The finite-difference time-domain (FDTD) method, which solves time-dependent Maxwell’s curl equations numerically,
has been proved to be a highly efficient technique for numerous applications in electromagnetic. Despite the simplicity
of the FDTD method, this technique suffers from serious limitations in case that substantial computer resource is
required to solve electromagnetic problems with medium or large computational dimensions, for example in high-index
optical devices. In our work, an efficient wavelet-based FDTD model has been implemented and extended in a parallel
computation environment, to analyze high-index optical devices. This model is based on Daubechies compactly
supported orthogonal wavelets and Deslauriers-Dubuc interpolating functions as biorthogonal wavelet bases, and thus is
a very efficient algorithm to solve differential equations numerically. This wavelet-based FDTD model is a
high-spatial-order FDTD indeed. Because of the highly linear numerical dispersion properties of this high-spatial-order
FDTD, the required discretization can be coarser than that required in the standard FDTD method. In our work, this
wavelet-based FDTD model achieved significant reduction in the number of cells, i.e. used memory. Also, as different
segments of the optical device can be computed simultaneously, there was a significant gain in computation time.
Substantially, we achieved speed-up factors higher than 30 in comparisons to using a single processor. Furthermore, the
efficiency of the parallelized computation such as the influence of the discretization and the load sharing between
different processors were analyzed. As a conclusion, this parallel-computing model is promising to analyze more
complicated optical devices with large dimensions.
We present the electromagnetic analysis of Talbot effect with the finite-difference time-domain (FDTD) method. To our knowledge, it is the first time that FDTD method is applied to analyze the performance of a Talbot illuminator. Furthermore, self-imaging performances of a grating with different flaws are analyzed. The FDTD method can be applied to analyze this kind of diffraction. Of course it also can be analyzed with the Fourier transform method. But for this non-period grating, it will be more complex. In addition, the grating employed here is a high-density grating. The Fourier transform method is not rigorous enough. For these reasons, the FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to attain with the conventional Fourier transform method.