2.28 Wire Grids (Asymptotic Boundary Conditions)

Asymptotic Boundary Conditions (ASBC) are defined by setting to zero one of the electric field components over the region covered by ASBC, and thus can be realised as wire grids. Regarding the orientation and geometry of ASBC, the following restrictions apply in QW‑3D:

·        ASBC can only be defined in planes perpendicular to one of the coordinate axes;

·        in vertical planes (parallel to XZ, YZ) ASBC must have a rectangular shape;

·        in horizontal planes (parallel to XY) arbitrarily-shaped ASBC can be drawn, but a stair-case approximation will be made.

Table below specifies the correspondence between the ASBC orientation (horizontal (H)/vertical (V)) and the electric field component effectively set to zero:

Note that formally speaking, ASBC can also be introduced by drawing appropriate grids of individual wires. There is, however, one major practical difficulty in such an approach: the user has to draw each wire separately, exactly following the existing FDTD mesh. After re-meshing of the project, the wire grid has to be re-drawn. Those problems are avoided by application of special elements, which we shall call “wire grids”. Drawing a wire grid really means drawing a frame (rectangular in XZ, YZ planes; arbitrarily-shaped in XY plane), which is then filled with wires of a horizontal (H) or vertical (V) orientation. The number and locations of wires in the grid automatically adjusts to the mesh and mesh changes. Their orientation is chosen by the user in Wire Change dialogue.

Wire grids can be defined through the ..elib/wires/wiregrid.udo file, prepared by QWED and delivered together with QW-3D software. Manual definition of wire grids is also possible although less convenient.

Definition of ASBC with wiregrid.udo

Rectangular wire grids can be defined in QW-3D with wiregrid.udo.

Invoking the Add Object dialogue and selecting wiregrid.udo shows the following dialogue with default parameters:

Pressing Draw creates a rectangular wire grid perpendicular to the X-axis, at x=X1=X2=2, based at level Z=0, with height h=1, between Y1=1 and Y2=3 (all in current project units). The grid will be filled with horizontal (Y -oriented – see table above) wires. If the FDTD mesh lines are at z=0,1,2,…, the y-oriented wires will appear at z=0,1.

The user can modify the parameters, creating different wire grids. Note that:

·      The grids must be planar (not volumetric). Consequently, we must make one of the three settings: h=0, or X1=X2, or Y1=Y2. Otherwise a warning will appear.

·      Orientation boxes allow to choose horizontal and/or vertical wires. Setting Orient_h/x=1 will create horizontal wires, Orient_v/y=1 will create vertical wires. If both orientations are set to 1, a 2D mesh of wires will be created - this will no longer imitate ASBC, but rather to a thin metal plate. If none of the orientations is checked, no wires will be created.

·      If d>0, all wires in the grid will have diameter d. In such a case, besides setting the tangential E-field components to zero, singularity corrections will be applied to the H-fields encircling the wire, and E-fields perpendicular to the wire.

·      The X and Y origin coordinates are irrelevant

·      Put and Get buttons cause standard UDO actions of, respectively, saving current Values of consecutive Parameters of the current wiregrid object to a *.udp file, and restoring the previously saved values from such a file.

Manual definition of XZ and YZ wire grids

A grid of wires parallel to the XZ plane can be created by drawing an X -oriented wire, in a standard manual way, but of non-zero height. Note that:

·      Default orientation of wires in the grid is horizontal (x-oriented). The uppermost wire will not be created. For example, if the wire element is drawn at level z=0, of height h=5, and the FDTD mesh is at z=0,1,2,3,4,5,… – the individual wires will be set only at z=1,2,3,4.

·      Wire orientation can be changed to vertical (Z -oriented) in the Edit Wire dialogue and can be invoked by selecting the wire element on the Select Element list, double-clicking with left mouse button, and clicking right mouse button). The vertical wires will be of user-defined height h. However, the last wire on the right will not be created. For example, if the wire element is drawn between x₁=1 and x₂=3, and the FDTD mesh lines are at x=0,1,2,3…. – the individual vertical wires will be set only at x=1,2.

Analogous rules apply to wire grids parallel to the YZ plane (Y replacing X in the above description).

Manual definition of XY wire grids

A grid of wires parallel to the XY plane can be created by drawing a metal element of zero height, of an arbitrary shape, in a standard manual way. The Element Change dialogue for such elements has now been supplemented with HV Grid button. It allows choosing between a metal patch or a wire grid, and to specify orientation and diameter of wires. Note that:

·      If only H or V orientation box is checked, the X- or Y -oriented wires are created, respectively. The last wire in the positive X - or Y-direction, respectively, is not created.

·      If both H and V orientation boxes are checked, a 2D grid of the X- and Y-oriented wires is created. Stair-case approximation of the shape is applied. The last wires in the positive X- and Y-directions are not created.

·      If none of the orientation boxes is checked (default), a thin metal patch is conformally modelled.