Inverse estimation of geometric parameters of aluminum matrix microscale structure grating
-
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。
-
关键词:
- 光栅结构反演 /
- 随机微粒群优化(SPSO)算法 /
- 严格耦合波分析(RCWA)法 /
- 光谱反射率 /
- 辐射特性
Abstract:Micro structure grating is a widely used electronic component. The geometric parameters of one-dimensional rectangular aluminum matrix grating are inversely estimated using stochastic particle swarm optimization (SPSO) algorithm. The theoretical overview of rigorous coupled wave analysis (RCWA) algorithm and particle swarm optimization algorithm is introduced, and RCWA algorithm is employed to solve the electromagnetic field problem within grating. The objective function is formulated based on the spectral reflectance obtained by the direct problem, and then the SPSO algorithm is used to optimize the objective function. The geometric parameters such as the grating period, ridge width and groove depth are retrieved simultaneously. The effects of population size and searching space on the inverse estimation results are also investigated. The retrieval results show that SPSO algorithm is effective and robust for estimating geometric parameters of grating and the population size is suggested as 30.
-
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 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 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 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 -
[1] 梁铨廷.物理光学[M].北京:电子工业出版社, 2009:1-11.LIANG Q T.Physical optics[M].Beijing:Publishing House of Electronics Industry, 2009:1-11(in Chinese). [2] LEE B J, WANG L P, ZHANG Z M.Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film[J].Optical Express, 2008, 16(15):11328-11336. doi: 10.1364/OE.16.011328 [3] JIAO Y, LIU L H, LIU L J, et al.Radiative properties tailoring of grating by comb-drive microactuator[J].Journal of Quantitative Spectroscopy and Radiative Transfer, 2014, 143:35-45. doi: 10.1016/j.jqsrt.2014.01.010 [4] CHEN Y B, ZHANG Z M.Design of tungsten complex gratings for thermophotovoltaic radiators[J].Optics Communications, 2007, 269(2):411-417. doi: 10.1016/j.optcom.2006.08.040 [5] QIU J, LIU L H, HSU P F.FDTD analysis of infrared radiative properties of microscale structure aluminum surfaces[J].Journal of Quantitative Spectroscopy and Radiative Transfer, 2010, 111(12-13):1912-1920. doi: 10.1016/j.jqsrt.2010.04.026 [6] ZHANG Z M.Nano/microscale heat transfer[M].New York:McGraw-Hill Professional, 2007:1-36. [7] 王强, 沈国土, 杨宝成, 等.遗传算法在光栅面形状优化设计中的应用[J].红外与激光工程, 2005, 34(4):410-414. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=hwyj200504008&dbname=CJFD&dbcode=CJFQWANG Q, SHEN G T, YANG B C, et al.Application of genetic algorithm in the design optimization of grating profile[J].Infrared and Laser Engineering, 2005, 34(4):410-414(in Chinese). http://kns.cnki.net/KCMS/detail/detail.aspx?filename=hwyj200504008&dbname=CJFD&dbcode=CJFQ [8] 董健. 一维微结构光栅辐射特性的反设计方法[D]. 哈尔滨: 哈尔滨工业大学, 2013. http://cdmd.cnki.com.cn/Article/CDMD-10213-1014001130.htmDONG J.Inverse design method on radiative properties of one dimensional micro/nano scale grating[D].Harbin:Harbin Institute of Technology, 2013(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10213-1014001130.htm [9] CHEN J S, LIN P D, CHIU F C, et al.Grating profile optimization for narrow-band or broad-band infrared emitters with differential evolution algorithms[J].Optical Letters, 2012, 37(16):3399-3401. doi: 10.1364/OL.37.003399 [10] KENNEDY J, EBERHART R C.Particle swarm optimization[C]//Proceedings of IEEE International Conference on Neural Networks.Piscataway, NJ:IEEE Press, 1995:1942-1948. [11] ZHAO J M, QIU J, LIU L H.Accurate geometry design of magnetic polariton with specified resonance wavelength:A combined LC circuit model and inverse technique[C]//ASME 20165th Micro/Nanoscale Heat and Mass Transfer International Conference.New York:ASME, 2016:V001T05A008. [12] 曾建潮, 崔志华.一种保证全局收敛的PSO算法[J].计算机研究与发展, 2004, 41(8):1333-1338. http://d.wanfangdata.com.cn/Periodical/jsjyjyfz200408003ZENG J C, CUI Z H.A guaranteed global convergence particle swarm optimizer[J].Journal of Computer Research and Development, 2004, 41(8):1333-1338(in Chinese). http://d.wanfangdata.com.cn/Periodical/jsjyjyfz200408003 [13] CUI Z H, ZENG J C, CAI X J.A new stochastic particle swarm optimizer[C]//Proceedings of IEEE International Congress on Evolutionary Computation.Piscataway, NJ:IEEE Press, 2004:316-319. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=1330873 [14] MOHARAM M G, GRANN E B, POMMET D A.Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings[J].Journal of the Optical Society of America A, 1995, 12(5):1068-1076. doi: 10.1364/JOSAA.12.001068 [15] SHI Y H, EBERHART R C.A modified particle swarm optimizer[C]//Proceedings of IEEE International Conference on Evolutionary Computation.Piscataway, NJ:IEEE Press, 1998:69-73. [16] WAKAKI M, KUDO K, SHIBUYA T.Physical properties and data of optical materials[M].Boca Raton:CRC Press, 2007:1-10. [17] ROBINSON J, SINTON S, RAHMAT-SAMⅡ Y.Particle swarm, genetic algorithm, and their hybrids:Optimization of a profiled corrugated horn antenna[C]//IEEE Antennas and Propagation Society International Symposium.Piscataway, NJ:IEEE Press, 2002:314-317. http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=1016311 [18] CHENG Q, LI P P, LU J, et al.Silicon complex grating with different groove depths as an absorber for solar cells[J].Journal of Quantitative Spectroscopy & Radiative Transfer, 2014, 132:70-79. https://www.sciencedirect.com/science/article/pii/S0022407313000496