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铝基微结构光栅几何参数反演

孙双成 齐宏 孙建平 阮世庭 吕中原 阮立明

孙双成, 齐宏, 孙建平, 等 . 铝基微结构光栅几何参数反演[J]. 北京航空航天大学学报, 2017, 43(11): 2199-2206. doi: 10.13700/j.bh.1001-5965.2017.0055
引用本文: 孙双成, 齐宏, 孙建平, 等 . 铝基微结构光栅几何参数反演[J]. 北京航空航天大学学报, 2017, 43(11): 2199-2206. doi: 10.13700/j.bh.1001-5965.2017.0055
SUN Shuangcheng, QI Hong, SUN Jianping, et al. Inverse estimation of geometric parameters of aluminum matrix microscale structure grating[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(11): 2199-2206. doi: 10.13700/j.bh.1001-5965.2017.0055(in Chinese)
Citation: SUN Shuangcheng, QI Hong, SUN Jianping, et al. Inverse estimation of geometric parameters of aluminum matrix microscale structure grating[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(11): 2199-2206. doi: 10.13700/j.bh.1001-5965.2017.0055(in Chinese)

铝基微结构光栅几何参数反演

doi: 10.13700/j.bh.1001-5965.2017.0055
基金项目: 

国家自然科学基金 51476043

详细信息
    作者简介:

    孙双成 男, 博士研究生。主要研究方向:辐射传输逆问题及智能优化算法

    齐宏 男, 博士, 教授, 博士生导师。主要研究方向:热辐射传输与耦合换热、高温弥散颗粒辐射物性及温度测量、辐射传输逆问题及智能优化算法、微藻新能源利用

    通讯作者:

    齐宏, E-mail: qihong@hit.edu.cn

  • 中图分类号: TK121

Inverse estimation of geometric parameters of aluminum matrix microscale structure grating

Funds: 

National Natural Science Foundation of China 51476043

More Information
  • 摘要:

    微结构光栅是一种广泛应用的电子元件。采用随机微粒群优化(SPSO)算法反演了一维铝基衬底矩形光栅的几何结构参数。首先介绍了严格耦合波分析(RCWA)法和微粒群优化算法的基本原理,并采用RCWA法求解了光栅内电磁场问题;然后根据正问题求得的光栅光谱反射率建立目标函数,并采用SPSO算法优化目标函数,反演得到单槽和双槽矩形光栅的周期、凸脊宽度和凹槽深度;最后分析了种群大小和搜索区间对反演结果的影响。结果表明,SPSO算法可以准确地反演光栅几何结构参数,并推荐种群数取30。

     

  • 图 1  TE波入射矩形光栅示意图

    Figure 1.  Schematic of rectangular grating with a TE wave irradiation

    图 2  PSO算法计算流程图

    Figure 2.  Calculation flowchart of PSO algorithm

    图 3  单槽光栅光谱反射率

    Figure 3.  Spectral reflectance of single-slot grating

    图 4  单槽光栅几何参数反演结果

    Figure 4.  Inverse estimation results of single-slot grating geometry parameters

    图 5  4种PSO算法目标函数值变化曲线

    Figure 5.  Changing curves of objective function values of four PSO algorithms

    图 6  不同种群大小下目标函数值变化曲线

    Figure 6.  Changing curves of objective function values under different population sizes

    图 7  双槽矩形光栅示意图

    Figure 7.  Schematic of rectangular double-slot grating

    图 8  双槽光栅光谱反射率

    Figure 8.  Spectral reflectance of double-slot grating

    图 9  双槽光栅几何参数反演结果

    Figure 9.  Inverse estimation results of double-slot grating geometry parameters

    表  1  SPSO算法参数设置

    Table  1.   Parameter setting of SPSO algorithm

    参数 数值
    M 50
    Vmax 3.0
    C1 1.2
    C2 0.8
    tmax 100
    ε1 10-6
    λ1/μm 0.1
    λ2/μm 5.0
    n 100
    下载: 导出CSV

    表  2  不同入射角度下反演结果

    Table  2.   Inverse estimation results with different incident angles

    入射角度/(°) aest/μm 平均相对误差/% 最大相对误差/%
    0 [1.000 6±1.26×10-3, 0.899 2±3.61×10-3, 0.600 4±2.51×10-3] 0.380 5 2.852 6
    30 [0.999 3±3.09×10-3, 0.899 3±4.59×10-3, 0.599 2±2.99×10-3] 0.368 9 2.863 1
    60 [0.999 4±2.90×10-3, 0.900 5±3.23×10-3, 0.599 3±3.02×10-3] 0.376 6 2.799 9
    下载: 导出CSV

    表  3  不同结构参数下反演结果

    Table  3.   Inverse estimation results with different structure parameters

    aexa/μm aest/μm 平均相对误差/% 最大相对误差/%
    [1.0, 0.9, 0.6] [0.999 3±3.09×10-3, 0.899 3±4.59×10-3, 0.599 2±2.99×10-3] 0.368 9 2.863 1
    [3.0, 2.5, 1.5] [2.999 1±3.11×10-3, 2.500 5±1.19×10-3, 1.499 4±2.95×10-3] 0.359 6 2.904 0
    [5.0, 4.0, 2.0] [5.000 6±3.33×10-3, 3.999 2±4.14×10-3, 2.000 6±3.20×10-3] 0.331 5 2.882 3
    下载: 导出CSV

    表  4  不同搜索区间下反演结果

    Table  4.   Inverse estimation results with different searching spaces

    算例 Λ /μm l /μm d/μm 迭代次数 目标函数值 平均相对误差/%
    算例1 [0.9, 1.1] [0.8, 1.0] [0.5, 0.7] 59 3.25×10-7 0.020 9
    算例2 [0.8, 1.2] [0.7, 1.1] [0.4, 0.8] 71 9.19×10-7 0.115 5
    算例3 [0.5, 1.5] [0.4, 1.4] [0.1, 1.1] 100 8.11×10-6 0.206 4
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-02-13
  • 录用日期:  2017-06-07
  • 刊出日期:  2017-11-20

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