An Improved Spectral Numerical Mode Matching Method for Simulating Fiber Bragg Gratings

An improved spectral numerical mode matching (SNMM) method is applied for the first time to simulate fiber Bragg gratings (FBGs). Based on using the relative permittivity perturbation as the source, the new SNMM is constructed to correlate the total electromagnetic (EM) field with the excitation (expansion) coefficients directly from Maxwell's equations instead of forward-and backward-propagating waves in the coupled mode theory. This work provides the EM field by mode excitation based on the corresponding eigenmodes according to the perturbation approximation. In the new SNMM method, the spectral element method (SEM) is used to solve the eigenvalue problem numerically, and the excitation coefficient functions are obtained by the Runge-Kutta method. Several numerical results demonstrate the validity, accuracy, and advantages of the proposed method by comparing it with the commercial software COMSOL and the transfer matrix method (TMM).