Excitation of modes at very low frequency in the earth-ionosphere wave guide

The concept of VLF radio waves propagating between the earth and the ionosphere in the manner of a wave guide has proved very useful. A much neglected aspect of the subject, however, is the manner in which the modes are excited. A valid analysis of this effect requires that the earth's curvature and the grazing nature of the modes be properly accounted for. By using Airy integral or third-order approximations for the spherical wave functions, an expression for the excitation factor is obtained. It is indicated that the modes of very low attenuation may be accompanied by excitation factors much less than unity. There is evidence of this phenomenon in some of the old experimental data of Round et al. at frequencies of the order of 25 kc/s. A mode of this type can be imagined as becoming ‘detached’ from the lower boundary of the earth-ionosphere wave guide. In this situation, the height-gain functions increase with height and the modal characteristics depend only slightly on ground characteristics.