## 1. Introduction

[2] Method of moments (MOM) techniques relying on integral equation formulations are very popular for full-wave field analysis in CAD tools. These formalisms only require the discretization of the fields along the boundaries of the metallic structures present in the configuration, provided the characteristics of the dielectric background medium are incorporated in the kernel functions of the integrals. Although the latter problem has been studied for quite a number of years, the calculation of the Green's function of the substrate still remains an important issue. Indeed, it is well known [*Michalski and Mosig*, 1997; *Faché et al.*, 1992] that the two-dimensional (2-D) Green's functions of multilayered media can be easily computed in the spectral domain; however, the inverse Fourier transform leads to Sommerfeld-type integrals, requiring complex and time-consuming integration schemes. Therefore a number of faster alternative approaches have been proposed, such as, for example, the fast Hankel transform [*Hsieh and Kuo*, 1998] and the complex image technique [*Chow et al.*, 1991; *Van Hese et al.*, 1994]. A new technique is proposed by *Derudder et al.* [1999, 2001] and *Bienstman et al.* [2001] to calculate the Green's function by using perfectly matched layers (PML) [*Bérenger*, 1996; *Gedney*, 1996; *Knockaert and De Zutter*, 2000] to obtain a closed waveguide configuration. The PML then mimics an open structure, while an efficient problem description in terms of a set of discrete modes of the closed waveguide containing the PML is possible.

[3] This approach is used by *Derudder et al.* [1999, 2001] and *Bienstman et al.* [2001] to construct the Green's function *G*_{xx} for a two-dimensional configuration, for the transverse electric (TE) polarization. The problem we are studying here consists of a 2-D configuration of metallic objects buried in a substrate, as defined in section 2. The main contribution of this paper then consists in relying on results obtained by *Rogier and De Zutter* [2002] to apply the new PML formalism within a 2-D Galerkin MOM approach with subdomain pulse basis functions in order to expand the currents on the boundaries of the objects buried in the substrate, as discussed in section 3. More specifically, we will show that the Green's function written down in section 4.1 as an expansion in leaky and Berenger modes [*Rogier and De Zutter*, 2001] and accelerated by the Shanks transform, discussed in section 4.2, can be used to calculate the interaction integrals between arbitrarily oriented segments placed anywhere in the substrate. This latter statement does not hold for the self-patch contribution, but there the quasi-static part suffices to calculate this interaction with sufficient accuracy. Since for all interactions, the Green's function is available under closed form, the technique allows for a drastic improvement in CPU time, as shown by the examples in section 5. Furthermore, it is shown that the PML formalism is also useful in the calculation of the fields anywhere in the substrate, once the unknown currents are solved for. Again, a different treatment is necessary for the self-patch contribution as well as for calculating the fields in the air region above the substrate.