Abstract-The application of the existing time-domain beampropagation 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 Padé (2,2) approximant is applied to the time axis. Although the truncation error in time is found to be (1 2 ),asinthecaseofthe Padé (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 TEand 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.
A wide-band time-domain beam-propagation method is proposed using the altematingdirection implicit method with the aid oj'an iteration algorithm. Substantial reduction in CPU time is found, compared to the conventional method.
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