In this section, we explore higher order wave forms that form the basis of the reformulated theory of radiation force fields beyond plane waves. We present higher order forms of the previous considerations of Maxwell waves and show that the original plane wave form requires descriptions of higher orders to describe the observable light-matter phenomenon in nature. Nuances of plane waves without extrapolations to higher geometric powers fall short of describing the optical and magnetic phenomenon in totality. We also extend our discussion to the realm of diffusion and wave equations with the latter being extrapolated to higher orders of the gradient operator. Results show the flow of geometric waves transitioning from one state to the other and the dissemination of information and waves in higher dimensions. Also discussed and highlighted is the nature of radiation and associated force fields that create it, and the distribution and redistribution of matter upon interaction with radiation force fields. The gist of this article is that one does not need the electromagnetic theory as it has been previously thought of. Rather, we base our discussion purely on matter waves by doing away with the concept of charge fields, and by focusing solely on matter vibrations and the geometric force fields thus generated.