模式转换器耦合波方程组的微波网络矩阵解法

A Microwave Network Matrix Solution to Coupling-wave Differential Equations for Mode Converter

求解具有边值条件的耦合波微分方程组是研究变截面波导或弯曲波导模式转换器的基本方法。利用微波网络理论,给出了一种求解边值条件耦合波微分方程组的新方法,以简化求解过程,并使得解的物理意义更加明确。对于一个考虑了N个微波模式相互作用的耦合波微分方程组,通过分别赋予其2N个不同的初值条件并求解,可得到该方程组所描述模式转换器的传输矩阵和散射矩阵,进一步利用散射矩阵可得到给定边值条件下微分方程组的解。

Solving coupling-wave differential equations with boundary-value conditions is a basic method for investigating waveguide mode converters with varying radius or bent axis.A matrix method according to microwave net theory is presented to make the solution simple and explicit with clearer physical meanings.For a group of coupling-wave differential equations in which N coupling waveguide modes are considered,the transmitting matrix and scattering matrix of the converter described by the equations can be obtained by solving the differential equations 2N times with different initial value conditions,respectively.Then with use of the scattering matrix,the solution of the coupling-wave differential equations with boundary-value conditions can be educed.