Application of multigrid method to lightwave propagation in optical waveguide

摘要

In this report, the multigrid method is applied to the lightwave propagation in the optical waveguide. This method is one of the rapid methods because of speeding up the convergence of the relaxation method. In general, the electromagnetic fields are composed of fast and slow spatial variations (high and low frequency components). The high frequency components can be caused by the local iterations in the geometry and the low frequency ones arise from the global interactions. When the high and low frequency modes are solved at the fine and coarse levels of discretization by using the iteration solvers, the electromagnetic fields can be obtained quickly. As the model to be applied, the lightwave coupling in the linear and nonlinear directional couplers is considered. It is shown that the multigrid method is very useful as the rapid method.