一维函数光子晶体的研究

本文提出一种新型函数光子晶体, 其折射率是空间位置函数. 由费马原理, 我们给出光在一维、 二维和三维函数光子晶体中的运动方程, 以及一维函数光子晶体的色散关系、 带隙结构和透射率, 再利用传输矩阵理论研究函数光子晶体周期数、 入射角和介质层的厚度等对透射率和禁带结构的影响, 计算发现通过选择不同的折射率空间分布函数, 可以得到比传统光子晶体更宽或更窄的禁带结构. 这样为我们设计不同带隙结构的光子晶体提供理论依据.

Research on one-dimensional function photonic crystals

In the paper, we present a new kind of function photonic crystal of which the refractive index is a function of space position. According to Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystal, we give the dispersion relation, the band gap structure and the transmissivity, and we obtain wider or narrower band gap structure than that of conventional photonic crystal. We study the effects of the refractive index, the number of period, the incidence angle and the thickness of medium layer on photonic crystal band gap, and obtain some valuable laws. Our results give the theoretical support designing the photonic crystals of different band gap structures.