应用电磁场理论和介质中的麦克斯韦方程组,推导了任意截面微腔的TM模光场分布。并以四极子状微腔截面为例,推导了含有传播常数的本征方程。用Mathematica软件模拟出具有不同变形因子的基模(m=1)和高阶模的光场分布图,得出基模在=45°,135°,225°,315°四个方向光辐射最强,具有“蝴蝶结模式”特征,并且当变形因子值取ε′为0.1~0.15时,该效应表现得更明显;而高阶模(m≥2)时微腔中没有这种光的定向输出现象,在任何变形因子情况下也不能形成稳定的“蝴蝶结模式”,为四极子微腔激光器的设计和制作提供了一定的理论依据。 Based on the theory of electromagnetic field and the Maxwell equations in the medium, the TM mode field distribution of microcavity with arbitrary cross section is deduced. Taking the quadrupole microcavity cross section as an example, the eigenvalue equation with propagation constant is deduced. The light field distributions of the fundamental modes (m = 1) and the higher order modes with different deformation factors were simulated by Mathematica software. The results show that the optical modes of the fundamental modes are the strongest in four directions of  = 45 °, 135 °, 225 ° and 315 ° , Which has the characteristic of “bow-tie mode”, and the effect is more obvious when the value of deformable factor ε ’is 0.1~0.15; however, in the high-order mode (m≥2), the directional output of this light is absent in Any deformation factor can not form a stable “bow pattern”, which provides a theoretical basis for the design and fabrication of quadrupole laser.