Application of the phase integral method to the analysis of the diffraction and refraction of wireless waves round the earth

Abstract

The increasing use of short waves of less than 10 m. has given a new stimulus to the problem of calculating the signal strength to be expected at a distance from a transmitter, and especially of determining the gain of signal strength with height above the ground. For short waves the predominant factor quite near to the transmitter is the diffraction of energy round the curve of the earth with heavy earth losses, so that the problem has to be approached by considering the complete solution for propagation over an imperfectly conducting curved earth. The solution of the problem was first put on an unimpeachable basis by Watson (1918), who expressed the expansion for the potential function as a contour integral leading to a more rapidly convergent series, and his work has been the starting-point for subsequent writers. His solution is formally complete, but the application of it to practical cases involves considerable mathematical difficulties. He gave the solution explicitly only for the case of long waves where the earth was so highly conducting that, for mathematical purposes, it approached the limit given by a perfect conductor. Also, without further reduction, the solution only expressed the potential function, and hence the electromagnetic field, at points on the surface of the earth.