先进引力波干涉仪非标准光学研究
Researches on Non-standard Optics for Advanced Gravitational Waves Interferometers
摘要：
本论文针对先进的引力波干涉探测器的非标准光学特性进行了大量的研究，其中，热噪声是影响探测器灵敏度的主要因素。定量分析了非高斯光束对不同热噪声的影响。我们开发了台面光束的理论，在先进的GW干涉仪的台面光束的想法，着眼于未来的实施，分析推导的量（即光束宽度，发散度，传播因子），这是选择作为ISO标准的参考参数的光束的特性。我们还解析地证明了非球面镜光学腔之间的一种新的对偶关系。GW社区对这种新光束技术的兴趣使我们建造和测试了一个带有墨西哥帽镜的原型台面光束法布里-珀罗腔。本论文的部分工作致力于开发新的光学系统仿真程序。这些程序提供了我们实验的理论预期行为，特别是腔模结构和失调灵敏度与实验结果相面对。除了光束整形之外，我们还探索了降低反射镜热噪声的另一种补充方法，即多层膜厚度优化。我们表明，它是有效的，在减少涂层噪声和探索GW干涉仪的灵敏度方面的可能影响。在此分析过程中，我们开发了一个独立的模型的涂层有效的弹性参数，这是基于均匀化理论的充分理解的主题。
英文摘要：
This thesis presents a collection of different researches on non-standard optics in view of enhancing the performances of the Advanced Gravitational waves interferometric detectors, where the thermal noise of the test masses is expected to be a limiting factor for their sensitivity. We provide a quantitative analysis of the impact of non-Gaussian beams on different kinds of thermal noises. We developed the theory of mesa beam, in view of a future implementation in advanced GW interferometers of the mesa beam idea, focusing on the analytical derivation of the quantities (i.e. beam width, divergence, propagation factor), which are chosen as ISO standard reference parameters for the characterization of an optical beam. We also analytically proved a new duality relation between optical cavities with non-spherical mirrors. The interest of the GW community in this new beam technology led us to the construction and testing of a prototype mesa beam Fabry-Perot cavity with Mexican-hat mirror. Part of the work of this thesis was devoted to the development of new simulation programs of optical systems. These programs provided the theoretical expected behaviour of our experiment, in particular cavity modes structure and misalignments sensitivity to be confronted with the experimental results. We also explored another complementary way of reducing the mirror thermal noise, beside the beam shaping, that is the multi-layered coating thickness optimization. We show it to be effective in reducing the coating noise and explore the possible implications for GW interferometers in terms of sensitivity. During this analysis we developed an independent model for the coating effective elastic parameters, which is based on the well understood subject of homogenization theory.
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