Modelling an optical fiber Bragg grating

A theoretical investigation of a single mode optical fiber with one and two superimposed Bragg grating is presented. The formulation relies in the determination of an approximate solution in the asymptotic region of one of the fiber parameters. A correction is then applied to the asymptotic solution using the Method of the Successive Approximations also known as the Piccard Method. The approximation was then compared to the numerical solution using the Runge-Kutta method. Assuming that each Bragg grating has modulation frequencies given by {dollar}Omegasb1{dollar} and {dollar}Omegasb2{dollar}, it has been found that the second Bragg grating shifts the peak reflectivity of the first one by a small amount. The direction of the shift depends on the relative value of {dollar}Omegasb1{dollar} and {dollar}Omegasb2{dollar}. The fiber Bragg grating solution has been succesfully applied to other fiber devices.