A new look at numerical analysis of uniform fiber Bragg gratings using coupled mode theory

Abstract

The coupled mode theory (CMT) is used to analyze uniform Fiber Bragg gratings. The multi-mode CMT is expressed as the first-order vector ordinary differential equations (ODEs) with coefficients depending on the propagation distance. We show in this paper that by changing variables, the original couple mode equations (CMEs) can be re-casted as constant coefficient ODEs. The eigenvalue and eigenvector technique (EVVT), the analytic method for solving constant coefficient ODEs, is then applied to solve the coupled mode equations. Furthermore, we also investigate the application of Runge-Kutta method (RKM) to the calculation of the global transfer-function matrix for CMEs. We compare the transmission and the reflection spectra obtained by EVVT with those by RKM. Both results agree within machine accuracy. Numerical simulations conclude that solving constant coeffcient ODEs improves the speed and accuracy of solutions to the original CMEs.