Numerical simulation on Multimode fiber Bragg gratings with nonuniform transverse profile of refractive index change

The reflection characteristics of Multi-mode fiber Bragg grating (MM-FBG) with non-uniform profile of index change were numerically studied in this work. The reflection spectrum of MM-FBG was obtained by solving the coupled mode equations (CMEs) using shooting method. For a standard multimode fiber with 342 guided modes, the initial problem within the shooting method frame is very slow when it was solved using numerical methods. We obtained the analytical solution of the initial problem of the CMEs by diagonalization so that the numerical simulation is fast enough to be finished within several hours using personal computer. The reflection was obtained for a standard multimode fiber with diameter of 62.5 micron. There are 35 reflection peaks in the spectrum where 18 of them are corresponding to forward-propagation mode coupled to same order backward mode and the other 17 peaks are corresponding to forward mode coupled to backward mode with diameter of 62.5 micron. There are 35 reflection peaks in the spectrum where 18 of them are corresponding to forward-propagation mode coupled to same order backward mode and the other 17 peaks are corresponding to forward mode coupled to backward mode with neighboring order.