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An investigation into the dynamic response and frequency split behavior of a cylindrical fused silica resonator is performed via simulations and experiments. For this purpose, a structure for the cylindrical resonators with appropriate dimensions has been designed and fabricated. A laser Doppler vibrometer is utilized for the experimental quantification of the physical characteristics of the resonator. Natural frequencies of n = 2 modes, frequency split and quality factor have been extracted from the measured frequency sweep. Then the influence of mass change on the frequency split is investigated by chemical trimming. Time response predictions utilizing a ring model is employed to predict the resonant amplitudes as well as the influence of driving force and input angular velocity variations. The numerical predictions of the relationship between the mass mismatch and the frequency split are found to be consistent with the exper imental results. Predictions of frequency split of resonators via the simulation model are envisaged to greatly increase the efficacy of the chemical trimming process.

The luminescence properties of Ba13.35Al30.7Si5.3O70:Eu2+ and Ba13.35Al30.7Si5.3O70:Eu2+,Tm3+ phosphors are presented. After being excited by a light source, Ba13.35Al30.7Si5.3O70:Eu2+,Tm3+ phosphors emit intense yellow long persistent luminescence covering the region from 450 to 700 nm, which can last about 8 h. Thermoluminescence curves were demonstrated to analyze the trapping nature of persistent luminescence. Tm3+ is added to improve the long persistent luminescence properties of phosphors. The mechanism of persistent luminescence has been studied.

A cylindrical shell piezoelectric vibration gyroscope is a kind of Coriolis vibration gyroscope. Its core components are the cylindrical quartz resonator (CQR) and the piezoelectric ceramic electrodes (PCEs). In order to develop a high-precision Cylindrical shell piezoelectric vibration gyroscope, it is very important to reduce the influence of the PCEs and obtain a high-quality-factor CQR. To achieve this goal, a novel high-temperature sintering method is proposed to combine the CQR and the PCEs, and the corresponding sintered resonators are fabricated. After sintering, results of the acoustic excitation experiment and piezoelectric excitation experiment are tested, and the influence of the sintered PCEs on the CQR is determined. A complete gyroscope is obtained by vacuum packaging the sintered resonator. Through the open-loop and closed-loop tests, the performance parameters of gyroscope are obtained. The feasibility of the high-temperature sintering method is proved by experiments.

The fused silica cylindrical resonator is a type of axisymmetric resonator that can be used for Coriolis vibratory gyroscopes. Although the resonant frequency, frequency mismatch, and Q factor are natural properties of the resonator, they can change with temperature. Therefore, the temperature drift severely limits the detection accuracy and bias stability of the gyroscope. In this paper, the influence of temperature variation on the vibrational characteristics of fused silica cylindrical resonators was investigated. Experiments were performed on a fused silica cylindrical resonator coated with Cr/Au films. It was shown that at the temperature range from 253.15 K to 353.15 K, the resonant frequency linearly increased with temperature, the frequency mismatch remained unchanged, and the Q factor gradually increased till about 333.15 K, when it began to decrease. Meanwhile, the change of thermoelastic damping with temperature may dominate the variation of Q factor at the temperature range from 253.15 K to 353.15 K. This phenomenon was theoretically analyzed and the variation trends of results were consistent with the theoretical analysis. This study indicates that, for the fused silica cylindrical resonator, to discover the influence of temperature variation on the resonant frequency, frequency mismatch, and Q factor, there are certain rules to follow and repeat. The relationship between temperature and frequency can be established, which provides the feasibility of using self-calibration based on temperature characteristics of the resonator for temperature drift compensations. Additionally, there is an optimum temperature that may improve the performance of the Coriolis vibratory gyroscope with the fused silica cylindrical resonator.

The Coriolis Vibratory Gyroscopes are a type of sensors that measure angular velocities through the Coriolis effect. The resonator is the critical component of the CVGs, the vibrational characteristics of which, including the resonant frequency, frequency mismatch, Q factor, and Q factor asymmetry, have a great influence on the performance of CVG. The frequency mismatch and Q factor of the resonator, in particular, directly determine the precision and drift characteristics of the gyroscope. Although the frequency mismatch and Q factor are natural properties of the resonator, they can change with external conditions, such as temperature, pressure, and external forces. In this paper, the influence of electrostatic forces on the vibrational characteristics of the fused silica cylindrical resonator is investigated. Experiments were performed on a fused silica cylindrical resonator coated with Cr/Au films. It was shown that the resonant frequency, frequency mismatch, and the decay time slightly decreased with electrostatic forces, while the decay time split increased. Lower capacitive gaps and larger applied voltages resulted in lower frequency mismatch and lower decay time. This phenomenon was theoretically analyzed, and the variation trends of results were consistent with the theoretical analysis. This study indicates that, for fused silica cylindrical resonator with electrostatic transduction, the electrostatic influence on the Q factor and frequency, although small, should be considered when designing the capacitive gap and choosing bias voltages.

The preparation and development of novel optical thin films are of great importance to functional optical and opto-electric components requiring a low refractive index. In this study, a typical metal-organic framework (MOF), MIL-101(Cr), is selected as the research model. The corresponding MOF nanoparticles are prepared by a hydrothermal method and the optical thin films are successfully prepared by spin-coating. The optical properties of the corresponding MOF thin films are controlled by changing the type of functional groups on the benzene ring of the ligand (terephthalic acid) on MOFs. The functional groups are hydrogen atoms (H), electron donating groups (–NH2, –OH) and electron withdrawing groups (–NO2, –(NO2)2 or F4), respectively. It is found that the effective refractive index ( n eff) of MOF thin films decreases along with the increasing voids among MOF nanoparticles. In addition, the extinction coefficient ( k ) increases with the addition of electron donating groups, and decreases with the addition of electron withdrawing groups. Among the MOFs used in this study, the n eff of NO2-MIL-101(Cr) containing electron withdrawing groups is as low as ~1.2, and value of k is particularly low, which suggests its potential application in antireflective devices. In addition, the intrinsic refractive index ( n dense) of the dense MOF materials evaluated according to their porosity increases with the number of the functional groups, and the n dense of the two nitro-substituted MOFs is greater than that of the single nitro-substituted one, and the latter is bigger than that of hydroxyl-substituted one, which is close to that of amino-functionalized one. The diversity of ligands in MOFs makes them a promising new generation of optical materials.

Cylindrical resonators are commonly used in Coriolis vibratory gyroscopes (CVGs), which measure angular velocity through the precession of solid waves. Quality factor and its homogeneity are critical indicators of the resonator. In this paper, we present the observation and analysis of the Q factor variation behavior around the resonator’s axis of symmetry. We measured the resonator’s Q factor by the amplitude frequency response (AFR), with an acoustic source for excitation and a laser Doppler vibrometer (LDV) for detection. We then theoretically analyzed the Q variation behavior based on the two-dimensional mass-spring model. The experimental results were consistent with the theoretical calculation. By comparing experimental results with numerical calculations, we showed that the nature of this Q variation was due to the fact that when the excitation direction is misaligned with principle axes, for each detection point, the vibration is the superposition of two eigen-modes, and fitting with a one-dimensional oscillator would result in repetitive errors. This work is significant for understanding the mechanism of resonator’s Q factor variation behavior, as well as improving CVG’s performances.

The quality factor (Q factor) of resonators in Cylindrical Vibration Gyroscope (CVG) directly determines the drift characteristics and noise performance of the gyroscope. Annealing can reduce the residual stress and internal friction loss of materials effectively, thus increasing the Q factor significantly. In this paper, a kind of fused silica cylindrical shell resonator was presented. The design of the resonator, fabricating steps, and the annealing experiment were introduced. A laser Doppler vibrometer was utilized to measure the resonant frequency and the Q factor of resonators before and after annealing. We performed the annealing experiment on three resonators, the best results showed that after annealing, the Q factor increased by 498.3% (from 28955 to 173232, measured in 120Pa).

The resonator is the key element of the Coriolis Vibratory Gyroscope (CVG). The vibrational characteristics of the resonator, including the resonant frequency, vibrational amplitude, and Q factor, have a great influence on CVG’s performance. Among them, the vibrational amplitude mainly affects the scale factor and the signal-to-noise ratio, and the Q factor directly determines the precision and drift characteristics of the gyroscope. In this paper, a finite element model of a cylindrical shell resonator actuated by piezoelectric electrodes with different thicknesses is built to investigate the vibrational characteristics. The simulation results indicate that the resonant frequency barely changes with the electrode thickness, whereas the vibrational amplitude is inversely proportional to the electrode thickness under the same driving voltage. Experiments were performed with four resonators and piezoelectric electrodes of four sizes, and results were consistent with simulations. The resonant frequencies of four resonators changed within 0.36% after attaching the piezoelectric electrodes. Meanwhile, with the same driving voltage, it was shown that the vibrational amplitude decreased with the increase of electrode thickness. Moreover, thinner electrodes resulted in better Q factor and therefore better performance. This study may provide useful reference on electrode design of the CVGs.

The existence of mode deflection angle in the cylindrical resonator gyroscope (CRG) leads to the signal drift on the detecting nodes of the gyro vibration and significantly decreases the performance of the CRG. Measuring the mode deflection angle efficiently is the foundation of tuning for the imperfect cylindrical shell resonator. In this paper, an optical method based on the measuring gyroscopic resonator’s vibration amplitude with the laser Doppler vibrometer and an electrical method based on measuring the output voltage of the electrodes on the resonator are both presented to measure the mode deflection angle. Comparative experiments were implemented to verify the methodology and the results show that both of the two methods could recognize the mode deflection angle efficiently. The precision of the optical method relies on the number and position of testing points distributed on the resonator. The electrical method with simple circuit shows high accuracy of measuring in a less time compared to the optical method and its error source arises from the influence of circuit noise as well as the inconsistent distribution of the piezoelectric electrodes.

Fused silica cylindrical resonant gyroscope (CRG) is a novel high-precision solid-wave gyroscope, whose performance is primarily determined by the cylindrical resonator&rsquo, s frequency split and quality factor (Q factor). The laser Doppler vibrometer (LDV) is extensively used to measure the dynamic behavior of fused silica cylindrical resonators. An electrical method was proposed to characterize the dynamic behavior of the cylindrical resonator to enhance the measurement efficiency and decrease the equipment cost. With the data acquisition system and the designed signal analysis program based on LabVIEW software, the dynamic behavior of the fused silica cylindrical resonator can be analyzed automatically and quickly. We compared all the electrical measurement results with the optical detection by LDV, demonstrating that the fast Fourier transform (FFT) result of the resonant frequency measured by the electrical method was 0.12 Hz higher than that with the optical method. Thus, the frequency split measured by the electrical and optical methods was the same in 0.18 Hz, and the measurement of the Q factor was basically the same in 730,000. We conducted all measurements under the same operation condition, and the optical method was used as a reference, demonstrating that the electrical method could characterize the dynamic behavior of the fused silica cylindrical resonator and enhance the measurement efficiency.

The hemispherical resonator gyroscope (HRG) has attracted the interest of the world inertial navigation community because of its exceptional performance, ultra-high reliability and its potential to be miniaturized. These devices achieve their best performance when the differences in the frequencies of the two degenerate working modes are eliminated. Mechanical treatment, laser ablation, ion-beams etching, etc., have all been applied for the frequency tuning of resonators, however, they either require costly equipment and procedures, or alter the quality factors of the resonators significantly. In this paper, we experimentally investigated for the first time the use of a chemical etching procedure to decrease the frequency splits of hemispherical resonators. We provide a theoretical analysis of the chemical etching procedure, as well as the relation between frequency splits and mass errors. Then we demonstrate that the frequency split could be decreased to below 0.05 Hz by the proposed chemical etching procedure. Results also showed that the chemical etching method caused no damage to the quality factors. Compared with other tuning methods, the chemical etching method is convenient to implement, requiring less time and labor input. It can be regarded as an effective trimming method for obtaining medium accuracy hemispherical resonator gyroscopes.

Cylindrical resonators are commonly used in Coriolis vibratory gyroscopes, which measure angular velocity through the precession of solid wave. Quality factor and its homogeneity are critical indicators of the resonator characteristics. In this paper, we report that the Q factor varies regularly around the resonator's axis of symmetry. We measured the resonator Q factor by the amplitude frequency response (AFR) using a non-contact method with an acoustic source for excitation and a laser Doppler vibrometer (LDV) for detection. By analyzing experimental results, we concluded that measuring Q factor at antinode can be a convenient and relatively accurate method for Q factor studies. However, one needs to be careful that the measurement point should be near the vibration antinode, otherwise the results may contain huge errors. We then built a theoretical model based on the two degree-of-freedom mass-spring system to analyze the Q variation behavior. The experimental results were consistent with the theoretical calculation. By comparing experimental results with numerical calculations, we showed that the circumferentially Q variation is due to the complex combined effect of frequency mismatch, Q factor mismatch, and the angle between excitation direction and the principle frequency axes (Qk) and the principle damping axes (Qc). We believed it is possible to combine the scan measurement of LDV with proposed model to determine the Q mismatch and direction of the damping axes without labor-consuming procedures, and therefore the proposed method can be developed for pre-screening of resonators for high-performance cylindrical resonator gyroscopes.

The cylindrical resonator gyroscope (CRG) is a typical Coriolis vibratory gyroscope whose performance is determined by the Q factor and frequency mismatch of the cylindrical resonator. Enhancing the Q factor is crucial for improving the rate sensitivity and noise performance of the CRG. In this paper, for the first time, a monolithic cylindrical fused silica resonator with a Q factor approaching 8 × 105 (ring-down time over 1 min) is reported. The resonator is made of fused silica with low internal friction and high isotropy, with a diameter of 25 mm and a center frequency of 3974.35 Hz. The structure of the resonator is first briefly introduced, and then the experimental non-contact characterization method is presented. In addition, the post-fabrication experimental procedure of Q factor improvement, including chemical and thermal treatment, is demonstrated. The Q factor improvement by both treatments is compared and the primary loss mechanism is analyzed. To the best of our knowledge, the work presented in this paper represents the highest reported Q factor for a cylindrical resonator. The proposed monolithic cylindrical fused silica resonator may enable high performance inertial sensing with standard manufacturing process and simple post-fabrication treatment.

The optimization of buffer gas pressure is very important to improve the performance of the rubidium (Rb) atomic magnetometer. In this paper we briefly introduce the basic principle and the experimental method of the rubidium magnetometer based on Faraday rotation effect, and describe the factors affecting the magnetometer sensitivity, then analyze and summarize the mechanism of the influence of spin-exchange, spin-destruction collisions, radiation trapping and the spin diffusion on spin relaxation of Rb atoms. Based on this, the relationship between the rubidium magnetometer sensitivity, the spin relaxation rate and the gas chamber conditions (buffer gas pressure, the bubble radius, measuring temperature) is established. Doing calculations by the simulation software, how the magnetometer sensitivity and the relaxation rate vary with the gas chamber conditions can be seen; finally, the optimal values of the buffer gas pressure under certain gas chamber conditions are obtained. The work is significant for the engineering development of rubidium magnetometer.

A finite element model of the hemispherical resonator gyro (HRG) is established and the natural frequencies and vibration modes are investigated. The matrix perturbation technology in the random finite element method is first introduced to analyze the statistical characteristics of the natural frequencies of HRG. The influences of random material parameters and dimensional parameters on the natural frequencies are quantitatively described based on the probability theory. The statistics expressions of the random parameters are given and the influences of three key parameters on natural frequency are pointed out. These results are important for design and improvement of high accuracy HRG.

We propose and analyze a superluminal ring laser gyroscope (RLG) using multilayer optical coatings with huge group delay (GD). This GD assisted superluminal RLG can measure the absolute rotation with a giant sensitivity-enhancement factor of ~103; while, the broadband FWHM of the enhancement factor can reach 20 MHz. This superluminal RLG is based on a traditional RLG with minimal re-engineering and beneficial for miniaturization according to theoretical calculation. The idea of using GD coatings as a fast-light medium will shed lights on the design and application of fast-light sensors.

Scatter property of folded-mirror coating in V-shaped cavity is studied with Kirchhoff diffraction theory. The interference effect of scatter lights can be used to explain the ripple effect existing in optical-feedback cavity ring-down spectroscopy.

A novel strategy of choosing ellipsometric data is presented for more accurate optical characterization of thin film materials based on partial derivatives analysis and selection.

High performance electro-optic modulator is achieved employing a thin multiferroic BiFeO3 film on thick Au. This arises from the strong absorption resonance in BiFeO3 and its electric tunable huge birefringence ( delta n =0.15-0.31).

We report a novel method of measuring the spin polarization of alkali-metal atoms by detecting the NMR frequency shifts of noble gases. We calculated the profile of 87Rb D1 line absorption cross sections. We then measured the absorption profile of the sample cell, from which we calculated the 87Rb number densities at different temperatures. Then we measured the frequency shifts resulted from the spin polarization of the 87Rb atoms and calculated its polarization degrees at different temperatures. The behavior of frequency shifts versus temperature in experiment was consistent with theoretical calculation, which may be used as compensative signal for the NMRG closed-loop control system.

A helium–neon ring laser cavity is modified by employing variable coupled passive cavities to introduce anomalous dispersion. An equivalent model for the coupled cavities is proposed, and new equations are performed. Theoretical analysis of the parameters is presented in detail, and a novel iterative method is proposed. Gyros using this ring laser are shown in different sensitivity enhancements with limited broadened passive cavity line-width, and the minimal measurable rotation rate is analyzed. The related quantum noise limited line-width is found to be broadened with limitations, which mainly depend on the round trip loss. Fluctuations are induced to analyze parameter influences on enhancements, and a novel modification method concerning mirror reflectivity is proposed for experimental setups. Finally several practical considerations are generally discussed, and some suggestions are proposed for realization. This fast light induced enhancement can be important for present gyros based on a He–Ne ring laser.