A finite-difference time-domain beam-propagation method for TE- and TM-wave analyses

The application of the existing time-domain beam-propagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Pade (2,2) approximant is applied to the time axis. Although the truncation error in time is found to be O(Δt
²
), as in the case of the Pade (1,1) approximant, this method allows us to use a large time step. A substantial reduction in CPU time is found when compared to the conventional method in which a broadly banded matrix is solved by the Bi-CGSTAB. The effectiveness in evaluating the TE- and TM-mode waves is shown through the analysis of the power reflectivity from a waveguide facet. This method is also applied to the analysis of a waveguide grating. The accuracy and efficiency of the TD-BPM are assessed in comparison with the finite-difference time-domain method.