Abstract: Photonic band gap (PBG) of one-dimensional ZnO/MgF₂ photonic crystal is studied with the optical transmission matrix method. A one-dimensional model consisting of ZnO and MgF₂ is proposed. The influence of PBG by the periodicity N is studied, and the effect of the PBG width and the center length by the film thickness is also discussed. In the end, the authors discuss the condition to get the maximum of the PBG width with the center length as a constant, and propose an explanation from physics mechanism. When the products of the refractive index and the thickness of the two different films are equal, the PBG reaches the maximum. When the product is 93 nm, the center length is at 385.05 nm with the PBG width of 138.7 nm.

Key words: photonic crystal, ZnO/MgF₂, optical transmission matrix, PBG

摘要： 利用光学传输矩阵理论对一维ZnO/MgF₂光子晶体的光子带隙进行了研究。文中给出了一个由ZnO和MgF₂组成的一维光子晶体模型，并在此基础上详细讨论了光子晶体的周期数，对光子带隙的形状及震荡频率的影响，以及薄膜的厚度对光子带隙的带隙宽度、中心波长等的影响。讨论了在保持光子带隙的中心波长不变的情况下，通过改变两种薄膜的厚度使得带隙宽度达到最大值的条件，并且从物理机制上给出了相应的解释。当两种薄膜的折射率和厚度的乘积相等时，所获得的光子带隙最大，当这个乘积等于93 nm时，所获得的光子带隙的中心波长在385.05 nm处，带隙宽度为138.7 nm。

关键词: 光子晶体, ZnO/MgF₂, 传输矩阵法, 光子带隙