Z-Transform Implementations of the CFS-PML

Four implementations of the complex frequency-shifted perfectly matched layer (CFS-PML) based on the uniaxial anisotropic PML (UPML) formulations and Z-transform methods are presented for truncating the finite-difference time-domain (FDTD) lattices. These formulations are independent of the material properties of the FDTD computational domain and hence can be applied to the modeling of general media. Particularly, a new algorithm to minimize memory requirement is introduced. Two numerical simulations of the dispersive media have been carried out in three dimensions to validate these formulations. It is shown that the proposed formulations with the CFS scheme are efficient in attenuating of evanescent waves and reducing late-time reflections.