Fourier pseudospectral time-domain techniques in computational electromagnetics.

摘要

In computational electromagnetics, the traditional finite-difference time-domain (FDTD) method is not suitable to solve electrically large problems due to its high sampling rate requirement. Recently, Fourier pseudospectral time-domain (PSTD) method was proposed to solve Maxwell's equations, which only require 2∼4 grid points per minimum wavelength. This translates into tremendous memory savings for 2D and 3D problems. Another advantage of the Fourier PSTD algorithm is that its numerical dispersion is isotropic. This dissertation presents techniques that can even further reduce the dispersion.; However, Fourier PSTD has several difficulties in applications, particularly in introducing soft sources, in modeling fine structures and in modeling high-contrast and metallic materials. This dissertation addresses these difficulties. Along these lines, we introduce a weighted total field/scattered field (TF/SF) formulation, which can solve the soft source problem. Then we propose a specially designed mapping technique that can help model fine structures. For high-contrast and metallic materials, we discover the connection between the magnitude of Gibbs phenomenon and the distribution of the non-uniform grid points and propose a method that can help reduce the effect of Gibbs phenomenon. Using a specially designed mapping technique, we apply the Mapped PSTD to metallic materials, and our numerical experiments prove its accuracy.; Having examined and solved most of the difficulties with the Fourier PSTD algorithm, we apply these techniques to the near field calculation of photolithography masks. This is a very important problem for the semiconductor industry, because current photolithography tools have reached the diffraction limit and resolution enhancement through optical proximity correction (OPC) has become indispensable. For this application, we invent a domain separation technique that will be very useful in real applications. Using this technique the results from subdomains can seamlessly reconstruct the whole-domain solution. For photo mask simulation problems, we also propose a hybrid PSTD-FDTD algorithm, which can combine the advantages of both algorithms. Numerical examples of 3D simulation of photo masks using the hybrid algorithm and the FDTD method are given and compared.; Lastly, we give some concluding remarks toward the current pseudospectral time-domain techniques, and discuss some possible future research directions.