Composite Refractive Index on Electromagnetic Wave Propagating in Spherical Medium

Calculating how electromagnetic waves propagate in spherical media is currently approached in two ways: by using eikonal equations based on a spherical coordinate system or by using parabolic equations based on a Cartesian coordinate system. However, eikonal equations can produce problems of accuracy and stability, while the modified refractive index used for parabolic equations is only suitable for low-altitude conditions. In this article, a comparison of the differential form of Bouguer’s law and Snell’s law is used to develop a composite refractive index. This enables the problem of how electromagnetic waves propagate in spherical medium to be converted into one of how they propagate in cuboid medium. By providing a way of solving eikonal equations according to a Cartesian coordinate system, the problems associated with traditional methods are overcome. It is proved that the modified refractive index widely used in the field of radio is the approximation of the composite refractive index, which breaks the height limit of parabolic equation method based on modified refractive index.