Application of the Leapfrog ADI FDTD Method to Periodic Structures

In this letter, the one-step leapfrog alternating direction implicit (ADI) finite-difference time-domain (FDTD) method has been introduced to solve periodic structures, resulting in a one-step leapfrog periodic ADI-FDTD method. In comparison to the original ADI-FDTD method, the one-step leapfrog ADI-FDTD method retains almost the same numerical modeling accuracy, but with higher computational efficiency. To simplify the issue, a reformation of the periodic one-step leapfrog ADI-FDTD method is also presented. Numerical results are given to demonstrate the proposed formulation. It is found that the periodic one-step leapfrog ADI-FDTD method requires less memory and CPU time than the conventional periodic ADI-FDTD method. To reduce the numerical dispersion error, an optimization procedure is applied.