应用于亚波长角向偏振金属光栅设计的快速收敛粒子群算法优化

Fast Convergent Particle Swarm Optimization Algorithm for Subwavelength Azimuthally Polarized Metal Grating Design

提出了分步寻优的基于粒子位置调整惯性权重的粒子群算法(PDW-PSO),通过调用严格耦合波方法(RCWA)计算衍射效率,进行了光栅结构参数的优化。将PDW-PSO与惯性权重不变的粒子群算法(PSO)和基于迭代次数调整惯性权重的粒子群算法(IDW-PSO)进行对比,结果表明PDW-PSO具有更快的收敛速度,相比于PSO和IDW-PSO,PDW-PSO的平均迭代次数分别从89.83和74减少至21.2,调用RCWA的次数分别从3144.05和2590下降至224。分析了波段匹配数对算法的影响, PSO和IDW-PSO的RCWA调用次数与波段匹配数呈等倍率增加,而PDW-PSO的RCWA调用次数的增加倍率小于波段匹配数的增加倍率。进行了算法准确度实验,在30次运行中,PDW-PSO与PSO、IDW-PSO正确收敛到最优值的次数相近,误差值不超过6.6%;随着粒子数的增加,三种方法的准确度都有所提高,粒子数达到27后基本都可以保证收敛到最优。

A particle swarm optimization algorithm(PDW-PSO), of which the inertia weight is modulated by particle position, is proposed for step-by-step optimization. The diffraction efficiency is calculated using rigorous coupled wave analysis(RCWA), and structural parameters of gratings are optimized. The comparison among PDW-PSO, traditional particle swarm optimization of which the inertial weight is unchanged(PSO), and particle swarm optimization of which the inertia weight is iteration-determined(IDW-PSO) shows that PDW-PSO has a faster convergence rate. Compared with PSO and IDW-PSO, the average number of iterations of PDW-PSO decreases from 89.83 and 74 to 21.2, and the number of calling RCWA drops from 3144.05 and 2590 to 224. The influence of wavelength matching number on the algorithm is analyzed. The magnification of RCWA calling numbers of PSO and IDW-PSO is equal to that of wavelength fitting number, while the magnification of RCWA calling numbers of PDW-PSO is less than that of wavelength fitting number. Experiments on algorithm accuracy are carried out. In 30 runs, PDW-PSO, PSO, and IDW-PSO have similar times of correct convergence to the optimal value, and the error is less than 6.6%. With the increasing particle number, the accuracy of the three methods improves, and the algorithm can be guaranteed to converge to the right optimal value after the particle number increasing to 27.