The time domain Green´s function and propagator for Maxwell´s equations

The free space time domain propagator and corresponding dyadic Green´s function for Maxwell´s differential equations are derived in one-, two-, and three-dimensions using the propagator method. The propagator method reveals terms that contribute in the source region, which to our knowledge have not been previously reported in the literature. It is shown that these terms are necessary to satisfy the initial condition, that the convolution of the Green´s function with the field must identically approach the initial field as the time interval approaches zero. It is also shown that without these terms, Huygen´s principle cannot be satisfied. To illustrate the value of this Green´s function two analytical examples are presented, that of a propagating plane wave and of a radiating point source. An accurate propagator is the key element in the time domain path integral formulation for the electromagnetic field.