Theory of directional pulse propagation

We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions, respectively, and use these to reformulate Maxwell's equations. These variables enable us to not only judge the effect and significance of backward-traveling field components, but also to discard them when appropriate. They thereby have the potential to simplify numerical simulations, leading to potential speed gains of up to 100% over standard finite difference time-domain (FDTD) or pseudospectral spatial-domain (PSSD) simulations. We present results for various illustrative situations, including an example application to second harmonic generation in periodically poled lithium niobate. These field variables are also used to derive both envelope equations useful for narrow-band pulse propagation, and a second order wave equation. Alternative definitions are also presented.