The radiation of Hertzian dipoles (vertical electric and magnetic and horizontal electric and magnetic) with impulsive currents in the presence of a nondispersive dielectric half‐space is considered. By taking the inverse Fourier transform of the Sommerfeld integrals, exact closed‐form solutions are obtained for particular locations of source and observation points. These solutions contain doublet and delta singularities whose magnitudes and arrival times are determined by geometrical optics followed by smoothly decaying waveforms whose final values are determined by static the