A local description of the directional characteristics of the propagation of electromagnetic fields

A method is presented for determining a local measure of the amount of electromagnetic field propagation as a function of direction. This determination is made for the region near a given point by using the known field in the vicinity of that point within a given plane. The method is developed by assuming the parabolic equation approximation. Then the resulting equations are cast in the path integral form. A reformation of the path integral formulation is then developed. This reformation contains a quantity which is interpreted as a reasonable measure of the amount of field (amplitude) propagating in each direction. The relationship of this model to the plane-wave expansion technique is noted. The use of the method in two dimensions is illustrated by several numerical calculations. These numerical calculations are shown to be consistent with the predictions of the geometric theory of diffraction