Time-Domain Green Function Corresponding to a Time-Harmonic Point Source in Complex Space

The time-domain counterpart of the scalar field arising from a time-harmonic point source in the complex space is derived. The solution corresponds to the complex-space source Green function, which has grown very important in various electromagnetic problems, because it can be applied to approximate the narrow radiation of the Gaussian beam type. The time-domain counterpart presented in the present paper is seen to be real and causal. The solution is demonstrated to an asymptotic case of the Sommerfeld half-space problem in time domain.