采用在椭圆柱坐标系中分离变量的方法,得到了填充多层介质共焦椭圆同轴线模式特征方程.研究表明:当椭圆退化为圆时,利用角向和径向马修函数的渐进关系,可得到填充多层介质的圆形同轴线的模式特征方程,由此可见,圆形同轴线可看作椭圆形同轴线的特例;当椭圆同轴线内导体半长轴大小为零时,则椭圆同轴线就变成椭圆波导,同样的方法,可得到填充多层介质的椭圆波导模式特征方程.当填充一层介质时,得到了椭圆同轴线和椭圆波导的模式特征方程,结果和相关文献所得结果相同.作为示例,对填充一层介质和两层介质的椭圆同轴线中一些模式色散特性进行了数值计算,分析了椭圆同轴线中介质参数的变化以及椭圆同轴结构的变化等对其传播特性的影响.
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