IBM Release 1.93 manual Perfectly-Matched Layers, Materials, Point Sources

3.3.1. Perfectly-Matched Layers

PMLs are fictitious anisotropic materials that (usually) absorb whatever radiation falls on them from pre-specified directions. They work extremely well when they work at all, which isn’t 100% of the time.

PMLs don’t absorb in every direction, so different parts of the domain need different PMLs. This is such a pain that POEMS makes a valiant effort to automate it for you. It works as follows:

(i)If a PML touches a boundary, it will be set to absorb energy falling on that boundary from the centre of the domain.

(ii)If a PML touches more than one boundary, rule(i) will be applied to all of them. (iii)PMLs that touch both the upper and lower boundary of an axis will be automatically split in half down the middle so that (ii) can be applied to both halves.

(iv)PMLs must touch at least one boundary.

A solid block of PML filling the whole space is thus split into 8 blocks, each absorbing diagonally outwards. You can manipulate these rules to customize PMLs for your use. One common desire is to have PMLs covering the whole outer skin of the domain, with the faces, edges, and vertices all absorbing in different directions (26 blocks altogether). This is fiddly, so the HOLLOWBOX statement was added to POEMS to take care of it.

HOLLOWBOX is implemented by splitting the box up and letting the automatic PML handler apply rules (i)-(iv) to each block. The TILEDPLANE statement does the same for planar PML regions.

POEMS has heuristics for generating reasonable PMLs automatically, but these are not always reliable. Signs of trouble are checkerboard patterns, fields apparently originating in PML regions, floating-point runtime errors, and the generation of NaNs. This will happen every time if you put a material boundary near a PML, or if you have sources inside it. A reasonably safe rule is to put a PML no closer than 1 wavelength from a material boundary or a source. Plane waves and PMLs are a difficult combination in

TEMPEST.

3.4. MATERIALS

Materials used in POEMS are treated as isotropic, linear and time-invariant. tempest supports photoresist materials and has limited support for anistotropic ones, so if this becomes important it can be added in a future release.

3.5. SOURCES

POEMS has a rich array of sources, and when the PUPILFUNCTION order becomes available, it will be able to generate essentially any monochromatic propagating field.

3.5.1. POINT SOURCES

In continuous-space electrodynamics, static point sources are mathematically very simple. In electrodynamics, there are no monopole sources, since a monopole field is purely radial, whereas electromagnetic waves are purely transverse. The simplest physical

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