Quantitative Analysis Of The Acceleration Sensitivity Of Optical Cavities

Ultra-stable narrow-line laser has been widely used in a variety of research fields such as high-resolution laser spectroscopy, optical atomic clock, cold-atom experimental systems, and gravitational wave detection.The Pound-Drever-Hall frequency locking method is one of the important ways to achieve ultra-stable narrow-line lasers. In this method the stability of the laser frequency is primarily determined by the length stability of optical resonator that is used as the frequency reference. However, the vibration can deform the optical resonator, introducing unwanted frequency noise. Apart from vibration isolation, an alternative and new approach has been adopted in recent years to lower the impact of the vibration to the laser frequency stability. By appropriate design of the geometry and supporting structure, the vibration sensitivity of the cavity itself can be reduced. The finite element analysis (FEA) is used in this approach to perform the numerical simulations that have greatly saved the design time and reduced the experimental cost, playing an important role in improving the length stability of the optical cavity.Although the numerical simulation using finite element analysis has been widely adopted in the design and optimization of optical cavities, the entire procedure needs a systematical and comprehensive description as well as in-depth investigations on specific ways of modeling, reliability examination, and experimental verification. For instance, in order to obtain the acceleration sensitivity of the cavity, the quantitative relationship between the cavity deformation and the resultant length change has to be derived. To determine the acceleration sensitivity of the cavity, the finite element analysis is then used to obtain the cavity deformation. In this second process there exists another issue that requires a close scrutiny. In the finite element analysis, the cavity support is predominately modeled by either directly fixing small areas on the surface of the cavity or by using some rigid support bonded to the cavity. However, support made of soft materials is widely adopted in the real situations, indicating potential inaccuracy of the results obtained by the numerical simulation. In addition, how to deal with the machining imperfections and installation errors in the numerical simulation and the subsequent optimization of cavity acceleration sensitivity remains to be further addressed.Firstly, the quantitative relationship between the cavity deformation and the resultant length change is derived. This result is universal in that it can be used to analyze the acceleration sensitivity of cavities with different geometries and supporting structures. With this result, the acceleration sensitivity of cavity can be determined from the vibration-induced deformation, which is obtained by using finite element analysis. Moreover, this analysis is extended to account for the vibration-induced length change with the existence of geometry imperfections and mirror displacements, which are introduced during the machining process and the installation, respectively.Secondly, to reduce the difference between the realistic system and the corresponding numerically-simulated one, we simulate a cavity that is supported by soft material, a model that is more close to the real situation. When subject to forces in certain directions, the cavity supported by soft material exhibits a relatively large global rotation, which interferes with the calculation of the length change. To cope with this inconvenience, a method of coordinate transformation is introduced to deduct the effect caused by the global rotation. With this procedure added, we analyze the acceleration sensitivities of a rectangular-bar cavity supported by soft material and compare the results with that obtained by directly fixing the cavity at the same locations.In addition, through a large number of numerical simulations, we investigate the sensitivities of the simulation to various modeling parameters including the size of mesh, the coefficient of friction, and the degree of structure simplification applied to the cavity support. To further verify the reliability of the method, we compare the results among different simulations as well as experimental results in a newly published investigation. When directly fixing small areas on the surface of the cavity, the current numerical result is identical to the published one. Furthermore, compared with the published simulation that fixes areas on the surface of the cavity, our model with a soft support yield results that are closer to the experimentally determined acceleration sensitivities.Last, the support of a 200-mm-long horizontally-installed cylindrical cavity with two notches is optimized by the method introduced in this thesis. The optimization explores and compares two different ways of modeling the cavity support by (1) directly fixing small areas on the surfaces of the cavity and by (2) using more-realistic soft supports.The methodology summarized here can be used for quantitatively analyzing the acceleration sensitivity of a variety of optical cavities, allowing for optimizing the cavity geometry and supporting structure. With more cases of experimental verifications and further improvements on modeling strategy and calculation technique, the accuracy of the simulation will be further improved and the method will definitely play more important roles in a broad range of basic research and practical application.