See the results of a complex 17 wavelength-diameter spherical dielectric lens designed in AutoCAD and run in XFdtd^®.

These images show the transient field progression and the steady-state electric field magnitudes of a 17 wavelength-diameter spherical dielectric lens excited by a 10 GHz signal emitted by an open rectangular waveguide. The lens has a dielectric value of 2.54 and is located 671 mm from the radiating waveguide. The focused fields from the lens are shown for two cases: the first with the lines perpendicular to the incoming wave and the second with the lens tilted by 45 degrees. The fields shown are in the central bisecting planes of the lens and waveguide for each case.

The XFdtd calculation is run as a full-sized model where the lens and waveguide are surrounded by free space. Due to the symmetry involved, this calculation could have also been run in XFdtd using an image plane which would have halved the size of the problem. The spherical lens was created in AutoCAD and imported into XFdtd using the 3D Solid CAD importer.

The first case with the lens perpendicular to the incident field was simulated using a problem space of 225x225x445 FDTD cells at a cellular resolution of 2.5 mm. The calculation was run for 1500 time steps which is approximately 75 cycles of the incident signal. The calculation was run on a 700 MHz Pentium II computer. The run time was 5 hours 15 minutes and required just under 600MB of memory.

The second case, with the lens tilted by 45 degrees to the incident field, was simulated in a problem space of 251x233x451 FDTD cells at 2.5 mm per cell. The calculation was run for 2500 timesteps or about 125 cycles of the input sine wave. The calculation was performed on a dual processor 700 MHz Pentium II computer using the Remcom Multi-Processor Module in 4 hours and 15 minutes. Approximately 680 MB of memory were required to run this calculation.

The output fields display the steady-state electric field magnitudes in the planes of the two cross-sectional cuts of the lens for each case. The incident field is focused by the lens, thus increasing the gain of the incident signal significantly. For the first case with the lens perpendicular, the gain is increased by approximately 16 dBi. For the case of the tilted lens, the pattern is focused about 7 degrees to the the side with a peak gain increase of approximately 7 dBi.

The time-domain field images display the progression of the incident field toward the lens and the interaction and focusing which occurs.