Physically interpretable alternative to Green´s dyadics, resulting representation theorems, and integral equations

An alternative to the concept and use of Green´s dyadics is presented. The major difference between the material presented here and the corresponding material usually presented with Green´s dyadics stems from the use of a dipole source term instead of a unit dyadic source. Another difference is related to the fact that derivations employing Green´s dyadics require that the dyadics satisfy a second-order curl curl equation. Here, the fields replacing the dyadics derive some of their attributes from solving Maxwell´s first-order differential equations. Simple manipulations of Maxwell´s first-order equations lead to the curl curl equation. What is accomplished is the derivation of equations that perform the same purposes as those requiring Green´s dyadics but that are simpler and contain physically interpretable fields and surface currents in place of the dyadics. The details of how to derive totally equivalent representation theorems are presented, and the way to derive integral equations having the same benefit is outlined. Key results of this work are the representation theorems when the observation point is in the far zone of the reference surface. For this case, simple expressions are given in which plane-wave-excited currents on a perfect conductor replace Green´s dyadics