Directive properties of antennas for transmission into a material half-space

The directive properties of antennas for transmission into a material half-space are investigated. In a practical situation, the antennas might be located in air with the directive transmission into the earth. The field of a general antenna over the half-space is expressed as a spectrum of plane waves. The integrals representing the field are evaluated asymptotically to obtain the "geometrical optics" field of the antenna, and this field is used to define quantities that describe the directive properties of the antenna (pattern function, gain, and directivity). Numerical results are presented for infinitesimal electric and magnetic horizontal dipole antennas in a dielectric half-space, region 1, with directive transmission into the adjacent dielectric half-space, region 2, and the ratio of permittivities
\epsilon_{2}/\epsilon_{1}
greater than one. The theory for the infinitesimal dipoles completely explains the directive properties previously obtained for the resonant circular-loop antenna over a material half-space. Measured field patterns and gains for dipole and loop antennas near an interface between air and fresh water are in good agreement with the theory.