Parallel Higher-Order FDTD Simulation For Optical Waveguides

The Finite-Difference Time-Domain (FDTD) method is a most popular numerical method for the simulation of optical waveguide devices. It was first proposed in 1966 by Yee to solve problems in electromagnetic scattering. The FDTD algorithm is based on the finite difference expression of the set of Maxwell's time-dependent curl equations. The FDTD method is excellent in computational efficiency and simplicity, and can be used for modeling on structural complicated materials like conductors, insulators and non-linear materials. With the increase in computer's computational power and decrease in the computer's price, it has been widely used in almost every area of computational electromagnetics, and larger and more complex problems have been solved by using the FDTD method.The FDTD method was originally proposed for electromagnetic waves with long wavelength such as RF and microwave. It can also be used for the analysis of optical devices. Due to the numerical dispersion limit in the FDTD method, the spatial discretization width is usually less than λ/10, which results in a large grid number in an electrically large device simulation. The spatial discretization width is extremely short when wavelength is of micrometer order. For large-scale optical waveguide simulations, such as simulations of three dimensional or large-scale two dimensional optical waveguide problems, extremely large computer memory space and a long computational time is required.The parallel computing techniques can be used to reduce the computation time significantly and have been widely applied in various complex FDTD applications. The current large parallel computer system no longer satisfies the demands of large optical devices simulation in the industry because the price of the system is too high. A research on a low-cost parallel FDTD computation system is needed for the FDTD application.Another effective method to reduce the numerical dispersion error is to use the higher-order FDTD methods. Higher-order methods exhibit low dispersion errors and can utilize coarser cell sizes than those needed by classical FDTD methods to achieve satisfactory levels of accuracy. The study of dispersion property of various higher-order FDTD methods has its special importance, and this still remains in the research area.