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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.

Surface roughness is really important to the ultra-low loss of multilayer optical coatings. Reflectance and transmittance model for multilayer optical coatings with surface roughness has been established at normal incidence by A. V. Tikhonravov et al. in 2003. However, under the condition of oblique incidence, no further model which is based on the model of Tikhonravov has ever been reported. In this paper, an approximate reflectance and transmittance model is established for the thin film system with roughness at oblique incidence by analogy and usage of the concept of equivalent refractive index. The small-scale roughness model's effectiveness has been theoretically demonstrated according to the effective medium theory. However, the large-scale roughness model's effectiveness needs other methods to be proved, as the scattering effect of different scale roughness is different. This model might play a significant role to research the scattering loss of oblique incident thin film systems, such as mirrors in ring lasers, deep ultraviolet lasers and interferometers with ultra long cavity length.

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.

We derive 1st and 2nd order approximation characteristic matrix of slightly inhomogeneous optical coating at oblique incidence, and test its effectiveness, accuracy and speed by comparison with published results.

We present a novel determination method of thin film optical parameters based on partial derivatives selection, which is with least impact of photometric measurement systematic errors on the characterization accuracy of thin film optical parameters. The spectral measurement data used in our numerical simulations are the single wavelength photometric data of P-polarization light measured at different incident angles. It is shown that, under the same level of systematic errors in the measurement data, the deviations of the fitted optical parameters values from real ones in spectral bands with opposite signs of partial derivatives for most incident angles at which measurement data are collected are much smaller than other spectral regions. The theoretical explanations are discussed. It is advisable to select spectrophotometric data from the recommended spectral bands and to remove the dangerous spectral bands according to derivatives information for optical characterization of thin films with best accuracy.

An ultra-high precision thin-film polarizing beam splitter (PBS) has been designed and fabricated. Using Needle optimization technology, we design the thin-film polarizing beam splitter that is transparent for P polarization and reflective for S polarization with ultra-high precision at 64.8° angle of incidence and 632.8 ± 10 nm wavelength band. The experiments with the fabricated thin-film PBS demonstrate that both the reflectance of P polarization and transmittance of S polarization at 64.8° angle of incidence and 632.8 nm wavelength point are less than 0.02%, which is ultra-high for reported PBSs.

To improve the current status of home multilayer optical coating design with low speed and poor efficiency when a large layer number occurs, the accurate calculation and fast realization of merit function’s gradient and Hesse matrix is pointed out. Based on the matrix method to calculate the spectral properties of multilayer optical coating, an analytic model is established theoretically. And the corresponding accurate and fast computation is successfully achieved by programming with Matlab. Theoretical and simulated results indicate that this model is mathematically strict and accurate, and its maximal precision can reach floating-point operations in the computer, with short time and fast speed. Thus it is very suitable to improve the optimal search speed and efficiency of local optimization methods based on the derivatives of merit function. It has outstanding performance in multilayer optical coating design with a large layer number.

Light scattering is an important and classical method for optical surface testing. Typical scheme of light scattering measurement often uses a single laser beam incidence, and then evaluates the surface quality via detecting and analyzing the scattering signal. In this work, a developed method for optical surface testing is proposed and demonstrated, and whose measuring principle is based on the scattering interference effect. In this approach, a single longitudinal mode laser beam is divided into two beams, when these beams irradiate the optical surface, their respective scattering fields would interfere with each other. If the phase between these incidence lights is scanned periodically, their scattering light interference signal would fluctuate simultaneously. Through analyzing this kind of scattering signal, our method can not only determine the scattering loss of optical surface, but also scale its inhomogeneity performance. A simply set of experimental apparatus is built up and used to demonstrated this method, which uses a single mode laser as the light source. Furthermore, to modulate the phase difference between two incidence beams, a piezoelectric ceramic is used. Some typical cases are then experimented and discussed, the results show that this method can be used to calibrate the quality of optical surface.

So-called spectral ripple a special phenomenon only existing in fold-type cavity ring-down spectrometer, and it is believed as deriving from the interference effect of different lights on the folded mirror. To investigate the influence of this phenomenon, on fold-type cavity ring-down measurement, some representative instances of laser linewidth are simulated and analyzed, and some experiments are carried on. It is found that the increasing of laser linewidth can make the amplitude of the spectral ripple decrease, more importantly, which can make the ring-down signal no longer decay as a single exponential but as the double exponential function.

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 present a novel fast robust design method of multilayer optical coatings. The sensitivity of optical films to production errors is controlled in the whole optimization design procedure. We derive an analytical calculation model for fast robust design of multilayer optical coatings. We demonstrate its effectiveness by successful application of the robust design method to a neutral beam splitter. It is showed that the novel robust design method owns an inherent fast computation characteristic and the designed film is insensitive to the monitoring thickness errors in deposition process. This method is especially of practical significance to improve the mass production yields and repetitive production of high-quality optical coatings.

A spectral ripple effect observed in fold-type continuous-wave cavity ring down spectroscopy is described and studied. Its period was measured as ∼0.02 cm−1 in a 49.1 cm long V-shaped glass ceramics cavity. To find its origin, various losses of high-reflectivity coating and their relations to the optical field in the V-shaped cavity, especially the optical field inside the folding mirror coating, have been discussed and analyzed according to the interference theory and the matrix calculation method. It is found that the ripple mainly comes from an interference effect at the folding mirror coating between the direct and the inverse light waves. The interference effect results in the periodic fluctuations of the scattering and absorption loss of the high-reflectivity coating, so it can be used to measure some special losses of the high-reflectivity coating and separate them from the total loss of the coating.