  This paper proposes a technique for designing flat lenses using Field
Transformation (FT), as opposed to Ray Optics (RO) or Transformation Optics
(TO). The lens design consists of 10 layers of graded index dielectric in the
radial direction and 5 layers in the longitudinal direction. The central layer
in the longitudinal direction primarily contributes to a bulk of the phase
transformation, while the other four layers, above and below this middle layer
on either side, act as matching layers that help reduce the reflections
introduced by the impedance mismatch at the interfaces of the middle layer. The
paper compares the performance of the lens, so designed, with those based on
the RO and TO techniques. We show that the proposed lens design using field
transformation is broadband, has a better than 1 dB higher gain compared to the
RO and TO based designs over a wider frequency band, and that its scan
capability is superior as well.
