The electromagnetic field in a 1-D lossy medium based on a Maxwell equation propagator

A propagator has been derived for the electromagnetic field in a 1D lossy region. The solution is exact, and does not require the evaluation of a differential or integral equation. In the limit as σ → 0 the result is seen to reduce to the D´Alembert solution for coupled equations in a homogeneous lossless medium. Good agreement with the ADS CAD program has been demonstrated. Because we get an exact solution, it is expected to be more accurate than integral or differential equation methods, not subject to numerical dispersion and simple to evaluate. By using the methods described here, derivations of the 2D and 3D cases should be straightforward.