A Finite-Difference Time-Domain Beam-Propagation Method for TE- and TM-Wave Analyses
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The application of the existing time-domain beampropagationmethod (TD-BPM) based on the finite-difference (FD)formula has been limited to the TE-mode analysis. To treat the TMmode as well as the TE mode, an improved TD-BPM is developedusing 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 thetruncation error in time is found to be ( 2), as in the case of thePadé (1,1) approximant, this method allows us to use a large timestep. A substantial reduction in CPU time is found when comparedto the conventional method in which a broadly banded matrix issolved by the Bi-CGSTAB. The effectiveness in evaluating the TEandTM-mode waves is shown through the analysis of the powerreflectivity from a waveguide facet. This method is also applied tothe analysis of a waveguide grating. The accuracy and efficiency ofthe TD-BPM are assessed in comparison with the finite-differencetime-domain method.
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