total of simultaneously and independently functioning generators within the electronic system are considered. The most common case is considered, in which the deviation of the true values of the nominal parameters of generators from the estimated values of these parameters has an unknown distribution law, and random deviations of frequency from the true nominal value are subject to the normal distribution law with the corresponding variance. The proposed method of obtaining parameters estimates of both independently functioning generators (true nominal frequency values and long-term instability, accidental deviation of frequency caused by short-term instability of the generator) is based on the measurement of the signals phases of each of the generators during several measuring intervals. The first step in obtaining estimates is to line the relationship between deviations of generator parameters from nominal values and the random deviation of the generator frequency by deviation of the measured phase value from the intended nominal value. This allows the formation of a system of linear algebraic equations relative to unknown values of frequency par deviations and relative instability, random deviation of frequency. Minimally necessary number of measuring intervals estimated in the materials of the article. The method proposed in the article is a further generalization of the previously proposed method of statistical frequency stabilization of the system of simultaneously and independently functioning generators, in which, based on finding the extremum of the multidimensional likelihood function, formed under the assumption of a normal distribution law for each of the arguments, the current duration of the measurement time interval, the nominal frequency and the relative instability of each of the generators. The suggested generalization is as follows: formation of an overdetermined system of equations, the unknowns in which are the deviation of the duration of the measurement time interval from the nominal value, the deviation of the values​​of the nominal frequencies of each of the generators from the corresponding assumed values, the deviation of the values ​​of the relative instabilities of each of the generators from the corresponding assumed values; formation of a system of normal equations, based on the results of the solution of which, a joint assessment of the duration of each of the measurement time intervals, frequency deviations and relative instabilities of each of the generators from the corresponding assumed values ​​is carried out; measurements of the signal phases of each of the generators at each time interval of the measurement. The proposed generalization allows us to abandon the following assumptions: exactly known values ​​of the nominal frequency and relative instability of each of the generators; about the known distribution law of the deviation of the values​​of the specified parameters from the assumed values. At the same time, the use of the proposed method leads to the need to measure the phases of the signals of each of the generators not in one, but in several measurement intervals. On the basis of numerical modeling, an increase in the accuracy of estimating the duration of time intervals of measurements and, accordingly, the frequency of generators is analyzed. It is shown that the refinement of the values ​​of the relative frequency instability of each of the generators does not lead to a practically significant increase in the accuracy of estimates of the current values ​​of the generator frequency. A transition to a simplified likelihood function is proposed, in which only the duration of the measurement time interval and the nominal frequency of each of the generators are estimated.

Increasing frequency stability of HF signals in the transmitting device of the localiser based on statistical estimation of phases

The article based on the method of statistical frequency stabilization deals with the issues of increasing frequency stability and synchronization of the forming HF signals in a transmitting device of a localizer using a multichannel variant of construction. It was demonstrated that the available digital unit of frequency and phase correction allows easy application of the proposed method. Two main features of the localizer operation affecting frequency stability and phase synchronization of HF signals are noted. The first factor is determined by deviation of the present -HF signal frequency (on the measurement interval) from the average (i) frequency value in n-channel. The second one is related to average frequency variation of each of the forming HF signals and its deviation within the (i) value from the nominal value during localizer operation. On the basis of HF signals description in channels of the transmitting device of a localizer ratios are obtained determining optimal values in terms of the method of least square method as (i) deviations of the present frequency values from the average value as well as variations of average frequency values during localizer operation. The article considers the most significant, from an applicatory point of view, case of assessment covering only deviations of the present HF signals frequency values from the average value on the measurement interval. It is shown that application of the method of statistical frequency stabilization allows the transmitting device of a localizer including N channels of HF signals formation to increase frequency stability and HF signals phase synchronization times. That enables to improve accuracy of forming integrated and difference directivity diagrams and setting heading in the runway direction as well. Apart from that, on the basis of the received values of frequency parameters estimation and relative instability of the forming HF signals a decision can be made about the condition of the controlled parameter by the criterion STANDARD-DETERIORATION-ACCIDENT.