Recently, an enhanced perfectly matched layer (PML) absorbing boundary condition (ABC) has been proposed [1], [2] for the 3-D wave equation in the time domain (WETD) derived for the vector potentials (VPs) [3], [4]. The derivation is based on the stretched coordinate approach [5]. Thus the PML is defined in the frequency domain and then six auxiliary variables are introduced to facilitate its mapping into the time domain. In [2], a new degree of freedom in the definition of the PML variable profiles has been introduced in the existing spatially polynomial scaling, and it is combined with modifications in the PML terminating walls. That improves the PML performance in applications involving the wave equation. However, an enhanced performance of this PML ABC is also observed when applied with the classical Yee’s finite-difference timedomain (FDTD) method to the solution of Maxwell’s equations [6].

In this work, the performance of this enhanced PML (EPML) ABC, when applied in Yee’s FDTD algorithm, is compared with existing PML ABCs like the original Berenger’s PML [7], the modified PML (MPML) [8] and the generalized PML (GPML) [9]. Also, a comparison of the reflection levels from the EPML ABC is made when one problem is modeled by Yee’s FDTD method and by the WETD method. Finally, the influences of the new degree of freedom and of the modified termination walls on the PML performance is studied and the best choices are singled out both in the case of Yee’s FDTD model and the WETD model.

In [1], [2] it has been proposed firstly the PML conductivity (responsible for the propagating waves attenuation) and the PML loss factor (responsible for the evanescent waves attenuation) to increase at different exponent rates within the PML medium. This in effect adds a new degree of freedom in the definition of the PML variable profiles. In addition, further performance enhancement is achieved by the use of modified PML terminations. Such a problem-independent approach to improve the PML performance is in contrast with the commonly used approach to optimize a single PML variable profile like in [10], [11], [12], and frequently it is done in a problem-specific environment [13], [14].

To illustrate the better performance of the proposed EPML ABC for Yee’s FDTD applications, the following examples are considered: an infinitesimal dipole radiating in open space and a microstrip line. It is shown that the proposed EPML has a superior performance in all major types of problems (3-D open problems and guided-wave problems) in comparison with commonly used PML ABCs such as MPML and GPML: it offers lower reflection levels in a broader frequency band.

Secondly, a comparison of the spectrum of the reflections is done when one and the same 3-D structure is modeled by Yee’s FDTD method and by the WETD method for the magnetic VP. Thus the equivalency of both methods is validated as well as the excellent performance of EPML in both models. The structure is chosen to be an optical buried waveguide terminated by a two-layer anti-reflection coating. The reason for this choice is that in such a problem the low reflection level from the ABC itself is of utmost importance since the reflections from the anti-reflection coating are of the order of the reflections from most of the commonly used ABCs. By initially terminating an infinite (longitudinally uniform) optical buried waveguide directly by EPML, it is shown that the level of the reflections caused by the EPML itself in both models is below –80 dB (corresponding to 10-4 magnitude).

Finally, the influence of the difference between the exponent rates of the PML conductivity and the PML loss factor on the overall EPML performance is considered both in the case of Yee’s FDTD model and the WETD model. It is shown that if the PML conductivity increases faster than the PML loss factor, the reflection levels can be decreased by half to full order of magnitude.