用于引力波探测器反射镜的三元四分之一波长薄膜：穷举搜索法优化设计
Ternary Quarter Wavelength Coatings for Gravitational Wave Detector Mirrors: Design Optimization via Exhaustive Search
摘要：
多材料光学薄膜是满足下一代引力波探测器反射镜在透射率、吸收率和热噪声方面的挑战性要求的一种有前途的可行选择。在本文中，我们专注于由四分之一波长厚层组成的三元涂层，其中第三种材料（H '）被添加到目前使用的两种材料中，即二氧化硅（L）和掺杂氧化钛的钽（H），具有更高的介电对比度（相对于二氧化硅）和更低的热噪声（与掺杂氧化钛的钽相比），但更高的光学损耗。我们寻求最佳的材料序列，具有最小的热（布朗）噪声下规定的透射率和吸收率的限制，通过详尽的模拟在所有可能的配置，对于不同的值（在一个有意义的范围内）的第三种材料的光密度和消光系数。在所研究的所有情况下，最优设计都是由（H '）|L）双峰，顶部是一叠（H| L）双峰，证实了先前的启发式假设，并且可实现的涂层噪声功率谱密度降低因子为\sim 0.5。还研究了所发现的最佳设计对层厚度沉积误差和第三材料的光学损耗中的不确定性和/或波动的鲁棒性。进一步降低热噪声的层厚度优化，和策略，以实现它的可能的利润率进行了讨论。
英文摘要：
Multimaterial optical coatings are a promising viable option to meet the challenging requirements (in terms of transmittance, absorbance and thermal noise) of next generation gravitational wave detector mirrors. In this paper we focus on ternary coatings consisting of quarter-wavelength thick layers, where a third material (H') is added to the two presently in use, namely Silica (L) and Titania-doped Tantala (H), featuring higher dielectric contrast (against Silica), and lower thermal noise (compared to Titania-doped Tantala), but higher optical losses. We seek the optimal material sequences, featuring minimal thermal (Brownian) noise under prescribed transmittance and absorbance constraints, by exhaustive simulation over all possible configurations, for different values (in a meaningful range) of the optical density and extinction coefficient of the third material. In all cases studied, the optimal designs consist of a stack of (H'|L) doublets topped by a stack of (H|L) doublets, confirming previous heuristic assumptions, and the achievable coating noise power spectral density reduction factor is \sim 0.5. The robustness of the found optimal designs against layer thickness deposition errors and uncertainties and/or fluctuations in the optical losses of the third material is also investigated. Possible margins for further thermal noise reduction by layer thickness optimization, and strategies to implement it, are discussed.
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