A higher-order FDTD technique for the implementation of enhanced dispersionless perfectly matched layers combined with efficient absorbing boundary conditions

The systematic construction of dispersionless Berenger and Maxwellian unsplit-field PMLs via a novel generalized higher-order FDTD technique, is presented in this paper. Both conventional and accurate nonstandard schemes are introduced. Unlike previous implementations, the proposed algorithm is derived from the complete form of Maxwell's equations. The wider spatial stencil near absorbing walls is limited by the use of compact operators. Improved accuracy is achieved by applying generalizations of the derivative definition and Pade approximations of FDTD stencils, while for the temporal integration the four-stage Runge-Kutta integrator is invoked. Efficient higher-order ABCs are imposed on the PML boundary in order to decrease absorbers' thickness and suppress the grazing incidence angle effect. A modified PML incorporating diverse conductivity profiles and a higher-order PML mesh expansion approach, are also discussed. Results demonstrate that the proposed algorithm significantly reduces dispersion errors and system computational requirements.