FDTD absorbing boundary conditions: From global lookback schemes to metamaterial PMLs

In this paper, the author reviewed his mathematical analysis with FDTD simulations on metamaterial perfect match layer (PML). It was demonstrated that a unixial medium with specifically designed permittivity and permeability values could produce the desired PML and permeability values could produce the desired PML behavior.The interesting aspect of this was not only the originally developed two-time derivative Lorentz material (2-TDLM) ABC, but the 2-TDLM model itself and a restricted version, the 1-TDLM model. These novel material models enabled the development of ABCs that were perfectly matched to lossy dielectric materials. Moreover, the 2-TDLM model and its proposed realizations were one of the precursors to artificial media that we now call metamaterials.