Radiation of a Dipole in a Lossy Half-Space

By the application of the method of operators asymptotic expressions of the Hertz vector for the radiation of a dipole in a lossy half-space are obtained under the exclusive condition k 2 R 0 ≫1, where k 2 is the wave number for free space, and R 0 is the distance from the median between the dipole and its image to the observing point. A method to obtain the asymptotic expansion for the Hertz vector in the general case is given, by means of which formulas applicable even to the near field are obtained in a relatively in a relatively simple from under the condition practically admitted, in particular without restrictions on the position of the receiving point in air. The result is compared with others previously appeared, and when k 2 R 0 ≪1 assures its agreement with the one derived by the quasi-static approach.