  The near fields of small-size extended hemielliptic lenses made of rexolite
and isotropic quartz and illuminated by E- and H-polarized plane waves are
studied. Variations in the focal domain size, shape, and location are presented
versus the angle of incidence of the incoming wave. The problem is solved
numerically in a two-dimensional formulation. The accuracy of results is
guaranteed by using a highly efficient numerical algorithm based on the
combination of the Muller boundary integral equations, the method of analytical
regularization, and the trigonometric Galerkin discretization scheme. The
analysis fully accounts for the finite size of the lens as well as its
curvature and thus can be considered as a reference solution for other
electromagnetic solvers. Moreover, the trusted description of the focusing
ability of a finite-size hemielliptic lens can be useful in the design of
antenna receivers.
