Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2006 · 20 citations · 0 references
ComputingComputational EngineeringElectrical EngineeringComputational ElectromagneticsComputational Materials ScienceMicrowave EngineeringConvergence AnalysisDielectricsElectromagnetic MethodsError EstimationFinite Difference MethodsFinite Difference Time Domain AnalysisConvergenceDielectric FunctionDiscretizationDiscretization ErrorFinite Difference SchemesFinite Difference Time Domain SimulationNumerical DiscretizationSmoothing
Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization ("pixellization"). We show that accuracy can be significantly improved by using a sub-pixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory, and compare it to other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.