Aluminum doped zinc oxide (AZO) is a heavily studied metamaterial for its unique optical properties. Some of these include lower losses, direct wide band energy, and the ability to spectrally alter its emission depending on doping concentrations. When nanolayering the aluminum within zinc oxide, the material exhibits a hyperbolic dispersion relation due to a differing permittivity in perpendicular directions. Potential applications of this metamaterial include blue LEDs, optical microcavities, and UV laser diodes. The goal of this thesis is to investigate the photoluminescence of AZO and changes in emission due to doping. A model is created using a set of rate equations that describe the dynamics between band structures. The model is first created by using the two-level system in which only the conduction band and valence band exist. The dynamic between these two bands are shown to be responsible for the emission in the UV/blue regime. The model is expanded to incorporate green emission by utilizing a three-level system. This third level exists due to zinc vacancies within the band gap structure, allowing for emission of lower energy photons. Solving this system of equations numerically using the fourth order Runge Kutta method, and changing values of the initial concentration, a suppression of the green emission and an increase of the UV emission is demonstrated. Numerical results show a crossover of the blue and green emission, depending on the pumping regime, as well as the existence of a fast and slow component to the decay rate, agreeing with experimental studies. Having a theoretical model allows for the systematic optimization of parameters that can be incorporated during manufacturing. An optical setup is created to optically pump an AZO sample manufactured using Atomic Layer Deposition. This setup employs a pulsed ND:YAG laser with an emission of 355 nanometers, which is larger than the band gap energy. The photoluminescence spectrum is analyzed using a McPherson spectrometer with a photomultiplier. Preliminary measurements have shown an emission line at 382 nanometers, as expected from experimental studies. Future experimental research will include studying the entire emission spectrum of several samples with different doping parameters.