Acoustic parabolic equation model with a directional source

: The acoustic parabolic equation method in the ocean is an efficient technique to calculate the acoustic field in the range-dependent environment, emanating from a point source. However, we often need to use the directional source with a main beam in the practical problem. In this paper, we present two methods to implement the directional source in the acoustic parabolic equation code easily. One is simply to filter the Delta function idealized as an omni-directional point source. Another method is based on the rational filtering of the self-starter solution. It has a limitation not to separate the up-going and the down-going wave for the depth, but would be useful in implementing the mode propagation. Numerical examples for validation are given in the Pekeris environment and the deep sea environment