Computation of transient far radiation field of anarbitrarily oriented dipole over the half-space using the reciprocity theorem and Fourier transform

Based on the reciprocity theorem, the far field formulation of an arbitrarily oriented electric dipole located above the interface of the half space in the frequency domain is deduced. The far field is composed of two parts: the directed wave and the reflected wave when the observed point located above the half-space. The transient far field of the directed wave can be obtained by analytical method, and then the waveform of reflected wave can be obtained by using the Fourier transform and the inverse Fourier transform with the consideration of time delay and the reflection of the half-space. Numerical results of a vertical dipole show that this method can be applied in fast calculation of the far field of electric dipole above the half space.