On the stretching of Maxwell's equations in general orthogonal coordinate systems and the perfectly matched layer

Abstract

It is shown that the complex coordinate stretching and diagonal anisotropy formulations of the perfectly matched layer are equivalent in a general orthogonal coordinate system setting.The results are obtained by taking advantage of the tensorial invariance of the line element.

Full-wave simulation of optical waveguides via truncation in the method of moments using PML absorbing boundary conditions

“…It can be shown [9,13] that by introducing these changes into Maxwell's equations, the characteristic impedance of the new medium remains unchanged w.r.t. to the background medium, irrespective ofχ(x).…”

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

“…A very efficient and elegant way to calculate Green functions, based on the use of perfectly matched layers (PML) [12]- [14], has been proposed in [15]- [17]. For a layered structure that is closed by a perfect electric conductor (PEC) plane at the top and bottom of the structure, the Sommerfeld integrals that arise in the Green function calculations can be expressed as a series of surface waves.…”

“…The branch cut causes the numerical evaluation of Sommerfeld-integrals [5], [35] and this complicates the application of the MLFMA to the acceleration of matrix-vector products (3). The crux of our new formalism is based on the application of PMLs [12]- [14]. The PML-concept is invoked to obtain an approximate analytical/closed-form expression for involving only discrete modes.…”

Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer

“…Let us now consider the configuration shown in Figure 2, consisting of a circular dielectric waveguide with a core section having refractive index n co , permeability co , and radius r. The cladding, with refractive index n cl and permeability cl , is terminated by a PML with thickness ⌬ and absorption 0 , to form a closed circular waveguide with radius R. In [6,11] it is shown that, by stretching the coordinates, the air cladding can be combined with the PML to form a cladding layer with complex thickness R Ϫ r ϭ R Ϫ r Ϫ j⌬( 0 / 0 ). By replacing the real radius R of the closed circular waveguide by a complex complex radius R , one can easily perform the modal analysis of the waveguide under consideration.…”

“…The propagation constants are determined up to an accuracy of 10 Ϫ11 . Using the technique described in section 2, it took 116 s to calculate the propagation constants of the first 150 Berenger HE modes based on transformation (10) and 135 s for the propagation constants Berenger HE modes based on transformation (11). Concerning the leaky modes, 133 s were needed to find the propagation constants of the first 150 modes based on transformation (9).…”