Inhomogeneous dielectrics

Electromagnetic analysis of models with inhomogeneous dielectric volumes is handled in Wave3D via solution of volume integral equation discretized with volumetric mesh of tetrahedral elements. The Luneburg lens is an example of such model.  The relative permittivity of the lens varies continuously according to dependence  $ \epsilon_r=2-\frac{r^2}{R^2}$, where  $R$ is the outer radius of the lens and  $r$ is radial coordinate. While the model of such lens in Wave3D could be created on arbitrary tetrahedral mesh, creation of the inhomogeneous permittivity is more expediently done through creation of multilayered sphere model shown in Fig. 1 below.

Fig. 1: Luneburg lens consisting of 15 layers each 0.1m thick (left), 55,515 tetrahedral element discretization (center), magnitude of volumetric polarization current and a slice of near scattered field (right) calculated with Wave3D at 200MHz.

Extensive data processing capabilities of ParaView software allow to visualize complex volumetric field distributions in various convenient forms including isosurfaces, solution threshold defined sub-volumes, plane slices, line slices and other methods.

Fig. 2: Subvolumes of the Luneburg lens within various ranges of polarization current intensity.

Fig. 3: Line slices of the polarization current density across the diameter of the lens alined with x-, y-, and z-axis. Plots are generated by ParaView from Wave3D solution.