Second-order PML: Optimal choice of nth-order PML for truncating FDTD domains

The nth-order PMLs based on the unsplit-field formulations and the Z-transform methods are proposed to truncate the finite-difference time-domain (FDTD) domains, which will be validated through numerical simulations whether the higher-order PML with more than two poles, such as n=. 3, will hold better absorption performance as compared with the conventional, complex frequency shifted (CFS), second-order perfectly matched layer (PMLs). The advantages and disadvantages of different PMLs are demonstrated. It has shown that the higher-order PMLs have the advantages of both the conventional and the CFS PMLs in terms of absorption performance, since the conventional PML is ineffective at absorbing the evanescent waves and the CFS-PML is incapable of absorbing low-frequency propagating waves. It is clearly shown that the second-order PML is overall the optimal choice for truncating arbitrary FDTD domains, since it not only requires less computational time and memory, but holds almost the same absorption performance as compared with the third-order PML. Three numerical simulations have been carried out in three-dimensional (3D) problems to confirm the analysis.