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基于深度学习的Fano共振超材料设计

杨知虎 傅佳慧 张玉萍 张会云

杨知虎, 傅佳慧, 张玉萍, 张会云. 基于深度学习的Fano共振超材料设计[J]. 中国光学(中英文), 2023, 16(4): 816-823. doi: 10.37188/CO.2022-0208
引用本文: 杨知虎, 傅佳慧, 张玉萍, 张会云. 基于深度学习的Fano共振超材料设计[J]. 中国光学(中英文), 2023, 16(4): 816-823. doi: 10.37188/CO.2022-0208
YANG Zhi-hu, FU Jia-hui, ZHANG Yu-ping, ZHANG Hui-yun. Fano resonances design of metamaterials based on deep learning[J]. Chinese Optics, 2023, 16(4): 816-823. doi: 10.37188/CO.2022-0208
Citation: YANG Zhi-hu, FU Jia-hui, ZHANG Yu-ping, ZHANG Hui-yun. Fano resonances design of metamaterials based on deep learning[J]. Chinese Optics, 2023, 16(4): 816-823. doi: 10.37188/CO.2022-0208

基于深度学习的Fano共振超材料设计

doi: 10.37188/CO.2022-0208
基金项目: 国家自然科学基金(No. 61875106,No. 62105187);山东省自然科学基金(No. ZR2021QF010)
详细信息
    作者简介:

    杨知虎(1998—),男,黑龙江牡丹江人,硕士研究生,2020年于山东科技大学获得学士学位,主要研究方向为基于深度学习的超材料设计。E-mail:383048999@qq.com

    张会云(1974—),男,山东沂水人,博士,教授,博士生导师,2008年于天津大学获得博士学位,主要从事太赫兹功能器件方面的研究。E-mail:sdust_thz@126.com

  • 中图分类号: O436.3

Fano resonances design of metamaterials based on deep learning

Funds: Supported by National Natural Science Foundation of China (No. 61875106, No. 62105187); Natural Science Foundation of Shandong Province (No. ZR2021QF010)
More Information
    Corresponding author: sdust_thz@126.com
  • 摘要:

    本文提出了一种基于深度学习的超材料Fano共振设计方法,能够获得高Q共振的线宽、振幅和光谱位置特性。利用深度神经网络建立结构参数和透射谱曲线之间的映射,正向网络实现对透射谱的预测,逆向网络实现对高Q共振按需设计,设计过程中实现了低均方误差(MSE),训练集的均方误差为 0.007。与传统方法需要耗时的逐个数值模拟相比,深度学习设计方法大大简化了设计过程,实现了高效、快速的设计目标。对Fano共振的设计也可推广应用到其它类型的超材料的自动逆向设计,显著提高了更复杂的超材料设计的可行性。

     

  • 图 1  用于双向神经网络设计的框架示意图。(a)ASRR的单位单元结构图;(b)正向神经网络图;(c)正向预测输出的透射谱;(d)逆向设计输出的最优参数;(e)逆向神经网络图;(f)逆向设计输入的透射谱

    Figure 1.  Schematic diagram of the framework used for the bidirectional neural network design process. (a) The unit cell structure diagram of ASRR; (b) the forward neural network diagram; (c) transmission spectrum of the forward prediction output; (d) optimal parameters of the reverse design output; (e) inverse neural network diagram; (f) transmission spectrum of the inverse design input

    图 2  神经网络模型

    Figure 2.  Neural network model

    图 3  Sigmoid激活函数

    Figure 3.  Sigmoid activation function

    图 4  DNN的结构参数

    Figure 4.  Structural parameters of DNN

    图 5  正向神经网络损失

    Figure 5.  Forward neural network loss

    图 6  不同网络层数对损失函数的影响对比

    Figure 6.  Comparison of the influence of different network layers on the loss function

    图 7  正向预测结果和数值模拟结果

    Figure 7.  Forward prediction results and numerical simulation results

    图 8  (a) 逆向神经网络的模型训练损失演变。(b) 逆向神经网络输出,CST仿真结果和目标频谱比较

    Figure 8.  (a) Evolution of model training loss for an inverse neural network. (b) Comparison of inverse neural network output,CST simulation results and target spectrum

    图 9  优化后的模型俯视图。沿y轴入射,周期性P=90 µm,铝环厚度H=14 µm,铝环臂宽W=6 µm,间隙G=3 µm,非对称性D=3 µm

    Figure 9.  Top view of the optimized model. Incident along the y-axis, periodicity P=90 µm. Aluminum ring thickness H=14 μm, aluminum ring arm width W=6 μm, gap G=3 μm, asymmetric tuning factor D=3 μm

    图 10  在0.97 THz处,结构参数为[70,14,6,3,3]晶格失配和[90,14,6,3,3]晶格匹配条件下,Fano的近场总电场和磁场振幅|E|和|B|。同一场的所有贴图共享相同范围的颜色比例。

    Figure 10.  The near-field total electric and magnetic field amplitude, |E| and |B| of the Fano resonance under the conditions of the structural parameters of [70, 14, 6, 3, 3] lattice mismatched and [90, 14, 6, 3, 3] lattice matched. All maps of the same field share a color scale with the same range

    表  1  训练神经网络的数据值

    Table  1.   Data values of training neural network (μm)

    PHWGD
    7010511
    7111622
    $ \vdots $$ \vdots $$ \vdots $$ \vdots $$ \vdots $
    12515733
    下载: 导出CSV
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  • 收稿日期:  2022-10-10
  • 修回日期:  2022-11-11
  • 网络出版日期:  2023-03-08

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