$Z$-Transform Implementation of the CFS-PML for Arbitrary Media

An efficient implementation of the complex frequency-shifted perfectly matched layer (CFS–PML) based on stretched coordinate PML (SC–PML) formulations and the
$Z$
-transform method is presented for truncating the finite-difference time domain (FDTD). This method is completely independent of the material properties of the FDTD computational domain and hence can be applied to the modeling of arbitrary media without any modification. A numerical test has been carried out in three dimensions to validate these formulations. It is shown that the proposed formulations with a CFS scheme are efficient in attenuating evanescent waves and reducing late-time reflections.