Effective implementation of the CFS-PML using DSP techniques for truncating dispersive medium FDTD domains

Efficient and unsplit-field finite-difference time-domain (FDTD) implementation of the complex frequency-shifted perfectly matched layer (CFS-PML), based on the digital signal processing (DSP) techniques and the material independence relations via applying the electric flux density (D) and the magnetic flux density (B), is proposed for truncating three dimensional FDTD computational domain entirely composed of dispersive material realized with a Drude model. The CFS-PML implementation is introduced based on the stretched coordinate PML (SC-PML) and the uniaxial anisotropic PML (UPML), respectively. The implementation of the proposed CFS-PML formulations is based on the SC-PML due to the fact that has advantage of simple implementation in the corners and the edges of the PML regions. Moreover, these proposed formulations are completely independent of the material properties of the FDTD computational domain and hence can be applied to truncate arbitrary media without any modification because of the D-B constitutive relations used in Maxwell's equations. Besides, the DSP techniques include the Bilinear Z-transform (BZT) method and the Matched Z-transform (MZT) method, respectively. However, from the point of view of the Courant-Friedrichs-Levy (CFL) condition, to the best of our knowledge, time step based on the BZT only needs to meet CFL condition, whereas time step based on the MZT method has to make it smaller for retaining stability and desirable accuracy. Consequently, the former one is introduced into the proposed formulations. A numerical example has been carried out in a three dimensional FDTD computational domain to validate the proposed formulations. It is clearly shown that the proposed formulations with CFS scheme are efficient in attenuating evanescent waves and reducing late-time reflections.