各向异性周期性结构RCWA算法及并行计算加速
发布时间：2018-09-01 06:41
【摘要】：严格耦合波分析法(RCWA)是一种非迭代的能稳定收敛的状态变量解法,是周期结构衍射模拟分析中应用最广的傅立叶空间的方法,这种方法非常适合于对亚波长量级的周期结构进行衍射模拟分析。但是RCWA算法仍然存在对折射率剧烈变化的周期结构数值计算收敛慢的问题。本文基于衍射光栅的严格耦合波分析法,把光栅介质从各向同性的情形推广到各向异性情形。从各向异性衍射区域中电磁场傅立叶级数展开和介电常数张量的傅立叶级数展开出发,利用周期性边界条件和电磁波的横波性等特性,把求解矢量麦克斯韦方程组问题转换为求解矩阵特征值问题,从而求出电磁场的衍射效率,清晰明了的展示了各向异性光栅严格耦合波方法的推导过程。并以LiNbO3晶体为例,在光轴与坐标重合情形下,改变入射光波长、入射角等光栅参数讨论体光栅和表面浮雕光栅的衍射特性。收敛速度和计算效率问题一直是严格耦合波法的焦点问题,研究人员一直在寻找计算方法来提高收敛速度和数值稳定性,本文将并行计算技术应用到RCWA算法计算效率的改进上来。LU分解和QR分解是RCWA算法中使用频率非常高并且非常耗时的模块,用NVIDIA公司的CUDA混合计算架构对这两部分进行优化,采取的策略包括制定合适的并行计算算法,利用分块技术和共享内存技术,利用CUDA GPU具有高并行、多线程、计算能力强、带宽高的优良特性,提高RCWA模拟技术的计算效率。最后,简要的介绍了RCWA在光折变晶体和动态极化铌酸锂晶体分析中应用,以PPLN晶体衍射效率随光波长的变化规律为例,分析PPLN晶体的波长选择性。
[Abstract]:Strictly coupled wave analysis (RCWA) is a non-iterative and stable convergent method of state variables, which is the most widely used Fourier space method in the diffraction simulation of periodic structures. This method is very suitable for diffraction simulation of periodic structures of subwavelength order. However, the RCWA algorithm still has the problem of slow convergence for the numerical computation of periodic structures with sharp refractive index changes. Based on the strictly coupled wave analysis of diffractive gratings, the grating medium is extended from isotropic to anisotropic. Based on the Fourier series expansion of electromagnetic field in anisotropic diffraction region and the Fourier series expansion of dielectric constant Zhang Liang, the properties of periodic boundary condition and transverse wave of electromagnetic wave are used. The problem of solving vector Maxwell equations is transformed into solving matrix eigenvalue problem, and the diffraction efficiency of electromagnetic field is obtained, which clearly shows the derivation process of the strictly coupled wave method of anisotropic grating. Taking LiNbO3 crystal as an example, the diffraction characteristics of volume grating and surface relief grating are discussed by changing the parameters of incident light wave length and incident angle when the optical axis and coordinate coincide with each other. The problem of convergence rate and computational efficiency has always been the focus of strictly coupled wave method. Researchers have been looking for calculation methods to improve the convergence rate and numerical stability. In this paper, parallel computing technology is applied to improve the computational efficiency of RCWA algorithm. LU decomposition and QR decomposition are very high frequency and time consuming modules in RCWA algorithm. These two modules are optimized by CUDA hybrid computing architecture of NVIDIA Company. The strategies adopted include making appropriate parallel computing algorithms, using partitioning technology and shared memory technology, using CUDA GPU with high parallelism, multi-thread, strong computing power and high bandwidth, and improving the computing efficiency of RCWA simulation technology. Finally, the application of RCWA in the analysis of photorefractive crystals and dynamically polarized lithium niobate crystals is briefly introduced. The wavelength selectivity of PPLN crystals is analyzed by taking the variation of diffraction efficiency of PPLN crystals as an example.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN253;O436.1
本文编号：2216423
[Abstract]:Strictly coupled wave analysis (RCWA) is a non-iterative and stable convergent method of state variables, which is the most widely used Fourier space method in the diffraction simulation of periodic structures. This method is very suitable for diffraction simulation of periodic structures of subwavelength order. However, the RCWA algorithm still has the problem of slow convergence for the numerical computation of periodic structures with sharp refractive index changes. Based on the strictly coupled wave analysis of diffractive gratings, the grating medium is extended from isotropic to anisotropic. Based on the Fourier series expansion of electromagnetic field in anisotropic diffraction region and the Fourier series expansion of dielectric constant Zhang Liang, the properties of periodic boundary condition and transverse wave of electromagnetic wave are used. The problem of solving vector Maxwell equations is transformed into solving matrix eigenvalue problem, and the diffraction efficiency of electromagnetic field is obtained, which clearly shows the derivation process of the strictly coupled wave method of anisotropic grating. Taking LiNbO3 crystal as an example, the diffraction characteristics of volume grating and surface relief grating are discussed by changing the parameters of incident light wave length and incident angle when the optical axis and coordinate coincide with each other. The problem of convergence rate and computational efficiency has always been the focus of strictly coupled wave method. Researchers have been looking for calculation methods to improve the convergence rate and numerical stability. In this paper, parallel computing technology is applied to improve the computational efficiency of RCWA algorithm. LU decomposition and QR decomposition are very high frequency and time consuming modules in RCWA algorithm. These two modules are optimized by CUDA hybrid computing architecture of NVIDIA Company. The strategies adopted include making appropriate parallel computing algorithms, using partitioning technology and shared memory technology, using CUDA GPU with high parallelism, multi-thread, strong computing power and high bandwidth, and improving the computing efficiency of RCWA simulation technology. Finally, the application of RCWA in the analysis of photorefractive crystals and dynamically polarized lithium niobate crystals is briefly introduced. The wavelength selectivity of PPLN crystals is analyzed by taking the variation of diffraction efficiency of PPLN crystals as an example.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN253;O436.1
【参考文献】
相关期刊论文 前1条
1 傅克祥,王植恒,张大跃,张靖,张奇志;大深度任意剖面形状光栅的模式理论和RTCM递推算法[J];中国科学(A辑);1999年04期
，本文编号：2216423
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