The nearly perfectly matched layer is a perfectly matched layer

An absorbing boundary condition for computational electromagnetics called the nearly perfectly matched layer (NPML) was recently introduced. This boundary condition, designed to be simple to implement in complex media, was regarded as not quite a perfectly matched layer because its formulation deviates from the standard PML through an inexact variable change. Analytical and numerical results are presented here that show that the NPML is equivalent to the standard perfectly matched layer (PML) in Cartesian coordinates for one-dimensional, two-dimensional, and three-dimensional problems through simple variable changes. Consequently, the NPML performs identically to the PML as an absorbing boundary condition while maintaining its simplicity of implementation.