【摘要】：嚴(yán)格耦合波分析法(RCWA)是一種非迭代的能穩(wěn)定收斂的狀態(tài)變量解法,是周期結(jié)構(gòu)衍射模擬分析中應(yīng)用最廣的傅立葉空間的方法,這種方法非常適合于對亞波長量級的周期結(jié)構(gòu)進(jìn)行衍射模擬分析。但是RCWA算法仍然存在對折射率劇烈變化的周期結(jié)構(gòu)數(shù)值計算收斂慢的問題。本文基于衍射光柵的嚴(yán)格耦合波分析法,把光柵介質(zhì)從各向同性的情形推廣到各向異性情形。從各向異性衍射區(qū)域中電磁場傅立葉級數(shù)展開和介電常數(shù)張量的傅立葉級數(shù)展開出發(fā),利用周期性邊界條件和電磁波的橫波性等特性,把求解矢量麥克斯韋方程組問題轉(zhuǎn)換為求解矩陣特征值問題,從而求出電磁場的衍射效率,清晰明了的展示了各向異性光柵嚴(yán)格耦合波方法的推導(dǎo)過程。并以LiNbO3晶體為例,在光軸與坐標(biāo)重合情形下,改變?nèi)肷涔獠ㄩL、入射角等光柵參數(shù)討論體光柵和表面浮雕光柵的衍射特性。收斂速度和計算效率問題一直是嚴(yán)格耦合波法的焦點(diǎn)問題,研究人員一直在尋找計算方法來提高收斂速度和數(shù)值穩(wěn)定性,本文將并行計算技術(shù)應(yīng)用到RCWA算法計算效率的改進(jìn)上來。LU分解和QR分解是RCWA算法中使用頻率非常高并且非常耗時的模塊,用NVIDIA公司的CUDA混合計算架構(gòu)對這兩部分進(jìn)行優(yōu)化,采取的策略包括制定合適的并行計算算法,利用分塊技術(shù)和共享內(nèi)存技術(shù),利用CUDA GPU具有高并行、多線程、計算能力強(qiáng)、帶寬高的優(yōu)良特性,提高RCWA模擬技術(shù)的計算效率。最后,簡要的介紹了RCWA在光折變晶體和動態(tài)極化鈮酸鋰晶體分析中應(yīng)用,以PPLN晶體衍射效率隨光波長的變化規(guī)律為例,分析PPLN晶體的波長選擇性。
[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.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TN253;O436.1

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本文編號：2216423