Abstract: The paper presents not only the ontire formula of the three-dimension complex ray expansion of the local vector plane wave with parallel beams, but also the formulas of the expansion truncation error and the discretized expansion error. The three-dimonsion complex source expansion parameter of the local vector plane wave, including complex source point parameter, expansion interval,and the expansion radius can ho determined if the expansion error and the maximum expansion interval is given previously. Thus the error requirement can be met by the synthesized field everywhere in space, which is from expansion place to the maximum expansion interval in the area of the required radius. This method is especially suitable for the analysis of wave propagation and target scattereing characteristics.

Key words: local vector piano wave, three-dimension complex ray, wave expansion