Independent mode frequency control will improve the ability to suppress parametric instabilities in gravitational wave detectors. In this article we investigate a formalism that allows multiple cavity optical modes to be thermally tuned independently based on the transformation between the change in mode spacing and the mirror surface deformation. An FFT based cavity simulation software is used to demonstrate the effectiveness of the formalism. A case study showed that it is possible to tune the HG 03 mode spacing by 100 Hz while maintaining other mode spacings with minimum change. Our investigation also indicates that the desired mirror surface deformation is experimentally realisable with a matrix heater.

中文翻译：

---

反射镜表面的轮廓热变形，可消除光腔中的参数不稳定性

独立模式频率控制将提高抑制重力波探测器中参数不稳定性的能力。在本文中，我们研究了一种形式主义，该形式主义允许基于模式间距变化和镜面变形之间的转换独立地对多个腔光学模式进行热调谐。基于FFT的腔体仿真软件用于证明形式主义的有效性。案例研究表明，可以将HG 03模式间隔调整100 Hz，同时以最小的变化保持其他模式间隔。我们的研究还表明，所需的镜面变形可以通过矩阵加热器在实验上实现。