Ray tracing on extended hemispherical and elliptical silicon dielectric lenses

In this paper, extended hemispherical and elliptical silicon dielectric lenses are compared by means of ray tracing. It is shown that the optical focuses of two lenses are not at same position though the elliptical lens is synthesized from an extended hemispherical lens by carefully choosing a particular extension length as stated in ref1]. It may be used to explain why the best compromise between alignment, directivity and Gaussian-coupling effciency will be obtained if the feed antenna is placed at the region between 2.2 mm and 2.4 mm of extension length (for 13.7 mm diameter lens, dielectric contant = 11.7).