Bilinear Transform Implementation of the SC-PML for General Media and General FDTD Schemes

With the complex-frequency-shifted perfectly matched layer (CFS-PML) implemented based on both the stretched coordinates and the bilinear transform method as the absorbing boundary condition (ABC), a novel unified finite-difference time-domain (FDTD) algorithm is developed for general FDTD spatial schemes and general media. The proposed FDTD-PML algorithm employs a general expression for the permittivity of arbitrary linear dispersive media and also takes the nonlinear effects into account. The bilinear transform used in this paper has better accuracy than the frequently used forward, backward, and central difference schemes. Compared with the recursive convolution implementation of the CFS-PML, the bilinear transform implementation involves much simpler FDTD expressions and has better absorbing performance with the same computational cost. Several two-dimensional (2-D) and 3-D simulations involving the anisotropic media, the Debye media, the Drude media, and the Kerr nonlinear media have been done to validate the presented algorithm, and indicate the advantages of the bilinear transform implementation of the CFS-PML. A simulation involving the Lorentz media calculated with the proposed algorithm adopting the wavelet-based high-order FDTD scheme is also included to validate the accuracy and effectiveness of the developed method.