正弦光栅标量衍射及等效介质理论有效性分析

王卫敏; 阮东升; 井绪峰

doi:doi:10.3788/gzxb20164507.0705001

光子学报, 2016, 45 (7): 070705001, 网络出版: 2016-08-18

正弦光栅标量衍射及等效介质理论有效性分析

Analysis of Accuracy of Scalar Diffraction Theory and Effective Medium Theory for Sinusoidal Grating

论文大纲

王卫敏 ^*阮东升井绪峰

作者单位

中国计量学院光学与电子科技学院, 杭州 310018

摘要

利用严格傅里叶模式理论研究了不同基底折射率、入射角度、归一化周期、归一化沟槽深度对正弦型光栅微结构衍射效率的影响, 并分析了该光栅的衍射特性.基于标量衍射理论和等效介质理论, 分别计算了光栅周期远远大于和远远小于入射波长时, 正弦型光栅的衍射效率, 并与傅里叶模式理论的计算结果进行比较, 分析标量衍射理论和等效介质理论的有效性.结果表明：在垂直入射条件下, 当光栅基质材料折射率为1.5时, 标量衍射理论在光栅归一化周期大于5时, 能够准确计算光栅衍射效率, 误差小于3%; 当基底折射率增大到3.42时, 只有在光栅归一化周期大于10时, 标量衍射理论才有效, 误差小于5%; 当正弦型光栅透射光中只有0级衍射光传播时, 等效介质理论能够准确计算其透射率; 随着入射角度的增大, 标量衍射理论和等效介质理论的有效性都不同程度地降低.

Abstract

By using the rigorous Fourier modal theory, the influence of the substrate refractive index, the incident angle, the normalized period and the normalized depth with different values on the diffraction efficiency of a sinusoidal grating microstructure was investigated. Also, the diffraction properties of the grating were analyzed. Based on the scalar diffraction theory and the effective medium theory, the diffraction efficiencies of the sinusoidal grating were calcualted at which the period is far greater than the incident wavelength and far smaller than the wavelength respectively. Using the different parameters of grating structure, comparing the results calculated by these two theories with that estimated by Fourier modal theory, the accuracy of the scalar diffraction theory and the effective medium theory was analyzed. The results show that when the refractive index of grating is about 1.5, the normalized depth is less than or equal to 1 and normalized period is greater than or equal to 5, the scalar diffraction theory can be used to calculate the diffraction efficiency of sinusoidal grating, the error is less than 3%; If the refractive index is increased to 3.42, only when the normalized period is greater than or equal to 10, the scalar diffraction theory can be used to estimate the diffraction efficiency and the error is less than 5%. Only zeroth transmittance light is propagating, effective medium theory is valid to evaluate the diffraction efficiency of sinusoidal grating. It is noted that the error of two simple methods is minimum at a normal incidence. Furthermore, the accuracy of scalar diffraction theory and effective medium theory decreases as the incident angle increasing.

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王卫敏, 阮东升, 井绪峰. 正弦光栅标量衍射及等效介质理论有效性分析[J]. 光子学报, 2016, 45(7): 070705001. WANG Wei-min, RUAN Dong-sheng, JING Xu-feng. Analysis of Accuracy of Scalar Diffraction Theory and Effective Medium Theory for Sinusoidal Grating[J]. ACTA PHOTONICA SINICA, 2016, 45(7): 070705001.

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