Finite-Difference and Fourier Modal Methods for the Analysis of Gratings Structures

• Main Authors: Chi-Kai Shen, 沈祺凱
• Other Authors: 邱奕鵬
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/38316957865189014178

碩士 === 臺灣大學 === 光電工程學研究所 === 98 === In this thesis, the finite-difference modal method (FDMM) with step-index formulation for simulating grating structures is proposed and compared with rigorous coupled-wave analysis (RCWA), also called Fourier modal method (FMM). It is verified that FDMM has better convergence and accuracy than RCWA for TE polarization in almost all cases and TM polarization for high conductive and lossless metallic materials. In the FDMM, the relation of interface conditions to arbitrary high orders is considered and combines with Taylor series expansion. The generalized Douglas (GD) scheme is also adopted to enhance the convergence order without considering more sampled points. With the techniques mentioned above, the sparse matrix of eigenvalue problem could be constructed to solve the fields and the propagation constants of modes inside each layer. In addition, the enhanced transmittance matrix approach proposed by Moharam emph{et al.} for RCWA is used to make matrix manipulation stable for multi-layer or even single layer gratings. The diffraction properties of gratings, such as accuracy, convergence, dependence of diffraction efficiencies on incident angle, thickness, duty cycle, etc, will be discussed for numerical assessment of FDMM. Moreover, two-dimensional finite-difference methods combined with periodic boundary conditions and absorbing boundary conditions will be executed for comparison.