Complete time domain free space dyadic Green's function for Maxwell's equations

This paper is intended to give a complete formula for the free-space time-domain dyadic Green's function (TDDGF) for Maxwell's equations. The vector potential approach is used in solving Maxwell's equations in TD resulting in a new form for the source region term. This new form is different from that resulting from the state-space approach recently applied in literature. The source region term in the recently reported TD-DGF seems to be inconsistent with the well-known frequency domain results. This paper is intended to give a formula that is completely consistent with the frequency domain results. Also, it gives an interpretation of the seemingly inconsistency of the reported TD-DGF. A main advantage of the introduced form over the recently reported form is that it is applicable for different coordinate systems representing the source current. The paper also shows that the second derivative term in the recently reported field propagator formula is completely unnecessary. This leads to a great simplification in calculations as shown in the paper.