Under a compulsive boundary condition,a simplified time-domain finite-difference beam propagation method (TD-FD-BPM) suitable for the analysis of fiber Bragg grating (FBG) is presented.In the alternating-direction implicit method (ADIM) and the generalized Douglas (GD) scheme, the time-domain beam propagation equation is discretized with a truncation error two orders lower than that of conventional finite-difference scheme.The compulsive boundary condition simplifies the boundary model,which is important in the numerical analysis of optical waveguides with open boundary conditions.We focused on the position of excitation,the shape of the pulse and its distribution in the radial direction,and the use of the one-way continuous-wave (CW) scheme.Using a modified sinusoidal pulse,a satisfactory reflective spectrum is obtained in a short symmetrical FBG through discrete Fourier transform.