Modeling of Fiber Bragg Gratings with Different Lengths for the Reflectivity Control for Fiber Lasers

An analytical formulation and modeling of an optical fiber Bragg gratings has been developed and is reported in this paper. Supported by the coupled-mode theory and considering that the mode fields of the unperturbed waveguide remain unchanged in the presence of weak perturbations, it is possible to obtain first-order differential equations that have solutions for some types of periodic perturbations. Finally, the model is applied to analyze the influence of structural parameters of fiber gratings, such as length, period and refractive index modulation on its reflectivity and bandwidth.