Abstract: In this paper, a novel quasi-three-dimensional finite-difference time-domain beam propagation method(Q-FDTD-BPM) is proposed. In the cylindrical coordinate, the azimuthal component of the vector field solution is separated and three-dimensional equation is decomposed into several two-dimensional equations, which simplify the 3D discrete equations. And the method presented is developed using an alternating-direction implicit method and generalized Douglas scheme,which achieves higher accuracy than the regular FD scheme. Next the transform scheme is used to obtain the 3D resolutions of the equation. Based on this method, the simulated results for the spectrum of MMFG is obtained with a good approximation to the results in the experiment.

Key words: multimode fiber grating, quasi-3D, alternating-direction implicit method, finite-difference time-domain beam propagation method, generalized Douglas scheme