Finite-difference computation of transient electromagnetic waves for cylindrical geometries in complex media

We present two novel, fully three-dimensional (3-D) finite-difference time-domain (FDTD) schemes in cylindrical coordinates for transient simulation of electromagnetic wave propagation in complex (inhomogeneous, dispersive, and conductive) and unbounded media. The proposed FDTD schemes incorporate an extension of the perfectly matched layer (PML) absorbing boundary condition (ABC) to three-dimensional (3-D) cylindrical coordinates. Dispersion on the media is modeled by using the piecewise-linear recursive convolution (PLRC) algorithm, accounting for multiterm Lorentz and/or Debye models. Split-field and unsplit (anisotropic medium) formulations of the cylindrical PML-PLRC-FDTD schemes are implemented and compared in the time domain. The comparison includes the late-time stability properties of the update schemes. Numerical simulations of subsurface electromagnetic problems are included. Because the proposed schemes retain the nearest-neighbor property of the ordinary FDTD, they are well suited for implementation on massively parallel computers.