Application of Fourier Mode Coupling Theory to Real-Time Analyses of Nonuniform Bragg Gratings

By applying Fourier mode coupling (FMC) theory to the Bragg gratings (BGs) with the effects of Gaussian-apodization, phase shift, superstructure, and linear chirp, the calculations of their reflectivities are fast and accurately achieved, and compared with the practical cases and those on the transfer matrix (TM) method used widely. The results indicate that the FMC theory can be used for the real-time analysis and control in the design and fabrications of nonuniform BG and its mask, of which the efficiency is about several-thousand times that of the TM method.