How to design the imperfect Berenger PML

In contrast to the previously popular second order Mur absorbing boundary condition (ABC), the recently introduced Berenger Perfectly Matched Layer (PML) ABC can be designed to lower the numerical reflection coefficient associated with mesh truncation by several orders in magnitude. Nonetheless the PML ABC is not perfect; it does have a numerical reflection coefficient. This reflection coefficient is characterized in the time and frequency domains for narrow and broad bandwidth pulses from several points of view including specifically its behavior in terms of the magnitude of the loss tangent in the PML and the thickness of the PML. It is demonstrated that for broad bandwidth pulses the PML ABC exhibits a low frequency increase in its reflection coefficient that is associated with the actual thickness of the PML layer in terms of the longest wavelengths contained in the signal incident upon it. Moreover, it is shown that the effectiveness of the PML ABC saturates when the loss parameters of the PML are significantly increased and that this behavior is connected with the size of the first discontinuity in the material properties encountered by a pulse as it propagates into the PML region. An optimal operating point for the design of the PML region is thus obtained.