A diffraction theory for LF sky-wave propagation

The concept that radio waves propagate from transmitter to receiver via discrete ionospheric reflections (i.e., hops) is put on a sound theoretical basis. The earth and the ionosphere are represented by two (smooth) concentric spherical surfaces. The (local) reflecting characteristics of these boundaries are assumed to be known. It is shown that the mth hop sky wave may be generally represented by a complex integral. The geometrical-optical representations for the field are retrieved as a special case. For low radio frequencies, it is shown that these optical-type formulas, which are often used, have severe limitations. Generally, they are not valid near the caustic points. Techniques for evaluating the complex integral for the sky waves near and beyond the caustics are then discussed in some detail. Where possible, a physical interpretation of the results is given.