爱因斯坦的广义相对论是二十世纪人类在自然科学领域取得的最辉煌的成就之一， 它深刻地揭示了力学的本质，开创了近代物理的新纪元。引力波作为广义相对论的重要 预言与唯一能指示宇宙大爆炸早期的指针，它的探测是当代物理学的重要最有意义的前 沿领域，世界各国的科学家正在为了这一目标共同努力。

从六十年代第一代引力波探测器“共振棒”兴起，到九十年代第二代探测器“激光干涉 仪”开始陆续建成并投入运行，物理学家从来没有停止过对引力波的探索。本世纪开始， 现有的第二代探测器都开始升级，采用更高功率的激光，更低损耗的测试质量，以及更 有效的降噪系统，将探测器的灵敏度较之前提高了一到两个数量级。这给引力波的首次 直接探测带来了新的希望。

在“升级版”第二代探测器运转之前，还有很多技术上的难题需要解决，参量不稳定就 是其中之一，它是探测器正常运转的重要威胁。组成激光谐振腔的镜体在受热时会发生 振动，这种振动模式会将打在它表面的激光散射，导致谐振腔内部谐振的激光模式不纯 净。在某些特定情况下，由激光基模和散射成的高阶模相互作用产生的光辐射压力将会 激励镜子的内部振动模式。尤其是当原激光和散射光的频率差等于镜子固有振动模式的 频率，并且散射出的光学模式和振动模式在空间分布上有重叠的时候，镜体的振动幅度 会成指数增长。这样将会导致谐振腔的不稳定，降低探测器灵敏度，导致探测失败。

本文从引力波基础理论开始，介绍了引力波探测的历史。结合激光谐振腔和机械谐 振子的基本性质，设计了一个能探究参量不稳定性的桌面实验装置。装置包含一个质量 为 1mg，大小为 1mm2 厚度为 0.5mm 硅机械谐振子，它具有较高的品质因子。谐振子放 置于一个长度为 200mm 的折叠光学谐振腔中。这样一个结构能够实现光声相互作用，并 且通过调节组成谐振腔的镜体之间的相对位置，能够连续的实现光声放大和光声冷却。 本文对该实验装置的各种性质进行了详细的介绍，对实验的可行性进行了分析。基于已 有的机械谐振子参数和光学谐振腔参数，本文预测了当输入激光功率为 1.6µW 时，将发 生参量不稳定，输入功率为 30mW 时将能实现冷却系数为 1.9 × 104 的激光冷却。

Einstein’s General Relativity is one of the greatest achievement humankind had made in natural science in the 20th century, it revealed profoundly of the nature of mechanics, created a new era of modern physics. Gravitational wave, as one of the most significant prediction of General Relativity, offers the only means of probing the birth of the universe in the earliest moments of the Big Bang where time began. Gravitational waves detection is the most important and promising project in the word, where thousands of scientists and hundreds of institutes are making joint efforts.

Starting from the first generation bar detectors in 1960s to the second generation laser interferometric detectors in 1990s, scientists never stopped the exploration of gravitational waves. From the beginning of this century, the existing second generation detectors are experiencing a comprehensive upgrades. By using higher power laser, ultra-low-loss test mass and more efficient noise-suppressing system, scientists hope to increase the sensitivity by one or two order of magnitude, which will bring hopes to the first direct detection of gravitational wave.

Before the fully operation of ”Advanced” gravitational wave detectors, some technical problems need to be solved, one of which is Parametric Instability. Three-mode parametric instability is a phenomena where the optical modes in an interferometer are weakly scattered by thermally induced acoustic vibrations of the mirrors. Under certain conditions, the test masses acoustic modes can be amplified by the radiation pressure forces due to the beating of scattered light with the fundamental modes of the cavity. This can occur particulary if the frequency of the scattered light matches that of a cavity high order mode. Then it can cause the amplitude of the mirror’s acoustic mode to increase exponentially. This could cause the gravitational wave detector to stop operation.

This thesis introduces the fundamental theory of gravitational wave and the history of gravitational wave detection. It also presents an experiment design to investigate parametric instability, based on the characters of silicon resonator and optical resonator. The setup consists of a 1mg, 0.5mm thick silicon resonator, placed in the end of a 200mm folded near-self-imaging cavity. This configuration allows tuning the mode spacing between amplification and self-cooling by only adjusting the relative position of the optical components. Based on the demonstrated resonator parameters, we predict that this device can achieve parametric instability with 1.6µW of input laser power and mode cooling by a factor of 1.9 × 104 with 30mW of input power.