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光栅模式的色散方程与对称性

Dispersion Equation and Symmetry of Grating Modes

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摘要

提出了横电、横磁偏振布拉格角入射下光栅模式的色散方程可进一步分解的理论,证明了分解得到的方程与光栅模式对称性间的等价关系。光栅模式的对称性有助于阐释光栅内部衍射过程的物理图像。通过讨论光栅模式方程的根的分布性质,提出了一种提高有效折射率计算效率的方法。

Abstract

The theory about the further factorization of the dispersion equation of the grating mode under the incidence of Bragg angle and transverse electric and transverse magnetic polarizations is proposed, and the equivalent relationship between the factorized equation and the symmetry of the grating mode is confirmed. The symmetry of grating modes is beneficial to illustrate the physical picture of the diffraction process within gratings. By the analysis of the distribution property of the root of the grating mode equation, a method to improve the computation efficiency of the effective refractive index is proposed.

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中图分类号:O436

DOI:10.3788/aos201838.0905001

所属栏目:衍射与光栅

基金项目:国家自然科学基金(61405217, 61405216)

收稿日期:2018-03-02

修改稿日期:2018-04-19

网络出版日期:2018-04-23

作者单位    点击查看

项长铖: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中国科学院大学, 北京 100049
周常河: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

联系人作者:周常河(chazhou@mail.shcnc.ac.cn); 项长铖(ccxiang@siom.ac.cn);

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引用该论文

Xiang Changcheng,Zhou Changhe. Dispersion Equation and Symmetry of Grating Modes[J]. Acta Optica Sinica, 2018, 38(9): 0905001

项长铖,周常河. 光栅模式的色散方程与对称性[J]. 光学学报, 2018, 38(9): 0905001

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