基于传输矩阵法, 数值研究了掺杂对一维光子晶体带隙特征的影响。研究表明：掺杂时, 禁带中心会出现一导带, 导带深度会随着掺杂位置、杂质折射率的变化而发生变化。当晶体结构给定时, 总存在一个掺杂位置, 使其禁带中心的导带深度达到最深; 而对于给定的掺杂位置, 当杂质折射率为某特定值时, 禁带中心同样也会出现一个深度最深的导带, 这种特性可应用于滤波器件和光学谐振腔的设计。

Based on transfer matrix method, the effects of doping on one-dimensional photonic crystal are researched numerically. It is shown that in doped photonic crystal, there is a conduction band in the center of band gap, and the depth of conduction band varies gradually with the doping position and refractive index. When the crystal structure is given, there is always a doping position which makes the conduction band depth maximal in the center of band gap. When the doping position is given, there is always a specific value of impurity refractive index which makes the conduction band depth maximal in the center of band gap. These characteristics of one-dimensional photonic crystals are applied for the design of filters and optical resonators.