大光斑临界稳定谐振腔的研究及其在精密测量中的应用

The detection of gravitational waves emitted by inspiralling black holes has initiated a new era of astronomy, as the first detection achieved in 2015 marked the start of a new way of observing the universe. The laser interferometric gravitational wave detector is currently the world’s most sensitive instruments that made by human beings. It’s sensitivity is limited largely by quantum noise and mirror thermal noise. The next generationl detector will be designed and built mainly to reduce these two kinds of noises. Optical cavities are at the heart of ground-based laser interferometric gravitational wave detectors. These devices are primarily used to enhance the interaction between the laser light and the gravitational waves. A typical advanced detector scheme employs at least six cavities, and the performance of each of them directly impacts on the detector sensitivity. The present project focuses on the behaviour of a particular type of marginally stable cavities, and their application to the sensitivity enhancement of current and future gravitational wave detectors. Marginally stable cavities have been proposed as an enabling technology for future gravitational wave detectors, as their compact structure and large beam spot can reduce the thermal noise floor of the interferometer. These cavities operate close to the edge of geometrical stability, and may be driven into instability via small cavity length perturbations or mirror surface distortions. They are at risk of suffering from problems such as high optical scattering loss and Gaussian mode degeneracy. The well-defined Gaussian beams can also be distorted through their interaction with the small imperfections of the mirror surfaces. These issues have an adverse impact on the detector sensitivity and controllability. In this project an experiment is designed and will be built to investigate the technical hurdles associated with marginally cavities. A marginally stable table-top cavity is built and accurate control achieved through length and alignment control systems. This experiment will provide a detailed account of the behaviour of the marginally cavity and of the difficulties that need to be overcome in order to achieve optimal operation. Additionally, the experiment will provide a new method of measuring scattering loss and mirror surface defects.

激光干涉引力波探测器是目前世界上灵敏度最高的超精密测量系统，探测精度已经达到经典物理所决定的噪声极限，其灵敏度曲线主要由量子噪声和分子热噪声决定，下一代引力波探测器将重点围绕降低这两大噪声进行设计和制造。临界稳定法布里-珀罗谐振腔能够产生较大的光斑半径，因而具有更低的镜面热噪声，在未来激光干涉引力波探测器、量子噪声测量装置中有重要的应用前景，美国激光干涉引力波观测站LIGO已明确提出在下一次升级中将使用该技术。临界稳定腔还因为对反射镜面型误差和散射损耗十分敏感，可用作面型检测领域的新技术手段，并解决高能谐振腔中散射损耗难以估算的问题。本项目将在实验室光学平台上搭建法布里-珀罗谐振腔及其精密控制系统，将激光谐振腔的稳定性置于稳定与非稳定临界状态，运用实验与仿真相结合方法，研究临界稳定腔的光学特性，判断其是否兼容下一代激光干涉引力波探测器，并探讨临界稳定腔应用于面型检测和散射损耗分析的可行性。

激光干涉引力波探测器是当今人类造出的最大、最精密的测量系统，能够检测10的负19次方米的长度变化，其检测精度为1纳米的十亿分之一。法布里-柏罗谐振腔和迈克尔逊干涉仪是当前引力波探测器的核心组成系统。本项目所研究的大光斑半径临界稳定谐振腔服务于超精密激光检测技术及仪器，在激光干涉引力波探测领域有重要研究意义。通过搭建桌面型长度1米的谐振腔及其精密控制系统，将激光谐振腔的稳定性置于稳定与非稳定临界状态，运用实验与仿真相结合的方法，研究法布里-珀罗谐振腔在临界稳定状态下的性能及表现。通过观察稳频、准直系统反馈控制回路信号的衰减程度，判断谐振腔在实验室实际可控制范围内的稳定边界。在已知反射镜面型误差的情况下，通过测量谐振腔不同稳定性下波像差的大小，研究波像差与稳定性变化规律。通过实验测量临界稳定腔中由于散射引起的谐振高斯光束同阶模的频率分化，研究了频率分化大小与Zernike系数之间的关系，推算反射镜面型误差大小。对比仿真与实验测量结果，探究了临界稳定腔用作面形检测和散射损耗分析新手段的可行性。并进一步研究了Zernike系数与波长的函数关系，通过对大量系统的模拟仿真得到了两个可以用于描述Zernike系数-波长曲线的公式，即Conrady公式和复消色差特性公式。另外，由于临界稳定腔对频率锁相稳定系统具有更高的要求，本项目改进了传统的PDH误差信号，显著增加整个系统的线性动态范围。针对这种新的误差信号更容易受到噪声影响的问题，本项目将卡尔曼滤波算法与新的误差信号相结合来估计反射镜的状态，并证明了其与传统方法相比的稳健性和有效性。采用该方法可以极大地拓宽原有控制系统的动态范围，且能够在镜面位置扰动很大且系统处于非线性区域的情况下重新锁定光腔，使整个控制系统更不易受到环境噪声的干扰。本项目研究成果为下一代引力波探测器中谐振腔的设计和控制提供了重要技术指标和参考。

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