中国科学院力学研究所机构知识库

       LISA (Laser Interferometer Space Antenna) 计划和太极计划是最具代表性的空间引力波探测计划，不仅可以直接验证爱因斯坦的广义相对论，而且可能开辟一个观测宇宙演变的新窗口——引力波天文学。LISA计划和太极计划采用了空间激光干涉方法学来探测0.1 mHz – 1 Hz频率范围内的引力波信号。激光干涉测量的首要噪声源是激光频率噪声，针对激光频率噪声过大导致引力波信号引起的相位变化被淹没这一问题，LISA计划采取了Pound-Drever-Hall (PDH) 预稳、激光锁臂控制技术以及TDI (Time Delay Interferometer) 技术三个步骤来逐级压制激光频率噪声。本文的主要研究对象之一是激光锁臂控制技术，该技术可以将PDH预稳后的激光频率噪声进一步压制到0.3 Hz/√Hz@10 mHz。另外，针对激光信号在百万公里量级的星间距往返传播后功率大幅度衰减以致于无法进行探测的问题，通过采用弱光锁相技术将远端卫星转换为具备信号放大功能的“相位转发器”，从而将往返光程的衰减转换为单程的衰减，使得长基线的激光干涉成为可能。弱光锁相技术是本文的另一个研究对象，该技术需要在0.1 mHz – 1 Hz频段内达到2π×10^-5 rad/√Hz@10 mHz锁相技术要求。因此，本文开展了激光锁臂控制技术的数值仿真研究，弱光锁相控制技术的数值仿真与地面实验研究，以及锁臂-锁相控制系统的联合仿真研究。

    首先，为了实现锁臂技术的原理和方法学验证，本文在锁臂臂传递函数的推导和系统稳定性分析的基础上，通过合理的锁臂控制器设计，利用MATLAB/Simulink软件构建了单、双臂锁定的数值仿真模型。仿真结果表明，在0.1 mHz – 0.03 Hz频率范围内单臂锁定系统可以将激光频率噪声压制到0.3 Hz/√Hz@10 mHz及以下，而在0.03 Hz – 1 Hz频率范围内由于存在以激光往返时间为特征的控制零点，不能在0.05 Hz及其倍频处对激光频率噪声进行有效压制。与单臂锁定相比，双臂锁定技术通过利用两个干涉臂上的干涉信号的线性组合，可以在目标探测频段0.1 mHz – 1 Hz内消除控制零点，进而获得更优秀的频率噪声抑制性能。仿真结果表明，双臂锁定技术能够在0.1 mHz – 1 Hz频率范围内将激光频率噪声抑制到0.3 Hz/√Hz@10 mHz及以下，满足太极计划的锁臂技术要求。另外，这些仿真结果也表明了本文所采用的补偿滤波器和两级积分器并联的新型控制器设计方案，可以在不增加增益的情况下能有效地抑制激光频率噪声，防止高增益对引力波信号地抑制。

    其次，根据太极探路者卫星的方案设计，并基于外差式弱光锁相的物理图像，本文利用MATLAB/Simulink软件设计并构建了弱光锁相控制的数值仿真模型。经噪声分析得知，锁相系统的相位噪声水平主要由激光相位噪声和时钟噪声主导。同时，仿真结果表明环外信号的相位噪声低于1×10^-4 rad/√Hz@10 mHz，而环内信号的相位噪声低于10 nrad/√Hz@0.1 mHz – 1 Hz，表明所设计的锁相控制器具有很好的锁相控制能力。另外，基于外差式弱光锁相的仿真模拟，本文构建了外差式弱光锁相控制地面实验系统。实验结果表明，当两束干涉光为10 nW 和10 µW、差分频率为16 MHz时，环内相位噪声低于 2×10^-5 rad/√Hz@0.1 mHz – 10 Hz，环外相位噪声低于2×10^-4 rad/√Hz@10 mHz，满足太极探路者任务的锁相控制要求。

     最后，基于激光锁臂系统和弱光锁相系统的数值仿真分析，并根据空间引力波探测中激光干涉仪的方案设计，本文使用MATLAB/Simulink软件设计并构建了激光锁臂-锁相控制系统的联合仿真模型。利用该模型，研究了当锁臂和锁相控制器同时存在于控制回路中时整个系统的锁相性能表现和激光频率噪声的压制效果。仿真结果表明，激光锁臂-锁相控制系统在0.1 mHz – 1 Hz频率范围内可以将激光频率噪声抑制在0.3 Hz/√Hz@10 mHz及以下，满足太极计划的锁臂技术要求。同时，系统锁相环路的输入信号和输出信号基本重合，证明了激光干涉系统中各锁相环均具备良好的锁相控制能力。另外，仿真结果也验证了锁臂与锁相系统协调工作的可行性。

   The LISA (Laser Interferometer Space Antenna) mission and the Taiji mission are the most representative space gravitation wave detection missions, which cannot only directly verify Einstein’s general theory of relativity, but also may open up a new window for observing the evolution of the universe of gravitational wave astronomy. In space gravitational wave detection, laser frequency instability noise is the primary noise source. The LISA mission and Taiji mission use space laser interferometry to detect gravitational wave signals in the frequency range of 0.1 mHz – 1 Hz. The primary noise of laser interferometry is laser frequency noise. Excessive laser frequency noise causes the phase change caused by the gravitational wave signal to be submerged. The LISA mission adopts the three steps of Pound-Drever-Hall (PDH) pre-stabilization, arm-locking technology and TDI (Time Delay Interferometer) technology to suppress laser frequency noise, of which arm-locking technology is one of the main research objects of the thesis. This technology can further suppress the laser frequency noise after PDH pre-stabilization to the level of 0.3 Hz/√Hz@10 mHz. In addition, the power of the laser signal, which travels back and forth between satellites on the order of millions of kilometers, is too weak to detect. To overcome this problem, the weak-light phase-locking (WLPL) technology can phase-locking the high power local light signal with the weak-light signal to achieve the amplification of weak-light signal. The WLPL is another research object of the thesis, which has to achieve the phase-locking noise level lower than 2π×10^-5 rad/√Hz@10 mHz in the frequency regime of 0.1 mHz – 1 Hz. Therefore, some numerical simulations of arm-locking and WLPL for Taiji mission were investigated in the thesis, as well as the joint numerical simulation of the arm-locking and phase-locking control system.

    First, as a proposed frequency stabilization technique, the scheme of arm-locking is to convert the stability of interferometer arm-length into the stability of laser frequency. To realize the principle and methodoldgy verification of the arm-locking technology, some numerical simulations of arm-locking for the Taiji mission were investigated in the MATLAB/Simulink software. The single arm-locking simulation results showed that the laser noise of closed loop was lower than 3.19 μm/√Hz@10 mHz only in the frequency range of 0.1 mHz – 0.03 Hz. However, due to the existence of the nulls, the laser frequency noise cannot be effectively suppressed in the frequency range of 0.03 Hz – 1 Hz. Compared to the single arm-locking, the dual arm-locking system can overcome the nulls by using a linear combination of two different arm’s interfering signals to have better frequency noise suppression capability. The dual arm-locking simulation results showed that the laser noise of closed loop was lower than 3.19 μm/√Hz@10 mHz in the full frequency range of 0.1 mHz – 1 Hz, meeting the requirement of Taiji mission. In addition, the simulation results also proved that the innovative controller consisted of a compensation filter and two-stage integrators in parallel could suppress the laser frequency noise without increasing gain and prevent the high gain from suppressing the gravitational waves signal.

  Secondly, according to the requirements of the Taiji Pathfinder mission and based on the principle of heterodyne WLPL technology, a numerical simulations of WLPL for the Taiji Pathfinder mission were investigated in the MATLAB/simulink software. The simulation results showed that the phase-locking noise level is dominated by the laser phase noise, clock noise. The phase-locking noise of the out-of-loop is lower than 1×10^-4 rad/√Hz@10 mHz. The phase noise of in-loop is lower than 10 nrad/√Hz in the frequency range of 0.1 mHz – 1 Hz, which indicates that the phase-locking controller can work well. In addition, based on the simulation analysis of heterodyne WLPL, the experimental system of heterodyne WLPL was constructed. The experimental results showed that a 10 nW weak-light beam and a 10 µW strong-light beam were phase locked for several hours with an offset frequency of 16 MHz between two Nd: YAG lasers. The phase noise of in-loop was lower than 2×10^-5 rad/√Hz inside the frequency regime of 0.1 mHz – 10 Hz, and the out-of-loop was lower than 2×10^-4 rad/√Hz@10 mHz, meeting the requirement of the Taiji Pathfinder mission.

   At last, based on the numerical simulations of arm-locking and WLPL system, the joint simulation model of the arm-locking and phase-locking control system was investigated in the MATLAB/Simulink software. This model is used to research the performance of phase-locking system and the suppression capability of laser frequency noise, when both the arm-locking controller and the phase-locked controller exist in the control loop. The simulation results showed that the joint control system of arm -locking and phase-locking can effectively suppress the laser frequency noise to lower than 3.19 μm/√Hz@10 mHz in the frequency range of 0.1 mHz –1 Hz, meeting the requirements of the Taiji mission. Meanwhile, the amplitude spectral density of the input and output signals of the phase-locking loop basically coincide within the frequency range of 0.1 mHz –1 Hz, which proves that the phase-locking loop can work well. In addition, the simulation results also verified the feasibility of the coordinated work between the arm-locking and the phase-locking system.