ELF and VLF fields of a horizontal electric dipole

The waves in the spherical guide between the earth and ionosphere are excited by a horizontal electric dipole. The guide boundaries are characterized by surface impedances and the resulting waves are expressed as a superposition of TM and TE modes. The wavenumbers, excitation factors, height-gain functions, and height-dependent impedances are examined for both types of modes. A thin-shell approximation of the radial wave functions is shown to be adequate for phase velocity estimates; but other propagation parameters are of restricted validity in the VLF range where Airy integral approximations provide more reliable data. A horizontal electric dipole is shown to provide a nearly omnidirectional coverage of horizontal field components in the frequency range of the lower Schumann resonances. For an elevated source the horizontal fields are essentially omnidirectional also in the VLF range. Near fields are expressed as a summation of waveguide modes. The vertical field components vanish at the antipode, but the horizontal components remain of finite magnitude.