Time-domain wave splitting of Maxwell’s equations

Wave splitting of the time dependent Maxwell’s equations in three dimensions with and without dispersive terms in the constitutive equation is treated. The procedure is similar to the method developed for the scalar wave equation except as follows. The up- and down-going wave condition is expressed in terms of a linear relation between the tangential components of E and H. The resulting system of differential-integral equations for the up- and down-going waves is directly obtained from Maxwell’s equations. This splitting (arising from the principal part of Maxwell’s equations) is applied to the case where there is dispersion. A formal derivation of the imbedding equation for the reflection operator in a medium with no dispersion is obtained.