An analytical formulation and modeling of an optical fiber Bragg gratings has been developed and is reported in this paper. Supported by the Finite-Difference Time-Domain (FDTD) method, it was possible to set a 1018 nm bragg grating and simulate an electromagnetic field going through this periodic refractive-index device to obtain reflectivity, transmittivity, and bandwidth. Moreover, the model is applied to analyze the influence of structural parameters of fiber gratings, such as length, grating period, and refractive index modulation on its spectral response.