【摘要】 提出了一种基于辛几何的高频近似的新方法 ,并用此方法求解了电磁波在一非均匀媒质中的传播问题。通过辛空间上的坐标变换 ,使电磁波传播中的焦散问题转化为非焦散的问题 ,并结合几何光学的方法 ,求得了包括焦散区在内的高频近似解。解决了几何光学法无法在焦散区求解的问题 ,还可以推广到二维及三维的情况更多还原

【Abstract】 A new symplectic geometrical high frequency approximation method for solving the propagation of electromagnetic wave in an inhomogeneous medium is presented. The propagating caustic problem of electromagnetic wave is translated into non caustic problem by the coordinate transform on the symplectic space. The high frequency approximation solution that includes the caustic region is obtained with the method combining the geometrical optics. The drawback that the solution in the caustic region can not be obtained with geometrical optics is overcome by this method. Furthermore, the method can further be extended to twodimensions and threedimensions.更多还原