Passive optical components can be broken down into two main groups: Refractive elements and diffractive elements. With recent advances in manufacturing technologies, diffractive optical elements are becoming increasingly more prevalent in optical systems. It is therefore important to be able to understand and model the behavior of these elements. In this report, we present a thorough analysis of a completely general diffractive optical element (DOE). The main goal of the analysis is to understand the diffraction efficiency and power distribution of the various modes affected by the DOE. This is critical to understanding cross talk and power issues when these elements are used in actual systems. As mentioned, the model is based on a completely general scenario for a DOE. This allows the user to specify the details to model a wide variety of diffractive elements. The analysis is implemented straightforwardly in Mathematica. This report includes the development of the analysis, the Mathematica implementation of the model and several examples using the Mathematical analysis tool. It is intended that this tool be a building block for more specialized analyses.