Radio-wave propagation and electromagnetic surface waves

Abstract

A Discrepancy and Its Resolution. - The problem of the propagation of radio-waves along the surface of the (plane) earth was first treated in a celebrated paper by A. Sommerfeld (1909).(1) Let the (r, φ)-plane of a cylindric system of coordinates coincide with the plane of the earth surface and let the z-axis point vertically upward. Sommerfeld considered a vertically oscillating dipole (radio-antenna) in the air, close to the origin (z = 0, r = 0) and asked what secondary waves were produced by the discontinuity due to the presence of the partially conducting earth. His investigation led to the result that the Hertzian vector II describing the electromagnetic field can be divided, in either medium (air and earth), into two parts: II = Q + P, where the part Q has the character of space-waves, which at large distances from the origin are proportional to R^-1, if R = (r^2 + z^2)^1/2. On the other hand, P is a surface-wave: at large distances it becomes proportional to r^-1/2 and is restricted to the vicinity of the earth surface.