Orthogonal decomposition of external oscillation

External oscillation is decomposed orthogonally using the theory of differential geometry. It is shown that the SEM (singularity expansion method) poles of a smooth scatterer in three-dimension have three indexes (l, m, n). The l indicates the order of the creeping wave on the surface, and m and n describe the modes of the standing waves in two orthogonal directions. It is noted that the SEM poles of a sphere have two indexes (l, n); for a smooth scatterer, the index number of SEM poles is the same as the dimension number of the oscillation trajectory, but for a scatterer having nonsmooth points on the trajectory the index number of SEM poles will be larger, because the diffraction fields caused by these points have a number of orders.<>