Abstract
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.
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