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

The propagator is a mathematical expression which, when convolved with any given present time field, evolves that field through a predetermined time increment. When the field is entirely causal, the free space propagator and free space Green´s function have a simple mathematical relationship. In this paper, a method for finding the full wave time domain propagator for the electromagnetic field is presented. Starting with Maxwell´s differential equations in tensor form, a state variable approach is used to derive expressions for the propagator in three dimensions. It is shown that the properties of the propagator, which satisfies a homogeneous hyperbolic matrix equation, and the Green´s function, which satisfies an inhomogeneous equation with the same operator, can be used to determine their mathematical relationship.