填充层状电介质矩形波导中的电磁波

Electromagnetic Ware in a Rectangular Wave Guide with Dielectric Tiers

令向量位的方向垂直于介质分界面 ,由Maxwell方程可以得到Ey和Hy模的场分量按本征函数系的展开式 .为了得到本征函数的本征值 ,必须导出在Ey模和Hy模中的本值方程 .在各层介质中kx有相同值 ,kz亦然 ,因此K2 =k2 x+k2 z也具有相同的值 .kx可以直接由边界条件得到 ,而各层介质中的K必须通过边界条件与连续性条件求解 .在由场分量的边界条件和连续性条件导出的线性方程组中将本征函数的系数视为未知数 ,令方程组具有不平凡解 ,得到ky的本征方程 ,利用k2i=K2 +k2 yi(i=1,2 ,3) ,再将此方程转换为本征方程 .

Let the direction of vector potential to be vertical to the dividing face of dielectric tiers.From Maxwell's equations,the expansion equations of the field comonents with orthogonal function system of E ymode and H ymode can be obtained .ln order to obtain the eigenvalue of the eigenfunctions,the eigenvalue equations in E ymode and H ymode must be derived .The eigen value k x in each dielectric tier has the same value as in another dielectric tier and the same as eigenvalue k z.For this reason,K 2=k 2 x+k 2 z in each dielectric tier has the same value as in another dielectric tier too.K xcan obtained from boundary conditions,but the eigenvalue k yin each dielectric tier must be found with boundary conditions and continuity conditions.When the coefficients in the linear equation system,which are derived with boundary conditions and continuity conditions,are taken as unknown numbers and the equation system is set to have nonordinary solutions, we can obtain k y's eigenvalue equations in E ymode and H ymode.After that,those equations can be changed into the eigenvalue equations of k y by using the relation k 2 i=K 2+k 2 yi(i=1,2,3).ln addition,the normalized coefficients of eigenfunctions are obtained with orthogonal property.