摘要时域有限差分法是研究光子晶体常用的有效方法，它利用时间和空间的离散 化，将偏微分方程转化为差分方程，用于求解电磁波的相关问题。光子晶体以光 子为信息载体，如同半导体控制电子一样，控制光子的运动。68513

本文利用软件 Rsoft 和 OptiFDTD 对不同材料的光子晶体建模、仿真，得到带 隙位置和透射谱。再将正方形和三角形晶格的结果相比较，证实了光子晶体具有 带隙特性，且后者比前者的带隙宽度更宽。对光子晶体导波特性的研究表明，光 子晶体还具有光子局域特性和弯曲效应。

最后本文根据光子晶体的局域特性和导波特性，寻找并设计滤波效果较好的 微腔滤波器。通过对不同微腔材料、微腔数量及微腔的对称性进行比较，最终找 到了针对特定波长的 SiO2 和 GaAs 光子晶体滤波器。

关键词 光子晶体 时域有限差分法 带隙 透射谱 滤波器

Title    The FDTD Modeling in Two-dimensional Photonic   Crystals  and the Calculation of the Transmission Spectrum

Abstract

Finite-Difference Time-Domain (FDTD) technique is a usual and useful way to study the photonic crystal (PC), which transforms the partial differential equation into difference equation with the discretization of time and space to solve problems concerning the electromagnetic wave. Photons are information carriers of PCs which control the movement of photons as the semiconductor to electrons.

Different material photonic crystals has been modeled and simulated by the    softwares

—— Rsoft and OptiFDTD, and we discovered the band gaps and the transmission spectrums. After that, the results of the square lattice structures were compared with those of the triangle ones, which confirmed that there are band gap characteristics in PCs, and the gap of the later is wider than that of the former. Based on the research of PCs' guided mode characteristics, the photon localization properties and the bending effects have been found in PCs as well.

According to the localization properties and the guided wave characteristics in the PCs, we searched and designed an effective photonic crystal cavity filter. Eventually, with the comparison of different materials, numbers and the symmetry of the cavities, we found the SiO2 and the GaAs photonic crystal filters out for specific wavelengths.

Keywords  Photonic crystal    FDTD    Bandgap      Transmission spectrum     Filter

目 次

1 绪论 1

1.1 本文的相关背景 1

1.2 光子晶体的概述 1

1.3 光子晶体的应用 1

1.4 本文主要任务安排 3

2 光子晶体与时域有限差分法 4

2.1 光子晶体的结构 4

2.2 光子晶体的分类 4

2.3