Abstract
An improved three-dimensional (3-D) locally one-dimensional finite-difference
time-domain (LOD-FDTD) method is developed and applied to the wideband analysis
of waveguide gratings. First, the formulation is presented, in which dispersion
control parameters are introduced to reduce the numerical dispersion error
and perfectly matched layers are simply implemented without the field components
being split. Next, as a preliminary calculation, the wavelength response of
the waveguide grating is analyzed in a two-dimensional problem. The dispersion
control contributes to the accuracy improvement even with a large time step
beyond the Courant–Friedrich–Levy limit. Finally, a 3-D waveguide
grating is analyzed. The use of the dispersion control parameters only in
the propagation direction enables us to employ a large time step for efficient
calculations, i.e., the computation time can be reduced to about half that
of the explicit counterpart. In the Appendix,
an acceptable maximum time step for providing a highly accurate result is
also predicted using the numerical dispersion analysis.
© 2011 IEEE
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