  We construct combined electric and magnetic field variables which
independently represent energy flows in the forward and backward directions
respectively, and use these to re-formulate Maxwell's equations. These
variables enable us to not only judge the effect and significance of
backward-travelling 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 FDTD or 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.
