多层膜体折射率弱不均匀度反演计算的近似模型及性能分析

简钰东; 汤建勋; 吴素勇; 江奇渊; 谭中奇

doi:doi:10.5768/jao201637.0105004

应用光学, 2016, 37 (1): 124, 网络出版: 2016-03-22

多层膜体折射率弱不均匀度反演计算的近似模型及性能分析

Approximation model for refractive index slight inhomogeneity reverse determination of multilayers

论文大纲

简钰东 ^*汤建勋吴素勇江奇渊谭中奇

作者单位

国防科学技术大学光电科学与工程学院, 湖南长沙 410073

薄膜光学缺陷反演模型 Schrder近似不均匀薄膜 thin film optics reverse determination model for multilayer defects Schrder approximation inhomogeneous film

摘要

实际应用中的薄膜或多或少存在体折射率不均匀缺陷, 其准确表征对于镀膜工艺参数调校、低损耗薄膜设计与制备分析等具有影响。从Schrder近似出发, 推导了体折射率弱不均匀薄膜的膜系特征矩阵, 通过特征矩阵法推广, 建立了体折射率弱不均匀多层膜光谱特性计算的近似模型。利用基于有效介质理论的多层均匀膜近似方法, 讨论了上述近似模型的有效性、计算精度和时间消耗特性。结果表明, 上述模型矩阵计算中引入体折射不均匀度这一参数, 为多层膜体折射率不均匀缺陷反演提供了一种有效的手段, 为基于宽带光谱测量数据拟合的膜层缺陷数值反演应用奠定了基础。

Abstract

Thin film coatings in actual application are always characterized by some kind of, slight or large, refractive index inhomogeneity. Its accurate characterization can be vital to the process parameters calibration of coating machine, and to the design and manufacture of ultra low loss coatings. According to Schr?der approximation, the characteristic matrix of a slightly inhomogeneous thin film was derived, and an approximation model for the spectral characteristics calculation of slightly inhomogeneous multilayer coatings was presented by the matrix method. Based on the effective medium approximation theory and infinite division into large homogeneous sublayers, the effectiveness, calculation accuracy and time consumption of the approximation model were discussed in details. It shows that this model presents a fast and effective tool for the reverse determination of the refractive index inhomogeneity defect of multilayer system, and lays a foundation for the numerical optimization algorithm application into the data fitting based on the measured broadband spectral characteristics of actual multilayer coatings.

参考文献

[1] Furman S, Tikhonravov A V. Basics of optics of multilayer systems [M]. France: Gif-sur-Yvette, 1992: 1-5.

[2] 吴素勇, 龙兴武, 黄云, 等. 膜系光谱系数对膜层参数的一阶和二阶偏导数的计算模型[J].强激光与粒子束, 2010, 22(1): 83-90.

Wu Suyong, Long Xingwu, Huang Yun, et al. Calculation model for spectral coefficient’s first and second order partial derivatives of multilayer optical coatings with respect to layer parameters [J]. High Power Laser and Particle Beams, 2010, 22(1): 83-90.

[3] 吴素勇, 龙兴武, 杨开勇, 等.光学多层薄膜反向工程中局部优化算法的性能分析[J].光学学报, 2011, 31(6): 0631001-1-8.

Wu Suyong, Long Xingwu, Yang Kaiyong, et al. Performance analysis of local optimization algorithm in reverse engineering of multilayer optical coatings [J]. Acta Optica Sinica, 2011, 31(6): 0631001-1-8.

[4] 周天宇, 杨开勇, 吴素勇.多层高反膜光学常数和厚度的反演[J].应用光学, 2011, 32(1): 128-132.

Zhou Tianyu, Yang Kaiyong, Wu Suyong. Determination of optical constants and thickness of high-reflection multilayer system[J].Journal of Applied Optics, 2011, 32(1): 128-132.

[5] Schrder H. Bemerkung Z.Theorie des lichtdurchgangs durch inhomogene durchsichlige schichten[J]. Ann. Phys, 1941, 39: 55-58.

[6] Carniglia C K. Ellipsometric calculations for nonabsorbing thin films with linear refractive-index gradients[J]. J. Opt. Soc. Am, 1990, A7: 848-856.

[7] Borgogno J P, Lazarides B, Pelletier E. Automatic determination of the optical constants of inhomogeneous thin films [J]. Applied Optics, 1982, 22(15): 4020-4029

[8] De Lariviere G P, Frigerio J M, Rivory J. Estimate of the degree of inhomogeneity of the refractive index of dielectric films from spectroscopic ellipsometry[J]. Applied Optics, 1992, 31(28): 6056-6061.

[9] Ohlídal I, Franta D. Matrix formalism for imperfect thin films[J].Acta Physica Slovaca, 2000, 50(4): 489-500.

[10] Franta D, Ohlídal I. Calculation of the optical quantities characterizing inhomogeneous thin films using a new mathematical procedure based on the matrix formalism and Drude approximation[J]. SPIE, 2001, 4356: 207-212.

[11] Tikhonravov A V, Trubetskov M K, Sullivan B T, et al. Influence of small inhomogeneities on the spectral characteristics of single thin films[J]. Applied Optics, 1997, 36(28): 7188-7198.

[12] 唐晋发, 顾培夫, 刘旭, 等. 现代光学薄膜技术[M]. 浙江大学出版社, 2006: 410.

Tang Jinfa, Gu Peifu, Liu Xu, et al, Modern Technology of optical thin film [M]. Hangzhou: Zhejiang University Press, 2006: 410.

[13] Tikhonravov A V, Trubetskov M K, Krasilnikova A V. Spectroscopic ellipsometry of slightly inhomogeneous nonabsorbing thin films with arbitrary refractive-index profiles: theoretical study[J]. Applied Optics, 1998, 37(25): 5902-5911.

简钰东, 汤建勋, 吴素勇, 江奇渊, 谭中奇. 多层膜体折射率弱不均匀度反演计算的近似模型及性能分析[J]. 应用光学, 2016, 37(1): 124. Jian Yudong, Tang Jianxun, Wu Suyong, Jiang Qiyuan, Tan Zhongqi. Approximation model for refractive index slight inhomogeneity reverse determination of multilayers[J]. Journal of Applied Optics, 2016, 37(1): 124.

多层膜体折射率弱不均匀度反演计算的近似模型及性能分析

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