Time Domain of Sommerfelds Problem of Lossy Half-Space

This paper solved the problem of the scattering of radiation from a material half-space by the transient spectral domain method. The transient spectral domain method is a general theoretical approach for the exact solution to the time-dependent source radiation in the presence of media. It is located in the air region in the vicinity of lossy half-space. The apply of the integral transform to the wave equation in the horizontal coordinates in space by a two-dimensional Fourier transform is theoretical formulation of the problem. A source used is an electrically short vertical magnetic dipole with Impulse current distribution in the domain. Leads, under consideration of initial boundary and transition condition, the form expressions is achieved in terms of spectral domain variable and time. The integral representation determines the electromagnetic field anywhere the closed-form expressions is an achieved in terms of spectral domain variable and time.