基于Khalili标准具与高阶LG模式的膜层热噪声抑制  

Reducing Coating Thermal Noise by Using Khalili Etalon and High-order Mode

作　　者：王凯 张玉驰[1] 郭奇 郑耀辉[2] 张天才[2] WANG Kai;ZHANG Yu-chi;GUO Qi;ZHENG Yao-hui;ZHANG Tian-cai(College of Physics and Electronic Engineering,Shanxi University,Taiyuan 030006,China;State Key Laboratory of Quantum Optics and Quantum Optics Devices,Institute of Opto-Electronics,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学物理电子工程学院,山西太原030006 [2]山西大学光电研究所量子光学与光量子器件国家重点实验室,山西太原030006

出　　处：《量子光学学报》2024年第4期27-37,共11页Journal of Quantum Optics

基　　金：国家自然科学基金(12274274,U22A6003,U21A60061)。

摘　　要：测试质量镜反射膜层的热噪声是引力波探测等高精度测量中重要的极限噪声源,已经成为了增强探测灵敏度的主要限制之一。本文针对第三代引力波激光干涉仪使用波长为1 550 nm的光源,结合具有分布式反射膜层的Khalili标准具(Khalili etalon,KE)和高阶拉盖尔-高斯(Laguerre-Gauss,LG)模式两种技术有效地抑制了热噪声。基于涨落耗散定理,确定了KE前、后反射膜层的分布,计算了高阶LG模式下KE的膜层热噪声,将噪声抑制到原来的1/3。Objective The thermal noise in the mirror coatings of a test mass is an important limiting noise source in high-precision measurements such as gravitational wave detection,and has become one of the main limitations of improving detection sensitivity.In order to improve the sensitivity of detection,it is necessary to adopt the thermal noise suppression technology,and even to adopt a combination of multiple non-interfering suppression techniques to reduce the thermal noise.So we combine the two suppression techniques of Khalili etalon(KE)with distributed reflective coating structure and high order Laguerre-Gaussian(LG)mode beam with wider and more uniform transverse intensity distribution compared to the base mode currently used.Methods In this paper,we calculated thermal noise based on the fluctuation-dissipation theorem.To calculate the thermal noise of the coating,the elastic equation of the substrate needs to be solved,and the coating thermal noise can be obtained by the boundary conditions between substrate and coatings.The boundary conditions for the substrate are determined according to the reflection of the beam in conventional mirror and KE respectively,and the beam intensity profile is expanded with the oscillation mode of test mass, which is described by the Bessel function. The strain and stress tensor and the elastic energy of substrate canbe obtained from the elastic equation and boundary conditions, the three corresponding mechanical quantities of the coating arederived from deve the boundary conditions between the coatings and substrate. We add up the elastic energies of all the coatingsto get the total coating thermal noise. The suppression factor is defined as the ratio of the original noise level to the noise levelafter suppression, and the distribution of the coating layers is determined by considering the factor and the absorption of substratedue to the reduction of the front coating layer.Results and Discussions Compared with the LG base mode currently used in aLIGO (Advanced laser interferome

关 键 词：膜层热噪声 涨落耗散定理 Khalili标准具 高阶模 

分 类 号：P142.84[天文地球—天体物理]