深度学习的亚波长窄带陷波滤光片设计

Design of Subwavelength Narrow Band Notch Filter Based on Depth Learning

亚波长光栅结构表现出优异的陷波滤光特性,其经典设计是设定亚波长的几何结构参数,求解麦克斯韦方程组,设定优化算法求解出最优解,需要消耗大量的时间和计算资源。提出一种基于深度学习的逆向设计方法,搭建了可以同时实现正向模拟与逆向设计的串联神经网络。基于python语言的Tensorflow库进行网络搭建;优化均匀波导层的高度、亚波长光栅的高度、折射率、周期以及占空比;研究亚波长光栅在0.45~0.7μm的陷波滤光特性。采用严格耦合波分析(RCWA)数值模拟生成23100组数据集,在生成的数据集中随机选择18480组数据作为训练集,4620组作为测试集,并对不同的网络层数,网络节点以及Batch_size进行了研究。结果显示经过1000次的迭代后,当网络的模型结构为5×50×200×500×200×26,Batch_size大小为128时,网络性能最佳。相比独立的网络模型,串联神经网络的正向模拟测试集损失率从0.03363降到了0.0045,逆向设计的测试集损失率从0.70298降到了0.05298,同时解决了由数据的非唯一性导致的网络逆向设计过程中无法收敛的问题。在完成训练的网络中输入任意的光谱曲线,网络平均在1.35 s内给出亚波长光栅的几何结构参数;并与RCWA数值模拟曲线进行相关性分析,曲线相似系数均大于0.6581,属于强相关。另外,设计红、绿、蓝三种颜色的陷波滤光片,其峰值反射率分别可以达到98.91%,99.98%和99.88%,与传统方法相比,该方法可以快速、精确的求解出光栅的几何参数,为亚波长光栅设计提供了新方法。

Subwavelength grating structures exhibit excellent notch filtering properties.The classical design is to find the optimal solution by setting the geometric structure parameters of the subwavelength,solving Maxwell’s equations,and setting an optimization algorithm.It consumes a lot of time and computing resources.This paper presents an inverse design method based on deep learning and constructs a series neural network which can realize both forward simulation and inverse design.The Tensorflow library based on Python language is constructed to optimize the height of uniform waveguide layer,the height of sub-wavelength grating,refractive index,period and duty cycle,and to study the characteristics of sub-wavelength grating notch filtering in the range of 0.45~0.7μm.Using rigorous coupled wave analysis(RCWA)numerical simulation to generate 23100 data sets,18480 data sets were randomly selected as training sets,and 4620 data sets were used as test sets,the network node and Batch were studied.The results show that the network performance is best when the network model structure is 5×50×200×500×200×26,and the Batch size is 128 after 1000 iterations.Compared with the independent network model,the loss rate of the forward simulation test set of the series neural network decreased from 0.03363 to 0.0045,and that of the reverse design decreased from 0.70298 to 0.05298.At the same time,the problem that the network can not converge in the reverse design process caused by the non-uniqueness of data is solved.The geometric structure parameters of the sub-wavelength grating are given in 1.35 s on average by inputting any spectral curve into the trained network,and the correlation between the parameters and the RCWA numerical simulation curve is analyzed,the similarity coefficients of the curves were all greater than 0.6581,which belonged to strong correlation.In addition,a red,green and blue notch filter is designed,whose peak reflectivity can reach 98.91%,99.98%and 99.88%respectively.Compared with the traditional method,this method can quickly and accurately calculate the geometric parameters of the grating.It provides a new method for sub-wavelength grating design.