This thesis was based on the work of Hollis C. Chen who developed the 'coordinate-free analysis approach' to solve the equations for a propagating electromagnetic plane wave. In the first chapter, the basic properties of the monochromatic plane wave were presented alongside the laws of reflection and refraction which are (as known) derived from the boundary conditions. At the end of this chapter I presented Chen's analytical model and then used it in my own specific application (which is the main theme of this thesis) in the second and third chapters to further apply the same analysis on two different plates: isotropic and uniaxial, respectively. After I presented Chen's system of equations and before I introduced my own application at the end of these chapters, I have literally derived step by step all of Chen's equations to facilitate a much easier access into this material (and more specifically to rectify a major flaw in Chen's derivations) for both of the professionals and beginners of Science and Engineering alike. I have also computationally simulated the mathematically-dynamic model of my application. Furthermore, I have visualized Chen's own mathematically-static abstract equations and corrected his aforementioned mistake.