<p> Optical gradient index media have the property where the spatial variation of the index of refraction is continuous along the direction transverse to the optical axis. Many emerging technologies in optics require gradient index components, and a firm understanding of the physics of light propagation in these components is required. Presented here are the mathematical foundations used to analyze light propagation in planar quadratic index profile waveguides. One transverse direction is used in this analysis, and light propagation is seen to have periodic behavior. Also presented here is a comparison of ray bundles and wave intensities in quadratic index waveguides, with the intent to use this machinery to further ray chaos theory.</p>