石英晶体椭偏测量中的穆勒矩阵模型  

Mueller Matrix Model in Ellipsometry Measurement of Quartz Crystal

作　　者：赵宇 张灵浩 曾爱军[1,2] 黄惠杰 Sergey Avakaw Zhao Yu;Zhang Linghao;Zeng Aijun;Huang Huijie;Avakaw Sergey(Laboratory of Information Optics and Optoelectronic Technology,Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,Shanghai 201800,China;Center of Materials Science and Optoelectronics Enginering,University of Chinese Academy of Sciences,Beijing 100049,China;Company of KBTEMOMO Republication Unitary Scientific and Production Enterprise,Minsk 220033,Belarus)

机构地区：[1]中国科学院上海光学精密机械研究所信息光学与光电技术实验室,上海201800 [2]中国科学院大学材料科学与光电工程中心,北京100049 [3]白俄罗斯共和国开放式股份公司“精密电子机械制造设计局-光学机械设备”,白俄罗斯明斯克220033

出　　处：《中国激光》2023年第14期118-124,共7页Chinese Journal of Lasers

基　　金：上海市集成电路科技支撑专项(20501110600);上海市政府间科技合作计划(20500711300)。

摘　　要：石英晶体是一种重要的双折射材料,广泛应用于光学相关领域。石英晶体在宽光谱下的参数测量通常使用椭圆偏振法,但现有的椭偏测量仪器往往假定晶体的光轴与测量光路对准,从而引入测量误差,这一问题在紫外波段尤为显著。为此提出了一种采用椭圆偏振法精确测量石英晶体参数的穆勒矩阵模型,运用坐标变换和Berreman4×4矩阵理论建立石英晶体参数与穆勒矩阵的关联,通过拟合计算可以得到晶体的厚度、光轴欧拉角和相位延迟量。实验结果显示,拟合得到的穆勒矩阵与测量结果高度一致,模型拟合的均方根误差<5,拟合厚度的相对误差<1%,拟合的欧拉角与测量结果吻合。该模型包含的信息丰富,拟合准确,对椭圆偏振法测量各向异性材料的精确参数具有重要参考价值。Objective Quartz crystal is an important birefringence material,which is widely used in optical related fields.The two main optical parameters of quartz crystal wave plate are phase retardation and fast axis azimuth.Due to the influence of manufacturing process,these two actual parameters will deviate from the theoretical value,so it is usually necessary to accurately measure the optical parameters before use.Ellipsometry is usually used to measure the parameters of quartz crystal in a wide spectrum,but the existing ellipsometric measuring instruments often assume that the optical axis of the crystal is aligned with the measuring optical path,which introduces measurement error,especially in the ultraviolet band.Therefore,it is necessary to propose a fitting model for accurate measurement of quartz crystal parameters.The model contains rich information and the fitting results are accurate.This model has important reference value for measuring the accurate parameters of anisotropic materials by ellipsometry.Methods A Mueller matrix model for accurate measurement of quartz crystal parameters by ellipsometry is proposed.Firstly,the crystal coordinate system (a,b,c) is transformed into the measurement coordinate system (x,y,z) by coordinate transformation,which involves three Euler anglesФ_E,θ_E,andψ_(E) (Fig.1).After coordinate transformation,the expression of dielectric tensor of quartz crystal in the measurement coordinate system can be obtained.Then,the Berreman 4×4 matrix theory is used to establish the correlation between quartz crystal parameters and Mueller matrix.The Mueller matrix measurement value of the sample is obtained by the Mueller matrix ellipsometer,and then the Mueller matrix model is used for iterative fitting.The Levenberg-Marquardt algorithm is used for fitting,and the evaluation function is defined as root mean square error (RMSE).The fitting parameters are adjusted by nonlinear iterative regression to minimize the evaluation function,that is,when the evaluation function converges to the gl

关 键 词：测量 椭偏技术 石英晶体 介电张量 相位延迟量 欧拉角 

分 类 号：TN247[电子电信—物理电子学] O436.3[机械工程—光学工程]