Uniaxial PML absorbing boundary condition for truncating the boundary of DNG metamaterials

Abstract

The conventional perfectly matched layer (PML) absorbing boundary condition is shown to be unstable when it is extended to truncate the boundary of the double negative (DNG) medium. It is a consequence of the reverse directions of the Poynting and phasevelocity vectors of plane waves propagating in such material. In this paper, a modified uniaxial PML (UPML), which is stable for the DNG medium, is derived. The auxiliary differential equation technique is introduced to derive the discrete field-update equations of DNG-UPML. Numerical results demonstrate the effectiveness and stability of the new UPML for the DNG medium.