Characteristic Investigation and Finite Element Method Modeling for Two-Dimensional Anisotropic Photonic Crystals

• Main Authors: Sen-ming Hsu, 許森明
• Other Authors: 張宏鈞
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/59580007313108063300

博士 === 國立臺灣大學 === 光電工程學研究所 === 96 === A generalized scalar finite element method (FEM) based eigenvalue algorithm for analyzing the band structures of two-dimensional (2D) anisotropic photonic crystals (PCs) when the wave modes in the PCs can be decoupled into the transverse-electric (TE) and transverse-magnetic (TM) ones is developed first to investigate the intrinsic effect of anisotropic materials on constructing complete band structures. The 2D anisotropic PCs with square and triangular lattices are analyzed, and the relationships among the distinct sub-zones of the first Brillouin zones (BZs) for these two lattices are examined. The concept of constructing complete band structures for isotropic PCs should be modified for anisotropic PCs by taking into accounts enough necessary sub-zones in the first BZ. Then a full-vectorial FEM based eigenvalue algorithm under the in-plane wave propagation is further proposed for the band structure analysis of 2D PCs with arbitrary 3D anisotropy. We attempt an idea of considering all the electric or magnetic field components simultaneously and formulate a matrix eigenvalue equation to deal with the most general 2D PC problems. The relationship between this full-vectorial algorithm and the generalized scalar one is clarified from the analysis of isotropic PCs, and the significance of this full-vectorial algorithm is demonstrated through the examination of an example anisotropic PC. It is seen that a deeper insight about 2D anisotropic PCs can be obtained utilizing this full-vectorial algorithm. Finally a full-vectorial FEM based eigenvalue algorithm under the out-of-plane wave propagation for the band edge diagram construction of 2D PCs with arbitrary 3D anisotropy is also presented. Based on this full-vectorial algorithm, the band edge diagrams of various PCs with different material combination and geometry definition can be conveniently and correctly constructed. Consequently, quite valuable guidelines for the analysis and design of photonic band gap (PBG) fibers can be acquired with the help of this full-vectorial algorithm.