Extension of Berenger's absorbing boundary conditions to match dielectric anisotropic media

Abstract

Abstract-The authors propose an extension of Berenger's perfectly matched layer (PML) absorbing boundary conditions (ABC's) to achieve a perfect matching of waves propagating in anisotropic media. Although the procedure to obtain the matching conditions is valid for any kind of anisotropic material, it has been validated with a lossless two-dimensional uniaxial medium, in which the optical axis is not contained in its plane section. The finite difference time domain method, with an alternative scheme for anisotropic media, is used to simulate the problem and to obtain the numerical reflection coefficient.Index Terms-Absorbing boundary conditions, anisotropic media, FDTD methods, perfect matching layers.

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

“…Extension of the PML to anisotropic media have been formulated in [284], [285] based on a impedance matching approach, in [286] based on a material-independent approach as suggested in [287], and in [288] based on the complex coordinate stretching approach.…”

Perfectly Matched Layer (PML) for Computational Electromagnetics

“…Several papers were published in the literature on the generalization of the split PML to anisotropic media [34][35][36][37][38][39]. Two approaches are possible for nondispersive media.…”

A general approach to extend Berenger's absorbing boundary condition to anisotropic and dispersive media

“…The equations presented in [10] are a two-dimensional (2-D) special case of the above if only the z coordinate is stretched. Alternatively, one can use the D and B fields (with component splitting into two subcomponents) directly in the update equations and apply the constitutive relations after each time step, as was done in [9].…”

“…Due to its high numerical efficiency, there has been much effort to extend its capabilities to more general geometries and media. These include extensions to cylindrical [2]- [6], spherical [5], and conformal mesh terminations [7], and to anisotropic [8]- [10] and dispersive media [11]- [13].…”

“…The derivation of the PML for dispersive media in [13] and for anisotropic media in [8] and [10] was carried out through an extension of the approach of [1] in the sense that a different set of constitutive parameters inside the PML (tensors in case of anisotropic media) was selected through an analysis of the reflection coefficient to obtain the perfect matching conditions at the interfaces. The constitutive parameters thus derived depend on the particular kind of anisotropy present in a medium or on the particular kind of model used for the dispersive media.…”