Implementation of UPML for weakly conditionally stable FDTD in periodic structures

In this paper, uniaxial perfectly matched layer (UPML) is applied in weakly conditionally stable finite-difference time-domain method for periodic structures. In order to solve the special non-tridiagonal matrix, the Sherman-Morrison formula is applied, so the computational efficiency is improved. The reflection error of the proposed UPML absorber can be almost the same as the UPML absorber in the conventional FDTD method when the UPML is 16-layer. Even when the UPML is 4-layer, the reflection error can below -50 dB. Numerical results of reflection coefficient for the periodic array of metallic patches are calculated, so as to verify the accuracy and efficiency of the proposed method.