BOR-FDTD analysis of nonlinear Fiber Bragg grating and distributed Bragg resonator

Recently, nonlinear materials have attracted a great deal of attention because of their importance in designing new devices to meet a need range of optical systems. An intense investigation of the possibility of using these materials for all optical ultrafast applications is achieved by allowing their dielectric characteristics to be varied in such a way that a periodic perturbation of their refractive index along the length of the waveguide will be formed. The Finite-Difference Time-Domain (FDTD) method, on the other hand, has been proven to be one of the most powerful numerical techniques that are usefully applied to a wide range of optical devices. In this paper, a FDTD technique, developed for nonlinear structures, is used to analyze a nonlinear waveguide and periodic nonlinear structures that exhibit attractive properties that make them suitable for novel devices with wavelength tunable characteristics. More specifically, the Bodies of Revolution (BOR) FDTD numerical simulation method will be used to model the fiber Bragg Grating (FBG) and the direct integration method will be employed to include the effect of Self Phase Modulation (SPM) in this model. The combination of these techniques will result in a model that is used to analyze two different types of periodic nonlinear structure, FBG and Distributed Bragg Resonator (DBR). The nonlinear effect provides the designer an added degree of design flexibility for devices with wavelength tunable characteristics, for example, in the design of tunable filters, WDM systems and optical sensors.