Replacement of the TD Wave Equation by a First Order Equation with Alternative Field Constituents

A pair of field consistuents, denoted herein as
$\mathbf{E}^{\mathrm{R}}$
and
$\mathbf{E}^{\mathrm{L}}$
, are suggested as an altenarive to the conventional pair E, H. These fields obey lower order equations, i.e., the first order Maxwell's curl equations are replaced by a zero order (algebraic) relationship, while the wave equation is now traded for a first order equation. As a result, the conventional use of the
$6\times 6$
scalar, real time domain set is now consolidated a
$3\times 3$
complex equations. This consolidated solution tracks exactly the one obtained with the original finite difference scheme.