Numerically modeling Brownian thermal noise in amorphous and crystalline thin coatings
Numerically modeling Brownian thermal noise in amorphous and crystalline thin coatings
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对非晶态和晶态薄涂层中的布朗热噪声进行数值模拟
DOI：
10.1088/1361-6382/aa9ccc
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发表时间：
2018
影响因子：
3.5
通讯作者：
Khan, Haroon
中科院分区：
文献类型：
--
作者：
Lovelace, Geoffrey;Demos, Nicholas;Khan, Haroon
热噪声预计将是限制高级LIGO(一旦调试完成)和第三代探测器的天体物理覆盖范围的噪声源之一。在薄的反射镜涂层中采用晶体材料，而不是电流产生探测器中使用的非晶态涂层，可能会潜在地降低热噪声。了解和减少热噪声需要精确的理论模型，但对晶体材料进行热噪声分析建模尤其具有挑战性。热噪声模型通常依赖于涨落耗散定理，该定理将热噪声的功率谱密度与辅助弹性问题联系起来。在这篇文章中，我们给出了一个新的开源工具的结果，该工具数值地解决了辅助弹性问题，以计算非晶态和晶态涂层的布朗热噪声。我们采用的是开源交易。II和PETSC框架，使用有限元方法、自适应网格加密和并行处理来解决辅助弹性问题，使我们能够使用能够分解薄反射涂层的高分辨率。我们验证了数值收敛，并通过在多达数百个计算核心上运行，将辅助问题中的涂层弹性能分解为约0.1%。我们与非晶态材料的近似解析解进行了比较，并验证了随着光束大小、镜面尺寸和涂层厚度的变化，我们的解的规模达到了预期。最后，我们在Cole等人报道的一个实验中对晶体涂层的热噪声进行了建模(2013 NAT。光子。7644-50)，将我们的结果与一个更简单的数值计算进行比较，该计算将涂层视为一种“有效的无定形”材料。我们发现，将涂层处理为立方晶体而不是有效的非晶态材料会使热噪声增加约3%。我们的结果是朝着更好地理解和减少热噪声迈出了一步，从而扩大了未来引力波探测器的覆盖范围。
Thermal noise is expected to be one of the noise sources limiting the astrophysical reach of Advanced LIGO (once commissioning is complete) and third-generation detectors. Adopting crystalline materials for thin, reflecting mirror coatings, rather than the amorphous coatings used in current-generation detectors, could potentially reduce thermal noise. Understanding and reducing thermal noise requires accurate theoretical models, but modeling thermal noise analytically is especially challenging with crystalline materials. Thermal noise models typically rely on the fluctuation-dissipation theorem, which relates the power spectral density of the thermal noise to an auxiliary elastic problem. In this paper, we present results from a new, open-source tool that numerically solves the auxiliary elastic problem to compute the Brownian thermal noise for both amorphous and crystalline coatings. We employ the open-source deal. ii and PETSc frameworks to solve the auxiliary elastic problem using a finite-element method, adaptive mesh refinement, and parallel processing that enables us to use high resolutions capable of resolving the thin reflective coating. We verify numerical convergence, and by running on up to hundreds of compute cores, we resolve the coating elastic energy in the auxiliary problem to approximately 0.1%. We compare with approximate analytic solutions for amorphous materials, and we verify that our solutions scale as expected with changing beam size, mirror dimensions, and coating thickness. Finally, we model the crystalline coating thermal noise in an experiment reported by Cole et al (2013 Nat. Photon. 7 644–50), comparing our results to a simpler numerical calculation that treats the coating as an'effectively amorphous' material. We find that treating the coating as a cubic crystal instead of as an effectively amorphous material increases the thermal noise by about 3%. Our results are a step toward better understanding and reducing thermal noise to increase the reach of future gravitational-wave detectors.
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