Fast PML-based series expansions for the Green´s functions of multilayered media: Efficient calculation of the leaky modes

By terminating an open multilayered dielectric medium by means of a perfectly matched layer (PML), a closed-form modal series expansion for its spatial-domain Green´s functions is obtained, thereby avoiding time-consuming Sommerfeld integration, as required in the conventional approach. The PML-based modal series apply to Green´s functions for 2D and 3D geometries, including periodic configurations. In this contribution, we present an overview on how to construct these modal series expansions for multilayered substrates, with a special emphasis on the efficient determination of the eigenmodes that exist in multilayered waveguides terminated by a PML. Specifically, a rapid algorithm is presented for finding the propagation constants of the leaky modes pertaining to multilayered dielectric substrates.