I develop a mathematical model of light incident on a periodic grating structure that can effectively model the Kerr effect—third order susceptibility effects where the intensity affects the medium's index of refraction. This model has applications in fiber optics, and I’ll expand the model to that beyond just periodic structures. Typically, most structures are rectangular gratings, but I’ll consider structures similar to that of sawtooth or sinusoidal gratings in this research. I’d also like to see if I can find data that can replicate findings for different tuned parameters for my model. This computational model examines the properties of light through time evolution, considering any diffractive/interference effects.