四极子微腔的光场分布

Optical-Field Distribution of Quadrupolar-Shaped Microcavity

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Φ=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。

Using the theory of electromagnetic field and Maxwell equations in medium, we derive the TM mode optical field distribution of resonators with arbitrary cross section. Moreover, taking quadrupolar-shaped microcavity as example, it deduces the eigenvalue equation which contains the propagation constant. Using the software Mathematica, it stimulates the optical field distribution of fundamental mode （m=1） and high-order mode with the different deformation factors, and it is found that the fundamental mode gets the maximum of light emission at Φ=45°, 135°, 225°, 315°, it has the feature of ＂bow-tie＂ mode. Furthermore, when the deformation factor is 0.1～0.15, the effect is more obviously; however there is not the phenomenon of drawing out the light directionally in the microcavity when m ≥2, and it does not form the stable ＂bow-tie＂ mode when the deformation factor gets any values. It provides a certain theoretical base for designing and making the quadrupolar-shaped microcavity lasers.