Implementation of Mur’s Absorbing Boundaries with Periodic Structures to Speed up the Design Process Using Finite-difference Time-domain Method

The finite-difference time-domain (FDTD) method is used to obtain numerical solutions of infinite periodic structures without resorting to the complex frequency-domain analysis, which is required in traditional frequency-domain techniques. The field transformation method is successfully used to model periodic structures with oblique incident waves/scan angles. Maxwell’s equations are transformed so that only a single period of the infinite periodic structure is modeled in FDTD by using periodic boundary conditions (PBCs). When modeling periodic structures with the transformed fields, the standard Mur second-order absorbing boundary condition cannot be used directly to absorb the outgoing waves. This paper presents a new implementation of Mur’s second-order absorbing boundary condition (ABC) with the transformed fields in the FDTD method. For designs that require multi-parametric studies, Mur’s ABCs are efficient and sufficient boundary conditions. If more accurate results are needed, the perfectly matched layer (PML) ABC can be used with the parameters obtained from the Mur solution.