Maxwell equations and the k function

Abstract

We use a general solution to the eikonal equation to define generalized coordinates in terms of which the Maxwell equations are then cast. These coordinates are then used to obtain expressions for the electric and magnetic field vectors and the Poynting vector. An arbitrary vector function V is introduced that is subject to certain side conditions derived in this process. The k function, the arbitrary function that arises in the solution of the eikonal equation, contains only information descriptive of the geometry of a wave-front train. The vector function V contains information pertaining to the physics of the propagating energy that is distinct from the geometry of the wave-front train.