Material independent PML absorbers for arbitrary anisotropic dielectric media

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.…”

Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media

“…In the time domain, the frequency-dependence of the PML response is well known to require additional storage (e.g. auxiliary fields) [2], but we show that our scheme involves requirements at least as good as previous correct split-field PML proposals for anisotropic media [13][14][15][16][20][21][22][23]. (Anisotropic media are becoming increasingly widespread in computational electromagnetism, both for anisotropic metamaterials [28][29][30] and even for nominally isotropic media, where in the latter case accurate subpixel averaging requires the discretization to use effective anisotropic media at material boundaries [31][32][33].)…”

“…doi:10.1016/j.jcp.2011.01.006 formulate (via complex coordinate-stretching) and validate a corrected unsplit-field uniaxial PML for arbitrary anisotropic, dispersive, and conducting media in the time domain. Although there exist other correct alternatives for PML in anisotropic media [13][14][15][16][18][19][20][21][22][23][24] (including correct split-field proposals [21,13,15] by the same authors as the later incorrect unsplitfield formulation), our unsplit PML formulation has the appeal of a simple correction to previous UPML-like proposals that were correct for isotropic media [25,26,10]. We demonstrate this PML formulation both for a planewave method in frequency domain and for a finite-difference time-domain method (with a free-software implementation [27]).…”

“…Several such proposals employed the split-field approach [20][21][22][23][13][14][15][16] or convolutional approach [18,19,24] to obtain timedomain equations, and split-field PMLs were also derived for homogeneous anisotropic media by directly computing the reflection coefficients at the PML interface [20,14,23]. The transformational-optics approach also leads to a simple uniaxial anisotropic PML medium in the frequency domain [40], and in this paper we point out that the same approach also yields a straightforward time-domain PML for anisotropic and dispersive media, although in time domain a new factorization is required in order to efficiently implement the frequency dependence.…”

“…The transformational-optics approach also leads to a simple uniaxial anisotropic PML medium in the frequency domain [40], and in this paper we point out that the same approach also yields a straightforward time-domain PML for anisotropic and dispersive media, although in time domain a new factorization is required in order to efficiently implement the frequency dependence. Zhao et al, in addition to proposing correct split-field PMLs for anisotropic media [21,13,15], also proposed an unsplit-field PML for anisotropic media in which the PML is encapsulated in conductivity factors for the equation updating the D field from r  H, separate from the (unmodified) constitutive relation giving E from D [10]. However, we show in this paper that the Zhao unsplit-PML proposal relies on a commutation of the coordinate-stretch matrix and the material tensor which is not generally correct in anisotropic media, and as a result the absorber is not reflectionless in the limit of high resolution.…”