2.3      Bodies of Revolution

Fundamentals of the FDTD method of analysis have been discussed in Fundamentals of the Method of Analysis. In Introduction to QW-V2D package it has been signalled that QW-V2D is applicable to the structures of axial symmetry (also called Bodies of Revolution or BOR). In such a case, the 3D electromagnetic problem reduces to two dimensions in cylindrical coordinates xr and the FDTD method reduces to a 2-dimensional (2D) one. In general, we can distinguish scalar 2D problems with only three non-zero field components, or more complicated vector 2D problems (V2D problems) in which we must consider all six field components. As suggested by its name, QW-V2D can deal with vector 2D problems, but the analysis of simpler scalar 2D problems is also possible.

The QW-Modeller allows for definition of V2D (BOR) structures, mesh generation, and specification of simulation parameters.

The V2D (BOR) projects, axisymmetrical two dimensional in cylindrical coordinates, are considered in cylindrical coordinates x,ρ,φ with the assumption that the dependence of fields on the coordinate φ is analytically known. Therefore in fact we consider the structure in two dimensions x and ρ. In terms of FDTD meshing we have just one layer of FDTD cells reproducing the shape of the structure in the plane x, ρ. The third dimension (with respect to φ) is always equal to 2π.

Here are some remarks concerning application of QW-Modeller in V2D (BOR) projects:

• basically most features and commands described for 3D project in x, y, z coordinates are valid here for x, ρ, φ coordinates respectively,

• the simulation of V2D (BOR) project will take the geometry at the level 0 (Z-coordinate),

• in x, ρ plane the part of the structure extending below the ρ=0 will be ignored.

The V2D (BOR) project geometries (i.e. cylinder) can be introduced as:

• full 3D structure with X-axis as an axial symmetry:

• part of 3D structure with X-axis as an axial symmetry:

• part of 3D structure with X-axis as an axial symmetry defined as a 2D long-section of the structure placed at Z=0 coordinate: