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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。结果表明，与传统方法需要耗时的逐个数值模拟相比，深度学习的设计方法大大简化了设计过程，实现了满足高效、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。
Abstract:In this paper, a metamaterial Fano resonance design method based on deep learning is proposed to obtain high-quality factor (high-Q) resonances with desired characteristics, such as linewidth, amplitude, and spectral position.The deep neural network is used to establish the mapping between the structural parameters and the transmission spectrum curve, and the forward network is used to predict the transmission spectrum.The inverse network achieves the on-demand design of high Q resonance. The low mean square error ( MSE ) is achieved in the design process, and the mean square error of the training set is 0.007.The results indicate that compared with the traditional design process, using deep learning to guide the design can achieve faster, more accurate, and more convenient purposes.The design of Fano resonance can also be extended to the automatic inverse design of other types of metamaterials, significantly improving the feasibility of more complex metamaterial designs.
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Key words:
- metamaterials /
- neural networks /
- Fano resonance /
- reverse engineering /
- deep learning
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图 1 用于双向神经网络设计过程的框架的示意图。（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 6 比较不同网络层数对损失函数的影响。
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的演变。（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) Inverse neural network output，CST simulation results and target spectrum comparison.
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 D=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 structural parameters are [70,14,6,3,3] lattice mismatched and [90,14,6,3,3] lattice matched conditions. 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 单位：μm
Table 1. Data values of training neural network unit: μm
P H W G D 70 10 5 1 1 71 11 6 2 2 $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 125 15 7 3 3 
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